I have installed ClearTune on my new Android phone. I want to tune the common 18th c. French temperament (tempérement ordinaire). Cleartune offers Rousseau II, III, and IV with no explanation of what these are. Internet seaching does not provide enlightenment (pun intended); apparently using Roman numerals is not the usual system to identify the temperaments published by Rousseau.
Can anybody clarify?
Rousseau published one inexact description of his preferred tuning in his Dictionary of Music under the topic of Temperament. Several people have offered interpretations of that description. I’m not sure where the numbering system came from, perhaps Jorgensen. The other two original sources are Rameau (another inexact description of what he describes and how musicians ordinarily tune - hence the term temperament ordinaire) and d’Alembert in the Encyclopédie. d’Alembert essentially plagiarized Rameau, including an error.
One of the problems with these descriptions is that they have too many just thirds for the remainder of the temperament to work out satisfactorily, and in accordance with how they describe the remaining thirds. Most people tend to make the initial thirds for ordinaire somewhat wider than just, more along the order of 1/5 - 1/6 comma meantone or so.
Perhaps someone has experience with ClearTune and can respond more practically to the question. I don’t have that app, but perhaps you can find the offsets of those three temperament patterns within the inner workings somewhere and post them.
Le 12/12/2020 17:03, David Perry via The Jackrail écrit :
[David_Perry] David_Perry
https://jackrail.space/u/david_perry
December 12I have installed ClearTune on my new Android phone. I want to tune the
common 18th c. French temperament (tempérement ordinaire). Cleartune
offers Rousseau II, III, and IV with no explanation of what these are.
Internet seaching does not provide enlightenment (pun intended);
apparently using Roman numerals is not the usual system to identify
the temperaments published by Rousseau.Can anybody clarify?
According to Paul Poletti’s review of Cleartune:
Additionally, the pre-programmed list of temperaments unfortunately
appears to have been drawn from the writings of Owen Jorgenson, and the
temperaments are labeled using Jorgenson’s quirky arcane names. No
information is provided about the structure of the temperaments, and
there is no way to view the cents deviation for each note, so if you
don’t happen to have Jorgenson’s Great Red
Tome*http://www.amazon.com/Tuning-Containing-Eighteenth-Century-Temperament-Nineteenth-Century/dp/0870132903**,
you’re screwed*; there is no way of knowing what curious sort of
temperamental beasts might be represented by “Aaron-Neidhardt”,
“Almost-equal”, “Shifted Vallotti-Young”, “Homogeneous French”, “Early
French”, etc. Luckily, the latest version of Cleartune now places the
user-programmed temperaments at the top of the list, so the
pre-programmed temperaments can simply be ignored. Even better would be
to give the user the option to simply trash them, as they are
undoubtedly programmed with constant A reference.
Jorgenson’s Great Red Tome*http://www.amazon.com/Tuning-Containing-Eighteenth-Century-Temperament-Nineteenth-Century/dp/0870132903**
The link indicates that two used copies of this (now rare) masterpiece are available at eye-watering prices of $412 and $600. To think that I paid a mere $20 for my copy when it was being remaindered, and sold it for about the same.
David
Indeed, the great Prof. Barbieri gave up decades ago, considering that Rousseau’s description is “too vague to be reducible to precise numbers”. Also decades ago, I read Klop, was not happy, made my own initial deduction, and over the decades refined it. The explanation about how, among different French sources, I find Rousseau the most accurate and amenable to be reduced to very accurate numbers also, takes some pages in my U.T. Book. I also explain why the same can be done with d’Alembert and Rameau, getting slightly different temperaments.
This said, I did not find any alternative for Rousseau, and cannot imagine why one would have I, II, III, whatever. Sheer reasoning and calculations, as well as comparisons between descriptions, inevitably bring to a single formulation. And indeed it is based on three central pure thirds: that these thirds are to be pure is also demonstrable.
Claudio,
I guess you base your assertion in your U.T. that Rousseau had three just thirds in his pattern on his wording “once you have arrived at the sharps” [“dès qu’on est arrivé sur les dièses”]. I am not sure that is warranted in view of the fact that he is clearly plagiarizing d’Alembert to the extent of using precisely the same words in most cases. (I think I wrote it the other way around in my earlier post, saying d’Alembert plagiarized Rousseau).
