RE: microtonality in popular music

John Loffink
john.loffink@compaq.com

> From: gbreed@cix.compulink.co.uk (Graham Breed)
>
> There are a load of tunes that already use "ethnic" samples. I'll
> bet a lot of them way off 12-equal.
[Loffink, John] I bet not. Most of those samples and loops are
painstakingly retuned to 12-equal.

> Seriously, movies have such a huge budget you can't expect too much
> experimentation, especially as the people who hold the purse strings
> aren't going to be big musos. Now, if an established film composer
> were to go microtonal, then we'd be in business. If the audience
> don't realise they're listening to microtonal music, they might
> accidentally like it!
>
[Loffink, John] If one includes classical music borrowed for the
movies, then microtonal music already has the examples of Ligeti used in
"2001" and Penderecki used in "The Excorcist."

John Loffink
john.loffink@compaq.com

>>I wrote,
>>
>>}I haven't read Huygens (apart from what Barbour says about him), but this
>>}seems a curious justification. Given that the minor seventh of the dominant
>>}seventh chord resolves inward and the augmented sixth of the German
>>}augmented sixth chord resolves outward, wouldn't one expect that, ideally,
>>}the augmented sixth to be a larger interval than the minor seventh? (If,
>>}indeed, one considers the seventh harmonic to be in need of resolution at
>>}all.)
>>
Paul answered:
>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.

>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. The example you gave from Huygens was specific in that the
augmented sixths in the keys of D and G (common keys, to be sure) would be
close to 7/4 ratios, while the dominant sevenths of those keys would be
larger intervals. What struck me is not that a 7/4 augmented sixth would be
unusable, but that Huygens would use it as a justification for the tuning.

>I also think that resolution has much more to do with position within a
>scale (in particular, a tonal mode) than with absolute interval size.
>WIthout a scalar context, I don't think intervals have any particular
>>tendency to resolve one way or the other.

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" -- thus the importance of
the leading tone and its sharpening in minor keys.

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?)

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. Finally, though, we failed to convince each other
to cross over what was ultimately a difference is aesthetic preference.
Perhaps he felt a greater attachment to the tonal-egalitarian traditions of
late romantic chromaticism, atonality, and serialism than do I.

Bill

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)607-7600 (fax) ^
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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.

On Tue, 31 Mar 1998, Paul H. Erlich wrote:
> SORRY ABOUT THAT LAST POST! HERE IT IS, WITHOUT THE SPAM.

Whew, what a relief. I was on tenterhooks waiting to hear what it was I
had said.

--pH http://library.wustl.edu/~manynote
O
/\ "You just ran nine racks but you won't give me a spot?"
-\-\-- o "I can't; I haven't seen you shoot yet."

NOTE: dehyphenate node to remove spamblock. <*>