Equal temperament

Posted by: Loren D

Equal temperament - 06/12/13 07:52 AM

We already have a thousand posts about this, so what will one more hurt? smile

I have a love-hate relationship with ET. The tech in me sees the practicality of it, but the pianist in me hates it. For me, music should sound musical; not practical.

Give me the shades, colors, and textures of the different keys.
Posted by: Emmery

Re: Equal temperament - 06/12/13 08:27 AM

I didn't realize that the term "musical" had only one narrow definition. Equal temperament allows full versatility to play in any key with aproximately the same amount of "un-musical" quality. Every other non ET is a compromise. If one is playing pieces that uses keys which have more favourable musical qualities, there would obviously be some small benefits.

Unfortuanately, I have yet to open a fake book or classical music book that has "All pieces in the key of Db" written on it.
Posted by: Loren D

Re: Equal temperament - 06/12/13 08:34 AM

Originally Posted By: Emmery
I didn't realize that the term "musical" had only one narrow definition. Equal temperament allows full versatility to play in any key with aproximately the same amount of "un-musical" quality. Every other non ET is a compromise. If one is playing pieces that uses keys which have more favourable musical qualities, there would obviously be some small benefits.

Unfortuanately, I have yet to open a fake book or classical music book that has "All pieces in the key of Db" written on it.


Key word being "un-musical."
Posted by: UnrightTooner

Re: Equal temperament - 06/12/13 10:14 AM

One key or another does not mean anything to me. but that is not so with those with absolute pitch. I have to suspect that those with AP tend to have a preference for UT.

But before I understood what ET really was, I used to wonder why the F and especially the Eb brass instruments couldn't play in tune while us Bb brass instruments could. And I also wondered why pieces with flats sounded sooo much better than pieces with sharps. I had a band director encourage us to try playing with the 12 note strob-o-scope to work on our intonation. There were some notes where this just didn't work, I would run out of "lip". It was much easier for woodwinds. I understand this all now.
Posted by: Minnesota Marty

Re: Equal temperament - 06/12/13 10:19 AM

Originally Posted By: Emmery
Every other non ET is a compromise.

It is ET which is the compromise. You seem to need a lesson in the history of Western music.
Posted by: Mwm

Re: Equal temperament - 06/12/13 12:37 PM

Originally Posted By: Minnesota Marty
Originally Posted By: Emmery
Every other non ET is a compromise.

It is ET which is the compromise. You seem to need a lesson in the history of Western music.

Careful now. Every temperament on a 12 tone per octave keyboard is a compromise of some kind versus just intonation.
Posted by: Minnesota Marty

Re: Equal temperament - 06/12/13 02:57 PM

Originally Posted By: Mwm
Originally Posted By: Minnesota Marty
Originally Posted By: Emmery
Every other non ET is a compromise.

It is ET which is the compromise. You seem to need a lesson in the history of Western music.

Careful now. Every temperament on a 12 tone per octave keyboard is a compromise of some kind versus just intonation.

The inference in the posting was the ET was not a compromise. ET is a temperament based on a compromise, which is based on a compromise, and yet another compromise, ad infinitum.

To think that ET is not a compromise begs the study of music history and musicology.
Posted by: Minnesota Marty

Re: Equal temperament - 06/12/13 03:02 PM

Alex McDonald, a competitor in the recent Cliburn Competition, made a comment in an interview about the piano choices available. He observed that a piano is an instrument which is, and can never be, in tune with itself. Yet the common feeling in this forum is that pianists can't tell if a piano is in tune or not. I always beg to differ.
Posted by: Mwm

Re: Equal temperament - 06/12/13 03:45 PM

Marty,

You are correct about the compromise of a compromise of a compromise...

I am not so sure about pianists knowing when a piano is as tuned as it can be. Now that I tune my own piano, I am starting to hear the tuning qualities of all the pianos I hear, and I hate that it is interfering with my enjoyment of the music. Until I started tuning, I was blissfully unaware of the subtle variations in the structure of a tuning. I just performed the music and the piano was the vehicle. It is different from the awareness of the tuning of an organ or harpsichord, which are inherently cleaner sounding.
Posted by: Mwm

Re: Equal temperament - 06/12/13 03:50 PM

Originally Posted By: Loren D
We already have a thousand posts about this, so what will one more hurt? smile

I have a love-hate relationship with ET. The tech in me sees the practicality of it, but the pianist in me hates it. For me, music should sound musical; not practical.

Give me the shades, colors, and textures of the different keys.

Loren,
You want the shades, colors,..., but using which UT?
Posted by: Gary Fowler

Re: Equal temperament - 06/12/13 06:19 PM

I have a feeling ET is here to stay. People just like to be able to play in every key!(playing f# chord should sound as good/bad as playing C chord)
Posted by: Minnesota Marty

Re: Equal temperament - 06/12/13 07:25 PM

Playing a F# chord should every bit as good as a C chord, but it should sound different other than just a difference in pitch.

There is no reason why you can't play any fixed pitch instrument with a non-ET tuning in every key! It just sounds better.

(Flame suit on)
Posted by: Loren D

Re: Equal temperament - 06/12/13 07:34 PM

Originally Posted By: Mwm
Originally Posted By: Loren D
We already have a thousand posts about this, so what will one more hurt? smile

I have a love-hate relationship with ET. The tech in me sees the practicality of it, but the pianist in me hates it. For me, music should sound musical; not practical.

Give me the shades, colors, and textures of the different keys.

Loren,
You want the shades, colors,..., but using which UT?


I like EBVT. Love it, actually.
Posted by: David Jenson

Re: Equal temperament - 06/12/13 07:59 PM

I use ET 'cause it has only two letters and is first alphabetically bufur UT!
Posted by: OperaTenor

Re: Equal temperament - 06/12/13 08:05 PM

I use ET because I like sterile environments...

Oh yeah, and octave stretching is for sissies!
Posted by: Mwm

Re: Equal temperament - 06/12/13 08:09 PM

Originally Posted By: Minnesota Marty
Playing a F# chord should every bit as good as a C chord, but it should sound different other than just a difference in pitch.

There is no reason why you can't play any fixed pitch instrument with a non-ET tuning in every key! It just sounds better.

(Flame suit on)

Of course you can! It is done all the time. 99+% of all tunings on a piano, by the time the tuner has left, are non-ET. And, if you really want key colour, tune your piano in 1/4 comma meantone, founded on C, and play all your pieces one half step higher or lower than written. Or better yet, for those people who don't transpose at sight, base your fundamental pitch on F#. Then you can play all the pieces as written.
Posted by: Minnesota Marty

Re: Equal temperament - 06/12/13 08:16 PM

Originally Posted By: David Jenson
I use ET 'cause it has only two letters and is first alphabetically bufur UT!

Just read about it à la Hebrew. Then you'll love it - Trust me!
Posted by: bkw58

Re: Equal temperament - 06/12/13 08:19 PM

I use ET because it's out of this world(!)where wolves roam not.
Posted by: David Jenson

Re: Equal temperament - 06/12/13 08:31 PM

Originally Posted By: OperaTenor
I use ET because I like sterile environments...

Oh yeah, and octave stretching is for sissies!

I agree with what I think you are saying. confused
Posted by: Loren D

Re: Equal temperament - 06/12/13 09:22 PM

Originally Posted By: David Jenson
I use ET 'cause it has only two letters and is first alphabetically bufur UT!


I understand completely! One of the reasons I became a piano technician was so I would be in the yellow pages between Physicians and Pizza. grin
Posted by: David Jenson

Re: Equal temperament - 06/12/13 09:36 PM

On a good day I tune ET. If I mess up? Hey, its ... UT! Yay!
Posted by: Mark R.

Re: Equal temperament - 06/13/13 08:03 AM

Originally Posted By: UnrightTooner
One key or another does not mean anything to me. but that is not so with those with absolute pitch. I have to suspect that those with AP tend to have a preference for UT.


I have pitch memory (prefer not to call it "absolute", because I can be 1 or 2 Hz off at A440) - certainly recognize keys immediately if the instrument is between about -50 cents and +20 cents. But I certainly prefer ET. To me, C major is C major, with no need for an overly sweet M3. And F# major is F# major, with no need for an overly sour M3.
I might be an exception to your rule/suspicion, but there you have it.

Originally Posted By: Minnesota Marty
Playing a F# chord should every bit as good as a C chord, but it should sound different other than just a difference in pitch.


I submit that you can't have both "every bit as good" and "different other than just pitch". I see one of two cases:

1) F# sounds every bit as good as C, in which case
... a) you have ET or
... b) you have UT but don't care about the widths of M3s or can't distinguish them,

or

2) it sounds different, in which case you have UT and can actually distinguish between close and remote keys. But amongst musicians who can distinguish M3s of different widths, I've never found one person who likes a 17 cent M3 just as much as a 14 cent or 10 cent M3. They all prefer the closer keys.

So, if you tune/use UT and can distinguish between M3s of different widths, then F# does not sound "every bit as good" as C. (That's the whole idea, I've been told.)
Posted by: RonTuner

Re: Equal temperament - 06/13/13 08:50 AM

Here's a question for the ET folks out there...

You say that C is the same (every bit as good) as F#, or any other triad (in a real ET) - how is that REALLY possible with the thirds all beating at different speeds from each other? Or do you mean something else?
Posted by: Ed Foote

Re: Equal temperament - 06/13/13 08:56 AM

[/quote] Playing a F# chord should every bit as good as a C chord, but it should sound different other than just a difference in pitch.

I submit that you can't have both "every bit as good" and "different other than just pitch". I see one of two cases:
1) F# sounds every bit as good as C, in which case
... a) you have ET or
... b) you have UT but don't care about the widths of M3s or can't distinguish them,

or

2) it sounds different, in which case you have UT and can actually distinguish between close and remote keys. But amongst musicians who can distinguish M3s of different widths, I've never found one person who likes a 17 cent M3 just as much as a 14 cent or 10 cent M3. They all prefer the closer keys.<<

So, if you tune/use UT and can distinguish between M3s of different widths, then F# does not sound "every bit as good" as C. (That's the whole idea, I've been told.)[/quote]

Greetings,
So, it appears that the value judgement has been placed="good" equal consonance? Thus, dissonance is "bad"? If so, why would anyone want to accept all the thirds being so dissonant? 14 cents is pretty far away from consonant. I think it is more a question of contrasts.

I have found that the ET advocates consider sameness to be good, even if it is dissonant, and inequality is bad, even if it reduces the overall dissonance in piano music. ( The only way that a UT creates dissonance on a par with ET is if the use of all 12 keys is totally democratic, and this is not the case in piano music.)

The greater decision is whether a listener is more emotionally moved by one or the other, and science has proven that emotional response varies with the level of dissonance. This alteration of response occurs involuntarily, and is virtually universal. So, while the resolutions in classical music are obviously intended to relax, having them accompanied by a reduction in tempering increases the effect, and we find that classical composers don't resolve to a key with a higher level of tempering, they always resolve to a calmer place. In the absence of contrast, emotional responses are forced to rely on intellectual response, which many of us have found to be a weaker, watered-down, effect.

I love the effect of F# in a strong UT when it indicates a very deep emotional turmoil. I love the pure calmness of the closer keys. What I find most disturbing about ET is the boring sameness when there is no difference other than pitch, and the busy-ness of tempering in passages that would be so much more beautiful if they were closer to pure. I like my classical music as complex as it can be, and ET, with its reduction of harmonic effect to a mathematically determined value, is the antithesis of this. Once understood, the UT casts a new light on phrasing......

And to the statement " I've never found one person who likes a 17 cent M3 just as much as a 14 cent or 10 cent M3. They all prefer the closer keys." I can only say that I must have run into all of them that do, because I have a majority of customers that will never go back to ET. If so many people like the 'closer keys', there must be something repulsive about dissonance, and the only way to accept ET, with its ever-present beating, is to stop listening to the tempering completely, (which is what happens).
Regards,


Posted by: Ed Foote

Re: Equal temperament - 06/13/13 09:03 AM

Originally Posted By: RonTuner
Here's a question for the ET folks out there...
You say that C is the same (every bit as good) as F#, or any other triad (in a real ET) - how is that REALLY possible with the thirds all beating at different speeds from each other? Or do you mean something else?


Hi Ron,
I think the explanation is that we hear the beating in logarithmic terms and pitch determines the effect, i.e. the C-E in the 4th octave, though beating twice as fast as the C-E an octave lower, is registered by the ear as the same tempering because the pitch is twice as high.
Regards,
Posted by: Loren D

Re: Equal temperament - 06/13/13 09:07 AM

This is turning into a really good discussion. Good question, Ron. And Ed, excellent post.
Posted by: Minnesota Marty

Re: Equal temperament - 06/13/13 09:34 AM

Originally Posted By: Mark R.
Originally Posted By: Minnesota Marty
Playing a F# chord should every bit as good as a C chord, but it should sound different other than just a difference in pitch.


I submit that you can't have both "every bit as good" and "different other than just pitch".

That is because you think/hear as a tuner and not as a musician. It is exactly the difference in intervals, such as thirds, which create the tonal colors of each individual key. I prefer to hear a distinction between C-minor and C#-minor. If memory serves, composers seem to choose from all keys. Why not just compose everything in C-Major or minor if ET is the best solution?

As an aside, I performed the Beethoven Concerto No. 4 in Prague on a Petrof P-282. The piano immediately brought forth incredible vibrancy. Unlike the USA, rehearsals are accorded much more time and the tuner is included in discussions with the pianist and conductor. I had time to pick the brain of the tuner to find out what was going on.

With an orchestra, he centers the temperament octave on A, rather than C. He used EBVT-III as the foundation temperament and then "listens to what the piano wants." What this created was an identification that G-Major was not a clone of C-Major in ET, merely at a higher pitch. He indicated that for a Wind Ensemble, he sets his temperament octave from Bb.

Keep in mind, I'm not a tuner. But, I am a pianist with an interest in non-ET tunings. If I have messed up the terminology, I apologize in advance.
Posted by: Emmery

Re: Equal temperament - 06/13/13 10:13 AM

Originally Posted By: Minnesota Marty
Originally Posted By: Emmery
Every other non ET is a compromise.

It is ET which is the compromise. You seem to need a lesson in the history of Western music.


You would seem to need a lesson in distinguishing between an inferances/observation and also the meanings of statements within greater context. When quoting a snippet of someones posting and leaving out its context, it is also appropriate to precede and follow the quote with 3 dots.

My statement stands, and relates to the versatilitya musician has to explore every key signature they come across without wondering if the piece will be more, or less musical for lack of unequalness.

