In a message dated 4/13/00 12:09:32 AM Central Daylight Time, fndango@azstarnet.com (Robert A. Anderson) writes: << I have a question. Is there a table or some reference, that says which HT, sounds best with which composer? How does a person determine which piece of music, sound best in a particular HT? Thank you. John M. Ross" I think that's a good question, but I think that there's a better way of going about it than looking for someone else's notion of what temperament should be used in which situation. Everyone who's interested should simply start trying them out, listening, and letting others listen. >> Your answer couldn't have been better nor more complete. Only when tuning for a specific period and for a performance where the tuning will serve only that performance do you really need to choose a temperament which is specific for that kind of music. 1/4 Comma Meantone for Baroque music, for example, Werkmeister for Bach, 1/5 Comma Meantone for Mozart, etc. Even the recent recommendation by Owen Jorgensen that the Kirnberger, an early Well-Temperament that would be suitable for Bach, Baroque or Classical periods to be used for Chopin demonstrates that a temperament may be chosen for its characteristics more than for the period of music it comes from. Generally, the earlier the period, the more unequal. The more unequal, the purer the sound from the simple keys, 0-3 sharps or flats and the more vibrant or harsh, the remote keys, 4-6 sharps or flats. This is true for both Meantone and Well-temperament. In Meantone, the larger the fraction, 1/3, 1/4 or 1/5, the purer the simple keys will sound and the harsher the remote keys and the stronger the "Wolf". the 1/6 Comma is about in the middle. The 1/7 Comma begins the kind of Meantone that might be considered "universal", that is, useful for playing all kinds of music on the modern piano. This temperament however might be considered at the extreme end of that spectrum. Some people may find its mild harshness in the remote and "Wolf" keys to be a bit too strong. The 1/8 Comma might be considered "Victorian", having plenty of color but not too much harshness. 1/9 and 1/10 Comma would be in the Quasi-Equal range ("quasi" means "almost"), offering only "pastel" shades of color and finally, the 1/11 is the virtual equivalent of ET. The value for the Syntonic Comma, 21.5 cents divided by 11 = 1.95 cents, the approximate size of an ET 5th. It should be said that all of these Meantone temperaments are defined by the Syntonic Comma, not the Pythagorean Comma which is a different value, 24 cents. Therefore, ET is a 1/12 Pythagorean Comma Meantone and a 1/11 Syntonic Comma Meantone. The Syntonic Comma is the amount short of an octave that you get when you tune 3 pure contiguous 3rds. That 21.5 cents (theoretical) difference, gap or shortfall is called the Comma. The Pythagorean Comma is the amount in excess of an octave that you get when you tune 12 pure 5ths, 24 cents. Because any Meantone Temperament is defined as a chain of 5ths (and/or 4ths) all tuned by the same amount (whichever fraction is chosen), they lend themselves easily to using an Electronic Tuning Device (ETD) for tuning them. I do not mean using deviations of an FAC program for this although that is possible too. It is a very simple idea and you do have to make an adjustment for inharmonicity. To me, however, this is a fascinating way of constructing a temperament where you are playing an active role in directing the ETD what to do rather than simply accepting the calculation handed to you. You will have to create your own octaves but this too puts you in charge where you can choose the kind of compromises you want to make rather than accepting whichever ones are fed to you. Once you have made your decisions, a programmable ETD such as any of the SAT's will preserve your work to be used over and over. If there is interest, I can spell out in another post how you do this and also how you can make variations of any Meantone temperament such as Tim Farley has done by inserting 1 pure 5th in the 1/7 Comma Meantone. This alteration mitigates by just a bit the harshness of the remote keys and the so-called "Wolf" interval. Bill Bremmer RPT Madison, Wisconsin
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