Rousseau adds a little more detailed description in places, and that instance of “when you reach the sharps” is one of them, but the fact that he reproduced exactly d’Alembert’s error (D flat when he meant E flat - and d’Alembert corrected the error in the second edition) suggests to me that Rousseau was not terribly sharp in these matters, thus not really a trustworthy source.
I find it amusing and telling that both of them describe tuning in the flat direction from C, citing F, B flat, “et cetera.” Why not write the words E flat? That’s the only additional note that hasn’t been tuned. Apparently it is because d’Alembert was thinking in terms of F, B flat, E flat, A flat, D flat, since he writes D flat as the proof note in relation to G sharp. Would any musician who actually tuned his own instrument make that mistake? Would any musician reading d’Alembert’s mistake fail to notice it and reproduce it in a Dictionary entry? Their mistaken notion that there were five rather than three fifths remaining to be tuned in the flat direction makes a little more sense out of how they describe them.
All told, I don’t think we should take Rousseau or d’Alembert as gospel with respect to their details, especially considering that d’Alembert was not a practicing musician, and Rousseau was more dilettante and theoretician than performer. d’Alembert probably consulted with a practicing musician, and didn’t quite get all the details right. Rousseau plagiarized and expanded on d’Alembert. Their evidence is useful, as it is the most detailed that has survived, but it is more suggestive than definitive.
What we can derive from the two of them is a pattern that probably has some connection with actual practice at the time: that the CE third should be just (or close), and that some of the 5ths in the flat direction from F or B flat should be wide, at least two of them, possibly all three. And that the thirds will become somewhat wide in the sharp direction (as the fifths are tuned less narrow), and considerably more wide in the flat direction (as the fifths are tuned wider in a pretty rapid progression - there are only three of them between C and E flat.) It is quite likely that what was actually done was more random and varied than that.
For those interested, here is my Rousseau text:
“Pour cela, premier on commence par l’ut du milieu du clavier, et l’on affaiblit les quatre premières quintes en montant jusqu’à ce que la quatrième mi fasse la tierce majeure bien juste avec le premier son ut; ce qu’on appelle la première preuve. Second En continuant d’accorder par quintes, dès qu’on est arrivé sur les dièses, on renforce un peu les quintes, quoique les tierces en souffrent; et, quand on est arrivé au sol dièse, on s’arrête: ce sol dièse doit faire avec le mi une tierce majeure juste ou du moins souffrable; c’est la seconde preuve. Troisième On reprend l’ut et l’on accorde les quintes au grave, savoir, fa, si bémol, et cetera, faibles d’abord; puis les renforçant par degrés, c’est-à-dire affaiblissant les sons jusqu’à ce qu’on soit parvenu au re bémol, lequel, pris comme ut dièse, doit se trouver d’accord et faire quinte avec le sol dièse, auquel on s’était ci-devant arrêté; c’est la troisième preuve. Les dernières quintes se trouveront un peu fortes, de même que les tierces majeures; c’est ce qui rend les tons majeurs de si bémol et de mi bémol sombres et même un peu durs; mais cette dureté sera supportables si la partition est bien faite; et d’ailleurs ces tierces, par leur situation, sont moins employées que les premières, et ne doivent l’être que par choix.”
d’Alembert:
“On commence par l’ut du milieu du clavier, et on affoiblit les quatre premieres quintes sol, ré, la, mi, jusqu’à ce que mi fasse la tierce majeure juste avec ut; partant ensuite de ce mi, on accorde les quintes si, fa #, ut #, sol #, mais en les affoiblissant moins que les premieres, de maniere que sol # fasse à peu près la tierce majeure juste avec mi. Quand on est arrivé au sol # on s’arrête; on reprend le premier ut, on accorde sa quinte fa en descendant, puis la quinte si bémol, et cetera et on renforce un peu toutes ces quintes jusqu’à ce qu’on soit arrivé au ré bémol, qui doit faire en descendant la quinte juste, ou à très-peu près, avec le sol # déjà accordé.”