As an analogy, I have 4 or 5 different eye glasses I wear that have various coatings, filters, prescriptions and tints on them. I do both day and night driving, competitive shooting in both bright sunlight and overcast conditions and numerous other tasks with varying conditions that would benefit from wearing one over the other. If I wore a bright amber high contrast lens on a bright day I would lose much of what I want to see in the same way as if I wore dark grey sunglasses at night. An UT basically does the same thing musically with pieces/key signatures that do not favour what it was intended to help. I would never dream of permanently having implant lenses in my eyes that addressed one condition, nor would I tune my home piano to address specific period pieces and have it muck up and cloud over the musical qualities of all the otherrs.
Posted by: Minnesota Marty

Re: Equal temperament - 06/13/13 10:32 AM

Emmery - Are you saying that ET is not a compromise?

--- I am quite familiar with the use of ellipses. Your sentence was quoted in its entirety and did not require an ellipsis or ellipses. It was not taken out of context, it was a complete statement and the source and additional text is available for all to read.

You should search for glasses which are tempered to adapt to all conditions. One doesn't need to change pianos when the instrument is tuned in a non-ET, and the point is, that on the same piano, key color is evident.
Posted by: Ed Foote

Re: Equal temperament - 06/13/13 10:54 AM

[quote=Emmery
As an analogy, I have 4 or 5 different eye glasses I wear that have various coatings, filters, prescriptions and tints on them. I do both day and night driving, competitive shooting in both bright sunlight and overcast conditions and numerous other tasks with varying conditions that would benefit from wearing one over the other. If I wore a bright amber high contrast lens on a bright day I would lose much of what I want to see in the same way as if I wore dark grey sunglasses at night. An UT basically does the same thing musically with pieces/key signatures that do not favour what it was intended to help. I would never dream of permanently having implant lenses in my eyes that addressed one condition, nor would I tune my home piano to address specific period pieces and have it muck up and cloud over the musical qualities of all the otherrs.
[/quote]

Greetings,
I think you have rebutted your own argument. On the one hand, you state that there is no universal pair of glasses that will do it all, yet attempt to say that ET will cover all the bases. One pair of glasses will not satisfy all your visual needs, why would one size third be optimum for all your musical needs?

Composers used different keys for different effects. You will never hear a funeral dirge composed in the key of C, nor a calm idyll composed in F#. Just like your lenses, the various keys are best suited for different musical expression, (see WTC). The UT is a harmonic tool box, offering various resources to the sensitive composer that knows how to best present a musical experience. It is far easier to compose with ET, since modulations don't make any difference other than pitch. Easier because of simplicity.

Using ET for everything is the equivalent of using a Crescent wrench instead of the individual sizes of tools. It works for everything but is optimum for nothing. Its use is for convenience, and that is all. It comes down to the difference between how music sounds and how music feels. Those of us that rely on the intellect pay more attention to the former, those that seek the emotional perspective will pay more attention to the latter.
Regards,
Posted by: Emmery

Re: Equal temperament - 06/13/13 11:20 AM

Originally Posted By: Ed Foote
[quote=Emmery
As an analogy, I have 4 or 5 different eye glasses I wear that have various coatings, filters, prescriptions and tints on them. I do both day and night driving, competitive shooting in both bright sunlight and overcast conditions and numerous other tasks with varying conditions that would benefit from wearing one over the other. If I wore a bright amber high contrast lens on a bright day I would lose much of what I want to see in the same way as if I wore dark grey sunglasses at night. An UT basically does the same thing musically with pieces/key signatures that do not favour what it was intended to help. I would never dream of permanently having implant lenses in my eyes that addressed one condition, nor would I tune my home piano to address specific period pieces and have it muck up and cloud over the musical qualities of all the otherrs.


Greetings,
I think you have rebutted your own argument. On the one hand, you state that there is no universal pair of glasses that will do it all, yet attempt to say that ET will cover all the bases. One pair of glasses will not satisfy all your visual needs, why would one size third be optimum for all your musical needs?

Composers used different keys for different effects. You will never hear a funeral dirge composed in the key of C, nor a calm idyll composed in F#. Just like your lenses, the various keys are best suited for different musical expression, (see WTC). The UT is a harmonic tool box, offering various resources to the sensitive composer that knows how to best present a musical experience. It is far easier to compose with ET, since modulations don't make any difference other than pitch. Easier because of simplicity.

Using ET for everything is the equivalent of using a Crescent wrench instead of the individual sizes of tools. It works for everything but is optimum for nothing. Its use is for convenience, and that is all. It comes down to the difference between how music sounds and how music feels. Those of us that rely on the intellect pay more attention to the former, those that seek the emotional perspective will pay more attention to the latter.
Regards, [/quote]

Greetings Ed,
I would agree with your comparison of an adjustable wrench to a specific box end wrench, but you skirt around a very important point....a 3/8" box end wrench will not work at all on any other nut than the 3/8" one it was made for. Every piece written in a different key signature is a different sized nut, so to speak. An UT is not a complete set of box end wrenches, it is the same having a full set of wrenches, and most of them missing.

I have a pair of clear prescription glasses that will work universally in all conditions, this is the equivelant of ET. The other glasses I have to address certain conditions can easily be switched out in seconds. A temperament and tuning on a piano cannot be switched so easily on a moments notice. An UT is a pair of handcuffs that ties a musician to appropriate pieces the UT favours. UT's are simply not practical for musicians who do not want doors shut in their face when fully exploring all the keys the piano has to offer.

To put it in a nutshell, no self respecting mechanic has an incomplete set of box end wrenches in their tool box....and to the same degree, no self respecting musician has a temperament on their piano that does not address all the keys available to him on the piano.
Posted by: Mark R.

Re: Equal temperament - 06/13/13 11:40 AM

To Ed Foote:

If it comes down to that: yes, I find dissonance "bad". In fact, I don't find even the ET M3 particularly beautiful. I agree with you, it's actually quite dissonant. What I dislike, is having to listen to M3s that are even wider than ET. What I like, is a tuning where such dissonance has been minimized.

Originally Posted By: Minnesota Marty
That is because you think/hear as a tuner and not as a musician.


Assume all you want, but you haven't a clue how I think/hear. My dislike of overly wide M3s, as I described to Ed above, is much, much older than any tuning I've ever done. I've only tuned some 20-odd pianos since I started in 2010, and one harpsichord in earlier years. In contrast, I've been making music in various degrees of (mostly im-)perfection since 1974, been aware of my pitch memory since about 1978 (but probably had it more or less from birth), been acutely aware of interval tempering and whether I like it or not since about 1984.

My value judgement on dissonance does not stem from any form of "tuner's hearing". To the contrary, I've made my tuning decisions (of recent years) based on my musical hearing preferences (developed over 30 years or more). Yes, I've tried EBVT-3, amongst others, but when I heard Ab major, I didn't want to continue playing. (Not to mention my favorite Christmas Chorale by JS Bach, in b minor, with its prominent F# dominant. To me, it was spoiled.)
Posted by: Mwm

Re: Equal temperament - 06/13/13 12:26 PM

UTs on instruments with little or no iH work very well. Bach's WTC in a common UT of the time has wonderful variations in tension and relaxation according to the key. But, on the piano, keys far from the base key really start to scream when the iH is added.
Posted by: Ed Foote

Re: Equal temperament - 06/13/13 12:27 PM

Originally Posted By: Emmery

To put it in a nutshell, no self respecting mechanic has an incomplete set of box end wrenches in their tool box....and to the same degree, no self respecting musician has a temperament on their piano that does not address all the keys available to him on the piano.


Well, you may believe that, but the facts in front of me prove this statement totally wrong. I have numerous professional musicians in my clientele, (including 2 Steinway artists), that have been profoundly influenced by an introduction to WT. These musicians have little use for ET, other than 20th century music. These jazz, country, and classical pianists have found all sorts of improvement in the sound and response of their pianos when I have shifted them out of ET. If you want to argue for a toolbox of all the same size wrenches, go ahead, but it has little pertinence to the world I live in.

For many, there is a great difference between unequal and restrictive, but since it is an esthetic difference, some listeners will not realize it. The fact is that the size of an ET third was derived by dividing an octave into an easy to handle number of notes, (a number determined by the number of fingers we have), not by its musical quality.
Regards,
Posted by: Mwm

Re: Equal temperament - 06/13/13 12:55 PM

Originally Posted By: Ed Foote

...The fact is that the size of an ET third was derived by dividing an octave into an easy to handle number of notes, (a number determined by the number of fingers we have), not by its musical quality.
Regards,

How many fingers do you have? I have 10. I admit my knowledge of musical history and anatomy is limited.
Posted by: Emmery

Re: Equal temperament - 06/13/13 12:59 PM

Ed, I'm thinking that yourself and these artists have mangaged to convince yourselves that there is some kind of parallel temperment dimension out there which does not follow the fixed rules of the science of sound. Those of us in the know on this understand that within the fixed confine points of an octave, you cannot venture away from ET tuning to better favour an interval, without the opposite effect on other interval(s) connected to that adjusted note. It is possible to split the bias of it amongst more intervals but then the UT becomes more and more restrictive in freedom to venture to other keys. Its a lose/lose situation for 99.9% of technicians and musicians out there, and that is the reality of UT's. The arguement stands that if the adjustment is not so much that it makes the one unacceptably/noticably worse, then the adjustment is not enough to make the other acceptably/noticably better.

Incidently, I was discussing with an otchestra conductor the other day the issue of the pianos tuning not precisely matching a fixed pitch instrument when one ventures away from A440. All I could say is be thankfull that ET minimizes this....imagine if its tuned in EBVT3 and you played C4, you would have the pianos unusual tuning working against you and then add almost 4 cents difference on top of that.
Posted by: Minnesota Marty

Re: Equal temperament - 06/13/13 01:13 PM

Emmery,

Please ask that conductor if he believes that his orchestra plays in ET. Have you ever heard one that does? Have you ever had the opportunity to hear a vocal ensemble singing in ET?

It just doesn't happen.

BTW - Orchestral instruments and the voice are not fixed pitch instruments.
Posted by: Mwm

Re: Equal temperament - 06/13/13 01:22 PM

Originally Posted By: Minnesota Marty
Emmery,

Please ask that conductor if he believes that his orchestra plays in ET. Have you ever heard one that does? Have you ever had the opportunity to hear a vocal ensemble singing in ET?

It just doesn't happen.

BTW - Orchestral instruments and the voice are not fixed pitch instruments.

Non keyboard Instrumentalists and singers pull their pitches into just intonation. In general, they hate, but accept, as a necessary evil of the job, playing closer to ET in order to match a piano.
Posted by: Minnesota Marty

Re: Equal temperament - 06/13/13 01:24 PM

Originally Posted By: Mwm
Originally Posted By: Minnesota Marty
Emmery,

Please ask that conductor if he believes that his orchestra plays in ET. Have you ever heard one that does? Have you ever had the opportunity to hear a vocal ensemble singing in ET?

It just doesn't happen.

BTW - Orchestral instruments and the voice are not fixed pitch instruments.

Non keyboard Instrumentalists and singers pull their pitches into just intonation. In general, they hate, but accept, as a necessary evil of the job, playing closer to ET in order to match a piano.

I know that. You know that. I'm sure Emmery's conductor knows it too. Does Emmery?
Posted by: Mwm

Re: Equal temperament - 06/13/13 01:28 PM

Even though I am a huge advocate of UTs, I am not convinced about its utility on a piano, simply because I have not experienced it and my wife doesn't want me to change our piano into something like EBVT III because of all the transposed pieces of her students.
Posted by: Ed Foote

Re: Equal temperament - 06/13/13 03:18 PM

Originally Posted By: Emmery
Ed, I'm thinking that yourself and these artists have mangaged to convince yourselves that there is some kind of parallel temperment dimension out there which does not follow the fixed rules of the science of sound. Those of us in the know on this understand that within the fixed confine points of an octave, you cannot venture away from ET tuning to better favour an interval, without the opposite effect on other interval(s) connected to that adjusted note. It is possible to split the bias of it amongst more intervals but then the UT becomes more and more restrictive in freedom to venture to other keys. Its a lose/lose situation for 99.9% of technicians and musicians out there, and that is the reality of UT's. The arguement stands that if the adjustment is not so much that it makes the one unacceptably/noticably worse, then the adjustment is not enough to make the other acceptably/noticably better.

Incidently, I was discussing with an otchestra conductor the other day the issue of the pianos tuning not precisely matching a fixed pitch instrument when one ventures away from A440. All I could say is be thankfull that ET minimizes this....imagine if its tuned in EBVT3 and you played C4, you would have the pianos unusual tuning working against you and then add almost 4 cents difference on top of that.


Greetings,
That is not the way it works, at least, not here at Vanderbilt.

Last point first: string players have often commented on how easy it was to play with a Coleman 11, one well known violinist on tour specifically told me that it was the first time he could remember of that "all the overtones lined up perfectly". He did not know the piano was tuned in any particular way, he and his pianist simply chose it out of the line-up, leaving behind a perfectly good ET and a subtle Victorian era quasi ET (Moore and Co.) The performance was of Carl Maria Von Weber's concerto for piano and violin, all sorts of key changes, modulations, etc.

Unfettered by expectations, his musical sense took control and I listened to it,(not being a real fan of violins, I was half expecting to snooze, until I noticed that they had chosen the Coleman), with a new appreciation of control. In a number of places, he and the piano took turns heading up or down the scale, and the intonation between the two was impeccable. I heard comments in the hall, afterwards to that effect, so I wasn't deluding myself in this single-blind event.

Rene Fleming, without knowing anything was "abnormal", specifically told the Dean that she just loved rehearsing and performing with the piano, saying how comfortable it was to sing with.

A full Young temperament, with its 21 cent F#, went in front of the Vandy orchestra for a concerto (Beethoven's III). The artist, Enid Katahn. The conductor, and the head of the brass dept. told me later that they had never heard the kids play so in-tune.
Audra McDonald performed here with the Moore and Co. behind her and I was told was "well pleased" with the piano.

Any of these could be discounted as an anomaly, but the pattern speaks for itself. None of these were tuners, they were all musicians, and none of them had been told that the pianos were not in ET. It makes me wonder why an ear has trouble with a 18 cent third, when the needs of the music call for that tonality, and much music does. I wouldn't want every third to be that wide, I don't like meantone, where they are all pure, but I have come to recognize that the width of the third is a musical value, and different musical "meanings" can best be expressed in this or that level of color.

