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#1870818 - 03/30/12 04:53 AM Re: I've made up my mind about Bach's WTC and ET [Re: RonTuner]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4908
Loc: Bradford County, PA
Originally Posted By: RonTuner
Originally Posted By: UnrightTooner
Andy:

There is a difference between someone disagreeing and putting forth their own views, and going to great lengths to convince another to change their mind.


For many of us here, there could not be a clearer description of what you have taken on in this thread! It is the zeal which you try and get others to agree with your ET quest that keeps this thing going - most wouldn't care a bit if you just said that you don't like listening to the WTC in anything but equal...

Ron Koval


Yes I know. It seems that when I say "I think..." it is read as "I think YOU should think..."

It is probably going to get worse after a few more posts.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1870825 - 03/30/12 05:32 AM Re: I've made up my mind about Bach's WTC and ET [Re: UnrightTooner]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4908
Loc: Bradford County, PA
Folks:

I did not go into a whole lot of detail when I described how and why I chose the type of analysis that I did. I was not expecting much interest. Much was for a simple, repeatable test case that does not require musical evaluation, something that a computer would do. The clearest way that I can explain is that these are the note numbers of the highest tonic notes whose fifth partial has a nearly coincidental partial in another note. I used the Alfred Masterwork Edition. All 48 pieces end in major chords in this edition, unless I made an error.

C 28, 40, 28, 40
C# 29, 41, 29, 29
D 30, 18, 42, 30
D# 31, 19, 31, 19
E 20, 20, 32, 20
F 21, 45, 33, 21
F# 46, 22, 22, 22
G 23, 35, 23, 23
G# 24, 24, 24, 24
A 25, 25, 37, 47
A# 50, 26, 26, 38
B 27, 51, 27, 39

So the average note number for the remote keys is 42, or D4 28 or C3.

And the average note number for the close keys is 47.25 or about G4 31.5 or between D#3 and E3.

Is this significant? Maybe yes, maybe no. In ET this would mean the remote keys were used more harmoniously. In WT, well I think it would depend on which WT. That is why I chose to use note numbers rather than beat rates. For beat rates comparison I think an approximation can be made by taking the average beatrates of the three M3s above and the three M3s below the average note number for each group. Then various WTs could be compared.

But before doing so the question should be raised as to what would it mean if the average beatrates were the same or if one was much greater than the other. If you wait until after they are known it can be just rationalization.

Thinking along these lines is why I am up so early. Also I may not get back to the keyboard much before Monday. (I am going to be getting some experience on function block programming on a particular PLC.) Here is the question that is going through my mind: During Bach’s time, was WT used for tonal color or was WT a compromise between MT and ET with the tonal color only an artifact? If Bach did compose WTC in WT, it may have only been because ET could not yet be tolerated with all the busy RBIs. But MT prohibited the convoluted passages that Bach desired. And tonal color was a by-product, not the intent. Later composers might have utilized the tonal shading more.

Now I am not saying that this very simplistic analysis would answer such a question. But trying to decide what the result might mean does. For instance if the average beatrates are the same, that could mean that the desire was not for tonal shading but for harmonious equality, a tendency towards ET. (hoohoo, I bet that’s what the beatrates will show. The interval from D4 to G4+ is about halfway around the circle…) But if tonal variation was the goal, wouldn’t the average note number be about the same so the remote keys DID beat more?
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1870830 - 03/30/12 06:04 AM Re: I've made up my mind about Bach's WTC and ET [Re: UnrightTooner]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1923
Loc: Suffolk, England
Originally Posted By: UnrightTooner
Here is the question that is going through my mind: During Bach’s time, was WT used for tonal color or was WT a compromise between MT and ET with the tonal color only an artifact? If Bach did compose WTC in WT, it may have only been because ET could not yet be tolerated with all the busy RBIs. But MT prohibited the convoluted passages that Bach desired. And tonal color was a by-product, not the intent. Later composers might have utilized the tonal shading more.