Le 12/12/2020 22:32, David Pickett via The Jackrail écrit :
/Jorgenson’s Great Red/ /Tome/*http://www.amazon.com/Tuning-Containing-Eighteenth-Century-Temperament-Nineteenth-Century/dp/0870132903**The link indicates that two used copies of this (now rare) masterpiece
are available at eye-watering prices of $412 and $600. To think that I
paid a mere $20 for my copy when it was being remaindered, and sold it
for about the same.
I don’t know why the link appeared so clearly, when it was nicely hidden
on PP’s site. Anyway, perhaps you or someone owning the Great Red Tome
could tell David what these three Rousseau temperaments are, so he won’t
be “screwed”.
Thanks.
Le 12/12/2020 22:54, Claudio Di Veroli via The Jackrail écrit :
I find Rousseau the most accurate and amenable to be reduced to very accurate numbers
As many have pointed out, Rousseau’s explanation makes little sense,
since he ask that two of the notes be tuned twice (G#/Ab, C#/Db), first
on the sharp side and then on the flat side. If we assume that you don’t
actually retune the two notes, there are only three notes to be tuned on
the flat side (F, Bb, Eb), so Rousseau’s method is flawed here, since he
says that several of the these fifths are “faibles” and several are
“fortes”, using the plural in both cases. It’s impossible to make sense
of this paragraph:
Troisième On reprend l’ut et l’on accorde les quintes au grave, savoir,
fa, si bémol, et cetera, faibles d’abord; puis les renforçant par
degrés, c’est-à-dire affaiblissant les sons jusqu’à ce qu’on soit
parvenu au re bémol, lequel, pris comme ut dièse, doit se trouver
d’accord et faire quinte avec le sol dièse, auquel on s’était ci-devant
arrêté; c’est la troisième preuve.
Once you’ve rewritten that and decided what to do with these three
fifths, there’s still a lot of room left for interpretation, since it’s
up to your own taste to decide if the E-G# third is “souffrable”
(bearable) or not, and how “sombres” or “dures” you accept the last thirds.
So much for “the most accurate” French temperament and its “very
accurate numbers”.
Dear Fred (and partially this applies to Dennis as well). We agree on some points, we do not in others. We agree that Rousseau and d’Alembert are sometimes not perfectly clear. However, my deduction process is based on statistics. Statistics is the way of deriving conclusions from incomplete data, and this is what I have done in my book. For example, I could not assert that Rousseau has three pure thirds without collating with other descriptions (where I verify implications on the number of thirds and on whether they are really pure or not). And it is also apparent that Rousseau is describing the “old practice” use c.1730-40. Most scholars agree that Rameau (less convicing than others in this respect) calls for 4 pure thirds, d’Alembert for 2. Rousseau appears to have described a pre-d’Alembert practice, and the fact that we can deduce a complete and accurate, yes, accurate temperament is most useful for present musicians.
This said, it is pretty obvious that there was variety. However, and importantly, also in my book I show that when you put all the info together the only possible variety was in one or two Cents off the less used major thirds, not something really relevant.
Is is also important to notice that there are mathematical descriptions of the mid-18th-century ordinaire: Gallimard. He fails in the very asymmetrical way he enlarges the fifths, due to a ridiculous mathematical progression, but otherwise he clearly shows the idea behind the system, and with mathematical accuracy. Corrette (although with more major thirds and obviously referring to the peculiar organ-tuning practice) also helps in many respects. All this is explained in my book. I know you have it (Fred was most helpful revising my initial crude prose!), but perhaps re-reading it would help.
And Dennis, your last paragraph echoes exactly what I wrote about Rousseau’s bad thirds and possible variety, but I like the way you put it anyway. However, I cannot agree with the dismissive tone about my “accurate” statements. Yes, they are accurate: again, statistics has shown for over a century now that it is indeed possible to derive accurate information from inaccurate data.
Just a detail (also explained in my book …) : that error in d’Alembert (reproduced in Rousseau) that produces the contradictory double-tuning observed by Dennis, was soon spotted and corrected in later editions of his Elements de Musique. One just has to apply to Rousseau the same correction.
