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#632974 - 06/11/03 05:11 PM Tuning with tuning forks
.rvaga* Offline
2000 Post Club Member

Registered: 01/14/02
Posts: 2046
Loc: Portland, Oregon
Perhaps an offbeat question. . .

When tuning by ear, why don't techs use a complete set of 13 tuning forks calibrated in equal temperament? Wouldn't this eliminate errors in listening to beats? Wouldn't this be a heck of a lot cheaper than an electronic device?

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#632975 - 06/11/03 07:32 PM Re: Tuning with tuning forks
Bill Bremmer RPT Offline
3000 Post Club Member

Registered: 08/21/02
Posts: 3226
Loc: Madison, WI USA
It's a natural question with very simple answer: such a set of tuning forks would not compensate for the all important factor known as Inharmonicity. If all you did was tune as perfect a unison as you could to each fork, then tune what you perceive to be "pure" octaves up and down after that, you'd end up with a tuning that would not sound very good at all.

The initial octave must be wider than what the tuning forks would provide and all of the other notes must be spaced accordingly. That is, if you really believe in Equal Temperament, which I do not.

In recent years, many technicians have discovered that a mild, Well Tempered Tuning makes all music sound more appealing. Couple that with advanced octave stretching techniques and you really have something with some musical appeal.

The idea you have satisfies the desire to be *theoretically* correct but that theory is 150 years old already and everyone who really understands piano tuning knows that there are finer points which such simple mathematical theory can't address.

The Schaff Piano Supply catelogue offers such a set of forks but I don't think they sell very many of them. Trying to duplicate what highly skilled aural tuners do with electronic tuning devices has been a long process. A lot of progress has been made but I am sure glad I learned to tune by ear because to me, there are no mysteries or unsolvable problems.

Piano tuning is an art and science too and there are no short cuts to quality, the same as there are no short cuts to virtuosity in musicianship.

If you are interested enough, see my website for ideas about both temperament and octave tuning.
_________________________
Bill Bremmer RPT
Madison WI USA
www.billbremmer.com

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#632976 - 06/12/03 02:00 AM Re: Tuning with tuning forks
BDB Online   content
Yikes! 10000 Post Club Member

Registered: 06/07/03
Posts: 21531
Loc: Oakland
Tuning forks do not free one from the necessity of listening to beats. A set of tuning forks may help in setting the initial octave, but you still have the rest of the piano to tune.

Listening is only half the job of tuning a piano. I've never found it to be the hardest part. Using the hammer (wrench) properly is at least as difficult, and not nearly as enjoyable as listening as you tune a piano.
_________________________
Semipro Tech

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#632977 - 06/13/03 07:50 AM Re: Tuning with tuning forks
Bob Offline
3000 Post Club Member

Registered: 06/01/01
Posts: 3867
Ditto, and include with the tuning forks cheap electronic tuners. For grins, I tried tuning temperments with one (a $100 model), but always ended up tweaking notes to get the beats right. I would imagine the more expensive tuners do a better job with the temperment, but I've never used one to know for sure. Any comments on that?
_________________________
www.PianoTunerOrlando.com






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#632978 - 06/13/03 09:18 AM Re: Tuning with tuning forks
Bill Bremmer RPT Offline
3000 Post Club Member

Registered: 08/21/02
Posts: 3226
Loc: Madison, WI USA
I received a private post from someone who tried to tune a severely out of tune piano with a pitch pipe. When I was rebuilding, I used a pitch pipe for the very first rough tuning while stringing called a "chip tuning". I don't have time to get into the explanation as to all of the reasons but it is not possible to tune a piano this way.

What was interesting about the remarks of the pitch pipe tuner was that afterwards, some chords sounded good while others sounded terrible. This is what happens when the focus is entirely upon Equal Temperament, e.g., there is no other temperament. When that's what you believe, you inevitably get someing quite *unequal* and as Murphy's law dictates, the "bad" keys will always be the ones you want to play in.

A Strobe type tuner, a Korg type electronic tuner or a set of chromatic tuning forks will never produce in a good piano tuning, most often one which is far from the ideal.

The essence of good aural tuning is the perception of and control of beats, not "counting" beats. Even with a good eclectronic tuner, you still have to tune the unisons by ear which involves listening to and controlling beats.