There is also the psycho-physiological aspect of contrast, I mentioned it earlier. When every third is the same, the brain no longer processes it as a factor in response, there is no new information and our conscious mind becomes inured to the dissonance. When that width is a variable, there is a part of the pitch processing center that is stimulated to cause responses, such as changes in heart rate, pupil dilation, etc. There is more brain activity involved in dealing with contrasting values than there is in hearing only one. It is not unlike the stone mason that ,while build a natural stone wall, is dealing with complexity that a brick layer doesn't have to bother with.
It is like a composer making decisions on how to modulate, and where the home key is, and how to leave it and come back to it in small enough steps so that the listener's emotional state isn't interrupted, but, rather, manipulated into as high a degree of involvement as possible. In ET, there need be no consideration of step size, making it easier to make music. If simplicity is the goal, ET is the answer.

Using ET for everything composed on the piano, though is, imho, a mistake, since I am one of those that feels that ET does more damage to Bach, Beethoven, etal., that a WT does to Debussy, Rachmaninoff, etc.
Posted by: UnrightTooner

Re: Equal temperament - 06/14/13 07:29 AM

Originally Posted By: Mwm
Originally Posted By: Minnesota Marty
Originally Posted By: Emmery
Every other non ET is a compromise.

It is ET which is the compromise. You seem to need a lesson in the history of Western music.

Careful now. Every temperament on a 12 tone per octave keyboard is a compromise of some kind versus just intonation.


The twelfth root of two is not a compromise, it is a number. But if we take into account inharmonicity, the resulting stretch can be a compromise, but need not be. Pure twelfths can be used to avoid any compromise whatsoever. But some people like prints rather than plaids. That is what we are really talking about here, preference.
Posted by: bkw58

Re: Equal temperament - 06/14/13 09:34 AM

Originally Posted By: UnrightTooner
Originally Posted By: Mwm
Originally Posted By: Minnesota Marty
Originally Posted By: Emmery
Every other non ET is a compromise.

It is ET which is the compromise. You seem to need a lesson in the history of Western music.

Careful now. Every temperament on a 12 tone per octave keyboard is a compromise of some kind versus just intonation.


The twelfth root of two is not a compromise, it is a number. But if we take into account inharmonicity, the resulting stretch can be a compromise, but need not be. Pure twelfths can be used to avoid any compromise whatsoever. But some people like prints rather than plaids. That is what we are really talking about here, preference.



Exactly.

If I may digress for a moment.

Why did the art and science of piano tuning arrive at such a widely accepted temperament to begin with - one that has stood an exceedingly long test of time? There may be several reasons, but the only one that really "adds up" is this: For the typical family, it provided an agreeable basis for all of their music. Dad played Bach; Mom, Beethoven; Junior, Brahms; Little Sally, a little bit of everything. Piano teachers? Ditto.
One piano accommodating a wide range of interests.


I don't know about the rest of the tuners that post here, but this arena generated most of my "tuning income." Inasmuch as I had neither the time nor working capital to change tradition, I went with what worked the best for the most.

For many reasons - growing interest in period instruments, et al. - variety in temperaments have gained in popularity in certain quarters. Times change. Needs change. This is perfectly fine. Such has certainly found a niche. To one degree or another, some techs desire to be in that niche. This is perfectly fine as well.

There is really no "right" or "wrong" here. Different temperaments are meeting the needs of different "temperaments."
As stated above: "But some people like prints rather than plaids. That is what we are really talking about here, preference. "
Posted by: Mwm

Re: Equal temperament - 06/14/13 03:27 PM

Ed,
You write well and passionately about how it is possible to marry the sound of a piano well with other instruments by using carefully chosen UTs. Thanks for that insight. I hope to hear live someday an example, and I may force my wife to allow me to move our piano to Young, or do you think Coleman 11 would be less jarring for her singing work? The problem is that she does a large amount of late 19th C through modern song as well as the standard vocal rep.
Thanks again for your thoughts.
Posted by: Mwm

Re: Equal temperament - 06/14/13 03:34 PM

Originally Posted By: UnrightTooner
Originally Posted By: Mwm
Originally Posted By: Minnesota Marty
Originally Posted By: Emmery
Every other non ET is a compromise.

It is ET which is the compromise. You seem to need a lesson in the history of Western music.

Careful now. Every temperament on a 12 tone per octave keyboard is a compromise of some kind versus just intonation.


The twelfth root of two is not a compromise, it is a number. But if we take into account inharmonicity, the resulting stretch can be a compromise, but need not be. Pure twelfths can be used to avoid any compromise whatsoever. But some people like prints rather than plaids. That is what we are really talking about here, preference.

I guess we will have to agree to disagree. The twelth root of two is a compromise choice, made by tuners using math, to divide up the notes on a 12 tone keyboard. Those pitches do not match the natural harmonic series that arise from a plucked string or blown pipe. Listen to a natural trumpet. Just intonation is the only non compromise. Tune ET on pianos if you want - I do - and I hate it.
Posted by: BDB

Re: Equal temperament - 06/14/13 03:53 PM

Originally Posted By: Mwm

I guess we will have to agree to disagree. The twelth root of two is a compromise choice, made by tuners using math, to divide up the notes on a 12 tone keyboard. Those pitches do not match the natural harmonic series that arise from a plucked string or blown pipe...


The plucked string and blown pipe are subject to a number of other effects that make them diverge from the theoretical natural harmonic series, some of which can be controlled, and some cannot.
Posted by: Mwm

Re: Equal temperament - 06/14/13 05:45 PM

You are correct, but as an ideal (thought experiment), given total constraints on the other variables (tension shift with plucking, wind pressure variation with pitch changes), they do produce pure harmonic structures, which the piano cannot, being limited by 12 notes per octave and iH.
Posted by: Ed Foote

Re: Equal temperament - 06/14/13 06:12 PM

Originally Posted By: Mwm
I hope to hear live someday an example, and I may force my wife to allow me to move our piano to Young, or do you think Coleman 11 would be less jarring for her singing work? The problem is that she does a large amount of late 19th C through modern song as well as the standard vocal rep.
Thanks again for your thoughts.


Greetings,
I think the first step should be the least alteration. Big thirds 15 cents or under.

It seems that the step between ET and the mildest UT is the biggest step of all. Something about leaving a specific "sound" behind. When it loses that seamless texture, the sound "feels" differently. Even though pianists have listened around the tuning, they rarely can point to anything that they hear as changed, but they do say that the instrument certainly has a new feel. It isn't a pitch thing, it is a relationship thing.

The distance from that to the next stronger temperament might be greater, numerically and harmonically, but emotionally, it will have lost the newness, that first kiss is usually the most memorable one, (and the first slap, as well). A pianist familiar with these tunings has said, flatly, that "you can play it harshly or you can play it expressively". The pianist can make more use of the texture if they understand what it does to the harmonic qualities, but we don't throw babies in the deep end, first, so i think it is better to leave the familiar in the smaller steps.

The Young has a 21 cent third at the F#, that is the historical limit to most of the UT's I have seen or heard, as such, it is the extreme. Keep that particular spice for a later introduction.

All normal UT's have about the same shape, just varied steps and evenness of progression. As the tempering gets more and more "colorful", we all reach a point where it calls attention to itself. It is this point that I use to define "out of tune". When the listener becomes more aware of the tuning than the music, even for a split second, the piano is out of tune. This means Dr. John's piano can have well-tempered unisons and I wouldn't notice. His music is, with the help of that loose piano, taking control of my full attention. Listening to a Brahms intermezzo, I don't wanna hear no meowing unisons, at all!
Regards,
Posted by: Minnesota Marty

Re: Equal temperament - 06/14/13 06:31 PM

Originally Posted By: BDB
The plucked string and blown pipe are subject to a number of other effects that make them diverge from the theoretical natural harmonic series, some of which can be controlled, and some cannot.

The natural harmonic series is not the least bit theoretical. Hence the term "natural." On fixed pitch instruments, tunings are based on the theory of what sounds best when confronted by a mathematical impossibility.
Posted by: Withindale

Re: Equal temperament - 06/14/13 07:42 PM

Originally Posted By: Minnesota Marty
... On fixed pitch instruments, tunings are based on the theory of what sounds best when confronted by a mathematical impossibility.


Originally Posted By: Minnesota Marty
Originally Posted By: Emmery
Every other non ET is a compromise.

It is ET which is the compromise....


Is ET based on a theory of what sounds best or is it just the generally accepted compromise?
Posted by: Minnesota Marty

Re: Equal temperament - 06/14/13 07:46 PM

All temperaments are a compromise.
Posted by: Withindale

Re: Equal temperament - 06/14/13 08:41 PM

Originally Posted By: Minnesota Marty
All temperaments are a compromise.

Sure, but what is a good example of a theory of what sounds best?

Even it was just a form of words, it would be interesting to know what you had in mind.

You get ET if you take the view that all notes are created equal but I am not so sure the notes themselves are always happy with that sort of democracy.
Posted by: Gary Fowler

Re: Equal temperament - 06/14/13 09:22 PM

Bottome line is that even musician's ears have grown accustomed to the equal temperment. It's what's acceptable. It is tried and proven.
Posted by: Gary Fowler

Re: Equal temperament - 06/14/13 09:27 PM

Monkeying around with equal temperment seems poinless is all I'm saying
Posted by: Mwm

Re: Equal temperament - 06/14/13 10:27 PM

Originally Posted By: BDB
Originally Posted By: Mwm

I guess we will have to agree to disagree. The twelth root of two is a compromise choice, made by tuners using math, to divide up the notes on a 12 tone keyboard. Those pitches do not match the natural harmonic series that arise from a plucked string or blown pipe...


The plucked string and blown pipe are subject to a number of other effects that make them diverge from the theoretical natural harmonic series, some of which can be controlled, and some cannot.

I erred when I said plucked string. I meant to say bowed string.
Posted by: Mwm

Re: Equal temperament - 06/14/13 10:37 PM

Thanks Ed. My wife (a singer) and I have performed French lute songs on clavichord at 392 using 1/4 comma meantone, and Jacquet de la Guerre on harpsichord at 415 using Kirnberger. Wonderful resonance. I agree a gentle UT on the piano shift first would be wise. I just would eventually like to try Young.
Posted by: Mwm

Re: Equal temperament - 06/14/13 10:43 PM

Originally Posted By: Withindale
Originally Posted By: Minnesota Marty
All temperaments are a compromise.

Sure, but what is a good example of a theory of what sounds best?

Even it was just a form of words, it would be interesting to know what you had in mind.

You get ET if you take the view that all notes are created equal but I am not so sure the notes themselves are always happy with that sort of democracy.

Listen to The King's Singers, or a good barbershop quartet. They sing in just intonation. THAT is what tuning should be. It is IMPOSSIBLE, on an acoustic piano (it is on a digital piano) to achieve just intonation. Every tuning of a piano is a compromise from just intonation. You need to understand that just intonation means that the interval CE in Cmajor sounds different from the interval CE in Fmajor.
Posted by: Minnesota Marty

Re: Equal temperament - 06/14/13 11:00 PM

Originally Posted By: Withindale
Originally Posted By: Minnesota Marty
All temperaments are a compromise.

Sure, but what is a good example of a theory of what sounds best?

Even it was just a form of words, it would be interesting to know what you had in mind.

You get ET if you take the view that all notes are created equal but I am not so sure the notes themselves are always happy with that sort of democracy.

Ian, it is not a form of words, it is a fact. You don't get a tidy, whole number (not a fraction) of pitch Hz, when you try to divvy up the "space" into 11 subdivisions between a perfect octave.

Let me say, again, all temperaments are unequal due to the laws of physics. Even though one carries the title of ET, it doesn't mean that it is. "Temperaments" are nothing but names which are applied to the many solutions of the quandary of how to tune a fixed pitch instrument in a 12 tone scale.

Our tonal structure (Western) is derived from the formalized singing of chant. The ear perceives in what we label as Just Intonation, and that is the basis of the structure as we define it. Most music historians/musicologists believe that plain song, at the infancy of polyphony, was the ear perceiving harmonic structure due to echo/resonance. A huge event was the codification of the major and minor third. To this day, it is the anguish of piano tuners. (Blame it on the Renaissance.)

Have you ever noticed, at a ball game during the singing of the National Anthem, thousands of untrained singers will sing in parallel fifths? Hmmm. The eardrum responds to the natural laws of physics and we recreate them with voice. We learn to "identify" consonance, dissonance and what we term as perfect intervals. The un-schooled ear will often confuse octaves and fifths. We identify a lack of dissonance quite naturally.

As far as temperaments, to the ear, it is nothing more than preference. To a tuner, it is what they have been trained to do and what is the most comfortable for them to recreate with consistency.

So, what do I prefer? A superb tuning in whichever temperament is selected. My own pianos are not tuned in ET, though they differ from each other in their "non-equality." That is due to my tuners being able to "listen" to what works best on each of the pianos.

Uniformity seems to be one of the hallmarks of our times.
Posted by: Minnesota Marty

Re: Equal temperament - 06/14/13 11:06 PM

Originally Posted By: Mwm
Originally Posted By: BDB
Originally Posted By: Mwm

I guess we will have to agree to disagree. The twelth root of two is a compromise choice, made by tuners using math, to divide up the notes on a 12 tone keyboard. Those pitches do not match the natural harmonic series that arise from a plucked string or blown pipe...


The plucked string and blown pipe are subject to a number of other effects that make them diverge from the theoretical natural harmonic series, some of which can be controlled, and some cannot.

I erred when I said plucked string. I meant to say bowed string.

Plucked or bowed makes no difference. They still follow the laws of physics. Temperaments are theoretical, physical properties are not. The first law of physics is that there is always an exception due to interactive and combinative physical properties.
Posted by: BDB

Re: Equal temperament - 06/15/13 12:43 AM

Originally Posted By: Minnesota Marty
Originally Posted By: BDB
The plucked string and blown pipe are subject to a number of other effects that make them diverge from the theoretical natural harmonic series, some of which can be controlled, and some cannot.

The natural harmonic series is not the least bit theoretical. Hence the term "natural." On fixed pitch instruments, tunings are based on the theory of what sounds best when confronted by a mathematical impossibility.


Whereas on instruments which are not fixed pitch, tunings are based on whatever pitch the player is able to make them play at the moment. That, in turn, makes the temperament arbitrary.
Posted by: Withindale

Re: Equal temperament - 06/15/13 05:13 AM

Originally Posted By: Mwm
Originally Posted By: Withindale
Originally Posted By: Minnesota Marty
All temperaments [on fixed pitch instruments] are a compromise.

Sure, but what is a good example of a theory of what sounds best? ... You get ET if you take the view that all notes are created equal but I am not so sure the notes themselves are always happy with that sort of democracy.

Listen to The King's Singers, or a good barbershop quartet. They sing in just intonation. THAT is what tuning should be. It is IMPOSSIBLE, on an acoustic piano (it is on a digital piano) to achieve just intonation. Every tuning of a piano is a compromise from just intonation. You need to understand that just intonation means that the interval CE in Cmajor sounds different from the interval CE in Fmajor.

