--- In harmonic_entropy@y..., "unidala" <JGill99@i...> wrote:
> --- In harmonic_entropy@y..., "Paul H. Erlich" <PERLICH@A...> wrote:
>
> >PE: 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.

> >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?

JG: Additionally, due to the nonlinear amplitude transfer function of
perceived loudness levels [shown as approximately equal to a value of
( (SPL)b/(SPL)a )^(2/3) at SPL levels greater than 20 PHONS (in SPL),
which is equal to 0.1 SONE (in LOUDNESS UNITS, being 20 dB above the
threshold of human hearing)] [from "Music, Physics, and Engineering",
Olson, 1967, page 252], is it not also true that, in order that "the
spectral amplitudes of each of the overtones of the individual
fundamental frequencies of such individual complex tones" remain
identical (or nearly identical) relative to the amplitudes of those
fundamental frequencies - that the two identical (steady-state as
well as transient) frequency spectrums of the (complex) tones number
1 and number 2 from which the dyad is constructed ALSO be of equal
(or near equal) scalar amplitude throughout the time period during
which each of the individual complex tones are sounded (steady-state
as well as transient)?

NOTE: The phrases "steady-state" as well as "transient" are utilized
above in an inclusive manner to describe all phases of the process of
time-varying amplitude envelopes multiplying each of the values of
the individual complex tones (existing for some given time duration)
from which the dyad is constructed.


Curiously, J Gill