There is no easy shortcut and no way to tune a piano without learning to control beats.
_________________________
Bill Bremmer RPT
Madison WI USA
www.billbremmer.com

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#632979 - 06/14/03 06:46 AM Re: Tuning with tuning forks
ChickGrand Offline
3000 Post Club Member

Registered: 05/02/03
Posts: 3217
Loc: Midwest U.S.
 Quote:
Originally posted by Bill Bremmer RPT:
The essence of good aural tuning is the perception of and control of beats, not "counting" beats. Even with a good eclectronic tuner, you still have to tune the unisons by ear which involves listening to and controlling beats.

There is no easy shortcut and no way to tune a piano without learning to control beats.[/b]
I'm always apologizing for long posts elsewhere here, but let me particularly apologize up front here for the following layered inquiry, which asks in part for some short answers that I think you may be able to provide as a concientious poster in this forum.

Your statement above makes sense to me so you are my victim of choice to finally discuss the following and ask a few questions regarding tuning and piano tech career development.

I also want to thank you in advance for any time you may invest in answering my questions here, and want to suggest that I'm in no particular hurry for answers, so please defer to some time when you feel inclined, IF at all. If not, I understand that too without question. "Pass" is always an acceptible answer.

I'm both an amateur player and an amateur tinkerer. I've had, at the height of it, 5 pianos at the same time. With one upright and one small grand I was willing to experiment on. (Couldn't have hurt either one, I promise!)

My hearing covers an extraordinary range from low to high on aural testing with great sensitivity to even the softest of sound, and I've always had a remarkable sense of pitch (voice teacher observation).

So I jumped in and initially tuned the little grand to ET with the aid of TuneLab Pro on a laptop, but using my ears to satisfy me on some intervals (which put TuneLab's indicator off by a cent here or there. I read as much as I could beforehand on-line, but so much of what is written is written in a manner that it seems only a tuner already trained in the language would understand. (I recognize I may need to do much more reading, of the right resources--suggestions for just a starting volume?).

I did a lot of reading about regulation, also online, (which was MUCH less obtuse) and made passes at that with good results and a bit of light hammer shaping with sandpaper, with very good results on all the acoustics I own. Replaced some "dead" wound strings on the small grand with a little guidance from a retired local tech who advised me about gauges and sound length placement, etc., and replaced one unwound that I broke (classic hammer on wrong pin--why isn't it rising!), to good final effect. Those mediocre little pianos turned out quite well and I sold both to the first looker, quickly, for my asking (a little hesitantly by then).

The one thing I have yet to see anywhere is the definition of a "beat", although I "think" I know "beatING" when I hear it, and since you stated the opinion above, I'm interested in your clarification of my thinking, if needed.

There does seem to be a cycle to a sound (either rising or falling) that is quite defined in the lower pitches. May I assume the cycle is a beat? I found with a little practice, I could get dead-on with unisons muting two, tuning one, comparing pairs, then the third by the same method with TuneLab (but faster with my ears) to eliminate this cycle of "overtones". I am just amazed anyone can count that cycle in the higher octaves. If beating is that sort of slide-guitar kind of "twanging" rising or falling cycle of overtones, I got rid of that very quickly and completely in the unisons and arrived at a tone that was strongest when most pure, but I certainly couldn't begin to count or understand just what I should count. The twang of overtones just seemed to be something to minimize by whatever means. My octaves turned out well with little effort--the second time--once I understood that the "width" of the octave determined the overall result (tough lesson by the time I got to AAA first pass and found it WAY low and started over narrowing the octaves.

What I realize is much more complicated, is arriving at the best compromise for the minimum or total absence the most places of that same "twang" if that's what we're referring to as "beat" on thirds, fourths, fifths, sixths and such where tuners talk about compromising on one beat or a half, depending on temperament, or 6 in higher octaves and such, given that the frequencies can not be perfectly even multiples everywhere due to the number of tones. My approach was just to minimize them to the point the overtones seemed to not rise or fall but become steady (least objectionable) whenever they could not be eliminated completely.

While I'd love to better understand "partials" and fundamentals and their relationship, at this point I just want to be clear about What constitutes the cycle of a "beat"? Is it this cycle of rise or fall I heard?

I ended up just tuning by playing all interval combinations (among any two adjacent octaves) to arrive at the least aurally inharmonious result for the greatest number of intervals. I kept thinking if I understood the math behind partials, fundamentals, counting beats, etc, I might eliminate some of this trial and error. Am I right to think that, and is there a reference that's particularly good for the beginner to learn these fundamentals--as in the terms/symbols and math of it if they are even necessary or maybe essential?

