Le 14/12/2020 10:55, Claudio Di Veroli via The Jackrail écrit :
In the pìcture, the Circles of Major Thirds: brown is Poletti, blue is my d’Alembert.!
Wouldn’t it make more sense, for our discussion of Rouseau, to compare
your Rosseau and Poletti’s, rather than your d’Alembert?
Thanks.
Thanks Dennis.
Nominally yes. Numerically not.
Rousseau has at least three pure major thirds.
This is my only difference between d’Alembert and Rousseau, and is not that much relevant in practice, I believe.
What is relevant is that what we are all aiming for: a recipe for a 18th French Baroque ordinaire. This has to be asymmetrical and all the tonalities are playable (though one or two barely so), with very few bad (yet still playable, not meantone-wolves) thirds.
There is more than one way to achieve this, but what my curves shows is that “Poletti-Rousseau II” is in my opinion not the way.
JORGENSEN. Who mentioned him?
Just in case some of us do not know, different knowledgeable writers (e.g. Rasch, our Fred Sturm) have shown that most of what he wrote is based on “pure fantasy”, “having hardly read any source” and the like. Barbieri was even more scathing: he finds Jorgensen absolutly worthless.
Le 14/12/2020 01:54, Carey Beebe via The Jackrail écrit :
Please draw your own conclusions!
Thanks, Carey. The conclusions seem quite obvious: there are several
possible interpretations of Rousseau’s (flawed) instructions.
Le 13/12/2020 18:53, Fred Sturm via The Jackrail écrit :
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.
But were they really trying to make meantone circular? D’Alembert
specifically states that the “tempérament ordinaire” doesn’t allow to
play in all keys:
“sur un clavecin accordé par le tempérament ordinaire, il y a cinq ou
six modes insupportables, et dans lesquels on ne peut rien exécuter.”
Five or six modes [keys] are unbearable, and nothing can be played in them.
In Poletti’s interpretations, there is at least one “hideous” third and
one or two “very bad” thirds (his own terms).
Please note that my Rousseau, was obtained collating Rousseau with other descriptions: more than an “accurate” reproduction of Rousseau (and I stand corrected w.r.t. what I posted before), I find my Rousseau a good reconstruction of an average 18th c. ordinaire, and as such I recommend it in my book.
This was established years ago (I think even before 2000!) on HPSCHD-L.
David
You are correct Dennis. As I explain in my book, the 18th c. ordinaire starts with Chaumont and F. Couperin just extending the playable major thirds from 8 to 10, but reducing the number of pure ones from 8 to 6. Then Rameau further reduces the pure ones, and Rousseau also. They were not aiming at enharmonicity, but yet at something which I call “barely circular”. Your quote from d’Alembert is correct and I reproduce it and analyse it in my book: however, “playing it” you find that all tonalities are playable, although two barely so. Yet you do not hear real wolves. d’Alembert cannot be trusted in an opinion about how the tuning really sounds like: at the time he wrote the account, he was a supporter of (sorry for the bad word!) Equal Temperament!! 
Le 14/12/2020 11:43, Claudio Di Veroli via The Jackrail écrit :
Thanks, Claudio.
This has to be asymmetrical and all the tonalities are playable (though one or two barely so), with very few bad (yet still playable, not meantone-wolves) thirds.
D’Alembert says that 5 or 6 “modes” are unplayable. I think this is the
key (so to speak) to many of the misunderstandings around the
“tempérament ordinaire”. We’d like to have a “French” temperament
allowing us to play in all keys, including the F# major section in
Couperin’s L’Epineuse, but the tempérament ordinaire is not meant for that.
Le 14/12/2020 11:51, Claudio Di Veroli via The Jackrail écrit :
JORGENSEN. Who mentioned him?
Just in case some of us do not know, different knowledgeable writers (e.g. Rasch, our Fred Sturm) have shown that most of what he wrote is based on “pure fantasy”, “having hardly read any source” and the like. Barbieri was even more scathing: he finds Jorgensen absolutly worthless.
I mentioned Jorgensen because Poletti claims that Cleartune took their
temperaments from his writings.
