Re: [harmonic_entropy] Digest Number 149

Here are my 2 cents worth of ideas about the problem you describe (you know
my "obsession" with combination tones ;-)) :

The highest amplitude combination tones of 7:9:11 are f1 + f2 - f3 = 5, f1 -
f2 + f3 = 9, -f1 + f2 + f3 = 13, thus forming a "chord" 5:7:9:11:13,
consisting of an unbroken series of odd harmonics of a base freqency 1 that
serves as a tonal point of gravity.

Subjecting 14:18:21 to the same procedure yields 11:14:17:18:21:25. There is
not even a hint of order or tonal relationship detectable.

Conclusion: A chord even when composed of excellent intervals, but missing
tonality, will be inferior to one consisting of lesser intervals that
observes tonal requirements.

Heinz

--- In harmonic_entropy@y..., HPBOHLEN@A... wrote:

> The highest amplitude combination tones of 7:9:11 are f1 + f2 - f3
= 5, f1 -
> f2 + f3 = 9, -f1 + f2 + f3 = 13,

how do you derive that? in a dyad, the highest amplitude combination
tone is most commonly 2f1 - f2, not f2 - f1 . . .

This is actually an answer to Digest # 150, where Paul Erlich asked:

"how do you derive that? in a dyad, the highest amplitude combination tone is
most commonly 2f1 - f2, not f2 - f1..."

This is true for a dyad. If a three-tone cord is involved, the amplitude of
products of the type f1 + f2 - f3 is twice as high (+ 6 dB) as that of the
type 2f1 - f2 etc. This is at least the result of chord calculations with a
little simulation program that I am using. The model on which it is based
features a very modest nonlinearity.

Anyway, I use that criterion only for a "quick & dirty" assessment of a
chord. The full treatment only (taking into account the gamut of harmonics
and combination tones) finally reveals what I believe is essential: the
"shape" (gestalt) of a chord. Going back to the chords originally discussed,
7:9:11 fares much better under that treatment than 14:18:21. AOL is bad with
attachments; I can fax you print-outs if you are interested.

Heinz