Long story even longer, the my results were a far sight (sound) better than the local tuning that I got on delivery of the little grand (the horror of which provoked me to do attempt something better myself) (Great in the store, hideous at home after the delivery tuning). Also achieved a good result on the much neglected, but never abused, little upright which required an amazingly exact full semi-tone pitch raise (per TuneLab--spot on one half low). (shifting the keybed up one key would have been the perfect quick solution as PTG often wistfully say theyd like to do at the expense or swapping of the cheekblocks).

On comparison of those two to the concert grand in the same room note by note (lots of shoving to line em up for one person to simultaneous play for comparison of pitch in a room that was a circus of pianos) I was surprised at how precisely I'd come by my inexperiences method to matching the pitch of the just-tuned concert grand(professional--out of towner, on delivery--still holding). And they were all a good match for the digital, as well (the fourth in the room!).

I then got bold and experimented with a mild Well Temperament on the small grand for pleasing results on Beethoven and other early 19th century music. The back to ET to do it again.

But none of this experience ever made it quite clear the beat--to even start counting that unless I interpret it as this rising or falling cycle. I more or less relied on the displays in TuneLab to fine-tune desired pitch (watching to not confuse partial and fundamental peaks) and to stop as much as possible the moving display that I took to be beating, but let my ears be the final judge based on the purity of the intervals. I sometimes chose to let this display move ever so slowly on notes to improve and maximize good intervals for tone, at the expense of perfectly centered pitch.

Am I even beginning to approach this with a little of the proper considerations?

I thoroughly enjoy lurking in the PTG archives and I learn a lot there about construction, design, repair, and redesign, and the need to refuse all on occassion even. I think I grasp a lot of the general discussion about harmonics, inharmonicity, and the wildly ranging design and varying execution issues that nfluence pitch, tone, and volume on a given instrument. I love the discussions about diversity of designs, contemporary and historic, room for new designs and potential improvements, and value of various levels of repair.

I've thought about apprenticing as a last career change to carry me into retirement (as if that could ever happen), but unfortunately this town has only ONE tuner/tech who serves a single piano dealer (along with the odd acquisition at the competing mostly-band-instrument store) and the local largish community. Room for another, certainly, but not much option for apprenticeship without either relocation or a very long commute (considering both). Do most techs/tuners apprentice, or do most go to schools, or perhaps factories to learn? Can an amateur join PTG and pay dues to attend meetings to go to workshops and such to learn, even without an apprenticeship, as a starting point? (Sounds like some good workshops at the meetings.)

All this interests me intensely, as I realize I'll never make a dime as a "concert pianist" however much progress I've made lately nor am I even trying to achieve that. I just love piano generally, lots of particular pianos, their history, and their variety, and think my best way to "make love" to a piano might be to lovingly maintain or restore some. Perhaps to open my own rebuild/repair shop eventually.

I formerly did a lot of furniture work and even did a two year stint as a housebuilder in one of my earlier 8 lives (feels like it), so I'm quite comfortable with any kind of woodworking, fine or otherwise. I've also rebuilt complex 12-cylinder Jaguars, so I'm fairly fearless as a mechanic on metal machines. I'm as much interested, or moreso, in learning rebuilding and restoration as anything. Is apprenticeship the best approach to this? Is 45 an unreasonable age to begin at least some subset of this type of business?

I make a living writing and doing graphics design and related stuff, but am just ready for a change to something I can get freshly passionate about.

Again, thank you much for your time to consider answering some of these questions, or none at all.

Rick W.

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#632980 - 06/14/03 11:55 AM Re: Tuning with tuning forks
Bill Bremmer RPT Offline
3000 Post Club Member

Registered: 08/21/02
Posts: 3226
Loc: Madison, WI USA
Rick,

Wow! What a load of questions! I usually read this forum in the morning and write a post if I'm inclined to but I didn't really have time to thoroughly read all of yours but will do so when I do get the time.

I does appear to me that you have some good instincts about piano tuning and other aspects of piano technology, so I'd say first off, trust your instincts.