Excellent exercise Dennis: 1) tune to something like my ordinaire/Rousseau: few excellent thirds the two worst ones not exceeding -30 Cents. 2) play L’Epineuse not once but two or three times. At this point something happens: we understand what they were trying to achieve!
Le 14/12/2020 12:00, Claudio Di Veroli via The Jackrail écrit :
Dennis: you asked for a comparison with my own Rousseau. Here it is!!!
Thank you, Claudio, much appreciated.
As an aside, I find this a very eloquent way of comparing two
temperaments. The varying qualities of the thirds are immediately apparent.
Indeed. Good old Circle of Major Thirds. Difficult to understand why something so obvious is not used more often, especially in modern times when we are “blessed” with spreadsheets.
Le 14/12/2020 12:12, Claudio Di Veroli via The Jackrail écrit :
You are correct Dennis. As I explain in my book, the 18th c. ordinaire starts with Chaumont and F. Couperin just extending the playable major thirds from 8 to 10, but reducing the number of pure ones from 8 to 6. Then Rameau further reduces the pure ones, and Rousseau also. They were not aiming at enharmonicity, but yet at something which I call “barely circular”. Your quote from d’Alembert is correct and I reproduce it and analyse it in my book: however, “playing it” you find that all tonalities are playable, although two barely so. Yet you do not hear real wolves. d’Alembert cannot be trusted in an opinion about how the tuning really sounds like: at the time he wrote the account, he was a supporter of (sorry for the bad word!) Equal Temperament!!
Indeed, d’Alembert’s view (or hearing) was biaised, since he points out
right after that that in Monsieur Rameau’s temperament [=ET] all the
keys are “equally perfect”…
Both circularity and unsupportable are relative terms. It seems fairly clear that the initial aim of the style of tuning we refer to as ordinaire was ability to use notes enharmonically (eg, G sharp for A flat, E flat for D sharp), at least in passing, and not have them sound horribly “out of tune” to anyone listening. This was partly impelled by the need to be able to transpose, partly by compositional desires, not wanting to stay strictly within the bounds of three sharps and two flats. Over time, the aim seems to have become true circularity: ability to move into the most remote keys at will, and have it sound “supportable.”
The fact that d’Alembert said the ordinaire tuning he described made several keys unplayable is telling - and he wrote that twenty years before Rousseau. d’Alembert obviously thinks this is a defect, so we can infer that many musicians of his time would think the same. Hence, it seems probable that they would have tuned in a more circular manner.
The three surviving “recipes” by Rameau, d’Alembert and Rousseau (vague directions for how to concoct the ordinaire temperament) should not be taken as authoritative. They merely provide a certain amount of evidence (backed up by some even less precise descriptions by other authors) of a certain style of tuning which begins as 1/4 comma meantone, and in which there were multiple wide fifths and some degree of circularity.
As a side note, curiously enough Vallotti’s tuning more or less had its roots in ordinaire. Italians Riccati and Barca read d’Alembert’s Encyclopédie article (research by Barbieri described in his Acustica, Accordatura e Temperamento nell’Illuminismo Veneto), and this led to discussions of various methods for making mean tone more circular. In their case, they chose to use fifths wider than 1/4 comma, generally 1/6. Vallotti begins with 1/6 mean tone fifths, then enlarges them around the circle - describing the division of the syntonic rather than the Pythagorean comma.
(have now deleted my two last verbose posts: hope things are better explained below).
I am baffled Fred. I studied thoroughly Barbieri’s “Acustica … Veneto” book when preparing my “The Vallotti Saga” section in my U.T. book, where I state that Riccati, Vallotti and Tartini appear to have been blissfully unaware of the Rameau-d’Alembert-Rousseau ordinaire temperament.
You now write that, according to Barbieri’s book, Riccati read d’Alembert 1752.
Even if he had, he Riccati had church organs tuned to his first temperament, before 1750.
