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On the tuning of augmented sixth chord (Paul E)

🔗Manuel.Op.de.Coul@ezh.nl (Manuel Op de Coul)

3/19/1997 4:50:26 AM
From: PAULE

No disrespect intended, but it is silly to try to calculate the "5-limit"
ratios of common-practice chromatically altered harmonies. I believe the
preponderance of this kind of numerology to hurt the case for alternative
tuning systems among the musical community.

a) The diatonic system is only a 5-limit system insofar as the consonant
harmonies approximate ratios of odd numbers 5 or less. Even calculating the
ratios of a purely diatonic progression such as I-IV-ii-V-I is a futile
exercise; in any meantone temperament, including 12-equal, the musical
reality obliterates all distinctions between varying quantifications of the
above progression, and is more beautiful than any of them to boot. To claim
(as many would) that the arithmetical construction is more valid than the
musical reality is to cease to have any relevance for the realm of music and
to engage in a meta-musical game reminiscent of the worst excesses of
serialism.

b) The fact is that certain chromatic alterations were chosen from a pool of
many possibilities that would satisfy the rules of melodic/contrapuntal
movement. The latter would dictate simply that two voices can be
chromatically altered in opposite directions if both resolve by step in the
direction of the alteration. But we don't have augmented thirds progressing
to perfect fifths, and instances of augmented seconds and augmented fourths
seem to be restricted to the case where at least one note is diatonic. The
augmented sixth distinguished itself from other possibilities for acoustical
reasons; namely, its proximity to a septimal ratio. If nothing else,
septimal ratios define a set of "not-too-dissonant" intervals outside the
5-limit system, and need not be taken as a foreign musical language.

I would suggest that people using the limit terminology review Partch's
original definition since the "prime" definition seems to lead to a lot of
confusion and unneeded complexity while the "odd" or Partch definition seems
more suited to musical practice and acoustical theory. The "prime"
definition is sometimes useful in describing a tuning system or the practice
of tuning itself, but musical reality as concerns the listener is better
understood in terms of the "odd" definition.

-Paul E.

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