Jeff:

I think the answer to your question is well put in the piece I quoted before:

The Revolution of Bach’s ‘Well-Tempered Clavier’
http://www.larouchepub.com/eiw/public/2010/2010_20-29/2010-24/2010-24/pdf/44_3724.pdf

In 1691, the German organist and mathematician Andreas Werckmeister published a treatise entitled, “Musical Temperament or . . . mathematical instruction how to produce . . . a well-tempered intonation on the clavier.” Bach, Werckmeister, and others who supported the well-tempered system, rejected the previously held idea that musical intervals in the physical universe, had to conform to abstract mathematical proportions. This idea had put a straitjacket on the musical universe, limiting it to only those keys in which “pure” intervals could be played.

The new movement, of which Bach was a leader, created systems in which it would be possible to play music in all keys. The “comma” (the part of the octave that is left over if only mathematically “pure” musical intervals are used) was distributed unequally throughout all of the keys. (Different keys had different-sized intervals, giving each key its own nuance or “color,” creating a “musical palette,” which is lost in the modern practice of “equal-tempering,” where all half-notes have the same value.) It were then possible both to write music in every key, and to modulate—to move from one key to any another—within the same piece of music, in a way not possible before.


From the structural point of view you mentioned my guess is that Bach would not have been too worried about the distinction between WT and ET (which is why concert pianists are happy to play WTC today). But that would be only half the story.

PS If JI and MT were a straitjacket of abstract mathematical proportions then so, arguably, is ET!


Edited by Withindale (03/30/12 06:13 AM)
Edit Reason: PS
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

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#1870836 - 03/30/12 06:28 AM Re: I've made up my mind about Bach's WTC and ET [Re: Withindale]
Exalted Wombat Offline
1000 Post Club Member

Registered: 02/28/09
Posts: 1194
Loc: London UK
Originally Posted By: Withindale
From the structural point of view you mentioned my guess is that Bach would not have been too worried about the distinction between WT and ET (which is why concert pianists are happy to play WTC today).


An instrument is never perfectly in tune. A "slightly-off" unison is, mathematically-speaking, much more dischordant than a perfectly-tuned major 7th. But human perception is a wonderful thing. We hear what we expect to hear, what we WANT to hear.

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#1870910 - 03/30/12 10:23 AM Re: I've made up my mind about Bach's WTC and ET [Re: Exalted Wombat]
rxd Offline
1000 Post Club Member

Registered: 03/11/09
Posts: 1703
Loc: London, England
Originally Posted By: Exalted Wombat
Originally Posted By: Withindale
From the structural point of view you mentioned my guess is that Bach would not have been too worried about the distinction between WT and ET (which is why concert pianists are happy to play WTC today).


An instrument is never perfectly in tune. A "slightly-off" unison is, mathematically-speaking, much more dischordant than a perfectly-tuned major 7th. But human perception is a wonderful thing. We hear what we expect to hear, what we WANT to hear.


thank you for your enlightenment.

Two things I don't understand, what coincident partials do you use to tune your perfect major 7th. And how does a piano technician tune and tone regulate a piano if they can only hear what they expect to hear or want to hear?
_________________________
Concert & Recording tuner-tech, London, England.
"in theory, practice and theory are the same thing. In practice, they're not." - Lawrence P. 'Yogi' Berra.

Eschew obfuscation.



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#1870944 - 03/30/12 11:40 AM Re: I've made up my mind about Bach's WTC and ET [Re: UnrightTooner]
UnrightTooner Offline
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Registered: 11/13/08
Posts: 4908
Loc: Bradford County, PA
If anyone is following what I am doing, here are the beatrates and their averages.

For the remote M3s, M10s or M17s centered around C3:

E3 7.3
D#3 7.1
C#3 7.9
B2 5.8
G#2 5.5
F#2 4.7
Average 6.4 bps

For the close M3s, M10s, or M17s centered around D#3-E3:

A3 7.8
G3 5.2
F3 4.7
D3 4.6
C3 2.9
A#2 4.3
Average 4.9 bps

Fwiw the distance between the ET M3s with these beatrates is a P4.

I still don’t know what it might mean. And when it comes down to it, this is examining evidence for WT, not for ET, which I think needs to come from the convoluted passages.
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#1871023 - 03/30/12 02:01 PM Re: I've made up my mind about Bach's WTC and ET [Re: Mark R.]
UnrightTooner Offline
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Registered: 11/13/08
Posts: 4908
Loc: Bradford County, PA
Originally Posted By: Mark R.
.....

