>Greetings, > > Does the scaling indicate that these pianos would favor non-equal tuning? __________________ Yes. Inharmonicity has the effect of reducing the size of both the pythagorean and syntonic commas. This observation seems a little confusing at first because these commas appear to work in opposite directions. As you know, the greater the inharmonicity of an instrument the wider you must cut the fifths in order to keep them all of exactly the same size. We can say that a highly inharmonic instrument favors unequal (tonal) tuning because we are able to enjoy the benefits of several pure intervals, and the proportional beating triads that pure intervals imply, without increasing beat speeds of the diminished fourths and tempered fifths as much as the same temperament require on an instrument with lower inharmonicity. In some cases, a Victorian temperament on a more inharmonic piano for example, the tempered fifths and larger thirds may beat no faster than what we would have expected from ET on a less inharmonic instrument. ______________________ > Does the inharmonicity pose a problem to achieving what we accept as ET >today? _______________________ I have said before tuners who think that they can do an accurate equal on a cheap spinet should try and measure the fifths. I will bet that even though the thirds may progress evenly, some of those fifths are pure. With beat speeds that slow it is too difficult to cut the fifths equal, -and who would care anyway? If you want equal on a cheap piano, try Marpurg I, one of the "rival" temperaments. The thirds are all equal, but half of the fifths are pure. Obviously, this is only a small part of the picture or we would prefer more inharmonic instruments. The message is that inharmonicity is not all bad, and that message is not new. ______________ To Ed, Stehpen, and the other tonal tuners out there: Unfortunately since we are just beginning to ask some of these interesting questions concerning the relationship between inharmonicity and unequal temperament as realized on both period and modern instruments, and what all this means to the music, it may be some time before we have meaningful answers. I would like to continue the discussion with a question of my own. Most of the time we are not tuning for one particular evening or performance, therefore when selecting an appropriate temperament we can take into account that player (or owners) musical taste as well as our own, but generally we are, or should be, tailoring the temperament to best compliment that particular instruments scale. I do not even know exactly what kind of temperament or direction I will take until I have tuned at least 3-4 notes (on a first-time tuning). My question is this: I have noticed that on Borsendorfer pianos I consistantly end up tuning ET. Why? Have others of you done the same thing? For some reason I do not get the same sense of aesthetic disinterest I normally associate with ET when tuning a modern Bosendorfer piano. Thanks Ed for keeping this thread going, Dennis Johnson St. Olaf College
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