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Reply to Bruce K.

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

2/14/1997 2:05:59 PM
From: PAULE

>> I suppose I may have been insufficiently clear in my writing.
>> My point is (and perhaps I misunderstood Neil's original statement) that
>> I don't see how one can say that the harmonic series is the "pure" basis
>> for music as opposed to, for instance, the priciple of small number
>> ratios. Certainly people can hear the harmonic partials of a complex tone

>> and infer melody and harmony from that, but they can also hear simple
tones
>> in "simple" pitch relationships and infer melody and harmony from this.

>Pardon me if I'm missing something here, but I was under the impression
>that small number ratios were precisely intervals found in the harmonic
>overtone series, ie. 8/5 being the relationship between the 8th and 5th
>harmonic of the series. Perhaps I don't understand the terminology
>properly.

>Bruce Kanzelmeyer

Bruce, I don't think you're missing anything, you're exactly right. If our
brains are built to recognize harmonic series, it doesn't matter if the
fundamental or some octave-equivalent is present or not. For example, given
a set of pure tones forming a harmonic series but with the fundamental
missing, say, 300, 500, 600, and 700 Hz, what we hear is a single pitch at
100Hz. This is called fundamental tracking, and has nothing to do with
difference tones. Other psychoacoustical examples that would prove you
right, Bruce, are nonlinearities and partials forming critical band
roughness. In these cases, assuming you have instruments with reasonably
harmonic partials, you get the smoothest effects with intervals from
anywhere in the (lower) harmonic series, whether the fundamental is
represented or not. But the harmonic series remains a fine way of
understanding these phenomena.

The only case where fundamentals might take on special importance in
applying the harmonic series to music is when trying to put a chord in
"root position." It helps the stability of a chord if the fundamental
or octave equivalent thereof is in the bass part. This explains why,
in the days when minor triads were very close to 10:12:15, pieces in
minor keys tended to end on a mjor triad, 4:5:6, for stability.
However, once minor triads began to be tuned close to 16:19:24 (as in
equal temperament), the root of the became was an octave-equivalent of
the fundamental, so it was okay to end a piece on a root-position
minor triad.


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