In a message dated 98-01-29 20:26:17 EST, you write: << Doesn't this amount to an evening out of the very effect you are trying create with the 1/7 meantone? It would seem to me, that if you want the full effect of this temperement to be appreciated, you might prefer a low inharmonicity instrument, which would also be more consistant with the inharmonicity of the more "historical" instrument on which this temperement was originally used. John McKone, RPT >> This is an often asked question so I'm glad you brought it up. On one hand, you might well want to preserve the original character of one of the ancient temperaments, especially when you are playing early music. At the Historical Temperament Recital in Dearborne, Owen Jorgensen had me tune two pianos, each one quite differently, one from the other. One was to be tuned in 1/4 comma Meantone, the other in Thomas Young #1 Well-Tempered tuning. The 1/4 Comma was to have "minimal stretch" and the Well-Temperament was to have "optimum stretch" by the artist's direction. By the way, in my previous post, I misidentified the results of the two "mitigations" you could use if you found that the 1/7 CMT was too "strong". They become 1/7 Comma Modified Meantone and 1/7 Comma Victorianized Modified Meantone. The Modified Meantones can sound a lot like Well-Temperaments and can usually be freely substituted for them but they are of different origins and so they are not one and the same. A modified Meantone also breaks some of the basic rules of a Well-Temperament but often the Victorianized type is mitigated to the point where it is in line with those rules and can thus be called a Well-Temperament too. By choosing the Kawai piano, the one available with the lowest inharmonicity, I could best preserve the apparent sound of the 9 pure 3rds that the 1/4 CMT is supposed to have. I say "apparent" because the Kawai piano, being a modern piano, does still have inharmonicity. Just as 3rds in ET cannot be the 13.6¢ wide of just intonation that is theoretical, they MUST be widened to some degree to accomodate inharmonicity, 9 absolutely pure 3rds cannot exist on a modern piano and create an accurately effected 1/4 CMT. They must be widened but must still sound pure to the ear. In this case, each 3rd was 0.8¢ wide, an amount that was imperceptible to the ear and consistently and accurately provided for by the SAT. It would be very difficult indeed to do the same thing aurally because there is no aural check for a pure 3rd. All you can do is tune it so that it has no apparent beat. Just as when attempting an ET by ear, the cummulative effects of the cummulative errors you make in your estimations of what you think the interval ought to sound like can result in a puzzling and perplexing, erroneous end. Owen confirmed that all of the aural tests he knew for the temperament checked out. He was delighted. I was also thrilled to see that my idea had worked. I felt like Dr. Frankenstein when he saw the Monster's hand move, "It's ALIVE!!!". The idea I had of pre-programming the SAT to produce any kind of meantone temperament was only a hypothesis. It has never failed, however to produce stunningly accurate results! Since I always read my 3rd, 4th & 5th octaves all on the 5th octave, (the same as is done for the RPT Exam but not the way the SAT is set up to do automatically) I can have absolute, rational control over my octave stretching. To have "minimal" stretch is easier than you could ever want it to be. Once you have calculated the figures for the temperament, all you have to do is enter the same numbers for each note in the 3rd, 4th & 5th octaves and tune to what ever it says. Then when you get to the 6th octave, you play the note an octave below the one you want to tune, stop the lights and tune to whatever it says and enter that value in the program. In the bass, you do similarly, play the note an octave above the one you want to tune, stop the lights and tune to whatever it says and enter that value in the program. This resulted in a very still, contracted sound, virtually devoid of the resonances that we usually expect to hear from the modern piano. It fit the music he played on it, however. It was the way the artist wanted it. The other piano, a Samick grand with somewhat higher inharmonicity, but still in the moderate range, was tuned entirely differently. It was a Well-Tempered Tuning. Just as has been recently advocated with ET, to stretch the octave out very widely and also stretch the outer octaves as much as possible, we can use the inharmonicity that the piano has to our advantage to play tricks with the comma. Here, retaining the sound of tempered 5ths in the outer octaves is definitely not what I wanted to do. That just makes the modern piano sound poorly tuned! That tempering must be present in the midrange but in the outer octaves, anything goes! This is absolutely no different than the way ET is manipulated contemporarily by skilled, artful technicians. Now, with the 1/7 Comma Meantone you have a clear choice you can make. You can try to preserve an "ancient"-like sound and still have a tuning that will be very versitile. Or you can take it and manipulate the outer octaves and use it as a substitute for a Well-Tempered tuning and play Romantic music, modern jazz or virtually anything else on it. The amount of inharmonicity the piano has need not dictate which bend you give to the outer octaves, you only need to be aware of what you have to work with and what your goals are. Bill Bremmer RPT Madison, Wisconsin
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