Yes, that is the point. C and F take a different view of what sounds best and would tune the other notes differently. ET based on the twelfth root of two, or the nineteenth root of three to allow for inharmonicity, may be least likely to offend with some dissonant interval or other. That principle makes ET generally acceptable, but it is scarcely a good enough theory of what sounds best to persuade C and F to agree on that compromise.

If I were C or F, I'd be pragmatic and go along with a tuning such as Marty describes:

Originally Posted By: Marty
My own pianos are not tuned in ET, though they differ from each other in their "non-equality." That is due to my tuners being able to "listen" to what works best on each of the pianos.
Posted by: Mark R.

Re: Equal temperament - 06/15/13 05:56 AM

Originally Posted By: Minnesota Marty
The first law of physics is that there is always an exception due to interactive and combinative physical properties.


I'm not sure what "first law of physics" you're referring to, but in my years of studying physics (including acoustics, harmonic and non-harmonic oscillators) at university, I've never heard of such a statement - least of all under the guise of "the first law of physics".
Posted by: Olek

Re: Equal temperament - 06/15/13 06:45 AM

I wonder if pianos have not yet enough tendency to just intonation since the iH level is enough, so if that is the goal he problem would be more to avoid overpassing it than the opposite.

Now one can make a tuning without any correction of frequencies but it will not sound very nice.
Posted by: Mwm

Re: Equal temperament - 06/15/13 08:37 AM

Originally Posted By: Olek
I wonder if pianos have not yet enough tendency to just intonation since the iH level is enough, so if that is the goal he problem would be more to avoid overpassing it than the opposite.

Now one can make a tuning without any correction of frequencies but it will not sound very nice.




It is the issue of inharmonicity that has caused me to ask so many questions here at PW on temperaments and UTs versus ETs. When tuning other instruments with no iH or that have short sustain, UTs sound much better than ET, since the purity of the intervals in the close keys sound so wonderful. But with the very long sustain on the piano, it seems that any temperament the tuner chooses to use will be heavily modified by his/her attempts to align the partials in a manner that makes a nice sound.
Posted by: Ed Foote

Re: Equal temperament - 06/15/13 09:31 AM

Originally Posted By: Mwm

It is the issue of inharmonicity that has caused me to ask so many questions here at PW on temperaments and UTs versus ETs. When tuning other instruments with no iH or that have short sustain, UTs sound much better than ET, since the purity of the intervals in the close keys sound so wonderful. But with the very long sustain on the piano, it seems that any temperament the tuner chooses to use will be heavily modified by his/her attempts to align the partials in a manner that makes a nice sound.


Greetings,
It depends on what you call "nice". If we oversimplify it to "consonance is good, dissonance is bad", we are either going to be disappointed by any piano tuning, or we are going to have to stop listening to what is really there. There is no way to tune a piano without dissonance, so all we can do is handle it in different ways. I think of it as salt, some like none, others put it on everything, while others, yet, prefer its tang to be selectively applied, leaving opportunity for both sweetness and edge. Great cuisine often mixes dissimilar tastes, why not great composition?

Purity is beautiful, but I, for one, lose interest when everything is consonant. As Plutarch said, "Music, to create harmony, must investigate discord". Meantone is attractive, but without some contrast or color, the music begins to lose its grip on my attention. It is so sedative that I begin to zone out. The same effect comes from ET, to me. There is no consonance, and it is stimulative, everywhere, all the time. Ear fatigue follows. This is why I like a tuning that encompasses some of both. Judging from the music, I think composers did, too.

There are classical passages where the quiver in the melodic line is more expressive than it would be if rendered purely. Perhaps it is the 10th, or 17th in a highly tempered key that gives that vocal vibrato effect. I can't quote the pieces, but I hear this in numerous places when listening to Brahms, or Schubert. Beethoven likes to crash contrasts together, etc. The right key, in the right temperament, can present this musical quality in a way that it would not otherwise be heard. Resolving from a very tense triad to a very consonant one creates a sense of resolution that isn't obtainable without harmonic contrast. I hear evidence that the composers thought so , too.

Dissonance has its place; anytime we hear composers writing minor 2nds, we can be assured that they were seeking a dissonant quality to their sound. What was Bach doing in the Tocatta in D? Regardless of temperament, huge smears of dissonance were there for a reason. So, composers were not afraid of it, and, I think, made use of it.

I also don't think that the presence of inharmonicity is of much importance in the choice of temperament, since the difference between ET and UT dwarfs any effect that inharmonicity has on the overall sound. Particularly with the larger pianos. I have stretched and compressed these tunings to slight comment from artists, but the alteration of the temperament is much more profound.
Regards,
Posted by: Minnesota Marty

Re: Equal temperament - 06/15/13 10:24 AM

Originally Posted By: Mark R.
Originally Posted By: Minnesota Marty
The first law of physics is that there is always an exception due to interactive and combinative physical properties.


I'm not sure what "first law of physics" you're referring to, but in my years of studying physics (including acoustics, harmonic and non-harmonic oscillators) at university, I've never heard of such a statement - least of all under the guise of "the first law of physics".

I was being entirely facetious for those who always find an exception to any rule. They are rife at PW.
Posted by: Mwm

Re: Equal temperament - 06/15/13 10:45 AM

Ed,
I agree that playing only in useable meantone keys is a bit too relaxing. I think Bach, in his WTC, was probably using a just barely non-wolf WT that allowed him to find huge variation in key colour. The way in which he wrote the different preludes, in particular, seems to indicate he was enjoying exploring the tensions of the traditionally remote keys.

Thanks for your comments on the small effect of iH on the various temperaments. I have increased hopes of trying a UT soon.

Cheers
Posted by: Mark R.

Re: Equal temperament - 06/15/13 11:01 AM

Originally Posted By: Minnesota Marty

I was being entirely facetious for those who always find an exception to any rule. They are rife at PW.


Ah, yet another humor failure on my part. Apologies!
(In bed with unequally tempered tonsils.)
Posted by: bkw58

Re: Equal temperament - 06/15/13 11:22 AM

Originally Posted By: Minnesota Marty
Originally Posted By: Mark R.
Originally Posted By: Minnesota Marty
The first law of physics is that there is always an exception due to interactive and combinative physical properties.


I'm not sure what "first law of physics" you're referring to, but in my years of studying physics (including acoustics, harmonic and non-harmonic oscillators) at university, I've never heard of such a statement - least of all under the guise of "the first law of physics".

I was being entirely facetious for those who always find an exception to any rule. They are rife at PW.



Yes. I'd like to lock the QP Box and throw away the key. smirk
Posted by: BDB

Re: Equal temperament - 06/15/13 11:29 AM

Originally Posted By: Withindale
...ET based on the twelfth root of two, or the nineteenth root of three to allow for inharmonicity...


The nineteenth root of three is purely arbitrary, and has nothing to do with inharmonicity, which varies from note to note. If you are allowing for inharmonicity, equal temperament is based on a relationship of intervals, not on any mathematical ratio.
Posted by: Withindale

Re: Equal temperament - 06/15/13 12:57 PM

Originally Posted By: BDB
Originally Posted By: Withindale
...ET based on the twelfth root of two, or the nineteenth root of three to allow for inharmonicity...

The nineteenth root of three is purely arbitrary, and has nothing to do with inharmonicity, which varies from note to note. If you are allowing for inharmonicity, equal temperament is based on a relationship of intervals, not on any mathematical ratio.

Quite so, but I'd note that a temperament based on twelfths must build in some stretch as the nineteenth root of three (1.059526) is slightly greater than the twelfth root of two (1.059463).
Posted by: Olek

Re: Equal temperament - 06/15/13 01:01 PM

Originally Posted By: Mwm
Originally Posted By: Olek
I wonder if pianos have not yet enough tendency to just intonation since the iH level is enough, so if that is the goal he problem would be more to avoid overpassing it than the opposite.

Now one can make a tuning without any correction of frequencies but it will not sound very nice.




It is the issue of inharmonicity that has caused me to ask so many questions here at PW on temperaments and UTs versus ETs. When tuning other instruments with no iH or that have short sustain, UTs sound much better than ET, since the purity of the intervals in the close keys sound so wonderful. But with the very long sustain on the piano, it seems that any temperament the tuner chooses to use will be heavily modified by his/her attempts to align the partials in a manner that makes a nice sound.


I dont know, iH is low enough in mediums to allow all kind of temperaments, but as soon as the treble is met , the piano seem to allow for some "double" pitch.

SO there is a clear tendency to enlarged intervals that do not beat, where on an organ they would be unaudible.

Anyway, before any of those enlightements the managment of the attack and the one of the decay are necessary.
They give by themselves so much musicality, that looking for specific temperaments seem to be unnecessary at that point.
I simply follow the piano and tune musically.

Some methods allow to work the partials match more preciselty ; other seem to regulate the beats created by partial match in a smooth progression.

I seem to believe that a 3d way exists, if you mostly consider energy and activity of the intervals, the tuning take in account voicing, and probably the tempering is installed by itself.

That last "organic" method allow to tune quietely, diorectly in the musical result.
Of course one may have a good pattern to follow, and know well the lower and higher limit allowed in intervals managment.

I have not enough experience in UT to talk about them on pianos, I heard some light UT that where sounding well, not better than a standard tuning, somply well.

Also tuning with the tone so much under developed that harmony loose meaning anyway. That is what made me cautious about that UT "movement" initially and make me unable to appreciate them (while I had fun with samples at the organ and harpsichord and readings on the subject)

If the piano have to be tuned as if it was a barocco era instrument, better use directly the original one, in my opinion.
Posted by: BDB

Re: Equal temperament - 06/15/13 01:46 PM

Originally Posted By: Withindale
Originally Posted By: BDB
Originally Posted By: Withindale
...ET based on the twelfth root of two, or the nineteenth root of three to allow for inharmonicity...

The nineteenth root of three is purely arbitrary, and has nothing to do with inharmonicity, which varies from note to note. If you are allowing for inharmonicity, equal temperament is based on a relationship of intervals, not on any mathematical ratio.

Quite so, but I'd note that a temperament based on twelfths must build in some stretch as the nineteenth root of three (1.059526) is slightly greater than the twelfth root of two (1.059463).


That is numerology, not science.
Posted by: Mark R.

Re: Equal temperament - 06/15/13 02:20 PM

Originally Posted By: BDB
Originally Posted By: Withindale
Originally Posted By: BDB
Originally Posted By: Withindale
...ET based on the twelfth root of two, or the nineteenth root of three to allow for inharmonicity...

The nineteenth root of three is purely arbitrary, and has nothing to do with inharmonicity, which varies from note to note. If you are allowing for inharmonicity, equal temperament is based on a relationship of intervals, not on any mathematical ratio.

Quite so, but I'd note that a temperament based on twelfths must build in some stretch as the nineteenth root of three (1.059526) is slightly greater than the twelfth root of two (1.059463).


That is numerology, not science.


Dividing a P12 into 19 equal parts (e.g. Stopper's OnlyPure) is just as much an ET as dividing a P8 into 12 equal parts. It's just that the former (19 equal semitones in a pure 12th) is a little more stretched than the latter (12 equal semitones in a pure octave).

Whence the assertion that this is numerology, not science?
Posted by: Withindale

Re: Equal temperament - 06/15/13 02:25 PM

Originally Posted By: BDB
Originally Posted By: Withindale
Originally Posted By: BDB
Originally Posted By: Withindale
...ET based on the twelfth root of two, or the nineteenth root of three to allow for inharmonicity...
The nineteenth root of three is purely arbitrary, and has nothing to do with inharmonicity, which varies from note to note. If you are allowing for inharmonicity, equal temperament is based on a relationship of intervals, not on any mathematical ratio.
Quite so, but I'd note that a temperament based on twelfths must build in some stretch as the nineteenth root of three (1.059526) is slightly greater than the twelfth root of two (1.059463).
That is numerology, not science.

All of which brings us back full circle to:

Originally Posted By: UnrightTooner
Originally Posted By: Minnesota Marty

It is ET which is the compromise....
The twelfth root of two is not a compromise, it is a number. But if we take into account inharmonicity, the resulting stretch can be a compromise, but need not be. Pure twelfths can be used to avoid any compromise whatsoever....
Posted by: Minnesota Marty

Re: Equal temperament - 06/15/13 04:21 PM

Originally Posted By: Withindale

All of which brings us back full circle to:

Originally Posted By: UnrightTooner
Originally Posted By: Minnesota Marty

It is ET which is the compromise....
The twelfth root of two is not a compromise, it is a number. But if we take into account inharmonicity, the resulting stretch can be a compromise, but need not be. Pure twelfths can be used to avoid any compromise whatsoever....

After all of the various convolutions, my statement remains that all temperaments applied to fixed pitch instruments are compromises and the named Equal T isn't equal at all.
Posted by: BDB

Re: Equal temperament - 06/15/13 11:31 PM

Originally Posted By: Mark R.
Originally Posted By: BDB
Originally Posted By: Withindale
Originally Posted By: BDB
Originally Posted By: Withindale
...ET based on the twelfth root of two, or the nineteenth root of three to allow for inharmonicity...

The nineteenth root of three is purely arbitrary, and has nothing to do with inharmonicity, which varies from note to note. If you are allowing for inharmonicity, equal temperament is based on a relationship of intervals, not on any mathematical ratio.

Quite so, but I'd note that a temperament based on twelfths must build in some stretch as the nineteenth root of three (1.059526) is slightly greater than the twelfth root of two (1.059463).


That is numerology, not science.


Dividing a P12 into 19 equal parts (e.g. Stopper's OnlyPure) is just as much an ET as dividing a P8 into 12 equal parts. It's just that the former (19 equal semitones in a pure 12th) is a little more stretched than the latter (12 equal semitones in a pure octave).

Whence the assertion that this is numerology, not science?


The number is arbitrary. If you cannot divide an octave into 12 equal parts for some reason, you cannot divide a 12th into 19 equal parts for the same reason. So you are making up a number and endowing it with some mystical property.
Posted by: Withindale

Re: Equal temperament - 06/16/13 06:38 AM

Originally Posted By: Minnesota Marty
Originally Posted By: Withindale
Originally Posted By: Minnesota Marty
All temperaments are a compromise.

Sure, but what is a good example of a theory of what sounds best?

Even it was just a form of words, it would be interesting to know what you had in mind.

You get ET if you take the view that all notes are created equal but I am not so sure the notes themselves are always happy with that sort of democracy.

