source file: m1491.txt Date: Fri, 31 Jul 1998 22:57:07 -0700 (PDT) Subject: Re: Dave Hill's Wolf sonority From: "M. Schulter" Hello, there. This post is a very enthusiastic response to Dave Hill's post in Tuning Digest 1488. One of the greatest pleasures is to see how a musical experience can be shared by people working with different tunings and styles. Such experiences can add to understanding on all sides while highlighting interesting common ground. > The b - fsharp - d resolving chord with the wide fourth > between b and fsharp is nearly the same as the wolf D minor chord > which occurs with a twelve per octave keyboard tuned to a just scale > on C. In first inversion, this chord from d down to a down to f has > the d to a fourth wide from just by a 21.5 cent comma, while the > interval from f to a is a just 5/4 major third. One fascinating point that Dave's posts have brought home to me: what tertian just intonation and the early 15th-century Pythagorean tuning with the Wolf at F#-B (actually Gb-B) share is a keyboard with prominent just fifths _and_ a number of pure or nearly-pure thirds. When I posted about this Wolf in a 15th-century setting, I didn't realize how similar a situation could arise with Dave's just piano tuning, and the connection is indeed a delightful one. > In the song My Country tis of Thee - God Save the Queen, which > begins C C D B C D, the first two notes are harmonized with C major > and the third note would normally be harmonized with D minor. On my > piano, which I am here translating to the terms of the just scale on > C, the D minor chord sounds bad if played with a D in the bass, but > if the F is played in the bass, that D minor chord sounds all right > to me - not perfectly consonant, but not egregiously out of tune, > and possibly as effective musically as it would sound if a lowered D > were used or raised F and A so that the chord would be a just minor > triad. Thanks to Dave for a very memorable example which neatly brings the concept home, and suggests that the acoustical factors at play in this Classic context might be similar to those in a late Gothic setting. Just today, on a Yamaha TX802 tuned to Pythagorean and the keyboard mapped to place the Wolf at F#-B (Gb-B), I tried the 15th-century cadential sonority d-f#-b, holding it for a long time before resolving it to c-g-c'. Curiously, it wasn't unpleasant at all, but just seemed maybe to lend a bit of extra flavor or energy to the cadence. While Mark Lindley's examples don't dwell on this sonority for too long, I wouldn't hesitant to use it in a more prolonged cadential context. This is radically different than the effect of a Wolf fourth (or fifth) as a bare interval, as I definitely noticed -- maybe nature's way of saying "12 notes per octave is not enough." Anyway, the tunings and musical settings are in some ways very different, but Dave's experience and mine "running with Wolves" seem strikingly similar. It's interesting, for example, that in Dave's setting f-a-d' or d-f#-b is the inversion of a minor triad; in mine, it's an active and expansive combination with two _major_ intervals both "stretching" as it were toward stable resolutions (M3-5, M6-8). Thank you, Dave, for a great post -- I'm looking forward avidly to the next chapter in your just intonation piano saga. Most appreciatively, Margo Schulter mschulter@value.net