In a message dated 3/20/99 7:42:44 AM Central Standard Time, jpage@capecod.net writes: << Is the 'wolf' the reason for a term I heard along time ago, I don't remember which musician or composer said it but something was referred to as the "pianists' vibrato". Jon Page >> No, the "pianist's vibrato" exists even in ET. It is essentially the resonance you hear from the Rapidly Beating Intervals (RBI) (not Runs Batted In), the 3rds, 6ths, 10ths & 17ths. In ET, they are all distributed very evenly. Every major and minor triad has its own equal share of them, regardless of which key you are in. In the HT's, they are distributed in alignment with the cycle of 5ths. A "wolf" is a dissonant interval that is created, not by tuning it but as a result of tuning other intervals the way you want them. In the Meantones, you tune a series of 11 5ths that are *narrower* than an ET 5th. The 12th one is what is left over and cannot be reconciled. Since all the others were narrow, it is wide. In the 1/7 Comma MT, it is only slightly wide (6-8 cents depending on the inharmonicity) and slightly dissonant and so, it can still serve as a playable interval. In 1/4 Comma MT, it is some 40 cents wide and extremely dissonant. Yet, some jazz and blues players can incorporate that sound since they play other kinds of chords that would have seemed wildly dissonant in past centuries but titillate our senses today. HT's have "wolf" 3rds too, which are again, not tuned that way but are left over as the result of tuning other 3rds more narrowly than in ET. If you tune a pure C3-E3 3rd and a pure E3-G#3 on top of it, the remaining Ab-C4 3rd will be very wide, some 26 cents. It will sound very harsh and sour to most people. It is really not a 3rd but a diminished 4th: G#3-C4. A "wolf" 3rd is wider than the 22 cent "Pythagorean 3rd" which is considered to be at the limit of tolerance for a usuable 3rd (see Rules for Well-Tempered Tuning). Bill Bremmer RPT Madison, Wisconsin
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