What do you mean by writing in a certain temperament, as opposed to writing for a specific temperament?


I remember a better example. Doel mentioned this in another Topic. I can't remember if it was the same one that discussed the difference between "texture" and "form" as it relates to pieces affected by WT.

If I remember right, Doel said that Bach wrote the C# Prelude and Fugue in C and then transposed it for C#. I have have every reason to believe him. And I am thinking more about what he said in regards to what I call "texture" vs. "form."

I can see how it all might sound like double talk. frown
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Jeff Deutschle
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Who taught the first chicken how to peck?

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#1872388 - 04/02/12 08:00 AM Re: I've made up my mind about Bach's WTC and ET [Re: UnrightTooner]
UnrightTooner Offline
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Registered: 11/13/08
Posts: 4908
Loc: Bradford County, PA
Phil, Andy:

You encouraged me to do the analysis. Any comments, or is it time to let this Topic die?
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1872601 - 04/02/12 02:37 PM Re: I've made up my mind about Bach's WTC and ET [Re: UnrightTooner]
Phil D Offline
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Registered: 01/15/10
Posts: 551
Loc: London, England
Sure Jeff, I read your analysis before the weekend but didn't get round to replying. I must say I do like your method now I understand it.

The difference in the averages is a quarter of an octave, so I think it is significant. Especially with so many inconsistencies between the different pieces in the same key throughout the works. But there are many anomalous results. The most glaring is the first D major prelude. That's a major 10th from the bottom D #18... but as you say, the beat rate is the same as if it was #30, so it should be the same result in the texture of the chord. Is there something I'm missing here? Would it not be better to treat it as if it was a M3rd on #30, and the same with any other M10th? I've just found a M17th as well... I guess it's not quite as clear cut as that, a M10th clearly has a thinner texture than a M3rd regardless of the beatrates.

Looking at the score, something else comes up about that chord - the presence of a minor third directly above it. It would be interesting to also look at whether these crop up more often in close or remote keys, and where in the compass.

I also see you don't make provision for pieces where there is just a unison or octave at the end without the 3rd in it.

Criticisms aside, it's certainly interesting. And I think further investigation would throw up some more results. I'd enjoy doing it, if I get round to it... so I might add to this topic in the future!

I also wondered whether the trend is different between the different sets of 12 - the first preludes, first fugues, second preludes and second fugues. So I split up your results, and took the averages again.

For the remote keys, the averages are, for the different sets in that order:
29.5 29.5 27.5 25.5
And for the close keys
29.5 31.5 31.5 33.16666667

So there's no difference in the preludes overall in the first book, and a tone difference in the fugues.
The second book has much bigger differences. A major third in the preludes, and just over a major 6th in the fugues.

So maybe Bach got more out of the WT over time. You could interpret that to mean he was being more expressive with the temperament the second time round, or he was just mitigating better against the unevenness of it. So I don't think it supports the idea that it was written for ET, but it could indicate a desire for it - he avoided the fast beats more over time, so if he'd had ET maybe he'd have liked it as he wouldn't have to work around the bad intervals.

So a little bit of objective data... but still totally subjective interpretation wink


Edited by Phil D (04/02/12 02:40 PM)
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Phil Dickson
The Cycling Piano Tuner

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#1872737 - 04/02/12 06:21 PM Re: I've made up my mind about Bach's WTC and ET [Re: UnrightTooner]
Chris Leslie Offline
500 Post Club Member

Registered: 01/01/11
Posts: 563
Loc: Canberra, ACT, Australia
Some inner voice tells me that it will be futile to become too analytical with WTC intervals, beat rates, modulations and keys etc. It might be intellectual fun to try but there will always be inconsistencies and exceptions as in so much of art and nature.

