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Consonance

🔗"Andrew L. Kaye" <androsky@...>

10/21/1997 7:06:02 AM
Carl Lumma writes:
I like equal-step tunings as much as the next guy. I even like 12. I am
always amazed at how good it sounds, and at how powerful it is...

Okay, so to you, 12-TET tunings are powerful (and this is cause for
amazement, presumably because of the high integer ratios it employs)

Carl Lumma writes:
Consonance is a factor of the size the number in an intervals ratio.

In a sense, yes, because the interval itself is a factor of the sizes of
the numbers in the ratio. But in another sense, no: the Random House
Dictionary and the New Harvard Dictionary of Music agree that consonance
is a factor of cultural conventions and the "mind of the beholder" (or
the musical equivalent of that)

Carl Lumma writes:
An interval 16 cents flat of the sublime 6/5 has frequency ratio
19723/16585. This, of course, is our quite dissonant 12et minor third.

So, 6/5 is sublime, and 19723/16585 is quite dissonant, yet powerful.

Carl Lumma writes:
An interval 18 cents flat of the 6/5 bears ratio 19/16. It is a very
consonant minor third found in the duple 16-32 of the harmonic series...

And 19/16 is very consonant.

Colleagues of the tuning list, the evidence suggests that musical beauty
is in the ear of the hearer. I see many claims that low integer ratios
produce more "natural" and "perfect" harmonies, but little proof that
people actually respond this way. This makes the tuning list sometimes
read like some medieval treatise on the nature of God. Why be amazed
then, that the Devil incarnate, 12TET, wields such power?


SMTPOriginator: tuning@eartha.mills.edu
From: Carl Lumma
Subject: Dictionary Devils
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