7:4 and 7:5, but not 7:6, 8:7, and 9:7

What strikes me in the speech paper we recently discussed is that the
statistics of the spectral data of human speech show (slight) peaks at the
ratios 7:4 and 7:5, but none at 7:6, 8:7, and 9:7.

The authors do not mention this peculiarity in the text of the paper. But it
is clearly visible in the figures 2C, 2D, 4, and 5A.

Any idea?

Martin

--- In tuning@yahoogroups.com, "Martin Braun" <nombraun@t...> wrote:
> What strikes me in the speech paper we recently discussed is that
the
> statistics of the spectral data of human speech show (slight) peaks
at the
> ratios 7:4 and 7:5, but none at 7:6, 8:7, and 9:7.
>
> The authors do not mention this peculiarity in the text of the
paper. But it
> is clearly visible in the figures 2C, 2D, 4, and 5A.
>
> Any idea?
>
> Martin

why is it a peculiarity? 7:4 and 7:5 are the simpler of these ratios
by most measures. and even if you assume total octave equivalence,
9:7 is still more complex than the other four you mentioned.

also, i've noticed that sometimes an infinitesimal change in the
numerical method can change a small peak into a small trough, or vice
versa. it might be interesting to reproduce their studies with
simulated, rather than real, sounds, to see what results.

Paul:

> why is it a peculiarity? 7:4 and 7:5 are the simpler of these ratios
> by most measures. and even if you assume total octave equivalence,
> 9:7 is still more complex than the other four you mentioned.
>
> also, i've noticed that sometimes an infinitesimal change in the
> numerical method can change a small peak into a small trough, or vice
> versa. it might be interesting to reproduce their studies with
> simulated, rather than real, sounds, to see what results.

Thanks, Paul. This makes sense to me. Still, I find it a bit smart (of
nature) that the borderline of the harmonicity of the human voice should be
between 7:5 and 7:6, of all places. Could it play a role that 7:4 (969 Cent)
and 7:5 (583 Cent) have no immediate simple-ratio neighbors on the Cent
scale, as opposed to 7:6?

Martin

Martin Braun wrote:

>What strikes me in the speech paper we recently discussed is that the
>statistics of the spectral data of human speech show (slight) peaks at the
>ratios 7:4 and 7:5, but none at 7:6, 8:7, and 9:7.
>
>The authors do not mention this peculiarity in the text of the paper. But it
>is clearly visible in the figures 2C, 2D, 4, and 5A.
> >
One of the lines (think it's Farsi) in Figure 4 does seem to show a kink around 7:6. But in general, yes.

>Any idea?
> >
The comment to figure 3 says "There are no peaks in Figure 2 at intervals corrsponding to the reciprocals of integers >6, reflecting the paucity of amplitude maxima at harmonic numbers >6." I'm not sure if this is saying that the resonant peak is never at the 7th partial (Figure 3A shows a small amount of energy there) but 8:7 and 9:7 are ruled out. 6:11 would actually be the next simplest ratio with a denominator of 6. So perhaps we can adjust that claim to >=6? The 6th harmonic is certainly weaker than the 5th, yet 6:5 isn't apparent in the female graph.

Graham

--- In tuning@yahoogroups.com, "Martin Braun" <nombraun@t...> wrote:
> Paul:
>
> > why is it a peculiarity? 7:4 and 7:5 are the simpler of these
ratios
> > by most measures. and even if you assume total octave equivalence,
> > 9:7 is still more complex than the other four you mentioned.
> >
> > also, i've noticed that sometimes an infinitesimal change in the
> > numerical method can change a small peak into a small trough, or
vice
> > versa. it might be interesting to reproduce their studies with
> > simulated, rather than real, sounds, to see what results.
>
> Thanks, Paul. This makes sense to me. Still, I find it a bit smart
(of
> nature) that the borderline of the harmonicity of the human voice
should be
> between 7:5 and 7:6, of all places.

i'm sure this borderline could be pushed around quite a bit by using
different methodologies in the study.

> Could it play a role that 7:4 (969 Cent)
> and 7:5 (583 Cent) have no immediate simple-ratio neighbors on the
Cent
> scale, as opposed to 7:6?
>
> Martin

yes, the crowdedness of ratios is what harmonic entropy measures (i
know i've told you about harmonic entropy), and the dips in the
harmonic entropy curve that are found at the simplest ratios get
smaller as p*q gets larger, until for some critical p*q (depending on
the standard deviation, or "fuzziness" in hearing, assumed), there
are no dips any longer. the graphs you're looking at might be
analogous to a harmonic entropy curve "tuned" so that there are dips
for all ratios p/q such that p*q<42.