If I could summarise all that I have ascertained from my studies and through this thread: All Bach was trying to demonstrate was that a keyboard could be tuned in a manner that reduced dissonance in remote keys to an acceptable level and yet did not unacceptably increase dissonance in close keys. A keyboard instrument is therefore capable of making acceptable music in any key. It is that simple. As a consequence I am not convinced that for WTC Bach was too concerned about exact tuning to any particular scheme and that a range of tempering could be acceptable which could be exact equal temperament if that were possible. Isn't it obvious that if Bach had a specific tuning in mind that he would have provided more instruction than a cryptic squiggle?
_________________________
Chris Leslie
Piano technician
http://www.chrisleslie.com.au

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#1872885 - 04/03/12 12:29 AM Re: I've made up my mind about Bach's WTC and ET [Re: UnrightTooner]
Cinnamonbear Offline
3000 Post Club Member

Registered: 01/09/10
Posts: 3847
Loc: Rockford, IL
Originally Posted By: UnrightTooner
Phil, Andy:

You encouraged me to do the analysis. Any comments, or is it time to let this Topic die?


Sorry, Jeff. Last weekend went something like this for me:

Click to reveal..


Click to reveal..


Kidding! I'm kidding! Actually, I was trying to puzzle out whether WTC-1 No. 9 is a Giga. And in searching out that question, I learned a few things that puts me somewhere near Chris Leslie's camp. But before summing up that thought, here's this one:

I still fervently encourage you to keep going at this idea of yours. Obviously, there is something there that you need to answer for yourself. I am just happy that you're taking your own question seriously, now. You've come a long way from "I made up my mind because I played a chord in this one prelude," to, "Hmmm. How can I test my idea?" I still don't quite understand your analysis, except to say that the focus seems so very narrow, and it might be too early to try to understand it. You have to start somewhere, though, and I'm really glad PhilD sees your trajectory. I would like to see you take a step back and restate your premise, define your thesis, and list your assumptions, which might help you gain a little more clarity. It might help you structure your test(s) and help you to explain your results to yourself and others. Personally, I feel you still need to make a qualifying nod to, and demonstrate an appreciation for, the historical refraction inherent in your inquiry, because the instrument (and its sound) was so very different. But there is much to be said for crashing around. (I do it a lot, myself...)

Now, why did I land near Chris Leslie's camp? (Hi, neighbor! grin ) It is because I discovered something about the WTC that was new to me, in a 1996 article by Yo Tomita. (He's written a lot about Bach.) Did you know that WTC was written for keyboard instruction? Did you know that Bach purposely left out many tempo indications as a kind of quiz, so that students would examine the music to figure out the proper interpretation? Here's how Yo Tomita said it:

The Well-Tempered Clavier, Book 1, by Yo Tomita, (1996)

Quote:
Bach's clavier pieces do not often bear tempo marks. This is partly due to the domestic and educational nature of these compositions. When learning pieces from the WTC, his pupils were expected to study not only how to play the correct notes, but also how to interpret individual pieces correctly. All this is actually contained in the form of musical notation. The source of information resides in the use of a variety of time-signatures, the way the main motifs are shaped, and the way the texture is formulated. The tempo signs written in the WTC I are all exceptional cases, which are intended to clarify the composer's intention. Here Bach used five kinds, namely Adagio, Largo, Andante, Allegro and Presto: they appear in preludes no. 2 (Presto, Adagio, Allegro), no. 10 (Presto), no. 24 (Andante) and its accompanying fugue (Largo). It is important to note that they do not indicate the absolute tempo, as we would understand it today. In Bach's time the tempo indication meant its emotional character, which in turn suggested the speed to which it belonged.



Which makes me think that the squiggle on the title page is an instructional illustration that would have been accompanied by a demonstration. As has been noted in this very thread, keyboard musicians had to tune their own instruments, and so tuning had to be part of the lessons, right? (Apparently, one of Bach's students, Heinrich Nicolaus Gerber, made a copy of WTC in 1725 (that would be a hand copy (which, btw, bears some of Bach's markings)), and this copy is in the Gemeente Museum in the Hague. Does anyone reading this know whether Gerber copied the squiggle?)

Also,

Quote:
There is some evidence in the WTC I suggesting that this was intended to be a mikrokosmos. The fact that the WTC I begins with the simplest of preludes and ends with a fugue of an extensive, most complicated nature cannot be a mere coincidence. The work also embraces pieces in diverse forms and styles, encompassing all the possible varieties of the day, including quasi-vocal fugue in stile antico, dance movement, virtuoso impromptu, and others.

