Re: Classical Uncertainty Principle and string timbre

Hi Bob,

Thanks, interesting about the string timbre.

Actually it has helped wonderfully with the FFT section of FTS as
I now realise that most of the timbres need a bandwidth set for the frequency,
- the FFT finds too many peaks close together, and I realise
this isn't soemthing in the FFT itself, but of the nature of
the timbre of many musical notes.

This is working and it is now finding the peaks without user
intervention - hurray!

For pitch, I've been doing some tests using midi ocarina
voice (close to sine wave).

One can expect a gradual rather than sharp cut off in pitch
resolution - e.g. if one can always distinguish 5 cents, one
will prob. sometimes be able to distinguish 4 cents..

Trying yesterday, I could distinguish 5 cents (240-tet steps) at 1 sec. note.
At 4 cents (300-tet), made a few mistakes, about one in ten wrong.
At 3 cents (400-tet), results close to random.

This is when very relaxed and listening in a quiet fashion, not
hassled.

If tired, or in one way or another can't concentrate on it,
I make mistakes even at 5 or 6 cents.

Trying again right now immediately after a long coding session
without a break (not very sensible, but there we are)
I find 6 cents even quite hard, making lots of mistakes,
and 10 cents (120-tet) is about equiv to 5 cents yesterday night.

So, my pitch accuracy varies a tremendous amount.

On rarer occasions, I remember hearing 400-tet as separate notes
(though with a few mistakes).

Did this test for notes all the same pitch, e.g. 440 Hz, 440 + 4 cents.
(about 441 Hz).

Might make more mistakes if one randomised the start pitch.

It's for melodic steps, the notes played one after another.

Seems 4 cents is quite good at least for a western musician,
though as I can get close to 3 cents, can well believe
others get better than that and reach 1 cent or less,
as they have said on this list.

However, I must say, I'm not good at all at distinguishing
interval sizes. Play an interval, then play it transposed
to another pitch, and I find it really hard to tell if it
is the same interval, if there is no context in which to place
it.

Can, in this completely out of musical context type test,
on some occasions for test using just two notes, and with
voice such as ocarina with no partials to cue one in,
confuse 9/8 and 4/3! (can tell if it is within singing
/ whistling range and I sing from one to the other).

I don't have perfect pitch, but am an amateur musician with
a rather undeveloped sense of relative pitch, and a fairly
good medium term memory for the absolute pitches of notes
Also tend to hear pitches as a type of timbre - could
get sound of say ocarina at one pitch confused with say violin
at another - not now, but can still hear that aspect to a sound,
and it caused a lot of confusion when younger.

Doesn't seem to interfere with my improvising and composing
somehow... Also seem to somehow feel the quality of a
temperament when improvising in it.

So not too bothered by it. Having a good medium term memory for
absolute pitch plus fairly fine pitch accuracy for that has
been useful when debugging music software, on many occaions.

I think there are many ways pitch entres into things.

There's the recognisable melodic absolute and relative pitch;
then the quality of a chord; then the reproducibility of a note; I'm sure
many others...

An interesting thing, sometimes one can distinguish two notes
by melodic comparison with neighbouring notes that one
can't distinguish from each other.

E.g. suppose you have instrument tuned to 4 cent intervals
as 0 cents 4 cents 8 cents 12 cents.

Then someone gives you another instrument with just one note,
and tells you it is one of those.

Suppose your pitch descrimination is 5 cents, so that there is
no chance of doing it by direct melodic comparision.

Then, try comparing it with 0, 4, 8 and 12 in turn.

If it is the 4 cents one, it will sound the same as 0, 4 and 8
but you will be able to distinguish it from the 12 cents one.

If the 8 cents one, same as 4, 8 and 12, but you can distinguish
it from the 0 cents one.

etc.

So one can tell which it is.

One can match a pitch to better accuracy than one can recognise it,
perhaps using something like this.

E.g. if one clicks randomly on a 300-tet note, then shows
another 300-tet scale, and tries to locate the original
note by sound, clicking on one note at a time until one finds
the one that sounds most like the original, this task is
quite easy to do, comparatively. I can do that now, while
tired.

In this task, one is allowed to go back and forth between
the two scales as often as one likes until one is sure
one has the closest match. But, hide the numbers on the
randomly clicked scale so that one can't see which one
was clicked until one has made ones decision.

This experiment isn't exactly scientifically rigorous
(perhaps one might judge by spacial position, but
that seems a bit unlikely for 300-tet)

I'm sure it could be made so.

Since my pitch resolution right now is about 8 cents or
so and I'm doing this to 4 cents easily, I wonder if one could do
it to 2 cents at 4 cents resolution.

