hig third sound examples

Graham Breed said:

>> > The high third example has a less clear peak.

To which I asked for clarification:
>>
>> More about "peak," please. (Perhaps I will be able to check that myself
>> when I get my Spectrogram up and running.)

Graham answered:
>
> As I said in the original message, there's a wide variation in pitch
> over small periods of time. I think this is from 6:5 (definitely this
> time) to 9:7. But, if you do the Fourier transform over a longer
> period of time, you see a constant but blurred trace. The most
> intense frequencies in that blur are colored differently, and fairly
> consistently correspond to a 5:4. Which is what we would have
> expected. Looks like the ear does a similar thing.
>
> The "blurring" would presumably be interpreted by the ear similarly to
> vibrato. However, it is qualitatively different. It looks like a
> fractal trace, rather than a sine wave. I'd like to hotwire a synth
> to emulate this. Maybe over the weekend. It must come from some
> feature of the vocal chords, and is present, to greater or lesser
> extent, in all the samples I've analysed that don't replace it with
> gratuitous vibrato or portamento. Not that I have any kind of
> statistically significant sample yet.
>
> I don't think this is an artifact of the measuring process, as it
> isn't present for synth generated sounds.

This sounds interesting, Graham. Hopefully, you will be able to explore
further.

-----------------

Graham further noted that:

> What happens is that the trace is relatively
> steady for a while, then wanders around a bit, and becomes steady
> again. With the low third, it keeps hitting the same point when it's
> steady. With the high third, I think there are three different steady
> regions.

This is interesting from the standpoint that the vocalization of the low 4:5
third is clearly a "representation" of nature while the high third is not
(as far as we know). Perhaps it suggests that I (like the choirs I heard
during the last two days) have a a variety of "preferred" high thirds
according to context.

> Each is consistent, in that the average pitch is the same at
> the beginning and end of the region, but the regions are not
> consistent with each other.

Which example are you referring to here? The adjusting one? The point of
that one, of course, is to show a difference at the beginning and the ending
"regions."

> I think this is audible: I heard the
> pitch rising,

Okay, I guess you are talking about the "adjusting" third extracted from the
example into which the fifth was introduced.

> and the chord becoming more dissonant. I think the
> computer showed the first region being 5:4,

Before the fifth entered, I presume.

> the middle around the 400
> cents,

In tempered "never-never land."

> and I forget for the last one. I don't have the trace open
> here to check.

Oh, no! This is the vital one. The Tuning LIst (at least me) awaits the
revelation of the "magic" number.
>
> One interesting thing is that the blurring is actually greater for the
> low third, only the peak is well defined. With the high third, the
> pitch fluctuates over a smaller range, but without a clear center.

Sure sounds like I had something in mind. The question is: what??????

> At
> least that's how I saw it. You can all check for yourselves.

I certainly hope I will be able to when I get my new software loaded.

-------------------

>> Divisions?
>
> Each time slice in the readout is a discrete Fourier transform at that
> point. This is equivalent to a Fourier series about some low
> fundamental. So you get equal divisions of frequency space. Each
> point is colored to show the intensities of that range of frequencies.
> Now, as I was measuring the fundamentals, the width of those
> frequency ranges amounts to a few cents. So I can tell the difference
> between a just and equal tempered major third, but can't tell whether
> the high third is really 24:19.

But......but.......but.......I can't wait to find out what I sang!!!!!!!!

I guess I'll just have to tune in for the next exciting episode of "The High
Third Performance." Don't you just love suspense????

Jerry