Le 13/12/2020 13:37, Claudio Di Veroli via The Jackrail écrit :
Just a detail (also explained in my book …) : that error in d’Alembert (reproduced in Rousseau) that produces the contradictory double-tuning observed by Dennis, was soon spotted and corrected in later editions of his Elements de Musique. One just has to apply to Rousseau the same correction.
But that’s not the only error that needs to be addressed, since
Rousseau’s explanation aggravates the error by adding at least a second
one, requiring several small fifths and *several *large fifths going
downwards from C to Eb. How do you tune the C-F, F-Bb and Bb-Eb
descending fifths in your interpretation without contradicting
Rousseau’s description?
Le 13/12/2020 13:23, Claudio Di Veroli via The Jackrail écrit :
Rousseau appears to have described a pre-d’Alembert practice, and the fact that we can deduce a complete and accurate, yes, accurate temperament is most useful for present musicians.
Many scholars think that, on the contrary, Rousseau plagiarized
d’Alembert, to the point of copying his mistaken Db instead of Eb. Of
course, d’Alembert could have been describing a pre-d’Alembert practice
himself…
Dear Dennis.
I will not keep answering one loose argument after the other.
It is apparent that you have not read my book.
I have a serious objection to this discussion, let us see what has happened so far:
In a few posts it was mentioned that there was a problem, Rousseau’s temperament, supposedly awaiting solution.
I remind that the solution was found. It was actually published in an article and in a book, favourably reviewed too.
At this point, the correct reaction should be to acknowledge the solution.
If anybody is not happy with the solution offered by a serious piece of lenghty research detailed in dozens of published pages, the correct procedure is
either to write a negative rewiew,
or even better to write down a new deduction about Rousseau,
then have it published.
Accordingly, I am out of this discussion.
Finally, please note that with the above I am strictly following the advice of the present-day leading scholar in the matter, Prof. Barbieri. Published and reviewed books are not discussed in a few lines online.
(I also have my part of guilt: I should have just mentioned my contribution on one line avoiding further participation).
Le 13/12/2020 13:23, Claudio Di Veroli via The Jackrail écrit :
However, I cannot agree with the dismissive tone about my “accurate” statements. Yes, they are accurate: again, statistics has shown for over a century now that it is indeed possible to derive accurate information from inaccurate data.
I wasn’t commenting directly on your statements, but on the so-called
Rousseau temperament, which can hardly be considered an “accurate”
description given that
I fail to see how statistics could be of any help here.
Dennis
Le 13/12/2020 15:23, Claudio Di Veroli via The Jackrail écrit :
I have a serious objection to this discussion, let us see what has happened so far:
In a few posts it was mentioned that there was a problem, Rousseau’s temperament, supposedly awaiting solution.
I remind that the solution was found. It was actually published in an article and in a book, favourably reviewed too.
That’s not what exactly what happened. David Perry asked what the
different “Rousseau temperaments” were in Cleartune. It appears (P.
Poletti) that the answer to this question is to be found in “the
writings of Owen Jorgenson”. So I’m hoping someone has the book and can
give David Perry the answer. Another question was raised in the
meantime: can there really be more than one interpretation of Rousseau’s
description? Apparently, many scholars think so, and, given that the
description isn’t accurate but involves subjective notions, including
that of a “bearable third”, I’m inclined to agree with them. But this is
irrelevant here, unless you or someone can come up and state that some
(or all) of OJ’s interpretations of Rousseau are wrong or at least
debatable, which is more than likely. This would also help David decide
which (if any) of these settings he is going to use.
I 'm not sure Rousseau was in Jorgensen’s “Big Red” book. It might have been in one of his earlier books, Tuning the Historical Temperaments by Ear or perhaps The Equal Beating Temperaments. Or ClearTune may have a different source.
I don’t believe Rousseau was reflecting something earlier than d’Alembert. I see his paragraph as a further corruption of d’Alembert’s corrupt description (but d’Alembert corrected his error). The fact that Rousseau did not notice the error is very important in assessing whether to trust his judgment and perspicacity.