Also I wonder if this experiment of doubling up by an extra
n-tet beyond ones usual pitch resolution and identifying notes
in it by matching could be a way to improve ones pitch resolution,
if one wanted to do that?

Robert

Hi, Robert! I'm really glad something I said may have opened up some
new possibilities for you. As to your pitch experiments, I found them
interesting. Perhaps I should clarify some of what I've said in
previous posts.

I don't have any problem with people being able to hear differences
of 5 cents with consecutive pitches that are shifting from each other
at 5 cents. I can easily hear less than this quite reliably. And I
certainly can hear fifths sounded simultaneously that are 5 cents
flat or more as they are in meantone. I can also hear 5 cent errors
when the fifths are melodic, that is, sequential, which is
considerably more challenging.

But I have trouble accepting that some people hear melodic pitch
errors at any interval except unison (as opposed to harmonic or
simultaneously sounded pitches), that are only 2 or 3 cents, or even
ONE cent! I'm not dogmatically saying they can't, but I'm from
Missouri on that one.

On the other hand, it is quite a different matter to say that one can
detect the cumulative effect on a scale or melodic pattern that
shifts with key as a result of uneven temperaments.

--- In tuning@y..., "Robert Walker" <robertwalker@n...> wrote:
> Hi Bob,
>
> Thanks, interesting about the string timbre.
>
> Actually it has helped wonderfully with the FFT section of FTS as
> I now realise that most of the timbres need a bandwidth set for the
frequency,
> - the FFT finds too many peaks close together, and I realise
> this isn't soemthing in the FFT itself, but of the nature of
> the timbre of many musical notes.
>
> This is working and it is now finding the peaks without user
> intervention - hurray!
>
> For pitch, I've been doing some tests using midi ocarina
> voice (close to sine wave).
>
> One can expect a gradual rather than sharp cut off in pitch
> resolution - e.g. if one can always distinguish 5 cents, one
> will prob. sometimes be able to distinguish 4 cents..
>
> Trying yesterday, I could distinguish 5 cents (240-tet steps) at 1
sec. note.
> At 4 cents (300-tet), made a few mistakes, about one in ten wrong.
> At 3 cents (400-tet), results close to random.
>
> This is when very relaxed and listening in a quiet fashion, not
> hassled.
>
> If tired, or in one way or another can't concentrate on it,
> I make mistakes even at 5 or 6 cents.
>
> Trying again right now immediately after a long coding session
> without a break (not very sensible, but there we are)
> I find 6 cents even quite hard, making lots of mistakes,
> and 10 cents (120-tet) is about equiv to 5 cents yesterday night.
>
> So, my pitch accuracy varies a tremendous amount.
>
> On rarer occasions, I remember hearing 400-tet as separate notes
> (though with a few mistakes).
>
> Did this test for notes all the same pitch, e.g. 440 Hz, 440 + 4
cents.
> (about 441 Hz).
>
> Might make more mistakes if one randomised the start pitch.
>
> It's for melodic steps, the notes played one after another.
>
> Seems 4 cents is quite good at least for a western musician,
> though as I can get close to 3 cents, can well believe
> others get better than that and reach 1 cent or less,
> as they have said on this list.
>
> However, I must say, I'm not good at all at distinguishing
> interval sizes. Play an interval, then play it transposed
> to another pitch, and I find it really hard to tell if it
> is the same interval, if there is no context in which to place
> it.
>
> Can, in this completely out of musical context type test,
> on some occasions for test using just two notes, and with
> voice such as ocarina with no partials to cue one in,
> confuse 9/8 and 4/3! (can tell if it is within singing
> / whistling range and I sing from one to the other).
>
> I don't have perfect pitch, but am an amateur musician with
> a rather undeveloped sense of relative pitch, and a fairly
> good medium term memory for the absolute pitches of notes
> Also tend to hear pitches as a type of timbre - could
> get sound of say ocarina at one pitch confused with say violin
> at another - not now, but can still hear that aspect to a sound,
> and it caused a lot of confusion when younger.
>
> Doesn't seem to interfere with my improvising and composing
> somehow... Also seem to somehow feel the quality of a
> temperament when improvising in it.
>
> So not too bothered by it. Having a good medium term memory for
> absolute pitch plus fairly fine pitch accuracy for that has
> been useful when debugging music software, on many occaions.
>
> I think there are many ways pitch entres into things.
>
> There's the recognisable melodic absolute and relative pitch;
> then the quality of a chord; then the reproducibility of a note;
I'm sure
> many others...
>
> An interesting thing, sometimes one can distinguish two notes
> by melodic comparison with neighbouring notes that one
> can't distinguish from each other.
>
> E.g. suppose you have instrument tuned to 4 cent intervals
> as 0 cents 4 cents 8 cents 12 cents.
>
> Then someone gives you another instrument with just one note,
> and tells you it is one of those.
>
> Suppose your pitch descrimination is 5 cents, so that there is
> no chance of doing it by direct melodic comparision.
>
> Then, try comparing it with 0, 4, 8 and 12 in turn.
>
> If it is the 4 cents one, it will sound the same as 0, 4 and 8
> but you will be able to distinguish it from the 12 cents one.
>
> If the 8 cents one, same as 4, 8 and 12, but you can distinguish
> it from the 0 cents one.
>
> etc.
>
> So one can tell which it is.
>
> One can match a pitch to better accuracy than one can recognise it,
> perhaps using something like this.
>
> E.g. if one clicks randomly on a 300-tet note, then shows
> another 300-tet scale, and tries to locate the original
> note by sound, clicking on one note at a time until one finds
> the one that sounds most like the original, this task is
> quite easy to do, comparatively. I can do that now, while
> tired.
>
> In this task, one is allowed to go back and forth between
> the two scales as often as one likes until one is sure
> one has the closest match. But, hide the numbers on the
> randomly clicked scale so that one can't see which one
> was clicked until one has made ones decision.
>
> This experiment isn't exactly scientifically rigorous
> (perhaps one might judge by spacial position, but
> that seems a bit unlikely for 300-tet)
>
> I'm sure it could be made so.
>
> Since my pitch resolution right now is about 8 cents or
> so and I'm doing this to 4 cents easily, I wonder if one could do
> it to 2 cents at 4 cents resolution.
>
> Also I wonder if this experiment of doubling up by an extra
> n-tet beyond ones usual pitch resolution and identifying notes
> in it by matching could be a way to improve ones pitch resolution,
> if one wanted to do that?
>
> Robert

