source file: m1371.txt
Date: Tue, 31 Mar 1998 15:55:53 -0500

Subject: Re: reply to Bill Alves

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

SORRY ABOUT THAT LAST POST! HERE IT IS, WITHOUT THE SPAM.
>
>}>I'm not sure why one would expect that. Is there some size of minor
>}>seventh that, to you, is a dividing line, such that a slightly smaller
>}>one resolves inward, while a slightly larger one resolves outward? Try
>}>answering this question:
>}>
>}>"Given that the diminished fifth resolves inward and the augmented
>}>fourth resolves outward, wouldn't one expect that, ideally, the
>}>augmented fourth to be a larger interval than the diminished fifth?"
>}>
>}Yes.
>
>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?
>
>}>If you answer that in the affirmative, then we just have to be content
>}>saying that meantone temperament does not have all the properties of an
>}>"ideal" tuning.
>
>}Yes, though there are different sized tritones in a given meantone tuning
>}of 12 keys.
>
>I'm not sure what you mean. In a given meantone tuning, there is only one
>size of augmented fourth, and one size of diminished fifth. Enharmonic
>equivalents (in the 12-tone sense) cannot be used in meantone temperament.
>
>}Of course, music is an art, and there are many different things in musical
>}context that contribute to the feeling of, what shall we call it, the
>}resolution tendency or naturalness of resolution. However, I do believe
>}that one of these criteria in music of this period is that the shortest
>}path to resolution tends to be the most "natural"
>
>So why doesn't a tritone resolve to a perfect fourth?
>
>}By the way, I talked to someone the other day who argued for equal
>}temperament because of the importance of the ambiguities possible in such
>}chords (the favorite Romantic trick of interpreting a dominant seventh as a
>}German augmented sixth or vice-versa). The ability to reinterpret such
>}chord structures multiple ways, he felt, was at the heart of our tonal
>}system. (I wonder how Huygens would have felt about that -- do you think
>}he's arguing for a distinction between the sounds of the two chords?)
>
>Such reinterpretation may be at the heart of what many Romantic composers
>were doing, but in Huygens' time composers had not yet availed themselves of
>such tricks. You should inform your friend of Handel's meantone organ with 16
>tones to the octave, and that tonal thinking arose in a meantone, not ET,
>environment. Had Huygens had a bit more influence over musicians, Romantic
>composers would have been working in 31-tone equal temperament, and other
>sorts of "puns," chromaticisms, and serialisms would have arisen than the
>ones your friend is accustomed to.
>
>I think Huygens was observing musical practice, not attempting to dictate it,
>but offering 31-equal as a practical tool for musicians to continue doing
>what they were doing, without ever having to worry about hitting any wolves.
>
>}I explained, recalling the thread here some time ago on the possibility of
>}musical puns in just intonation, that such reinterpretations were not
>}impossible in JI, especially if the number of tones in the tuning system
>}were greater than twelve.
>
>I'm not sure what you mean by this, but after Daniel Wolf posted an expanded
>definition of "pun" to include some JI situations, Paul Hahn (if I recall
>correctly) gave a good argument for why the term "pun" should be reserved for
>cases where a tempered interval is used to represent two or more different
>ratios. Normal diatonic usage, by the way, requires punning of ratios
>differing by a syntonic comma, whether meantone or ET is used.