Note that these two paragraphs describing tuning are very minor parts of much longer and more detailed accounts of the problems of temperament, both of them relying very heavily on Rameau. It makes sense to me to accept what they wrote as descriptive of what musicians were doing in a broad sense, but that the details are quite obviously not to be relied on.
I think Carey Beebe’s “solution” is probably as good a model as any for ordinaire. Unfortunately for purposes of using an app, he does not provide offsets. Paul Poletti does for his interpretation, which is closer to the text of Rousseau than Carey’s.
Le 13/12/2020 17:28, Fred Sturm via The Jackrail écrit :
I think Carey Beebe’s “solution” is probably as good a model as any for ordinaire.
It may be a very good model, but it hardly agrees with Rousseau’s
description on the flat side
Carey Beebe:
4. Tune the three perfect fifths on the flat side of C so that each of
these fifths is slightly wide the same small amount.
Whereas Rousseau says that these fifths on the flat side are "faibles
d’abord’ (“weak to begin with”, in the plural): “On reprend l’ut et l’on
accorde les quintes au grave, savoir, fa, si bémol, et cetera, faibles
d’abord”.
Right, it does not conform to Rousseau, but it may well reflect what practicing musicians were doing better than Rousseau’s description. I believe the real aim is to get at what French (and possibly non-French) tuners were doing in trying to make mean tone circular during the 18th century. Rousseau is merely one source, and his instructions are vague and impossible to carry out literally. Better to take all the sources, including others beyond Rameau, d’Alembert and Rousseau.
The other sources are even less precise, but they provide additional evidence for the basic pattern. The most notable element is the considerably wide fifth, skewed to the flat side of the circle, together with [probably} at least one just third on CE. This makes for a very wide range of sizes of thirds, greater than in any other circular temperament style.
Dear All
An interesting discussion which raises the problem that many tuning apps have obscure sources for their temperaments, and the specs cannot be readily found.
There is considerable discussion about Rousseau in several sections of Jorgensen’s 1991 tome “Tuning — Containing The Perfection of Eighteenth-Century Temperament, The Lost Art of Nineteenth-Century Temperament and The Science of Equal Temperament”, and no mention in his 1977 “Tuning the Historical Temperaments by Ear”.
The Cleartune temperament derivation of Rousseau II, III & IV is not obvious. It is, however, possible to reverse engineer an app’s temperament by making it squawk each note of the scale so the deviation from ET can be determined.
I’ve done this for Rousseau II for the purpose of comparison with both the D’Alembert/Rousseau described on my website, and Paul Poletti’s Rousseau 1767. (Contrary to Paul’s preference for a C base, I’ve provided offsets from A as otherwise in performance the pitch of the A will vary according to temperament.)
| D’A/R [CB] | Note | Polletti | Cleartune Rousseau II |
|---|---|---|---|
| 11.73 | C | 10.26 | 10.2 |
| -3.91 | C# | -7.69 | -8.3 |
| 3.91 | D | 3.42 | 3.4 |
| 0.00 | Eb | 2.52 | -2.2 |
| -3.91 | E | -3.43 | -3.4 |
| 7.82 | F | 11.18 | 8.3 |
| -3.91 | F# | -8.27 | -8.5 |
| 7.82 | G | 6.84 | 6.8 |
| -3.91 | G# | -6.05 | -6.4 |
| 0.00 | A | 0.00 | 0.00 |
| 3.91 | Bb | 9.10 | 4.2 |
| -3.91 | B | -6.85 | -6.8 |
Please draw your own conclusions!
Regards
Carey
Obviously nobody cared to read my conclusions already found in my old U.T: book of 1978. Rousseau is audibly asymmetrical, as observed since by many scholars: the fifths enlarge slower towards the sharps, in agreement with the distribution of accidentals and tonalities found in French Baroque music. This asymmetry is also found in mid-18th C French sources unrelated to the Rameau-d’Alembert-Rousseau “line of thought”, e.g. Gallimard. At this point I find two serious issues with the Poletti-RousseauII version: 1) it is almost perfectly symmetrical, and 2) favouring unnecessary the flats yields on the other side 2 unnecessarily very bad major thirds.
In the pìcture, the Circles of Major Thirds: brown is Poletti, blue is my d’Alembert.