I often give a short explanation to youngsters who ask me, "Ho do you know when a note is *right*?" I have to explain what a "beat" is. I first explain that what I am talking about is not the "beat" you hear in music such as, "I like that song because it has a good "beat" to it. That kind of "beat" is the pulse felt by rhythm, mostly from the Bass and percussion instruments.

The "beats" referred to in Piano Tuning are quite another phenomenon. Every piano string produces a complex tone. The "fundamental" is the pitch we think of and that is usually the predominant (loudest). Take the note, A4 on the piano, the note we start with. Its fundamental is supposed to vibrate at 440 cycles per second.

But every string also has a whole spectrum of secondary tones at higher frequencies which are multiples of the fundamental. These secondary frequencies are called by various names which are all interchangeable. "Harmonics", "Overtones", "Partials", all three mean the same thing and are used when discussing tuning.

In theory, the next partial higher from 440 would be an exact multiple, 880. But piano strings are steel wire and thus have a stiffness factor which distorts the frequencies of the higher partials. Any sensitive electronic tuner will show this. Read A4 at the fundamental (on the pitch for A4), tune or calibrate it to be exact, then read the same pitch on the note A5. It will probably show that it is 2 cents or so sharp. Continue up another octave and it will probably read somewhere about 6 cents sharp. The higher you go, the sharper the higher partials will get.

In fact, if you read Middle C (C4) and calibrate it to 0.0 and read the same note at C8 (the highest note on the piano), it will read at an incredibly sharp frequency of about 75 cents! The series of overtones actually makes a chord much like a chord which you would play in actual music. If you play Middle C (C4), what you actually hear are: C4-C5-G5-C6-E6-G6-A#(Bb)6-C7 and beyond. The higher the overtone, the sharper it is but also the fainter. This sharpness of the overtones is known as "Inharmonicity". Indeed, piano strings do not have "harmonics", they have "IN-harmonics".

Back to Middle C (C4). When you have one string of the unison tuned to the desired pitch, you attempt to tune the next exactly the same. If the two strings are tuned to exactly the same pitch, they will sound as one, which is what "unison" means, "one sound". If the next string is higher or lower in pitch by any amount at all, you will hear a pulse or phasing kind of sound (some people call it a "chorus" effect). This is what is known as the "Beat" in piano tuning. A unison should be *beatless*, at least in theory.

When all 3 strings are tuned exactly to the same pitch, there is a quieter, more still sound than if there is any kind of beat. Normally, this is the goal. But pianos have imperfections, even the very best of them. There are what are called, "False Beats", which can easily confuse a tuner. A falsely beating string will show up as some kind of oscillation or pulse on an electronic tuner. A skilled aural tuner can tune a unison so that a false beat is largely, if not completely canceled out.

Other intervals that tuners use, octaves, 4ths, 5ths, 3rds, 6ths, 10ths, 17ths, double octaves, octaves and a 5th, even octaves and a minor 7th and still others can all be tuned so that they have apparently no beat all the way up to very rapid beating. Take the C4-C5 octave for example: If you tune the fundamental of C5 so that it is at exactly the same frequency as the second partial of C4, you will probably have what sounds like a "pure" or beatless octave. Those two matching partials are what are known as "Coincident Partials".

But that same C4-C5 interval has several sets of coincident partials. The example I gave was a 2:1 octave, that is, the 2nd partial of the lower note matches (is tuned to exactly the same frequency as) the fundamental (1st partial) of the upper note. In octave tuning discussions, you will often see various types of octaves suggested, 2:1, 4:2, 6:3, 8:4 and beyond. In each case, what is being referred to is a specific set of matching partials.

There is no specific kind of match which is right, correct or best under all circumstances. The "purest" sound may in fact be an octave tuned so that *none* of the partials actually match but a compromise resulting in the stillest sound is achieved. Putting a slight, barely perceptible beat in an octave is an example of what is called a "Stretched Octave". Usually, anything beyond a 4:2 octave will have that very slight beat. Skilled tuners stretch their octaves in order to achieve a certain effect and to make the overall compromise which there must be to compensate for Inharmonicity.

Any and all other intervals which tuners use also have matching sets of coincident partials. 4ths & 5ths are usually tuned so that there is a very slow, nearly imperceptible beat. I call these the Slowly Beating Intervals (SBI). 3rds, 6ths, 10ths and 17ths will generally beat very rapidly but will have a pleasant, musical effect which to me, sounds like the Vibrato you hear from a musician or vocalist. However, when a violinist, for example wiggles his/her finger on the string, that causes its pitch to rise and fall. The vibrato-like effect of the Rapidly Beating Intervals (RBI) is a kind of oscillation which is heard due to coincident partials which are significantly mismatched.

