Piano World Home Page Forums Our Most Popular Forums Piano Tuner-Technicians Forum Temperament ordinaire? Trying to learn just what it is...

I've been experimenting with what I think is temperament ordinaire as outlined by Rousseau--a departure from meantone that seems to have a wolf on close voiced chords that include an Ab (if I'm tuning it correctly), but which has great thirds and fifths and brings out some interesting resonances if I spread it from the center with 12ths similar to Alfredo's.

One thing that seems to "work" is to flatten that Ab a bit. But I'm worried--should I be hearing a wolf on that Ab at all, or does that wolf mean that I'm tuning it wrong? (And if I flatten it, can the entire tuning still be called called a temperament ordinaire, or is it becoming a variety of well?

In fact, the more I read about it, the less sure I am about just what constitutes a temperament ordinaire: Some sources speak of it as being the same thing as a Rameau temperament. Others say it's 1/4 meantone. Rousseau himself speaks of widening several fifths (from pure?), and little more. ( http://2place.org/wiki/Temperament_Ordinaire )

I guess I'm trying to ask if there is an agreed upon definition. And does anyone know of recordings that use the temperament? (As those of you who know me know, I'm of course using software, here, so I can't really claim to be tuning at all. However, I'd like to try to approximate the tuning, if I can determine just what it is...)

Ah, those French cognates (words in English and French which are the same or similar). Sometimes they do mean the same thing, sometimes they have quite different meanings. Temperament Ordinaire would be translated in North American English as: "usual temperament" or "typical temperament".

This would be a lot like the way we think of the temperament sequence we may use today to tune ET. There is a typical way that a tuner would tune through the cycle of 5ths and then try to "back up" through it to resolve dilemmas. While there are descriptions of how to specifically resolve and "check" errors along the way, (the French would use the word, contrôle), many tuners do not know these checks or if they do, they don't perceive them very well and end up with a haphazard system of evening things out the best they can.

In the era where the Temperament Ordinaire was used, ET was not the goal but 1/4 Comma Meantone was also viewed as too restrictive or limiting. There was a desire to have more or all of the keys useful but not the same.

Well Temperament (WT) was one idea that provided for that. The white key side of the cycle of 5ths was tuned the way 1/4, 1/5 or 1/6 Comma Meantone was tuned. That left the black key side with the problem of what to do there. The WT solution was to tune all or most of those 5ths pure. That left the M3s among them wider than they would be in ET.

Before the WT idea, a Meantone temperament would leave one of the 5ths irresolvable. It was most often left between G# (A-flat) and E-flat but sometimes between another interval. Since all of the 5ths would have been tempered more than they are in ET, the irresolvable 5th would be very wide and beating badly. That is the "wolf" 5th and the key of A-flat would usually not sound good at all. To solve that problem, some tuners found a way to distribute that dilemma between two or three 5ths. They would each be wide 5ths and the M3s would also be quite wide but the result would be that all keys were now tolerable. That is the description of what is known as a "Modified Meantone".

So, the answer to your question (at least from what I know) is that the Temperament Ordinaire was not a rigid set of rules at all. So, if during your experiments with it, you find your own way of smoothing things out, you would be doing what any tuner of that time may have done and there would be nothing wrong or unauthentic about it.

Have you checked http://www.rollingball.com/TemperamentsFrames.htm ?



What I have read agrees with what Bill says: tempérament ordinaire means "the usual/normal way to tune", quite a bunch of different tunings were called the same (we have now more classifications for them), and people tried to "smooth things" out using different approaches (some people took a more "theoretical" approach, and gave "alternatives" that were of no use at all).

Thanks for the reminder about those great charts. (I must say that I wish that they showed the minor thirds below the 0.0 line. A chart that shows a positive value for negative numbers for the sake of appearances is confusing, to me. Or is there another, unstated reason--is the relation of m3's to M5's significant in such a way that seeing their relative values overlapping overrides the visual logic?)

More generally, I wish that there was a chart that more simply showed the wolf tones and near-wolf (dog?) tones of each meantone and each well temperament, with all of these temperaments laid side by side. The rollingball charts are great in displaying the qualities of each temperament, but doing a comparison is difficult.

Sorry for the double-post, but I just ran across these visualization tools created in Mathematica. None of the existing tools show the wolf tones, but the program seems to offer many possibilities. Opens to one already-created tool, but others are listed on the right:

http://demonstrations.wolfram.com/PythagoreanMeantoneAndEqualTemperamentMusicalScales/

Jake,

what an interesting link! It seems simple too. Thanks a lot. a.c.

All the negative values in that chart are actually plotted below zero. That is what I saw and had not paid attention to the lack of signs before the numbers! That is kind of weird.

I think it's just to avoid cluttering. The magnitude is indicated just to help read the graph, I guess.

Erus,

this link you provided:

http://www.rollingball.com/TemperamentsFrames.htm ?

places ET between 1910 and 1920. Am I wrong?

Edit: then I went to "Homage to Jorgensen" and I could read:..."I have summarized Jorgensen's wording and decided in many places to eliminate...".

Do you know the author of this site?

I also went to "About "Key Color", and I cound not believe my eyes.

"All the negative values in that chart are actually plotted below zero."

Typo? If I'm reading it correctly, the negative value minor thirds are shown above the O line, while the narrow M5's are shown below it.(By "plotted," I meant, that "they are shown by their place on the graph above the 0 line.") There's an explanation in the section called "Reading the Charts."

Jake:

You are right, I immediately focused on the fifths and ignored the minor thirds.

Alfredo:

Jason Kanter
jkanter {{at}} rollingball.com

Took me a while to understand the charts, too, and I still have to glance over at the key to be sure of which color is what. Great reference, however. Many thanks, Jason Kanter, although Schubart's description of Ab Major (Key of the grave. Death, grave, putrefaction, judgment, eternity lie in its radius) makes me hesitate to sit down at a piano. Occurs to me that the goal might not have been to describe the sound, but to instead deter people from ever playing the notes.

Still looking for a side-by-side comparison that shows the wolves. Not sure, really, what kind of chart could best show them all at once unless it was just a list of which interval sounds the most off to the modern ear in each temperament.

One thing I did find through the variation of temperament ordinaire I tried, though, is that triads that include the Ab only sound really terrible in basic 1-3-5 closed positions. The inversions sound much better, which makes me think again about meantone temperaments and the departures from them--I'm wondering if they may not have notes or keys to be avoided as much as they have intervals and chords that may be best voiced in specific ways.

That sounds more like some aspects of counterpoint. I guess chord base approaches became more relevant after Rameau's treatise (1720's).