Ian, it is not a form of words, it is a fact. You don't get a tidy, whole number (not a fraction) of pitch Hz, when you try to divvy up the "space" into 11 subdivisions between a perfect octave.

Let me say, again, all temperaments are unequal due to the laws of physics. Even though one carries the title of ET, it doesn't mean that it is. "Temperaments" are nothing but names which are applied to the many solutions of the quandary of how to tune a fixed pitch instrument in a 12 tone scale.

Our tonal structure (Western) is derived from the formalized singing of chant. The ear perceives in what we label as Just Intonation, and that is the basis of the structure as we define it. Most music historians/musicologists believe that plain song, at the infancy of polyphony, was the ear perceiving harmonic structure due to echo/resonance. A huge event was the codification of the major and minor third. To this day, it is the anguish of piano tuners. (Blame it on the Renaissance.)

Have you ever noticed, at a ball game during the singing of the National Anthem, thousands of untrained singers will sing in parallel fifths? Hmmm. The eardrum responds to the natural laws of physics and we recreate them with voice. We learn to "identify" consonance, dissonance and what we term as perfect intervals. The un-schooled ear will often confuse octaves and fifths. We identify a lack of dissonance quite naturally.

As far as temperaments, to the ear, it is nothing more than preference. To a tuner, it is what they have been trained to do and what is the most comfortable for them to recreate with consistency.

So, what do I prefer? A superb tuning in whichever temperament is selected. My own pianos are not tuned in ET, though they differ from each other in their "non-equality." That is due to my tuners being able to "listen" to what works best on each of the pianos.

Uniformity seems to be one of the hallmarks of our times.

After yesterday's diversions, Marty, I'd like to comment on your post about theories of what sounds best. Let's pass on all the stuff about numbers and the laws of physics and accept pianos for the instruments they are.

Thanks for reminding us that it's our ears telling us what sound best. I think that will do for theory in this discussion which, therefore as a result of the way our ears work, is about the consonance of intervals, starting from the octave.

Reading your description of your pianos again, are you saying that the basic temperament is ET, which is how I took it at first, or a UT?

I think it is now pretty much established that the most consonant tuning is an approximation to ET; the "non-equality", as you put it, depending on the actual sounds of the piano. Last year's paper describing the application of Shannon's principles of communication to an upright piano showed that.

That paper also indicated that there is no single best tuning. There are many high points in a hilly landscape, providing plenty of scope for choosing the best panorama.

The conclusion is a tuning is a tuning provided, in your words, it is a superb one. The story would end there in uniformity if such tunings are to be the only "hallmarks of our times".

The paper mentioned that the result tended to just intonation when the number of intervals were restricted to certain keys, but I suspect you would come up with a range of WTs when you ascribe different weights to the keys round the circle of fifths.

My guess is that the result will be something like EBVT III when you impose beat relationships on the intervals.

Vive la différence.
Posted by: David Jenson

Re: Equal temperament - 06/16/13 07:02 AM

With apologies to the math-whiz techs, I'm afraid all the numbers thrown up about tuning are lost on me. I'm impressed, and gratified that there are geniuses in the profession. I'm even slightly envious, but I plod on listening to the individual musical voice of the piano and tuning accordingly.
Posted by: rxd

Re: Equal temperament - 06/16/13 08:26 AM

I can't help wondering what to do if the pianos' musical voice keeps on demanding that it be tuned in reverse well????
Posted by: Mwm

Re: Equal temperament - 06/16/13 09:56 AM

Originally Posted By: David Jenson
With apologies to the math-whiz techs, I'm afraid all the numbers thrown up about tuning are lost on me. I'm impressed, and gratified that there are geniuses in the profession. I'm even slightly envious, but I plod on listening to the individual musical voice of the piano and tuning accordingly.

Herein lies the problem for me as a pianist and would be tuner. Many posters imply (and I agree) that each piano asks to be tuned in a particular way each time it is tuned. That would imply a single unique un-equal, non-named Temperament. But, it would also appear that one can set a named Temperament of choice in the middle register, and then listen to the piano for the required stretch in the remainder. Am I missing something here?
Posted by: Withindale

Re: Equal temperament - 06/16/13 11:16 AM

Originally Posted By: Mwm
Originally Posted By: David Jenson
With apologies to the math-whiz techs, I'm afraid all the numbers thrown up about tuning are lost on me. I'm impressed, and gratified that there are geniuses in the profession. I'm even slightly envious, but I plod on listening to the individual musical voice of the piano and tuning accordingly.

Herein lies the problem for me as a pianist and would be tuner. Many posters imply (and I agree) that each piano asks to be tuned in a particular way each time it is tuned. That would imply a single unique un-equal, non-named Temperament. But, it would also appear that one can set a named Temperament of choice in the middle register, and then listen to the piano for the required stretch in the remainder. Am I missing something here?

What the numbers tell you is that you can tune a piano in many ways. Some will be better than others but there is no indication that any single temperament or tuning is best. Quite the contrary.
Posted by: rxd

Re: Equal temperament - 06/16/13 12:06 PM

Many of the pianos I tune have been tuned only a matter of hours before by me or one of my colleagues and the implied terms of our jobs are equal temperemt within specific pitch parameters. All this is decided by musicians, conductors, soloists, producers, chief concert techs. It would be incredibly arrogant of me to go against these decisions no matter how clever I think I am. It is simply not my decision to make.
If the piano meets these parameters, I am quite at liberty to walk away having done nothing. This, however is rarely the case, there is always some slight drift.

Yes, the piano dictates to us all quite precisely the way the treble lines up and I and my colleagues are in agreement and accept each others work as it stands. We are, however, completely at liberty to subtly change the character of the piano by the way we choose to tune the area we call the "long steels", (the octave below the temperament octave). Without getting pretentious about this, a quick glance at the programme or listening to the player if they are still playing when I arrive will give a hint but I am tuning according to the program, not what the piano is "telling me". That would be almost like saying I do what the voices in my head are telling me.
The long steels are the most flexible part of the piano and are the first notes to drift so they always need some attention anyway.

Having said that, the way the covered strings are tune depends on how they were wound so it could be said the piano is telling me but it is really the string winder that is dictating the parameters and, depending how old the piano is, quite possibly from beyond the grave!!!

As someone in these pages said a couple of years ago, don't anthropomorphise pianos, they hate it when you do that.
Posted by: Minnesota Marty

Re: Equal temperament - 06/16/13 12:46 PM

Originally Posted By: Withindale
Reading your description of your pianos again are you saying that the basic temperament is ET, which is how I took it at first, or a UT?

Ian,

All three are non-ET. I am not sure of the exact names of the temperaments on the 'M's,' but the 'C' is EBVT-III. The big differences I hear are the ways the temperament scales evolve as they expand from the temperament octave on each piano. My conjecture is that is where "listening to the piano" comes into play. I have my 'C' tuned with the temperament octave set from A-4 rather than middle C. That makes a huge difference, and is really evident in the voice of the larger piano.

I have wondered, though never tried, if there would be a difference if the temperament octave were centered on A-3 rather than A-4? Maybe some of our esteemed professionals could venture an opinion?

BTW - All three of my pianos are tuned to A-442.
Posted by: Phil D

Re: Equal temperament - 06/16/13 01:35 PM

It's a bit disturbing with people talking about just intonation, that nobody mentions the commas. The pythagorean comma, and the syntotic comma, being the driving force between finding suitable keyboard temperaments. Those are the source of the need to compromise intervals. Just the fact that twelve times 3/2 is not the same as seven times two is problematic.

Edit: 3/2 to the twelfth is not the same as two to the seventh. Thanks, BDB. Also, my last sentence was nonsense anyway.
Posted by: BDB

Re: Equal temperament - 06/16/13 01:55 PM

Should be 3/2 to the 12th is not 2 to the 7th.
Posted by: Ed Foote

Re: Equal temperament - 06/16/13 02:11 PM

Originally Posted By: Minnesota Marty
I have my 'C' tuned with the temperament octave set from A-4 rather than middle C. That makes a huge difference, and is really evident in the voice of the larger piano.


Greetings,
If the difference is huge, it must be easy to describe is some detail. What is the difference that that different temperament octaves make?
Regards,
Posted by: Minnesota Marty

Re: Equal temperament - 06/16/13 02:54 PM

Hi Ed,

Words still become a problem with sonic descriptions. From your past postings, I understand that you appreciate the 'color' of different keys which develop from non-ET tunings. Imagine the colorations of the different keys with C as the center of the temperament octave. C-Major is the 'still' key. Now shift those same offsets centered from A. Suddenly C-Major is a very different beast.

Orchestra musicians are totally focused on A being the center of the universe. It's the string thing. Just conjecture, but could Well Temperament, if we even know what it really is, be thought of as coming from A rather than C? Familiar key color is drastically changed. Some good, some bad, but all different to the ear.

I didn't hear these things until I requested that the temperament be centered from A on one of my pianos. Needless to say, this was new to my tuner also, and he really tried to talk me out of it. As a reference, he used the A-442 tuning fork that I keep in my flute case. The results were very audible.

Since then, I have performed the Beethoven Concerto No. 4 (G-Major) in Prague and the tuner also tempered from A. Unlike the rushed rehearsal/performance schedule in the US, in Eastern and Northern Europe, you actually have the chance to work with and get to know the tuners. This tuner indicated that with a Wind Ensemble, he sets the temperament from Bb.

You might give it a try and find out the differences that you hear as you play in different keys. It becomes a very different world in the Chopin Etudes and the WTC.
Posted by: Mwm

Re: Equal temperament - 06/16/13 03:20 PM

Marty,
Regarding the temperament centre choice, my reading of history seems to indicate that C has been the centre for most UTs and WTs, hence the preponderance of music written in keys closely related to C (G, D, Am ). If they had been centred on A, the majority of works would have been written in A, E, B and F#m.

You raise an interesting point. I will ask the tuner for Tafelmusik, who tunes Valotti, what centre he uses. The orchestra tunes on A, but the continuo strings tune each string to the corresponding organ or harpsichord note.

When I get up the courage to change my piano from quasi-ET to a well, I will centre it on C.
Posted by: Minnesota Marty

Re: Equal temperament - 06/16/13 04:48 PM

Mwm,

The preponderance of compositions in the keys you list is the ease of performance, rather than tuning temperament. It's where beginning students start, and for the overwhelming majority of pianists, it is still the comfort zone. G-Maj. and F-Maj. are the second easiest keys and they are pretty far from C.

I mean, ya know, who wants to bother to comprehend double sharps and flats and play those key signatures with lots of stuff that looks scary anyway. Then there is the problem of starting a scale on a black key! Egad-fingering! It's just plain easier for all but advanced players.

The whole temperament thing leads one to become a mindless mass of quivering gelatin with the realization that D#-Major should sound different from Eb-Major. But, alas, the best that can be done is a non-equal temperament. ET sucks the life out of what little remains.

Do you have any sources citing the references to C as the historical temperament center? I would love to do further reading.

Cheers,
Posted by: Phil D

Re: Equal temperament - 06/16/13 05:20 PM

I find C# major to be the key that fits most easily under my hands. I love improvising in it. But reading it is a nightmare!
Posted by: Mwm

Re: Equal temperament - 06/16/13 10:51 PM

If you check rollingball.com, for example, most of the temperaments except ET show minimal temperament of intervals in keys near C and highest temperament in the keys near F# . It implies that C is the base for historic temperaments. All other historical documents I have read which give instructions on tuning use C as the starting point.
Posted by: bkw58

Re: Equal temperament - 06/17/13 12:17 AM

It doesn't get any more subjective than this.

Most of us are taught first piano lessons in C major; accordingly, it becomes an auto-basis for sensing flat and sharp. Setting my ET to the C fork seemed like a natural - and it worked quite well - later extending to "between the breaks" - but C always remained the basis.
Posted by: rxd

Re: Equal temperament - 06/17/13 12:25 AM

Just look at an UT and it will be readily apparent that the vast majority are centred on C.
Modern instructions for constructing a temperament only start on A because that is the note used for specifying pitch. They may start on A but are tonally centred mostly on C.
Posted by: Bill Bremmer RPT

Re: Equal temperament - 06/17/13 12:29 AM

Originally Posted By: rxd
I can't help wondering what to do if the pianos' musical voice keeps on demanding that it be tuned in reverse well????


Well, well, Reverse Well! I have been quite busy recently and had seen this topic but not had time to jump in. So, I am glad someone else gratuitously made the very first comment I might have. Most (9 in 10 at the least) aural tunings which one would swear on a stack of Bibles, a couple of Korans and a Torah to boot to be ET are in fact, Reverse Well!

I certainly did skip through all of the numbers postings because they mean nothing to me either. Surely, I recognize tuning program numeric data but all of the theoretical numbers are just that, numbers. What matters is what the piano is actually tuned to!

I find it an especially opportune time to say that what I have said all along is no joke. It is the unfortunate reality. I received an urgent call yesterday to tune a Steinway Model D for a concert today. (Sunday Concert Tuning!) The usual aural tuner not being available for a very regularly tuned instrument. What did I find? You guessed it, Reverse Well!

I temper that remark by saying that at least, this time, it was not a very blatant example of it, perhaps Victorian Reverse Well if there could be such a thing but I have often been quite surprised at how really Reverse some of the Reverse Well temperaments I have encountered could be!

And they were all deemed to be, believed to be, meant to be attempted to be, sworn to be, foot stomping madly proclaimed to be and paid for to be ET!

The reason why? One sole publication: Piano and Allied Arts by William Braide White. It should really be entitled, "A Recipe for Reverse Well" because that is what it truly is and has become. Surely not for every last piano technician, no.

The most enlightened of these found information elsewhere that facilitated the supplementary knowledge required to actually tune some semblance of ET but for most, the truncated instructions found on a couple of pages in the middle of the book were all that were ever studied or retained.

What is most important about that book was not what was in in it but what it deliberately left out! That was the infinitely large gap between 1/4 Comma Meantone (which was basically laughed at as being thoroughly useless) and the supposed ideal of the glorious ET! Complete freedom of modulation! AH! Each pitch unequivocally equidistant from the other! AH! The "Final Solution" AH!

Forget that all 16th Century music to the present is basically tonal. We need atonality! (So that maybe somebody might come along and play some kind of weird, atonal music and we would never hear it whenever they modulated). All key signatures should sound equal! We need to be able to play in ALL the keys, not just some! (And to do that, we must destroy all semblance of key color). A neutral palette. AH! One where all expression is either louder faster or slower and softer but NEVER from key signature!

The unfortunate result is that from the single minded, heck bent orientation to complete equality of temperament, the favoring and desire for a pure fifth has prevailed. Since that pure fifth cannot exist entirely throughout the circle of fifths, it is placed on the OPPOSITE side of the circle of fifths from where it had been in all Well Tempered Tunings!

