Jason,
Fifteen years age and more, I thought the same as you do. Then I started investigating, and found out that a lot of what I was reading was seriously mistaken, at odds with the facts without any question. When I say "the facts" I mean surviving documentation interpreted in a reasonable way. That's the main thing we have to go on in making the past real, together with physical objects - but tuning of stringed instruments doesn't survive other than through documentation.
So I set out to make myself an expert. I decided to try to base my research almost entirely on practical tuning instructions, with the idea that if there weren't methods for accomplishing a tuning, it was just so many words and theoretical ideas. Luckily, more and more things have been scanned and made available, so I was able to access a very wide range of material. The result was the
nine articles I published in the Journal starting in 2010. In the process of research I also consulted with several experts in the field, and ran all my articles past them before publication. So I believe that that work was pretty solid.
That project led me to my Montal translation, during which I made an effort to become acquainted with whatever tuning documentation there was for his time and surrounding eras. I have continued searching ever since then, rather obsessively. So when I state something, it is based on copious research that I am constantly questioning and following up on.
While you are correct that not all procedures are/were well documented, and certainly not all are/were standardized, tuning was a pretty public activity. A lot was written about it, in educational texts, in manuals concerning how to learn to play the piano, in encyclopedia and dictionary entries, in articles in the various musical newspapers (there were three to four weeklies of this type in Paris in the mid 19th century, similar publications in Britain, Germany, and the US). And those were virtually unanimous in agreeing that ET had been adopted universally since something like 1800, that it was the best choice, and that everything else was obsolete.
Where is there any hint of practical procedures for tuning in some other fashion, in print, post 1800? There are some references to Kirnberger II - in which ten just fifths and a just third are tuned, then the remainder fudged between D, A and E - but I have found exactly nothing that would help someone understand how to create a sophisticated circulating temperament. If there was a stealth non-equal circulating temperament underground, it was very secretive.
That obviously doesn't mean that a refined ET was practiced by all tuners. And, no doubt, there were pockets of people still tuning mean tone, and probably "modified mean tone" (where the wolf at the end is split between two or more fifths, making it roughly circular). But by far the majority of tuners were attempting to tune ET, making it as even as they could. That is certainly what they said they were doing.
I'll describe a couple of exceptions I have found - and note that these are very rare exceptions, in the midst of hundreds of examples that advocated for ET:
In 1774, Henrich Laag gave a brief temperament description with six just fifths on the white keys, F to B, the remainder tempered evenly. That constitutes a "reverse Vallotti."
Ignace Pleyel and Dussek gave one in 1799, comprised of fifths with intervening octaves as needed. The fifths are described as AE wide, AD wide, DG narrow, GC wide, CF wide, FB flat wide, B flat E flat wide, EB narrow, BF# narrow, then the rest of the fifths with no instructions, except that the last fifth, D#G# is supposed to be just. No additional information (as in how wide, how narrow, etc.)
Can you make head or tails out of that? Six wide fifths, four of them between white keys, would likely make for thirds on the white keys wider than Pythagorean, worse than what Laag suggested. The last few fifths would have to be quite narrow to make up for six wide ones, as the total of the fifths needs to be narrow by 24¢, and any wide one must be made up for.
My impression from reading these is that most musicians didn't have a clue - as almost none do today. They may have notions of what sound they would like in one context or another, but no concept of how to achieve it, and no knowledge of how much the whole process is filled with compromise, where every action has multiple results, every gain causes an equal loss.
ET, however closely or roughly achieved, was adopted essentially universally for one and only one reason: it was the least bad way to tune a fixed pitch instrument so that music could be played in all keys without "surprises" and nasty sounds. It never pretended to be any better than that.
A fairly wide variety of tuning will be accepted and interpreted as ET by the vast majority of people. Exactly how wide has never been established, and it is unclear whether or not variations, either conscious and designed, or random due to lack of skill, are significant to more than a small minority of listeners and musicians. They may be, but I think the significance is far less than what is claimed by the temperament obsessed.
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Fred Sturm
University of New Mexico
fssturm@unm.eduhttp://fredsturm.nethttp://www.artoftuning.com"We either make ourselves happy or miserable. The amount of work is the same." - Carlos Casteneda
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Original Message:
Sent: 02-19-2019 16:38
From: Jason Leininger
Subject: Erard tuning instructions from 1927
What I find concerning about this whole discussion is the fact that while Fred may have some written technical information that leans towards the use of equal temperament from the beginning of the 19th century, any student of the history of the trades will know that just because there are documents that discuss certain practices, does not mean that is what everyone practiced. Actually often the exact opposite is true. The people doing it often don't bother to write about what they are doing and the intellectuals, academics, and innovators write about practices that they want to have disseminated and put into use. If circulating and unequal temperaments were in fact being used extensively, during the late 18th through the 19th century, I wouldn't expect to see much at all in the way of describing it in writing, or if there were descriptions, I would expect them to be vague...which is exactly what we find. This is a common thread that runs through other historic trades. Extreme standardization was not the norm in any of the trades until at least the end of the 19th century and some even later. Different countries and even different areas of the same country had widely different practices in the various trades. The simple answer is that it is highly likely that different circulating temperaments, and some form of (less than precise according to today's standards) ET were used side by through this time period. I don't need documents to prove what is common sense understanding of the history of the practical arts. Was Montal a famous technician/tuner, that used ET?.....yes, but that doesn't mean that was common practice or even desired by a large part of the musical world at the time. I don't have an agenda here to push, and don't really care one way or another whether ET was universal by the 19th century, just interjecting an important historical perspective.