The whole discussion and controversy over Equal Temperament (ET) and any other kind of temperament has to do with what is believed or not believed to be the best compromise for tuning the modern piano. Ancient keyboard tunings had 3rds, 4ths and 5ths tuned beatless. All one has to do is a little experimenting to find out that you can only tune a few beatless intervals before you run into the dilemma of not being able to reconcile the rest.

Early keyboard music simply used the combinations which worked and avoided the ones which didn't. By the time of J.S. Bach, there was a desire to be able to use all 24 Major and minor keys. Tuning theorists such as Kirnberger and Werkmeister came up with ideas which they called Well Tempered Tuning (WT) which replaced a system which was previously in use where 3rds were tuned beatless called, Meantone (MT).

The kinds WT used in the time of Bach was not what we think of today as ET but were *mistakenly* called that and in time, even dictionaries and other reliable textbooks used the terms WT and ET interchangeably. The piano as we know it today only came into existence during the late 19th Century, the "Victorian" era. It was considered at the time and still is today that the best tuning compromise would be ET, therefore, it has usually been the one and only method taught.

However, earlier music was never composed or performed in true ET. The other temperament solutions, mild Meantones, Modified Meantones and a myriad of WT's all had an effect on how the music sounded. Using a modern piano to play earlier music has its own effect too. So, playing Bach or any other 17th, 18th or early 19th Century composer's music on a modern piano in ET has a doubly altering effect to the music. This kind of altered sound is what we are used to hearing, however.

Even with the acceptance of the idea and principle of ET, the perfection of it has always been elusive and difficult, even today and even with the best of Electronic Tuning Devices (ETD). What I have observed as a life long piano technician is that because people have been taught the one and only concept of ET but often not what it takes to really achieve it, common errors are made which have their own unintended and unrecognized effects on the way the piano sounds and consequently on the music.

The in depth study of all aspects of Piano Technology but particularly in the understanding of temperament and octaves, which include your question about the perception and control of beats, will allow a skilled piano technician to produce a more musically pleasing and satisfying sound. Please see my website for articles I have written on these subjects, The True Meaning of Well Tempered Tuning, What is Key Color?, How To Tune Tempered Octaves and What the HELL is Reverse Well? Also see Skip Becker's articles on the History of Tuning.

Please keep your questions coming, there are no "dumb" questions. I don't know of a single book which tells it all.Rick,

Wow! What a load of questions! I usually read this forum in the morning and write a post if I'm inclined to but I didn't really have time to thoroughly read all of yours but will do so when I do get the time.

I does appear to me that you have some good instincts about piano tuning and other aspects of piano technology, so I'd say first off, trust your instincts.

I often give a short explanation to youngsters who ask me, "Ho do you know when a note is *right*?" I have to explain what a "beat" is. I first explain that what I am talking about is not the "beat" you hear in music such as, "I like that song because it has a good "beat" to it. That kind of "beat" is the pulse felt by rhythm, mostly from the Bass and percussion instruments.

The "beats" referred to in Piano Tuning are quite another phenomenon. Every piano string produces a complex tone. The "fundamental" is the pitch we think of and that is usually the predominant (loudest). Take the note, A4 on the piano, the note we start with. Its fundamental is supposed to vibrate at 440 cycles per second.

But every string also has a whole spectrum of secondary tones at higher frequencies which are multiples of the fundamental. These secondary frequencies are called by various names which are all interchangeable. "Harmonics", "Overtones", "Partials", all three mean the same thing and are used when discussing tuning.

In theory, the next partial higher from 440 would be an exact multiple, 880. But piano strings are steel wire and thus have a stiffness factor which distorts the frequencies of the higher partials. Any sensitive electronic tuner will show this. Read A4 at the fundamental (on the pitch for A4), tune or calibrate it to be exact, then read the same pitch on the note A5. It will probably show that it is 2 cents or so sharp. Continue up another octave and it will probably read somewhere about 6 cents sharp. The higher you go, the sharper the higher partials will get.