Most piano technicians today have no knowledge whatsoever about what a Well Tempered Tuning really is. All they know is that they would never do that. Unfortunately what they also don't know is that in the quest for a purer sounding fifth, they inevitably create the unintended and unrecognized MONSTER known as Reverse Well!

Reverse Well is tuned in homes, churches, schools, piano dealerships and concert halls everywhere. It has been throughout the entire 20th Century. People have grown up with pianos tuned in Reverse Well! Not just in certain places but everywhere! They have become accustomed to a kind of atonality imposed by reverse tonality. Everything sounds out of tune and that is the norm! In recent years, it is only the ETD that has curtailed that trend.

We can go back to William Braid White and thank him for at least one thing, his suggestion that we all buy a Strobe Tuner! Since very few people could ever really tune a true ET following his instructions, the Strobe Tuner might be the best we could actually do!

Thankfully, it took the work of the late Dr. Al Sanderson (a Harvard University Scientist) in compilation with a man who actually understood aural tuning, Mr. Bill Garlick, RPT (former instructor at the North Bennett Street School of Piano Technology and subsequently as the Education Director at the Steinway Factory in New York) to actually facilitate the tuning of ET with the use of an ETD so that the majority of people who tune pianos could actually produce a temperament that is not in fact, Reverse Well!

Recently (in the past few weeks), I have been dismayed to read on the PTG Tuning Examiner exclusive blog about examiners not being able to find other RPT's who know the most basic of ET tuning checks! All otherwise well qualified technicians have abandoned aural tuning altogether and forgotten any aural tuning checks for ET they may have once known and practiced!

It all boils down to a definition of ET that does not match the science of it it any way, shape or form! All of the theoretical numbers produced on previous pages here are candles in the wind! They bear no relationship whatsoever to what piano technicians actually do on a day to day basis, not even to what the best of us do when we perform our finest work!

That is not to say that theoretical calculations are useless, it is only to say that when it comes down to it as a practical matter they will be completely ignored!

For a period of about 20 years, I refused entirely to tune any piano in ET! If ET had really and truly been a requirement, I would have either been out of business very shortly or forced to change course. What I found instead was that the majority of my clients found a Well Tempered Tuning to be more musically satisfying. That extended to professional artists and concert stages as well.

Today, I believe that any piano technician should have a versatile and adaptable set of skills and techniques to be able to respond to any request or demand from a client. I truly believe in the power of Cycle of 5ths based temperament. There is no doubt about that in my mind. I worked for many years to perfect a system that worked and could be easily replicated. I have many enthusiasts and followers of that system.

Whether anyone uses the Well Temperament system I developed or not, is not my primary concern. There are many Well Temperaments, Meantone and Modified Meantone temperaments available. The temperament I am most well known for was designed mostly for ease of replication but as it turns out, the Equal Beating properties it has have their own specific benefits. I also use other temperaments when I sense the need for them. I respond as well for specific requests for a specific temperament.

To say that one will use only one method, one temperament, one amount of octave stretch on EVERY piano, regardless of circumstances to me is self-limiting to the point of being self destructive! Pianos are by their very nature different, one from another. The way in which they are used and enjoyed is also different from one circumstance to another.

It simply does not make sense to impose a "one size fits all" policy on each of them. It makes far less sense to impose a misguided attempt at ET that results in Reverse Well on any of them!
Posted by: BDB

Re: Equal temperament - 06/17/13 02:13 AM

It seems odd that someone would spend 1300 words writing about something that most of his customers apparently cannot differentiate.

There are so many other things that go wrong with pianos. It seems a shame to waste so much energy on temperament, which is no more than a preference.
Posted by: Olek

Re: Equal temperament - 06/17/13 05:51 AM

Based on C

That said older music I (mean before Internet) is played with A=415 Hz , half a tone lower.
Posted by: Olek

Re: Equal temperament - 06/17/13 05:57 AM

Originally Posted By: rxd


That would be almost like saying I do what the voices in my head are telling me.
.
the string winder that is dictating the parameters and, depending how old the piano is, quite possibly from beyond the grave!!!



Phew ! I did not realize, the situation begins to be severe wink.

An interesting movie could be done "a journey in the head of the piano tuner" !!! (really ! no joking, that would be an instructive document for apprentice, some may understand it may be necessary to know about some music to be a piano tuner)

your phrasing made me smile right !
Posted by: Mark R.

Re: Equal temperament - 06/17/13 07:05 AM

Originally Posted By: Minnesota Marty
G-Maj. and F-Maj. are the second easiest keys and they are pretty far from C.


Am I missing something? G and F are as close to C as one can get.
Posted by: Mwm

Re: Equal temperament - 06/17/13 07:52 AM

Originally Posted By: Olek
Based on C

That said older music I (mean before Internet) is played with A=415 Hz , half a tone lower.






We perform French Baroque music at A=392 Hz.
Posted by: Mwm

Re: Equal temperament - 06/17/13 07:56 AM

Originally Posted By: Mark R.
Originally Posted By: Minnesota Marty
G-Maj. and F-Maj. are the second easiest keys and they are pretty far from C.


Am I missing something? G and F are as close to C as one can get.

Actually, on a modern piano they are both about 7cm away from C. C# is much closer, being only 1cm away. It is surprising that more pieces weren't written in C# in the Baroque era.
Regards.
Posted by: Minnesota Marty

Re: Equal temperament - 06/17/13 08:45 AM

Originally Posted By: BDB
It seems odd that someone would spend 1300 words writing about something that most of his customers apparently cannot differentiate.

It seems odd that someone would take the time to count the words in a post.
Posted by: Minnesota Marty

Re: Equal temperament - 06/17/13 08:48 AM

Originally Posted By: Mark R.
Originally Posted By: Minnesota Marty
G-Maj. and F-Maj. are the second easiest keys and they are pretty far from C.


Am I missing something? G and F are as close to C as one can get.

You are missing the fact that I am referring to keyboard location and that they are the next easiest keys for a pianist to play.

Playing a Theremin solves the problem completely and never needs to be tuned!
Posted by: RonTuner

Re: Equal temperament - 06/17/13 08:56 AM

Originally Posted By: Minnesota Marty
Mwm,

The preponderance of compositions in the keys you list is the ease of performance, rather than tuning temperament. It's where beginning students start, and for the overwhelming majority of pianists, it is still the comfort zone. G-Maj. and F-Maj. are the second easiest keys and they are pretty far from C.



When you think of key signatures in the order of the circle of fifths, then C is right between G and F! Does that clear this up?
Posted by: Minnesota Marty

Re: Equal temperament - 06/17/13 09:01 AM

Originally Posted By: RonTuner
Originally Posted By: Minnesota Marty
Mwm,

The preponderance of compositions in the keys you list is the ease of performance, rather than tuning temperament. It's where beginning students start, and for the overwhelming majority of pianists, it is still the comfort zone. G-Maj. and F-Maj. are the second easiest keys and they are pretty far from C.



When you think of key signatures in the order of the circle of fifths, then C is right between G and F! Does that clear this up?

I am not talking about the circle of fifths. I'm talking about the damn keyboard. Read what I wrote!
Posted by: Mwm

Re: Equal temperament - 06/17/13 09:38 AM

OK people. Calm down. We are likely talking at cross purposes here. A discussion of ET,WT,UT always seems to degenerate by this point. I too contribute to that sad decline.
Posted by: Phil D

Re: Equal temperament - 06/17/13 10:14 AM

All discussion of ET/UT tends to degenerate from the first post. Loren is well aware of this - some people just love the controversy!
Posted by: Ed Foote

Re: Equal temperament - 06/17/13 10:16 AM

Originally Posted By: Minnesota Marty
Originally Posted By: RonTuner
Originally Posted By: Minnesota Marty
Mwm,
The preponderance of compositions in the keys you list is the ease of performance, rather than tuning temperament. It's where beginning students start, and for the overwhelming majority of pianists, it is still the comfort zone. G-Maj. and F-Maj. are the second easiest keys and they are pretty far from C.

When you think of key signatures in the order of the circle of fifths, then C is right between G and F! Does that clear this up?

I am not talking about the circle of fifths. I'm talking about the damn keyboard. Read what I wrote!


Greetings,
When we talk about distance between keys in a temperament discussion, it is generally accepted that we are not talking about physical distance between the keys, but the distance around the circle off fifths, ie, F# is as far from C as possible, and almost as far from F. This position in the circle correlates to the width of the tonic third.

The majority of piano music is written in keys that are closer to C than F#. If you compile the usage charts, you will see that C was the most commonly used key, F and G are second, and D and Bb follow them in use. This progression continues through all the keys, with B, F#, C# being the least used. This holds true for Schubert, Mozart, Beethoven, and most others. Chopin is the exception, but only in the polarity, his usage of the keys is almost exactly opposite all the others.

If we plot the prevalence of keys's use through the ages, we find that in the Meantone era, 1300-1700, the eight keys closest to C were virtually all that was used, clear evidence of the restrictive wolf in that 1/4 C tuning. Beginning around 1700, or perhaps a few decades before, we begin to see a more democratic use, as the circulating tunings came into use. This use was still lopsided, with the remote keys being rarely used. The usage becomes gradually more democratic over the next 200 years, and by the 1900's there was little pattern or correlation between the temperament and the key's selection. I suspect that as music left the strict tonal forms of the Classical era behind, the UT's value and influence faded, and ET became more prevalent.

Beethoven actually preferred Eb more than any other key, and I suspect that harmonically, it offered a wider palette for modulation, in that moving in one direction heightened musical tension, while going the other way entered very calm spaces. In most WT, Eb (and A) are virtually identical to ET, and for LVB, Eb could possibly have been the harmonic home base that was easiest to start from.
Regards,
Posted by: bkw58

Re: Equal temperament - 06/17/13 10:21 AM

Contending for a point without becoming contentious is a challenge for us all - especially on Monday mornings. smile
Posted by: Mark R.

Re: Equal temperament - 06/17/13 11:30 AM

Originally Posted By: Minnesota Marty
Originally Posted By: BDB
It seems odd that someone would spend 1300 words writing about something that most of his customers apparently cannot differentiate.

It seems odd that someone would take the time to count the words in a post.


10 seconds of copying and pasting is all it takes - even the most basic word processor has a word counting tool.

But I'm sure BDB didn't know this, and counted through Bill's post by hand. smile

P.S.: When learning the piano, I never progressed from C major to B major or C# major just because they were the "closest" on the (damn) keyboard. Perhaps my teacher was wrong to let me progress more or less along the circle of fifths? Pity she isn't alive anymore, otherwise I'd demand my parents' money back. wink
Posted by: BDB

Re: Equal temperament - 06/17/13 12:07 PM

It does not take 10 seconds nor cutting nor pasting. I used an OS X service to give me the statistics for the selection.
Posted by: Minnesota Marty

Re: Equal temperament - 06/17/13 12:28 PM

Let me try this again.

* Beginning piano students, especially children, are not taught the circle of fifths before they learn that the key of G has one sharp.

* A piano teacher does not teach beginning students the key of F or G because the teacher understands the harmonic relation within the circle of fifths.

* Those keys are the next easiest to learn to play, that is the only reason they are taught in that sequence.

* It happens before any discussion of major or minor keys. Accidentals are still further down the road. No, the F# in the key of G-Major is not an accidental.

* It certainly has nothing to do with temperament.

I posted that I asked for one of my pianos to be tuned in a non-equal temperament using A-442 as the basis for the setting of the temperament octave. Though my tuner was hesitant, he did what I asked. He knew me, my pianistic skills, and I had the checkbook. (Sorry to be so crass)

The reason I wanted to try this is because I have a great deal of experience as an orchestral instrumentalist, as well as a pianist. As I stated previously, orchestral musicians temper their concept of key color from A as being the center, not from C.

I used the example of playing a concerto in G-Major on a piano which had a non-equal temperament based on A. This shifts the whole key color (aural) identification. It becomes more natural to the ear of orchestral musicians than does a non-equal temperament based on C.

To be honest, it doesn't matter at all about the history of tuning temperaments on fixed pitch instruments, such as the piano. It was nothing more than a request, an attempt, to more closely match one of my pianos to how I hear key color (temperament) as expressed in orchestral performance. It is a departure from standard practice which achieved it's goal.

For those of you who are comfortable tuning in non-equal temperaments, you might give it a try and make your own assessment on the results.
Posted by: UnrightTooner

Re: Equal temperament - 06/17/13 12:38 PM

All:

If you want just intonation with fixed pitch instruments, you can only have a few notes. (Work it out yourself.) And if you want just intonation with changeable pitched intruments (or voice), you can have only major and minor triads - no sixths or sevenths. Only the simpliest music can be in just intonation. What some may consider to be just intonation is the real compromise. I see nothing in ET that is a compromise. Equal is equal, not a compromise.
Posted by: BDB

Re: Equal temperament - 06/17/13 12:41 PM

Originally Posted By: UnrightTooner
All:

If you want just intonation with fixed pitch instruments, you can only have a few notes.


Or a whole bunch. Harry Partch used 69 notes per octave.
Posted by: Mwm

Re: Equal temperament - 06/17/13 01:39 PM

Originally Posted By: Mwm
Originally Posted By: Mark R.
Originally Posted By: Minnesota Marty
G-Maj. and F-Maj. are the second easiest keys and they are pretty far from C.


Am I missing something? G and F are as close to C as one can get.

Actually, on a modern piano they are both about 7cm away from C. C# is much closer, being only 1cm away. It is surprising that more pieces weren't written in C# in the Baroque era.
Regards.

I do hope that those of you who mentioned the physical distance of keys from C realized that I was joking.
Posted by: Mwm

Re: Equal temperament - 06/17/13 01:41 PM

It is possible to play a DP in just intonation using Justonics software. You tell the software where the modulations are, and how you want to shift to occur. Then when you play the work, it adjusts the pitch of each note/chord on the fly. Very cool.
Posted by: Mark R.

Re: Equal temperament - 06/17/13 02:29 PM

Originally Posted By: Minnesota Marty
As I stated previously, orchestral musicians temper their concept of key color from A as being the center, not from C.


My checkbook isn't nearly as expansive as yours, but I've played in five symphony orchestras, albeit provincial ones, for the better part of 20 years.

