--- In harmonic_entropy@y..., "Paul H. Erlich" <PERLICH@A...> wrote:

> Waveform has nothing to do with it. Harmonic entropy is the simplest
> possible model of consonance and cannot be regarded as specific to
> any waveform.


> >JG had asked:...what relation does the term "harmonic" have to
> >your "Harmonic Entropy" concept?

> PE:(a) the dyad is compared with intervals in the harmonic series

JG: Of one, the other, or both fundamental frequencies of the two
tones from which the dyad is constructed?

> PE:(b) the dyad is harmonic, not melodic.

JG: Do you mean by this simply that the dyad is (potentially, but not
necessarily) constructed of complex (as opposed to sinusoidal) tones?

>PE:...harmonic partials will lead to the same set of ratio-
>interpretations for the dyad as the bare dyad,
>but with tighter standard deviation because
>
> (a) there will normally be some partials in, or at least closer to,
> the 3000Hz frequency range
>
> (b) the multiplicity of partials will represent several independent
> sources of information for the same ratio-interpretations


JG: Would not (b) directly above imply that - for the equivalence
of "ratio-interpretations" to exist from "several independent sources
of information" (those sources being the individual complex tones
from which the dyad is constructed) - the spectral amplitudes of each
of the overtones of the individual fundamental frequencies of such
individual complex tones must be equivalent. That is - the (steady
state, as well as the transient) frequency spectrums of the (complex)
tones number 1 and number 2 from which the dyad is constructed must
be identical (or nearly identical) in order for your assumption (b)
directly above to be valid?


Curiously, J Gill