Re: Overtones and chords

Subject: Re: Overtones and chords
From: Jay Smalridge (
Date: Mon Jul 19 2004 - 15:38:27 EDT

Concerning the 3rd and 5th harmonic, I thought that they were the third and fifth from the root in equally tempered? Or is it different because of the "true" 5th and "true" 3rd.

On Friday, July 16, 2004, at 09:45AM, lawrence casserley <> wrote:

>Hi Jay
>First of all, you are confusing the issue a bit with your different
>categories, which don't have a real meaning. The simple overtones of a
>given fundamental (ignoring for the moment inharmonic overtones and
>certain deviations caused by the acoustic peculiarities of individual
>instruments) are simple multiples of the fundamental frequency, ie:
>82 Hz 1st harmonic (fundamental)
>164 Hz = 82x2 2nd harmonic (1 octave above)
>246 Hz=82x3 3rd harmonic (true fifth - ie not equally tempered)
>328 Hz=82x4 4th harmonic (2 octaves above)
>410 Hz=82x5 5th harmonic (true M3rd - ie not equally tempered)
>492 Hz=82x6 6th harmonic (octave above 3rd harmonic)
>574 Hz=82x7 7th harmonic ("flat" 7th)
>656 Hz=82x8 8th harmonic (3 octaves above)
>738 Hz=82x9 9th harmonic (close to an equally tempered M2nd)
>820 Hz=82x10 10th harmonic (octave above 5th harmonic)
>etc, etc................
>All these are "harmonic" overtones - although they don't fit exactly
>with equally tempered notes, because these were manufactured by putting
>everything out of tune a littlle bit. Yes, the first thing to emerge is
>an untempered (natural) major triad, but as you go farther up the
>series all sorts of other possibilities arise.
>Inharmonic overtones are a bigger issue, because they emerge often due
>to special physical factors on each instrument, which can distort the
>"true" tuning of harmonics, or to noise content (and are part of the
>character of particular instruments). but this is the simple basis.
>Lots and lots of stuff about all this out there.
>Lawrence Casserley -
>Lawrence Electronic Operations -
>Colourscape Music Festivals -

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