Restricting our discussion to preludes, we can classify them in terms of their form, as follows: homophonic pieces — nos. 1, 2, 5, 6, 10, 15, 21; polyphonic 2-part Inventions — nos. 3, 11, 13, 14, 20; 3-part Sinfonias — nos. 9, 18, 19, 23; various kinds of arioso — nos. 4, 8, 16, 22; a concerto — no. 17; a trio sonata — no. 24; a sonorous, 4-part contrapuntal piece — no. 12; and a toccata-like introduction with a double fugue — no. 7.

Fugues are often classified according to the number of voices and the contrapuntal techniques used. It is also possible to some extent to approach from so-called 'Charakterthema' in H. Besseler's term, or from a stylistic classification, as viewed from a chronological perspective.

The musical form of the prelude-fugue pair traditionally meant what the term implies; preludes were originally short, mirroring the early development process of WTC I already discussed. The original function of preludes was to establish the tonic key on which the fugue exposed its rich musical discourse. In the WTC I however, the preludes began to acquire the character of an étude as well as that of an artistic piece in its own right. This tendency is even more clearly seen in the WTC II.



Clearly, Old Wig had a lot going on under there, and WTC is, indeed, a multi-faceted work.


So, Jeff, press on! Great discoveries come from burning questions.

--Andy
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I may not be fast,
but at least I'm slow.

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#1872968 - 04/03/12 07:52 AM Re: I've made up my mind about Bach's WTC and ET [Re: UnrightTooner]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4908
Loc: Bradford County, PA
Phil, Chris, Andy:

My responses to you three overlap so much that I better make it a group response.

Remember this analysis is just an example. And it would be a way of looking for evidence that WTC was written for WT, not of evidence of being written for ET. I would look for that evidence in the convoluted passages. So I am not going to continue this sort of analysis. Sorry, it is not the direction I am looking.

I have been taking steps back for a better perspective and see things much as Chris mentioned. Let me explain what I learned from the type of analysis that I used as an example. If the amount of tempering is changed, the results change also. Consider what is being observed objectively: The number of half steps between the average remote key roots and the average close key roots. Then comes the temperament part: The average beatrate for the chosen temperament. Change the temperament and the analysis changes.

For instance, the remote key’s average note is lower than the closer keys. Yet, for the chosen temperament the average beatrate is still faster than for the close keys. It could be argued that the chosen temperament was too strong. The correct, milder temperament is the one where the average beatrates would be the same. But the average note is only a little more than three semitones, and two semitones is insignificant. (I mentioned this before.) This is close enough to show that ET was the intent.

Then I consider No 1. I was thinking about my reaction to hearing it on Lindley's site. It sounded too bland in WT to me. But what would it sound like to those used to MT? It might have sounded too raucous! I can’t say that No 1 was a “sound check” for the chosen temperament, but I do wonder. Like, if No 1 is acceptable, the rest will be acceptable.

And this ties into what my intuition is telling me. The use of key color is not integral to the composition. It is only a comfort factor for the listener. It is a “season to taste” thing in the recipe. Regardless of what temperament it was written in, it was written for the universal temperament: ET.
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Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1873006 - 04/03/12 09:35 AM Re: I've made up my mind about Bach's WTC and ET [Re: Phil D]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4908
Loc: Bradford County, PA
Originally Posted By: Phil D
.....

I also see you don't make provision for pieces where there is just a unison or octave at the end without the 3rd in it.

.....


To keep things simple, I used the last time the third step was played.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1873292 - 04/03/12 07:51 PM Re: I've made up my mind about Bach's WTC and ET [Re: UnrightTooner]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1657
Loc: Vancouver, Canada
Originally Posted By: UnrightTooner
The use of key color is not integral to the composition. It is only a comfort factor for the listener. It is a “season to taste” thing in the recipe. Regardless of what temperament it was written in, it was written for the universal temperament: ET.