If (IF!!) this assertion of yours were true, it would mean that A major represents the most "well" key. It would further mean that each of these pairs are equally "colored":
E major (+1, 4 sharps) and D Major (-1, 2 sharps)
B major (+2, 5 sharps) and G major (-2, 1 sharp)
F# major (+3, 6 sharps) and C major (-3, no sharps/flats)
C# major (+4, 7 sharps) and F major (-4, 1 flat)
G# major (+5, 8 sharps) and Bb major (-5, 2 flats)

Truth be told, I have never heard of such a notion.
Posted by: Minnesota Marty

Re: Equal temperament - 06/17/13 02:57 PM

Well Mark R., that means that you heard "such a notion" here first. Congratulations!

In all five of your provincial orchestras, to what note did you tune?

That is the choice I made with my own piano. It works well.
Posted by: Mwm

Re: Equal temperament - 06/17/13 04:59 PM

Originally Posted By: Minnesota Marty
Well Mark R., that means that you heard "such a notion" here first. Congratulations!

In all five of your provincial orchestras, to what note did you tune?

That is the choice I made with my own piano. It works well.

Marty,
I think we may not be on the same page here. Are you saying that you could or would play Mozart Piano Concerto Op. 5, No. 4 in E flat on a piano using 1/4 comma meantone based on A? If you do, you will playing with the tonic on the 'wolf'. Even using just about any other WT, such as Young 1799, which would work beautifully with orchestra based on C, but would still be fairly wild based on A. Your thoughts?
Posted by: DoelKees

Re: Equal temperament - 06/17/13 06:18 PM

Originally Posted By: Mwm
Originally Posted By: Olek
Based on C

That said older music I (mean before Internet) is played with A=415 Hz , half a tone lower.






We perform French Baroque music at A=392 Hz.

And Italian early baroque a minor third higher.

Kees
Posted by: kohog

Re: Equal temperament - 06/17/13 06:26 PM

Originally Posted By: Bill Bremmer RPT

What is most important about that book was not what was in in it but what it deliberately left out! That was the infinitely large gap between 1/4 Comma Meantone (which was basically laughed at as being thoroughly useless) and the supposed ideal of the glorious ET! Complete freedom of modulation! AH! Each pitch unequivocally equidistant from the other! AH! The "Final Solution" AH!

If you had actually read the book, you would know that he recommended tuning meantone and described it as "very useful," not "thoroughly useless":
Quote:

The meantone system gives a "sweet" and harmonious effect for nearly all keys, with 16 tones to the octave, although of course this number still lacks 11 tones to make it quite adequate.
However, even with 12 tones to the octave, an experiment in meantone temperament can be tried, and will sound very attractive so long as one keeps within the range of keys allowable.
[...]
This is a very useful experiment and if tried out carefully will enable the student to play old music in the tuning for which it was intended; an experience sometimes most illuminating and delightful.


And this is what he had to say about ET:
Quote:
So long, of course, as the manufacture of pianos and organs is stressed rather on its industrial than on its artistic side we shall probably have to remain content with Equal Temperament. But it might as well be observed that if the piano and organ were out of the way, music throughout the world would be on some basis of tuning other than Equal Temperament within ten years.
[...]
tuners could do something to prepare the world for a better system if they wished to; and if they knew that improvement is actually possible. What we need is to realize that the Equal Temperament is a purely artificial system resting upon a consent gained rather on account of the absolute necessity for the piano having it than for any fundamental musical reason. To get something better we need a method which will either (1) allow more strings to the octave or (2) will give us a mechanism capable of making instant changes as required in the pitch of given strings, so that modulation may be as facile as it is now.
Posted by: Minnesota Marty

Re: Equal temperament - 06/17/13 06:43 PM

Mwm, my thoughts -

I am not a tuner and I don't know how the temperaments you mentioned would sound even if based on C. The temperament which was used was EBVT-III. I will not conjecture on that which I have no experience.

There is no Mozart Piano Concerto Op. 5, No. 4. in Eb. The Mozart Piano Concerto No. 5, K 175, is in D Major. The Mozart piano concertos in Eb Major are; Nos. 9, 10 (two pianos), 14, and 22.

There is absolutely nothing unpleasant or overly dissonant when playing in D Major or Eb Major. Though, they do sound different at the keyboard than EBTV-III based on C, but that transfers to what one hears when listening to recorded performances of these concertos performed with fine chamber orchestras. The sense of key color, and where the tonal structure leads the ear, are the same. That is exactly the point.

Have you tried it, or are you trying to imagine it theoretically?
Posted by: Mwm

Re: Equal temperament - 06/17/13 08:21 PM

Originally Posted By: DoelKees
Originally Posted By: Mwm
Originally Posted By: Olek
Based on C

That said older music I (mean before Internet) is played with A=415 Hz , half a tone lower.






We perform French Baroque music at A=392 Hz.

And Italian early baroque a minor third higher.

Kees

If I remember correctly, the organ at Peterborough Cathedral is tuned a quarter tone above 440 Hz. The quire rehearses at 440, then processes to the Cathedral to sing more brightly!
Posted by: Mwm

Re: Equal temperament - 06/17/13 08:33 PM

Originally Posted By: Minnesota Marty
Mwm, my thoughts -

I am not a tuner and I don't know how the temperaments you mentioned would sound even if based on C. The temperament which was used was EBVT-III. I will not conjecture on that which I have no experience.

There is no Mozart Piano Concerto Op. 5, No. 4. in Eb. The Mozart Piano Concerto No. 5, K 175, is in D Major. The Mozart piano concertos in Eb Major are; Nos. 9, 10 (two pianos), 14, and 22.

There is absolutely nothing unpleasant or overly dissonant when playing in D Major or Eb Major. Though, they do sound different at the keyboard than EBTV-III based on C, but that transfers to what one hears when listening to recorded performances of these concertos performed with fine chamber orchestras. The sense of key color, and where the tonal structure leads the ear, are the same. That is exactly the point.

Have you tried it, or are you trying to imagine it theoretically?


I was thinking of K. 107, the third one in E flat Major.

I haven't tried tuning a UT based on A, only C. All the UTs I have tuned are not even close to EVBT III, and have thirds beating upwards of 21 bps in the far keys, which would include E flat, if A was the tonal base. I can accept that EVBT III might sound fine based on A, though I don't see the point, since orchestral members, if they are world class, play in just intonation, so the whole point of temperament is moot.
Posted by: Mwm

Re: Equal temperament - 06/17/13 08:35 PM

I notice that Loren has thrown out the morsel of food, and let us scrap for it. Interesting.
Posted by: rxd

Re: Equal temperament - 06/18/13 04:26 AM

The UT movement is like any other religious movement. There are the one or two extremely knowledgeable high priests,

Then the enthusiastic followers, many of whom start proselytising before they know much about it and do the movement much harm when they attempt to explain it. They often simply appear as fools to anyone with the knowledge but is not a believer.

Some become heretics and, while appearing to abide by the basic tenets, start to extrapolate and make up their own interpretations which often make a nonsense of the central idea.

Then there are the lunatic fringe who will drop bombs on infidels and unbelievers often at the expense of their own credibility.
The list goes on.....

Me? I'm a non practicing believer.
Posted by: Mark R.

Re: Equal temperament - 06/18/13 05:13 AM

Originally Posted By: Minnesota Marty
Well Mark R., that means that you heard "such a notion" here first. Congratulations!

In all five of your provincial orchestras, to what note did you tune?

That is the choice I made with my own piano. It works well.


Our pitch reference was, of course, G## at 439.947 Hz (give or take 1.273 Hz, but always adding 0.026 Hz for Beethoven overtures on rainy days).

Oh, and for some weird reason, some of the brass always tuned to Cbb...

Feeble attempts at humor aside, we both know that orchestras tune to concert A of whichever definition. There was really no need to ask.

That aside, I don't see that pitch reference has anything to do with choice or center of temperament - especially on non-fixed-pitch instruments.

In my orchestras, anyway, any discussion of tempered intervals was pretty much a non-flier. When I pleaded for tuning open strings to somewhat narrow fifths in the violas and celli, in order to avoid an overly wide third between our C-strings and the violins' E-strings, and when I demonstrated that I could significantly raise my C-string (C3) by tuning ever-so-slightly narrower but still non-beating fifths from A4 to D4 to G3 to C3, I just received blank stares... By insisting on their pure fifths, often tuned from the wide side, the violists and cellists were effectively creating a reverse well, and made perplexed faces when the open strings (especially as roots of major chords) sounded horribly flat during play...
Posted by: Olek

Re: Equal temperament - 06/18/13 06:22 AM

Last time I asked the 5ths where not tuned pure at the violin, anyway for the soloist.
Posted by: Loren D

Re: Equal temperament - 06/18/13 06:57 AM

Originally Posted By: Mwm
I notice that Loren has thrown out the morsel of food, and let us scrap for it. Interesting.


Loren has a life! I've been here long enough for people to know that I post infrequently as time allows. I've commented several times on this thread.
Posted by: rxd

Re: Equal temperament - 06/18/13 08:02 AM

The only reason for using A as the tuning note is that all orchestral string instruments have an A string in a range convenient for tuning. It could almost as easily be a D or a G but they don't because the higher strings on an instrument are clearer sounding for pitch definition. (bass players often use the 3rd partial of their D string).

This convenient convention is just what it is. Strings don't use a temperament as such and have no requirement for a tonal centre in the quite the same way a fixed pitch instrument in an unequal temperament does. Bb transposing instruments sound their B, Eb instruments need to use f#. They don't make those notes their tonal centre. Wouldn't even dream of it.

Mark R., the string players I have conversed with about this do contract their 5ths very slightly. Maybe the seeds you have sown are now flowering down the generations. .
Posted by: Minnesota Marty

Re: Equal temperament - 06/18/13 11:20 AM

OK Good. We have now all agreed that orchestras tune to A, of whatever pitch. Phew!

My question remains, why not set a non-equal temperament from A rather than C? (Those who believe that ET is a gift from God, need not respond to this question.) There seems to be much resistance to this concept, but all of the replies have been theoretical, rather than actual. Ya know, actually playing the piano.

I have a series of rehearsals and performances approaching of the Poulenc Sextet. I am considering having my piano tuned with Bb as the temperament center. If this is successful, the primary performance piano could likewise be tuned. Thoughts?
Posted by: Mwm

Re: Equal temperament - 06/18/13 11:30 AM

Originally Posted By: Minnesota Marty
OK Good. We have now all agreed that orchestras tune to A, of whatever pitch. Phew!

My question remains, why not set a non-equal temperament from A rather than C? (Those who believe that ET is a gift from God, need not respond to this question.) There seems to be much resistance to this concept, but all of the replies have been theoretical, rather than actual. Ya know, actually playing the piano.

I have a series of rehearsals and performances approaching of the Poulenc Sextet. I am considering having my piano tuned with Bb as the temperament center. If this is successful, the primary performance piano could likewise be tuned. Thoughts?

Unfortunately, for me, that scenario is hypothetical, so I can't comment. Are you going to use EVBT III? Let us know what the interaction with the ensemble is like. My experience is with temperaments with a strong wolf, though I have played the WTC even with the wolf, and, while the sound is quite unusual, I don't mind it because of the huge colour shift, and the fact, if you will, that Bach was aware of the colours and used them to his advantage in the way in which he wrote each prelude in particular.

Ok, I looked at the Poulenc. It is very tonal, heavily biased toward B Flat, F, and D flat, with the odd momentary excursion to distant tonalities. My opinion is that it would work extremely well in even a strong UT, much better that ET. GO FOR IT!
Posted by: Ed Foote

Re: Equal temperament - 06/18/13 11:34 AM

[quote=Minnesota Marty]

My question remains, why not set a non-equal temperament from A rather than C? There seems to be much resistance to this concept, but all of the replies have been theoretical, rather than actual. Ya know, actually playing the piano. /quote]

Greetings,
It would alter piano music that was composed under the influence of the WT's between 1700 and 1850 or so. The tonal center of C was so common that tuning a WT so that the center was shifted to A, making the A-C# third the smallest, puts everything three harmonic steps away from the commonly expected placement. Nothing wrong with having the center elsewhere, per se, but don't expect the modulations to be helped by the normal resolution into consonance.

Shifting between Vallotti and Young is fairly simple, and I have rarely had anyone notice one was not the other, but the difference there is only one step, and most modulatons behave as expected.
REgards,
Posted by: Minnesota Marty

Re: Equal temperament - 06/18/13 11:40 AM

MWM, I totally agree with you about composers selecting keys for their tonal color. For the vast history of Western music, ET just didn't exist. It's a Johnny-come-lately. Using Bach or Mozart as examples, since both were certainly familiar with writing for strings, should we make the assumption that "well" temperament was based on middle C? I'm doing an experiment since I have different instruments available to give it a try.

Using EBVT is undecided. That will be a discussion with the tuners. For clarity, the pianos are in three different locations and each has a different tuner.
Posted by: Mwm

Re: Equal temperament - 06/18/13 11:44 AM

Did you see my edit. A strong UT based on B flat would be very wonderful.
Posted by: Withindale

Re: Equal temperament - 06/18/13 11:54 AM

Originally Posted By: Minnesota Marty
... I have a series of rehearsals and performances approaching of the Poulenc Sextet. I am considering having my piano tuned with Bb as the temperament center. If this is successful, the primary performance piano could likewise be tuned. Thoughts?

Perhaps this is a question I should not ask if I don't know the answer, but do you mean replacing C with Bb (and so on) in the circle of fifths?

When you come to a composition for the piano in C, do you play it in C or Bb?

Poulenc aside, what about the composer's notions of colour, consonance and dissonance?
Posted by: Mwm

Re: Equal temperament - 06/18/13 12:06 PM

Originally Posted By: Withindale
Originally Posted By: Minnesota Marty
... I have a series of rehearsals and performances approaching of the Poulenc Sextet. I am considering having my piano tuned with Bb as the temperament center. If this is successful, the primary performance piano could likewise be tuned. Thoughts?

Perhaps this is a question I should not ask if I don't know the answer, but do you mean replacing C with Bb (and so on) in the circle of fifths?

When you come to a composition for the piano in C, do you play it in C or Bb?

Poulenc aside, what about the composer's notions of colour, consonance and dissonance?

In this particular case, I would argue that the colour, consonance and dissonance would be enhanced by shifting the temperament base to B flat. If we keep in mind that the wind players prefer to be playing, to the extent possible, in just intonation, having the purest keys based on B flat would make that job more easy.
Posted by: Minnesota Marty

Re: Equal temperament - 06/18/13 12:06 PM

Originally Posted By: Ed Foote
Nothing wrong with having the center elsewhere, per se, but don't expect the modulations to be helped by the normal resolution into consonance.

Thanks Ed.