In fact, if you read Middle C (C4) and calibrate it to 0.0 and read the same note at C8 (the highest note on the piano), it will read at an incredibly sharp frequency of about 75 cents! The series of overtones actually makes a chord much like a chord which you would play in actual music. If you play Middle C (C4), what you actually hear are: C4-C5-G5-C6-E6-G6-A#(Bb)6-C7 and beyond. The higher the overtone, the sharper it is but also the fainter. This sharpness of the overtones is known as "Inharmonicity". Indeed, piano strings do not have "harmonics", they have "IN-harmonics".

Back to Middle C (C4). When you have one string of the unison tuned to the desired pitch, you attempt to tune the next exactly the same. If the two strings are tuned to exactly the same pitch, they will sound as one, which is what "unison" means, "one sound". If the next string is higher or lower in pitch by any amount at all, you will hear a pulse or phasing kind of sound (some people call it a "chorus" effect). This is what is known as the "Beat" in piano tuning. A unison should be *beatless*, at least in theory.

When all 3 strings are tuned exactly to the same pitch, there is a quieter, more still sound than if there is any kind of beat. Normally, this is the goal. But pianos have imperfections, even the very best of them. There are what are called, "False Beats", which can easily confuse a tuner. A falsely beating string will show up as some kind of oscillation or pulse on an electronic tuner. A skilled aural tuner can tune a unison so that a false beat is largely, if not completely canceled out.

Other intervals that tuners use, octaves, 4ths, 5ths, 3rds, 6ths, 10ths, 17ths, double octaves, octaves and a 5th, even octaves and a minor 7th and still others can all be tuned so that they have apparently no beat all the way up to very rapid beating. Take the C4-C5 octave for example: If you tune the fundamental of C5 so that it is at exactly the same frequency as the second partial of C4, you will probably have what sounds like a "pure" or beatless octave. Those two matching partials are what are known as "Coincident Partials".

But that same C4-C5 interval has several sets of coincident partials. The example I gave was a 2:1 octave, that is, the 2nd partial of the lower note matches (is tuned to exactly the same frequency as) the fundamental (1st partial) of the upper note. In octave tuning discussions, you will often see various types of octaves suggested, 2:1, 4:2, 6:3, 8:4 and beyond. In each case, what is being referred to is a specific set of matching partials.

There is no specific kind of match which is right, correct or best under all circumstances. The "purest" sound may in fact be an octave tuned so that *none* of the partials actually match but a compromise resulting in the stillest sound is achieved. Putting a slight, barely perceptible beat in an octave is an example of what is called a "Stretched Octave". Usually, anything beyond a 4:2 octave will have that very slight beat. Skilled tuners stretch their octaves in order to achieve a certain effect and to make the overall compromise which there must be to compensate for Inharmonicity.

Any and all other intervals which tuners use also have matching sets of coincident partials. 4ths & 5ths are usually tuned so that there is a very slow, nearly imperceptible beat. I call these the Slowly Beating Intervals (SBI). 3rds, 6ths, 10ths and 17ths will generally beat very rapidly but will have a pleasant, musical effect which to me, sounds like the Vibrato you hear from a musician or vocalist. However, when a violinist, for example wiggles his/her finger on the string, that causes its pitch to rise and fall. The vibrato-like effect of the Rapidly Beating Intervals (RBI) is a kind of oscillation which is heard due to coincident partials which are significantly mismatched.

The whole discussion and controversy over Equal Temperament (ET) and any other kind of temperament has to do with what is believed or not believed to be the best compromise for tuning the modern piano. Ancient keyboard tunings had 3rds, 4ths and 5ths tuned beatless. All one has to do is a little experimenting to find out that you can only tune a few beatless intervals before you run into the dilemma of not being able to reconcile the rest.

Early keyboard music simply used the combinations which worked and avoided the ones which didn't. By the time of J.S. Bach, there was a desire to be able to use all 24 Major and minor keys. Tuning theorists such as Kirnberger and Werkmeister came up with ideas which they called Well Tempered Tuning (WT) which replaced a system which was previously in use where 3rds were tuned beatless called, Meantone (MT).

The kinds WT used in the time of Bach was not what we think of today as ET but were *mistakenly* called that and in time, even dictionaries and other reliable textbooks used the terms WT and ET interchangeably. The piano as we know it today only came into existence during the late 19th Century, the "Victorian" era. It was considered at the time and still is today that the best tuning compromise would be ET, therefore, it has usually been the one and only method taught.