I agree mostly, except in my personal opinion it was written in and for just intonation. Reasons: 1) It is known Bach always composed in his head, not at the keyboard (hence the "in"). 2) It is known he liked the clavichord and just intonation is realizable on the clavichord (hence the "for").

Kees

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#1873410 - 04/03/12 11:59 PM Re: I've made up my mind about Bach's WTC and ET [Re: DoelKees]
Bill Bremmer RPT Offline
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Registered: 08/21/02
Posts: 3186
Loc: Madison, WI USA
Originally Posted By: DoelKees

I agree mostly, except in my personal opinion it was written in and for just intonation. Reasons: 1) It is known Bach always composed in his head, not at the keyboard (hence the "in"). 2) It is known he liked the clavichord and just intonation is realizable on the clavichord (hence the "for").

Kees


I can understand that easily. As a vocalist, I never thing about temperament when singing. All intervals are pure. The piano has to be tempered, of course. However, I disagree that the choice of ET is the best compromise or the only logical one. I have 23 years of experience that has proved that to me.
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#1873514 - 04/04/12 07:30 AM Re: I've made up my mind about Bach's WTC and ET [Re: UnrightTooner]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4908
Loc: Bradford County, PA
I sing in ET. I was taught that way. I have heard complex choral pieces fall apart tonally when Just Intonation is attempted.

Considerng the frequent use of dim7 chords and the occasional use of augmented chords I do not think WTC was written either in or for JI. It is impossible to have these chords just.
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Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1873580 - 04/04/12 11:12 AM Re: I've made up my mind about Bach's WTC and ET [Re: UnrightTooner]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1657
Loc: Vancouver, Canada
Fine with me. We have freedom of religion here.

Kees

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#1873596 - 04/04/12 11:43 AM Re: I've made up my mind about Bach's WTC and ET [Re: DoelKees]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4908
Loc: Bradford County, PA
Originally Posted By: DoelKees
Fine with me. We have freedom of religion here.

Kees


Ah... A breath of fresh air!
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Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1874138 - 04/05/12 11:12 AM Re: I've made up my mind about Bach's WTC and ET [Re: UnrightTooner]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1657
Loc: Vancouver, Canada
Originally Posted By: UnrightTooner
Originally Posted By: DoelKees
Fine with me. We have freedom of religion here.

Kees


Ah... A breath of fresh air!

Talking about religion... Tomorrow I'll attend a performance of Mozart's Requiem at a local church. Tuning: Kellner (1/5' WT).

Kees

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#1875256 - 04/07/12 05:36 PM Re: I've made up my mind about Bach's WTC and ET [Re: UnrightTooner]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1059
Loc: Sicily - Italy
..."Tuning: Kellner (1/5' WT)."...

Hmmm, interesting. How is it expanded all across the keyboard? Pure octaves? Or? (please answer through a different thread)

Hi All.

Linked below you''ll find a work on temperaments (pdf. available), perhaps in the spirit of this thread. During those years the "pure 12ths" ET tuning model was elaborated by Bernhard Stopper.

..."...human voices in concert have no difficulty in making pitch adjustments necessary to achieve consonance, but the keyboard with its twelve pre-set notes is inhibited."..."...at least in Werckmeister's casey temperaments were assessed not only for their faithfulness to the accepted standards of consonance, but for their ability to give to certain keys certain affective characteristics."...

Science, opinion or cliché?

"Pollard, Joseph Victor (1985) Tuning and temperament in southern Germany to the end of the seventeenth century. PhD thesis, University of Leeds":

http://etheses.whiterose.ac.uk/325/

Off Topic: Best wishes for a serene Easter.

Regards, a.c.


Edited by alfredo capurso (04/07/12 06:53 PM)
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alfredo

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#1875331 - 04/07/12 09:06 PM Re: I've made up my mind about Bach's WTC and ET [Re: UnrightTooner]
Eric D. Offline
Junior Member

Registered: 04/01/12
Posts: 16
IMO one of the points of the cycle is to test out Well-Temperments.

If all 24 pieces sound good in your tuning, then you've got a "Well-Temperment"!

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#1876070 - 04/09/12 08:14 AM Re: I've made up my mind about Bach's WTC and ET [Re: Eric D.]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4908
Loc: Bradford County, PA
Originally Posted By: Eric D.
IMO one of the points of the cycle is to test out Well-Temperments.