--
"For I am not ashamed of the gospel, for it is the power of God for salvation to everyone who believes." -Romans 1:16
Original Message------
David,
I realize that on first glance, the notion of a temperament sequence containing seven just fourths and five tempered fifths brings to mind one of your favorite temperaments, Kellner. The problem is that the tempered and just 5ths/4ths alternate in Blondel's sequence. The Kellner/Vallotti/Kirnberger III progression of major third beat rates is a result of a string of just 5ths, and then a string of tempered 5ths to take up the rest of the Pythagorean comma evenly. The alternation of strings of 5ths is what produces the even variation of beat rates that many consider to provide "key color."
Since the Blondel instructions pique your interest so much, and since the university is closed today because of snow. I did a quick and dirty calculation of how those instructions might be interpreted. I went by the somewhat plausible assumption that since there are a total of seven just 4ths (meaning that, contrary to the opinion of Blondel/Armellino/LaSalette, their complementary 5ths must also be just), we might decide that the remaining five 5ths must be tempered to "take up the slack": they must total about -24¢ ( the Pythagorean Comma) between them. Since there are five of them, they should each be narrow by about 5¢ each. (ET 5ths and 4ths are about 2¢ narrow/wide, respectively.) Here's what we get, following the tuning sequence in order (numbers are cents offset from ET):
A 0
D +3
E +2
B +4
F# +1
C# +3
G# 0
D# +2
A# +4
F +1
C -1
G -4
And we end up with the G D 4th/5th closing the circle at +7 narrow/wide. That won't sound good, and contradicts the instructions, that claim the final 4th will be just. This is because the theory behind the tuning sequence is faulty, and simply can't be made to work.
Widths of major thirds compared to ET, given contiguously - the sets of three should and do add up to zero:
FA -1, AC# +3, C#F -2
CE +3, EG# -2, G#C -1
GB +8, BD# -2, D#G -6
DF# -2, F#A# +3, A#D -1
IOW, it would be a "colorful" mess. GB being 8¢ wider than ET will sound pretty wild.
As an alternative, I'd suggest that you tune it by ear, following the instructions, and see what you come up with. That is what would have been done at the time. Try to figure out how to make all the thirds and sixths wide by the same amount. Do it several times in succession, and measure each. Average them. Consider the result "proof" of something or other. At least, you can guarantee it won't be the evil ET.
You asked about "accounts of what tunings were used by amatuer and professional musicians from the different eras." There are none I have run across that would give enough detail to be useful in any way, and I doubt very much anyone has looked more thoroughly than I have - particularly for the eras from 1750 on.
You say you don't want "theoretical documents," and complain about equal temperament instructions "written by theorists." The instructions written by what I assume you would call "non-theorists" mostly just give a circle of 5ths, sometimes saying something vague about playing some chords. Some are incoherent, and some have very strange "errors" like Blondel's. Others are straightforward and fairly easy to comprehend, if not to execute. You can find and read several on the PTG Foundation library menu, "
tuning and repair manuals." Many of these are aimed at the amateur.
Among them is Montal's Art of Tuning, probably the most detailed and descriptive of all, and the more complete title is the Art of Tuning Your Own Piano Yourself . . ., so he obviously aimed it at the amateur. Montal was both a theorist (he understood tuning and temperament in its mathematical complexity) and a practical tuner who had taught himself to listen and tune, then taught others, then wrote down his method meticulously. He knew and tuned for professional musicians. He tuned for the piano professors of the Paris Conservatory, who called him the best tuner in France.
The evidence you want to find is something that isn't there. You want musicians and tuners to have consciously tuned their fixed pitch instruments in such a way as " to diversify or expand musical expression, or increase variation of musical experience." There is no evidence that happened in the 19th through late 20th century - on fixed pitch instruments. So I'd say you should look to the late 20th and early 21st century for your sources. Or you could take random variation in accordance with one of the more obscure written methods as your touchstone. Or abandon fixed pitch instruments, and take up one that can change pitch expressively on the fly. Perhaps the
fluid piano.