That is exactly what I am hearing. The difference in the "pull" toward resolution is exactly what I find so intriguing. I have used playing in G-Major as an example. It is used so commonly in the Baroque and Classical eras for keyboard composition, and this temperament center, on keyboard, causes it to be much "brighter" than is usually heard. There is much more tension leading to consonance/resolution, also. I used chamber orchestra performance as an example, as the piano seems to match more closely the juxtaposition and intonation of intervals as is heard in a fine ensemble.

The important factor, as always, is that there is no "just" temperament employed in instrumental or vocal performance. Pitch is constantly fluid and "temperament" is ever changing. Vocalists and instrumentalists are not taught "temperament" to be employed in performance. Key color is stressed. One learns to hear, and implement, the difference between C-Major and Eb-Major, as example. Temperament is a concept learned in Musicology classes, not in the teaching studios.
Posted by: Mwm

Re: Equal temperament - 06/18/13 12:10 PM

Originally Posted By: Minnesota Marty
Originally Posted By: Ed Foote
Nothing wrong with having the center elsewhere, per se, but don't expect the modulations to be helped by the normal resolution into consonance.

Thanks Ed.

That is exactly what I am hearing. The difference in the "pull" toward resolution is exactly what I find so intriguing. I have used playing in G-Major as an example. It is used so commonly in the Baroque and Classical eras for keyboard composition, and this temperament center, on keyboard, causes it to be much "brighter" than is usually heard. There is much more tension leading to consonance/resolution, also. I used chamber orchestra performance as an example, as the piano seems to match more closely the juxtaposition and intonation of intervals as is heard in a fine ensemble.

The important factor, as always, is that there is no "just" temperament employed in instrumental or vocal performance. Pitch is constantly fluid and "temperament" is ever changing. Vocalists and instrumentalists are not taught "temperament" to be employed in performance. Key color is stressed. One learns to hear, and implement, the difference between C-Major and Eb-Major, as example. Temperament is a concept learned in Musicology classes, not in the teaching studios.

Marty,
the tonal centre, when playing or singing in just intonation is always shifting. I guess you could call that the temperament shifting, but I prefer to think of it as a leaning toward thenew key.
Posted by: Minnesota Marty

Re: Equal temperament - 06/18/13 12:22 PM

Originally Posted By: Withindale
Perhaps this is a question I should not ask if I don't know the answer, but do you mean replacing C with Bb (and so on) in the circle of fifths?

The circle of fifths is the circle of fifths. All I'm suggesting is placing the temperament center on Bb. Wind ensembles tune to Bb rather than A. It is with that understand that I would like to try the keyboard temperament based on Bb.

Originally Posted By: Withindale
When you come to a composition for the piano in C, do you play it in C or Bb?

In C. Why would I transpose it?

Originally Posted By: Withindale
Poulenc aside, what about the composer's notions of colour, consonance and dissonance?

That is exactly what I am trying to explore.
Posted by: Minnesota Marty

Re: Equal temperament - 06/18/13 12:27 PM

Originally Posted By: Mwm
Marty,
the tonal centre, when playing or singing in just intonation is always shifting. I guess you could call that the temperament shifting, but I prefer to think of it as a leaning toward thenew key.

Yep, and that is exactly what I said in my reply to Ed Foote.
Posted by: Withindale

Re: Equal temperament - 06/18/13 12:49 PM

Originally Posted By: Minnesota Marty
... All I'm suggesting is placing the temperament center on Bb. Wind ensembles tune to Bb rather than A. It is with that understand that I would like to try the keyboard temperament based on Bb.

Originally Posted By: Withindale
When you come to a composition for the piano in C, do you play it in C or Bb [when the temperament center is Bb]?

In C. Why would I transpose it?

To explore, as you say!
Posted by: Minnesota Marty

Re: Equal temperament - 06/18/13 12:52 PM

Originally Posted By: Withindale
Originally Posted By: Minnesota Marty
... All I'm suggesting is placing the temperament center on Bb. Wind ensembles tune to Bb rather than A. It is with that understand that I would like to try the keyboard temperament based on Bb.

Originally Posted By: Withindale
When you come to a composition for the piano in C, do you play it in C or Bb [when the temperament center is Bb]?

In C. Why would I transpose it?

To explore, as you say!

I tend to reserve that skill for aging sopranos and tenors and tell them nothing! wink
Posted by: keystring

Re: Equal temperament - 06/18/13 01:02 PM

I read through this thread after bumping into the reference to Bb. Marty, there is an earlier post of yours where you write about a long conversation you had with a conductor:
Originally Posted By: Minnesota Marty
He indicated that for a Wind Ensemble, he sets his temperament octave from Bb.

I can see it for wind, and have talked to brass players. My other instrument is violin. Here are the characteristics of that instrument: The strings are G, D, A, E. This sets up certain patterns of resonance through sympathetic vibrations. You get a richer sound resonating through the entire instrument. It is not just the strings but the wood itself, which is chosen as tone wood. In general, keys with sharps in the signature work better than those with flats, because of this. It is not just that we can use more open strings as pitch reference for ease of playing. When I learned the Db major key, my teacher warned me that the whole thing would sound "dull". (So would C# major, ofc). In F major we still have: G, A, D, E as degrees 2,3,6,7, but I,IV,V are all notes that won't resonate in the instrument (F,Bb,C). After that, in flats keys, there are diminishing returns.

So I'm thinking that if you're looking at what happens with other instruments, you might want to look beyond wind into strings, for that side of it.
Posted by: Minnesota Marty

Re: Equal temperament - 06/18/13 01:37 PM

Keystring,

The comment you quoted was not by a conductor, but rather a tuner in Prague. It was his approach to the temperament center as selected for wind ensemble, rather than orchestra.

If you read this thread, there has been much discussion of the whys and wherefores of an orchestra tuning to A.
Posted by: Mark R.

Re: Equal temperament - 06/18/13 02:13 PM

Originally Posted By: Minnesota Marty
Originally Posted By: Withindale
When you come to a composition for the piano in C, do you play it in C or Bb?

In C. Why would I transpose it?


Because you've just gone and put a Bb-centered UT on you piano, to suit a composition in Bb major.

Really, a rather supreme irony:

You're contemplating tuning your piano for a composition in Bb, and then playing a composition in C (generally accepted as the home key for UTs or WTs!), for which your piano would eminently not be optimally tuned. In fact, on your Bb-tuned piano, C major and its dominant, G major, would sound very much like ET. (Which is, perhaps, why Ian asked you in the first place.)

On the other hand, you deem fit to degrade ET, which caters for all keys, as a "Johnny come lately".

[Edit: just reading the most recent responses. An ET remains an ET, independent of the pitch reference that was used to tune it. There are well-documented procedures for tuning ET from C or from A, and even from other notes. This technician's forum on PianoWorld has had some of these discussions before (starting point of the temperament octave - even a temperament 10th or temperament 12th). I know, because I asked a few of the many pursuant questions, and read the ensuing answers with great interest. So, I repeat: I see no reason to confuse pitch reference with the tonal center of whichever UT is chosen. It was already written here that A is chosen as tuning note because all string instruments have some form of A-string or suitable partial.]
Posted by: DoelKees

Re: Equal temperament - 06/18/13 03:03 PM

IMO in a normal WT (invariably centered on C major of course) C major sounds better than C# major. So I play the C# major pieces of the WTC clavier in C instead because it sounds better. If I really had to play it in C# major I would retune the harpsichord centered on C#. This is what Gustav Leonhardt did in his landmark recording of the 48.

In WTC I the prelude in Eb minor is followed by the fugue in D# minor. Did you know the reason is the originals were written in E minor and D minor and Bach just transposed them to stuff them in the WTC? Makes you (at least me) think about arguments that the key and tuning was allegedly so important to the composer.

Also in Bach's cantata performances (by himself) the instruments were tuned a semitone below A440 (because he bought them from France) and the organ a semitone above. So in the scores you see the organ being written in a different key than the rest. How to reconcile that with the idea that the key of a piece is so important to the composer is beyond me.

Kees
Posted by: Minnesota Marty

Re: Equal temperament - 06/18/13 04:32 PM

Mark R. -

You have completely misunderstood what I have written. I'm not having my piano tuned to a non-equal temperament based from Bb because of any single composition, it is because it is the tuning center used in a Wind Ensemble. Obviously you have no familiarity with the Poulenc. It is all over the place harmonically. Though it can be analyzed harmonically and structurally, it is not identified by specific key.

The use of "Johnny-come-lately" in reference to ET is not disparaging, it is a matter of historical fact.

You seem to maintain that there is something wrong with basing a non-equal temperament on anything other than C. I am in the process of finding out if that it is true. I don't believe it is problematic at all.

My preference is tuning other than in ET. The temperament octave, in ET, could be placed anywhere and the results would be the same. It wouldn't matter what tuning fork is carried in the tuner's tool bag.

Kees,

There is a big difference between the necessities of a given performance and the intention of the composer. Odd compromises occur all the time.

Why would Bach write the Well Tempered Clavier if not to demonstrate that a keyboard could be tuned to accommodate all keys? Other than glorious music, that is its purpose. The result of his creation has led to what we now refer to as "key color." Our concepts of, and attitudes toward, keys which sound "dark," mysterious," or "bright" are based on understandings and labels which have been passed down through generations.

When Bach studied in Lüneburg, the available organs were of very divergent temperaments. The WTC seems to be an attempt at some sort of standardization of tuning for keyboard instruments. It is one of the hallmarks of the late Baroque.
Posted by: Mwm

Re: Equal temperament - 06/18/13 06:26 PM

Kees,
All of the Cantatas were written in closely related keys to C. For the most part Bach transposed, wrote, or sight transposed the organ part down a whole tone in order to match the nominal A=415 of the other instrumentalists, being that most of the organs he played were in the A=460-480 Hz range. I can't see a huge issue with colour in that case. The problem would be if the transposition had to be to a far key. I have haven't read anything to indicate he did that, but there is much (almost everything) that I don't know.
Posted by: Ed Foote

Re: Equal temperament - 06/18/13 06:35 PM

Originally Posted By: DoelKees
IMO in a normal WT (invariably centered on C major of course) C major sounds better than C# major. So I play the C# major pieces of the WTC clavier in C instead because it sounds better. If I really had to play it in C# major I would retune the harpsichord centered on C#. This is what Gustav Leonhardt did in his landmark recording of the 48.


Greetings,
I hear it differently. The wider third of the C# (in most WT), really makes that prelude bright and aggressive. I have had a Yamaha Disklavier to use at a PTG convention, and it was tuned in fairly colorful WT. We played that C# stuff back and forth on C and C# and it was all agreed that the C# piece sounded a lot better in C# than in the calmer C. The Prelude in C sounded terrible when moved up to C#. I think Bach knew what he was doing, and I think he was suggesting ways to use the particular characteristics of each key in a well-tempered keyboard. Some compositions can move around, and did, but others really only shine in the original key.

>>Other than glorious music, that is its purpose. The result of his creation has led to what we now refer to as "key color." Our concepts of, and attitudes toward, keys which sound "dark," mysterious," or "bright" are based on understandings and labels which have been passed down through generations. <<

It may also be due to the subliminal effects of dissonance still at work, after all these years...
Regards,
Posted by: Minnesota Marty

Re: Equal temperament - 06/18/13 06:42 PM

Originally Posted By: Ed Foote
It may also be due to the subliminal effects of dissonance still at work, after all these years...

Ah Yes -- And one of the reasons we still have war and conflict. Sometimes tradition overcomes reason. (No, that is not a lead in for ET enthusiasts!)
Posted by: DoelKees

Re: Equal temperament - 06/19/13 06:10 AM

Originally Posted By: Minnesota Marty

Why would Bach write the Well Tempered Clavier if not to demonstrate that a keyboard could be tuned to accommodate all keys?

Perhaps to demonstrate very remote keys don't sound very good in a strong WT? Perhaps to show you need to retune the instrument on a different key center for for example C# major? Or, most likely to me, because it was a fashionable thing at the time to write collections of compositions in all keys. Eg Schickhard produced a set of 24 sonatas in all keys.

Perhaps. All I know for sure is nobody knows for sure why he wrote it.

Kees
Posted by: Ed Foote

Re: Equal temperament - 06/19/13 10:08 AM

Originally Posted By: DoelKees
Originally Posted By: Minnesota Marty

Why would Bach write the Well Tempered Clavier if not to demonstrate that a keyboard could be tuned to accommodate all keys?

Perhaps to demonstrate very remote keys don't sound very good in a strong WT? Perhaps to show you need to retune the instrument on a different key center for for example C# major? Or, most likely to me, because it was a fashionable thing at the time to write collections of compositions in all keys. Eg Schickhard produced a set of 24 sonatas in all keys.
Perhaps. All I know for sure is nobody knows for sure why he wrote it.
Kees


Greetings,
I don't think it was written to show the need to retune, since playing the C# prelude on the most consonant center makes it a dull, lifeless piece. Many of those "strong" keys provide a beauty that isn't available without contrasts of harmonic values.

What is important is that we know all the plausible possibilities inre temperament, that Bach could have considered. And now, for the first time in history, we can listen to his compositions performed on all these varied approaches and make a value judgement based on our own tastes. Thus, rather than rejecting a temperament on theoretical grounds, we have to expose ourselves to the music and say what we prefer. I haven't heard more than 10 percent of listeners prefer Bach's music performed in ET when given a side by side choice with a WT, ( and I have presented this choice numerous times to classes of technicians and music teachers).

Try them all, make a choice, it is the way that the modern world offers a route to expand our horizons. Trying to ascertain what Bach had in mind by logical reason will only go so far, then we have only to describe our own sensual response. But, that is why music exists.
Regards,
Posted by: Mwm

Re: Equal temperament - 06/19/13 03:56 PM

Ed. Well said. A fitting end to this discussion one would hope..
Posted by: Unequally tempered

Re: Equal temperament - 06/19/13 03:57 PM

Hi!

In a good unequal temperament C# provides a key in which thinks can skate, as on ice, without foundation or sticking harmonically together. B major too.

The whole point about Bach's well tempered tuning was that each key was equally usable, not necessarily that each key was exactly the same.

Look up YouTube Chopin 24 preludes unequal temperament for how all keys are playable but all sound a little different.

The contrast for Bach was meantone, in which 4 major keys are most definitely unplayable. That contrast was a good temperament in which all keys were playable, not equal temperament in which they all sound the same

Best wishes

David P
Posted by: BDB

Re: Equal temperament - 06/19/13 08:30 PM

The Chopin Preludes all sound different no matter what the temperament!

I suppose one could take a piece and transpose it into 12 different keys, and show that there is a difference, but I suspect most people would notice the difference in pitch. Or someone with a lot of time on their hands could tune the piano starting with a different pitch 12 times, and play the same piece over and over, showing the different colors that it makes. Even so, I think most people would get bored pretty quickly.