RE: a question about limit of pitch perception

On Sat, 24 Dec 2005, "Mohajeri Shahin" wrote:
>
> Dear yahya
>
> As you know , jnd is very personal and is related to physical ,
> acoustical , psyco-physiological (training of the hearing system , from
> brain to ear !) parameters . wallyesterpaulrus wrote about harmonic and
> melodic jnd . my melodic jnd starts very badly at about 2 cent and at 5
> cent I have a good pitch discrimination.
>
> But I wonder if your jnd of 2 cent as paul mentioned it as harmonic jnd
> , is related to beating and time-interval of each beat ? but if so isn't
> it realted to octave :
>
> F1(HZ)........F2(F1+2 CENT)(HZ) ...................NUMBER OF BEAT PER
SECOND..........TIME INTERVAL OF EACH BEAT(SECOND)
>
> 50.............50.05779564..........
> ..........................0.057795643...................................
> ............17.30234242
>
> 100......... 100.1155913.....................................0.115591285
> ...............................................8.651171208
>
> 200.........
> 200.2311826.......................................0.231182571...........
> .....................................4.325585604
>
> 400.........
> 400.4623651.........................................0.462365142.........
> ......................................2.162792802
>
> 800.........
> 800.9247303..........................................0.924730283........
> ...................................1.081396401
>
> 1600.......1601.849461...........................................1.84946
> 0566.............................................0.540698201
>
> Shaahin Mohaajeri

Dear Shahin,

If you are tuning up an orchestra, or a string
instrument such as a guitar, these are indeed
the sorts of beat rates you'd be looking at.
I think - but am not sure - that most acoustic
guitarists wouldn't be looking for better than
1 beat in two seconds when tuning. The notes
die away too soon to be able to hear anything
slower very clearly. Also, the precision of the
tuning is limited to that provided by the
mechanical advantage of the tuning pegs - the
screw is an adaptation of the principle of the
lever.

When tuning a guitar, I tune the low E string
to a reference pitch, of whatever instrument
I'm playing with, then tune up in fourths and
a third. In so doing, I adjust each string until
it vibrates sympathetically with the stopped
string below it. For example, in tuning the
second string, the A, I stop the low E string on
the fifth fret to produce a pure 12-EDO A.
I then tune the A string until playing the A on
the low string makes the second string vibrate
sympathetically. It does this so well that the
motion is clearly visible (even in a noisy and
crowded room). To confirm the note is good,
I pluck, and then damp, the lower string; the
higher string should continue to vibrate,
producing a clear, ringing tone. Because the
sympathetic vibration occurs, not just exactly
at the exciting pitch, but across a narrow band
of pitches, and more strongly in the middle of
that band, if the sympathetic vibration is weak,
I could see (even with earplugs in) that the note
is not near enough to correct.

But this is just the beginning! :-) If the room's
not TOO noisy, I can clearly hear whether the
higher string is sharp or flat, and will adjust it
accordingly. I won't leave a small difference,
that corresponds to about a twentieth of a turn
of the tuning peg, or less. It seems to be about
the same as a difference of two cents that I
hear when adjusting the tuning on my Roland
keyboard.

Finally, having tuned all strings in pairs, I play
some simple test chords: E and G major, and
check that there are no strong beats; then A
and E minor, and check that the beats are not
objectionable.

However, within chords, the beat rates you're
listening for aren't those between supposed
unisons, but between overtones of the chord
tones. These are often weaker. Playing a 3:2
interval, eg E3:A3, also involves playing the
second overtone of the 3 (E3) and the third
overtone of the 2 (A3), which _should_ coincide
at E4. Depending on the harmonic spectrum of
the instrument, and also on the relative height
of the chord voicing, these partials may not be
strong enough to produce noticeable beating
even when slightly mistuned. Even with perfect
hearing (such as most eight-year-olds have), in
fast music there simply isn't time for beats to
be heard.

Just for fun, I tried listening to my lowest
tuned pair, at A3, for as long as it would ring.
It lasted about ten or twelve seconds, and in
that time, I heard no rhythmic variation.
Since that is around 220 Hz, and according to
your calculations above, I should have heard
three cycles of a 2-cent variation, if one were
present.

What I did hear, though, was that the _timbre_
of the unison changed continuously; in the end,
it favoured the higher overtones, becoming
lighter. I guess the lower partials are being
damped more quickly? When I checked by
playing just one string at a time, the same
effect was there. But the net result was a
curious effect of the tone changing in pitch,
like a (very slow) "smear" or glide. This, I hasten
to add, was in a very QUIET room, late on
Christmas Day, when everyone but me (even the
cat) was asleep in bed. Curious! I don't know
enough about guitar acoustics to explain this
with any confidence.

Your observation, about the jnd being related
to the octave (pitch range) you're in, makes
sense to me. We all have greater difficulty in
discriminating low pitches. Your figures, of 8
to 17 seconds for the period of beats with a
2-cent error at 50 to 100 Hz, explains why we
hear a wider range of low pitches as being "the
same".

[snip]
> > > [Shaahin, earlier]
> > > As I'm searching for jnd of pitch perception and you wrote about 2
> > > cent, and as it is mentioned in theoretical texts about jnd of 5 cent,
> > > may you guide me with your refrence about jnd of 2 cent?
> > >
> > [snip]
> > [Yahya, earlier]
> > > > The difference, 2 cents, is about the agreed
> > > > limit of our ability to perceive.
> >
> > My guide in this matter has been mostly some
> > discussions I've had with Paul Erlich over the
> > last few months. I do not remember whether
> > they were on this list, or in private email. But
> > I'm sure that Paul, or one of the other list
> > members, will be able to quote a suitable
> > reference for this fact.
> >
> > My own experience tells me that I can readily
> > discern intervals smaller than 5 cents in slow
> > music with timbres of moderate complexity.
> > What does your ear tell you?

Regards,
Yahya

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