However, earlier music was never composed or performed in true ET. The other temperament solutions, mild Meantones, Modified Meantones and a myriad of WT's all had an effect on how the music sounded. Using a modern piano to play earlier music has its own effect too. So, playing Bach or any other 17th, 18th or early 19th Century composer's music on a modern piano in ET has a doubly altering effect to the music. This kind of altered sound is what we are used to hearing, however.

Even with the acceptance of the idea and principle of ET, the perfection of it has always been elusive and difficult, even today and even with the best of Electronic Tuning Devices (ETD). What I have observed as a life long piano technician is that because people have been taught the one and only concept of ET but often not what it takes to really achieve it, common errors are made which have their own unintended and unrecognized effects on the way the piano sounds and consequently on the music.

The in depth study of all aspects of Piano Technology but particularly in the understanding of temperament and octaves, which include your question about the perception and control of beats, will allow a skilled piano technician to produce a more musically pleasing and satisfying sound. Please see my website for articles I have written on these subjects, The True Meaning of Well Tempered Tuning, What is Key Color?, How To Tune Tempered Octaves and What the HELL is Reverse Well? Also see Skip Becker's articles on the History of Tuning.

Please keep your questions coming, there are no "dumb" questions. I don't know of a single book which tells it all.
_________________________
Bill Bremmer RPT
Madison WI USA
www.billbremmer.com

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#632981 - 06/15/03 03:05 PM Re: Tuning with tuning forks
ChickGrand Offline
3000 Post Club Member

Registered: 05/02/03
Posts: 3217
Loc: Midwest U.S.
Thanks, Bill, for your reply to my post. Particularly for explaining the octaves ratio. I've seen references to it everywhere, but no discussion about what it actually means. Your explanation makes perfect sense to me.

I visited your website several days ago and read most of it and bookmarked it for future reference. I was particularly interested in your description of the E.B.V.T. (I may try it.)

I've always been a tinkerer by nature and look forward to learning more about piano technology.

I have a very good friend at the forefront of nanomaterials technology who received a major award in Japan last year for his contributions to the field. He's also a very gifted musician who has made some significant innovations in guitar and violin design. I'm just itching to steer him to exploring new material for piano soundboards that combines geometric stability with superior resonance characteristics while being a bit less impervious to atmospheric deterioration than spruce. His depth of understanding of designing tailor-made characteristics into the molecular structure and "lattice" structure of materials to suit a given purpose (like geometric strength accompanied by resilient flexibility) is where his genius lies. He has so many irons in the fire it may take a while before I can get him interested in this particular challenge, but I'm working on it. After that, perhaps on to the materials that go into the action...The goal would be to design an acoustic piano much less subject to environmental variations to rival the stability of a digital but with the richness of expressiveness that only an acoustic can provide.

Rick W.

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#632982 - 06/15/03 11:51 PM Re: Tuning with tuning forks
Ralph Offline
1000 Post Club Member

Registered: 12/09/01
Posts: 1299
Loc: Delaware (slower/lower)
Bill, great post and website you have.

I have a question if you don't mind. When octave ratios such as 2:1, 4:2, 8:4, ect are referred to, which fundamental pitch is the starting point? Now I understand the numbers such as 2:1 refer to the 2nd partial of the lower tone to and the 1st partial of the second tone, but what are the tones exactly? Is there an excepted octave or double octave on the keyboard these ratios represent by convention? I'm quessing these tuning measurments occur across the breaks. I quess I'm asking what is the note of the first number in the ratio? Many Thanks.

Ralph
_________________________
Do or do not. There is no try.

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#632983 - 06/16/03 01:40 AM Re: Tuning with tuning forks
BDB Online   content
Yikes! 10000 Post Club Member

Registered: 06/07/03
Posts: 21531
Loc: Oakland
2:1, 4:2 and 8:4 are all the same thing. The left side is the octave, the right side is the fundamental. It doesn't matter what the pitch is, the octave vibrates at twice the frequency of the fundamental. 4:1 would be two octaves.

3:1 is the ratio of an octave and a (pure) fifth and the fundamental. The ration of the fifth to the fundamental is therefore an octave below that, or 3:2. It's not a part of the harmonic series of the fundamental, but its octave is.

