source file: m1373.txt
Date: Fri, 3 Apr 1998 09:36:58 -0500

Subject: RE: reply to Bill Alves

From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>

>}>>}You really do believe that? So now tell me, what is, ideally, the
>dividing
>}>>line between minor sevenths }which tend to resolve inwards and those that
>}>>tend to resolve outwards?
>
>}As I said, I think that the shortest path to resolution tends to be the
>}most "natural." A resolution of a leading tone to the tonic is journey of a
>}semitone, and more natural than the resolution of the sub-tonic to the
>}tonic, a whole tone. By extension, a resolution by 76 cents, say, is
>}slightly more natural than one by 117 cents (though I do agree that is just
>}one factor in the musical context). I believe that string players, for
>}example, have a natural tendency to slightly sharpen or flatten notes in
>}the direction of the resolution.
>
>You didn't answer my question.
>
>}Handel's 16-key organ was the exception, not the rule, and the vast
>}majority of meantone keyboards had 12 keys. Thus musicians had to decide
>}whether to tune a given tritone to an augmented fourth or diminished fifth,
>}and so they might encounter music where they had to play a Db when they had
>}tuned an C#. Thus enharmonics, while theoretically distinct, had to be
>}treated as the same for practical purposes on most keyboards.
>
>Do you have an example where more than two different augmented sixths appear
>in the notation of a piece written for a twelve-tone keyboard in meantone
>temperament?