If all 24 pieces sound good in your tuning, then you've got a "Well-Temperment"!

I am thinking along the same lines now, like: If all 24 pieces sound GREAT in your tuning, then you've got an "EQUAL-Temperment"!
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1876440 - 04/09/12 08:26 PM Re: I've made up my mind about Bach's WTC and ET [Re: UnrightTooner]
Eric D. Offline
Junior Member

Registered: 04/01/12
Posts: 16
I prefer a well-temperment with the WTC, since it gives each key it's own effect, but it certainly works in EQ too.

To each his own.

I think Bach would have been fine with either; if it was terribly important, he would have written down explicit instructions, not some cryptic squiggle wink

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#1876510 - 04/09/12 10:22 PM Re: I've made up my mind about Bach's WTC and ET [Re: alfredo capurso]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1657
Loc: Vancouver, Canada
Originally Posted By: alfredo capurso
..."Tuning: Kellner (1/5' WT)."...

Hmmm, interesting. How is it expanded all across the keyboard? Pure octaves? Or? (please answer through a different thread)


The 8ft principal in the great is tuned first in the temperament octave, then octaves are tuned pure. Then the other stops are tuned to the 8' principal.

Kees

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#1876519 - 04/09/12 10:35 PM Re: I've made up my mind about Bach's WTC and ET [Re: UnrightTooner]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1657
Loc: Vancouver, Canada
Originally Posted By: UnrightTooner
Originally Posted By: Eric D.
IMO one of the points of the cycle is to test out Well-Temperments.

If all 24 pieces sound good in your tuning, then you've got a "Well-Temperment"!

I am thinking along the same lines now, like: If all 24 pieces sound GREAT in your tuning, then you've got an "EQUAL-Temperment"!

Agreed. In 1/4' WT like Werckmeister 3, as for example Ton Koopman's recording is tuned, it sounds it bit too rough esp. in f minor for some reason. Not EQUAL enough!

1/6' temperaments sound good to me (I'm talking about hpschd of course, he didn't write for piano). EQUAL enough! Still the normal keys sound a bit better, which is fine with me as I can't play in those remote keys anyways.

If I could and someone insisted I play all 24 pieces without retuning (a very unrealistic scenario) and without favouring keys the logical choice would be ET for me.

Kees

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#1876520 - 04/09/12 10:39 PM Re: I've made up my mind about Bach's WTC and ET [Re: UnrightTooner]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1657
Loc: Vancouver, Canada
Slightly tangential, but a better candidate for intended ET in Bach's music is,
IMHO of course, his Art of Fugue. Despite being entirely in d minor (1 flat) the pieces seem to want good P5's more than good M3's. Esp the DA fifth is so prominent that a
1/4' WT (which has DA 3X narrower than in ET) is a bit offensive.

Kees

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#1876794 - 04/10/12 01:00 PM Re: I've made up my mind about Bach's WTC and ET [Re: UnrightTooner]
Eric D. Offline
Junior Member

Registered: 04/01/12
Posts: 16
FWIW, this is a Well Temperment I arrived at after much fiddling around in scala. I really like it, all the major/minor chords sound good in it and have their own character.

Code:
0:          1/1               0.000  unison, perfect prime
  1:        106.647 cents     106.647
  2:          9/8             203.910  major whole tone
  3:        301.173 cents     301.173
  4:         81/64            407.820  Pythagorean major third
  5:          4/3             498.045  perfect fourth
  6:        609.384 cents     609.384
  7:          3/2             701.955  perfect fifth
  8:        803.910 cents     803.910
  9:         27/16            905.865  Pythagorean major sixth
 10:        998.436 cents     998.436
 11:        243/128          1109.775  Pythagorean major seventh
 12:          2/1            1200.000  octave


Edited by Eric D. (04/10/12 01:01 PM)

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#1876800 - 04/10/12 01:14 PM Re: I've made up my mind about Bach's WTC and ET [Re: UnrightTooner]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4908
Loc: Bradford County, PA
Folks:

Really! If you want a Topic on Well Temperaments, go start one!
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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