--- In tuning@y..., BobWendell@t... wrote:

> But I have trouble accepting that some people hear melodic pitch
> errors at any interval except unison (as opposed to harmonic or
> simultaneously sounded pitches), that are only 2 or 3 cents, or
even
> ONE cent!

I agree with Bob Wendell here. And, NB Bob Walker, in the end no one
claimed they could hear such things -- someone claimed they could
produce them on their instrument, but that's a totally different
matter.

On the other hand, for harmonic or simultaneously sounded intervals,
one can certainly get to within a fraction of a cent of JI by
eliminating beats (including beats between difference tones), in some
circumstances.

Hi Bob,

> Hi, Robert! I'm really glad something I said may have opened up some
> new possibilities for you. As to your pitch experiments, I found them
> interesting. Perhaps I should clarify some of what I've said in
> previous posts.

Yes, it's nice when that happens.

Thanks for explaining a bit more. I expect fifth is the easiest to
hear of the melodic ones after the unison.

> But I have trouble accepting that some people hear melodic pitch
> errors at any interval except unison (as opposed to harmonic or
> simultaneously sounded pitches), that are only 2 or 3 cents, or even
> ONE cent! I'm not dogmatically saying they can't, but I'm from
> Missouri on that one.

Well, going beyond it for unison is also going beyond the FFT limitation
of 4 cents for 1 sec. notes without peak interpolation.

Anyway, can easily go beyond it as it becomes 24 cents for sixth second notes,
and surely most musicians can distinguish two sixth second notes an eighth tone
apart?

So ear must be doing something extra, possibly peak interpolation, possibly
something else.

I've been following your posts about the details of why the QM model doesn't apply
and they were interesting.

Still leaves question about how one manages to go beyond the FFT bin limitation,
as we clearly do. Ear can't just go for the highest peak in the fourier analysis
if it does anything of that ilk, but must be doing something a bit more subtle
than that.

I'd be interested to hear if anyone can hear a one cent interval
at the unison.

I.e. play randomly, either

0 cents 1 cent

or

1 cent, 0 cents

as melodic steps, and can one tell which is which?

I can't do this, and am at the 3 to 4 cents level for this one when alert
and fresh (so at about same as the FFT bin limit), and at 6 to 8 cents when less alert.

I don't know if that is typical, good, or poor, but that's
where I'm at.

I got the impression from Johnny's posts about his experiments with splitting
the difference between the 12-tet fifth and the natural one, and playing
a succession of notes at steps of one cent on the recorder, that he could,
but I may have misunderstood...

Not that it is particularly relevant to the discussion, main thing is that
one can at any rate go beyond the FFT bin limitation for shorter notes than this,
which one surely can at 24 cents for sixth second notes (say).

Robert