The basis of the scale that we use is that 12 pure fifths are incredibly close to 7 octaves, just a bit over. Mathematically, that is (3/2)^12 is just over 2^7 (about 129.75 versus 128). Equal temperment spreads that difference equally, and it is not perceptible for all intents and purposes. However, the kicker is that three pure major thirds are considerably short of an octave. Other temperments are used to improve the thirds.
_________________________
Semipro Tech

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#632984 - 06/16/03 08:29 PM Re: Tuning with tuning forks
Ralph Offline
1000 Post Club Member

Registered: 12/09/01
Posts: 1299
Loc: Delaware (slower/lower)
Thanks. I guess I misunderstood Bill's explanation. I was thinking the ratio numbers represented the partials which were tuned to one another. It makes sense the ratios are multiples of the respective octave frequencies.
_________________________
Do or do not. There is no try.

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#632985 - 06/17/03 07:22 PM Re: Tuning with tuning forks
Bill Bremmer RPT Offline
3000 Post Club Member

Registered: 08/21/02
Posts: 3226
Loc: Madison, WI USA
 Quote:
Originally posted by Ralph:
Thanks. I guess I misunderstood Bill's explanation. I was thinking the ratio numbers represented the partials which were tuned to one another. It makes sense the ratios are multiples of the respective octave frequencies.[/b]
No, you understood me correctly. It is true that the ratios 2:1, 4:2, 6:3, 8:4 are all equivilent but when these numbers are used to describe octave types, there certainly is a difference. When tuners are discussing the choice of octave type, these figures refer to which partials are matched. The fundamental is the first partial.

In the real world, the purest (stillest or most beatless) octave may not have any of the partials perfectly matched. Indeed, when tuning ET, I recommend the first two octaves to be tuned, A3-A4 and F3-F4 as a *compromise* between a 4:2 and 6:3 octave. Generally, any octave type beyond a 4:2 will have a slight beat in it. That is what is called a stretched octave.
_________________________
Bill Bremmer RPT
Madison WI USA
www.billbremmer.com

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#632986 - 06/17/03 08:19 PM Re: Tuning with tuning forks
Ralph Offline
1000 Post Club Member

Registered: 12/09/01
Posts: 1299
Loc: Delaware (slower/lower)
Now I got it! \:\) Octave type, OK.

The reason I asked is because I use Tunelab to tune my piano. It was recently rebuilt and needs tuning frequently. The deviation curve to calculate the proper stretch is calculated using 6:3 single octaves in the bass and 4:1 double octaves in the treble. That can be changed if desired. It's starting to make sense.
_________________________
Do or do not. There is no try.

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#632987 - 06/18/03 08:08 PM Re: Tuning with tuning forks
Bill Bremmer RPT Offline
3000 Post Club Member

Registered: 08/21/02
Posts: 3226
Loc: Madison, WI USA
 Quote:
Originally posted by Ralph:
Now I got it! \:\) Octave type, OK.

The reason I asked is because I use Tunelab to tune my piano. It was recently rebuilt and needs tuning frequently. The deviation curve to calculate the proper stretch is calculated using 6:3 single octaves in the bass and 4:1 double octaves in the treble. That can be changed if desired. It's starting to make sense.[/b]
Those are good *default* settings. Just as I learned with the computer, if you don't know better than the default settings, use them!

I know Robert Scott, the designer of Tunelab, he has asked to put my EBVT in his list of alternative temperaments. He is a scientist who readily admits he has no preferences in tuning, he just wants to enable people who do.

I have a unique solution for octave tuning which is really very simple and actually uses Inharmonicity to make the piano sound cleaner, brighter and sweeter. It's the classic technique called Equal Beating. I stretch the octave enough that it slows down the beating of the tempered 5th until both beat exactly the same which is at a very slow rate.

Once enough notes are tuned, I compare the Double Octave and the Octave and 5th, stretch the Double Octave just slightly until the Octave and 5th is less tempered by the same, slight amount. Both intervals sound apparently in tune. The end result is that Triple Octaves are perfectly in tune. That makes perfect 8:1 Triple Octaves accross the whole piano.

Regardless of temperament, this gives the piano the clearest, brightest sound. Other great masters of the tuning profession such as Steve Fairchild RPT and the renowned Virgil Smith RPT also use this technique. Most Electronic Tuning Devices (ETD) can help you find that sweet spot between the octave and 5th and its multiples.

See the article in my website called "How to Tune Tempered Octaves".
_________________________
Bill Bremmer RPT
Madison WI USA
www.billbremmer.com

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