Actually, throughout Chapter III.D, the one in his book where Barbieri compares Italy evolution with “temperamenti circolanti europei”, he mentions similarities, not mutual knowledge. Later Barbieri includes in his book the main writings and letters by Riccati, 1751-54. I have been unable in Barbieri’s text and in his reproductions of Riccati to find any sentence stating that Riccati (or Vallotti, or Tartini) ever read d’Alembert or any other French source on the ordinaire. If there is such a sentence, please let me know the page number, thanks!
It is also relevant that Riccati does not work like the French, who just start tuning meantone and then modify the fifths through decades of tuning practice. Riccati spent years working with fractions, later logarithms. His writings are highly mathematical: practical application and the final Vallotti temperament came later.
Hi Claudio,
Apparently my memory from when I read Barbieri’s book over ten years was corrupted in the meantime. Presumably you are correct. I had the book out on interlibrary loan, as it was (and still is) unavailable for purchase. Perhaps I am conflating with a different source, or perhaps my memory is simply playing tricks with me,.
In any case, it is true that Vallotti can be looked at as essentially an extension of the French Ordinaire pattern, which was the real point of my side remark.
Indeed Fred. Although Vallotti (in its Young Pythagorean version in common used today with six pure “chromatic fifths”) prima facie looks like a German Good temperament à la Werckmeister, the “Vallotti saga” I describe in my book clearly shows that it originated (as you correctly wrote in a previous post) in syntonic-comma meantone-variant-modification work, and is therefore the same principle that the French used, as you correctly point out.
Anyway, it is important to bear in mind the important difference I noted before. Although the principle is similar, the working method of the “Vallotti gang” was different: mathematics rather than decades of tuning practice. Eventually the French also adopted mathematics for the ordinaire (Gallimard), but at this point they were fast adopting Equal Temperament (apologise again for cursing!).
I find that I did photocopy the chapter of Barbieri’s book in which he discusses the history of what we call French Ordinaire. It opens with Barca, in the 1750’s, finding d’Alembert’s described temperament abominable - it is noteworthy for performance practice that in the mid-1750s we find two musical writers of the same opinion about this pattern described by d’Alembert, including d’Alembert himself, while twenty years later Rousseau plagiarizes and elaborates on the same pattern, and considers it a good tuning. I think we can safely say that Rousseau was definitely outside the mainstream of opinion at the time he was writing.
Barbieri finds evidence of the beginnings of the pattern we call ordinaire in an Italian text as early as the 1620s, with CE described as just and both FA and GB described as wide. Barbieri cites a number of other Italian and French sources describing tuning of this sort in the interim leading up to d’Alembert. Hence, it is clear that there was a practice, even if not well or accurately documented, in which circularity is approached, that this practice occurred parallel to what seems to have been the predominant tradition of mean tone, and that this was occurring in Italy as well as France. (Indeed, this kind of tuning is also documented earlier, going back to Schlick in Germany).
It may well be that the irregular tuning practice described in Italy was introduced by Italians into France, since many Italian musicians made their way into the French musical life of the time, in court and beyond, during the 17th and 18th centuries.
While the derivation of Vallotti was mathematical calculation, he drew from a long tradition of tuning practice in which circularity is aimed at, starting with better thirds and proceeding to wider ones. Ordinaire derives from mean tone (a series of equally narrow fifths), with the effort to make it circular by varying the sizes of the fifths, trying by ear to start with “good thirds” and then close the circle in some way that is musically viable, rather than accept the clear limitations of mean tone. (Split keys, the alternative for at least extending the number of sharps and flats, are not terribly practical from any perspective). Vallotti came up with an elegant solution in which this is done very symmetrically.
Equal temperament is not a curse word, it is a solution to the problem of temperament. I see no reason to consider unequal temperament as “good by definition” and ET as “bad by definition.” All temperament is “bad by definition.” It necessarily involves compromise because of the nature of reality. Thirds, fifths and octaves are not compatible with one another. ET is the compromise in which everything is made the “least bad.” UETs make some things less bad by making other things worse.
In looking for what tuning to use for what music, we are trying to find out what compromise the composer and performing musicians of the time are likely to have used or preferred. There should be no particular judgmental criteria applied in examining the evidence.
