Re: Bell timbre

Hi Paul,

Found a good set of partials for a bell timbre at this web site:

http://www.oakcroft13.fsnet.co.uk/strike.htm

It also has some relevant interesting puzzles - seems there is a
lot still to find out about how the pitch of a bell is heard -
the pitch one hears isn't _any_ of the partials sometimes,
and doesn't bear any clear relation such as difference
tone to any of them either!

Anyway, I did a timbre in FTS using the partials in the
table:

Data was:
176.6 hz 390.2 hz 640.9 hz 949.0 hz 1302.4 hz 1690.9 hz 2110.2 hz 2604.6 hz 3380.0 hz
which I converted to cents:
->
1/1 1372.47 cents 2231.54 cents 2911.11 cents 3459.14 cents 3911.08 cents 4294.59 cents
4659.01 cents 5110.16 cents

Played on nine flutes, this gives:
http://homepage.ntlworld.com/robertwalker/agogo/9_flutes_bell_h.mid

Then the subharmonic series, again on nine flutes:
http://homepage.ntlworld.com/robertwalker/agogo/9_flutes_bell_subh.mid
1/1 -1372.47 cents -2231.54 cents -2911.11 cents -3459.14 cents -3911.08 cents -4294.59
cents -4659.01 cents -5110.16 cents

The flutes all play identical volumes - to be more realistic one would need
the actual volumes measured, which I found on another web page:
http://www.oakcroft13.fsnet.co.uk/pandc.htm

But I'll try that tomorrow.

Not sure what this all means exactly, but it sure is interesting!

I'm surprised that only 9 notes were enough to make a recognisable
bell sound. Could actually do it in a performance if one had good
performers! Now that would surprise everyone!

Robert

Hi Christopher:

> Anyway, here are some experiements I did:

> http://music.columbia.edu/cmc/courses/g6610/fall1999/week3/metals.html

Enjoying these!

Surprised how gong like the first example was, even before you added all
the subtleties to it.

Also enjoyed your little 12-tet fugue:
http://music.columbia.edu/~chris/tunes.html

I see you've got your l-system improviser up at
http://music.columbia.edu/~chris/lsys.html

I was very impressed by it when you first posted it to the TL.

One of the FTS additions of a fibonacci tonescape was originally inspired by
it if I remember rightly - idea is you go up or down in pitch, with the ratio varying
depending
on whether it is an L or S beat.

E.g. L = 10/11 and S = 7/6 works for the normal fibonacci rhythm.

FTS works out which ratio will be good for the S when you type in the
one for the L, or vice versa.

The ratios need to be exactly right, worked out from the proportions of
L and S beats in the rhythm, or else the tune rapidly moves down
or up in pitch (would yours do that if it went on for long enough?)

Robert

Robert wrote,

>It also has some relevant interesting puzzles - seems there is a
>lot still to find out about how the pitch of a bell is heard -
>the pitch one hears isn't _any_ of the partials sometimes,
>and doesn't bear any clear relation such as difference
>tone to any of them either!

Yes Robert this is exactly the point I've been trying to make -- this is the
virtual pitch phenomenon! Very important.

There is an inherent unfairness to your bell timbre vs. upside-down bell
timbre comparison here -- the bell timbre has closer partials higher up, so
its mirror-image will be at a disadvantage, since the critical band of
roughness is wider in the lower registers.

Hi Paul,

re:
http://www.oakcroft13.fsnet.co.uk/strike.htm

I agree, this is a virtual pitch phenomenon of some kind.

But how is it working??

It's a bit strange that the ear is lead down to half the pitch
of the nominal if there are no partials that have that pitch as a difference tone.

They don't particularly seem to much resemble a harmonic series either...

To within 6 cents, the steps are:
1/1 42/19~ 23/14~ 37/25~ 11/8~ 13/10~ 5/4~ 16/13~ 13/10~

Looking at consecutive partials, the only candidate I find is that there is an
approximate 5/4 between the note above the octave nominal and the
next note in the sequence:

2110.2/1690.9 hz = 383.506 cents
5/4 = 386.314 cents

but that would suggest a pitch of 1690.9/4 hz = 422.725 hz,
and the percieved pitch is 320.5 hz

Harmonic series on 320.5 is:
320.5 Hz 641 Hz 961.5 Hz 1282 Hz 1602.5 Hz 1923 Hz 2243.5 Hz 2564 Hz 2884.5 Hz 3205 Hz
3525.5 Hz 3846 Hz

Measured partials:
176.6 hz 390.2 hz 640.9 hz 949.0 hz 1302.4 hz 1690.9 hz 2110.2 hz 2604.6 hz 3380.0 hz

Ratios of partials to closest member of harmonic series on 320.5 hz (leaving out the 176.6
hz hum)

390.2/320.5 640.9/641 949/961.5, 1302.4/1282 1690.8/1602.5 2110.2/2243.5
2604.6/2564 3380/3205
=
0 cents 340.7 cents -0.2701 cents -22.65 cents 27.33 cents 92.86 cents -106 cents 27.2
cents 92.04 cents

The -0.2701 cents is the nominal.

Nothing else within 20 cents of the harmonic series, and one can hear the pitch of the
bell to within much less than 20 cents. To test that, I tried using the FTS version
with 9 flutes played simultaneously, and then compared it with 320.5, and then
with the next 31-tet note. The next 31-tet note was way out.

See what you think:
This has all the partials sounding at equal volume.
http://homepage.ntlworld.com/robertwalker/agogo/9_flutes_bell_640.9_hz_nom.mid

Or try the clips on the web page above, but it is nice also to try them all equal
volume as then there are no volume cues involved, in case that is a factor
somehow.

This is what most take to be the perceived pitch of the bell, and I'd agree:

http://homepage.ntlworld.com/robertwalker/agogo/320.5_hz.mid
(may sound a few cents sharper than the .wav sound if like me you
have a soundcard that is consistently sharp by 2 or 3 cents across its range)

and this is 20 cents sharp:
http://homepage.ntlworld.com/robertwalker/agogo/324.2_hz.mid

I'd understand if one heard the nominal as the pitch of the bell, and doubtless it
must be guiding ones perception of the pitch, but why to an octave below it,
with no other partials around to support it?

Especially since it works with the partials all the same volume.

I think the pure harmonic series _can't_ be the complete explanation, important though it
surely is. There must be some other effects involved as well. Could be interesting
thing to investigate, if one can find out where to get started on it.

>its mirror-image will be at a disadvantage, since the critical band of
>roughness is wider in the lower registers.

Yes, that's true.

>>bells, but one of
>>them would make a more "natural" bell sound than the other.

Just mean, the one that was an actual recorded bell sound would be
the more natural one.

If they were synthesised, it's another matter.

I suppose Christopher Bailey's first gong with random partials
could be turned upside down and sound equally good, since
random.

In fact, that would be a very good example to use, to see if hearing a timbre
in advance affects the percieved consonance / dissonance of the "otonal"
and "utonal" chords

>cents, there will always be coinciding partials, e.g., the fifth partial of
>the fourth member of the otonal series will always coincide with the fourth
>partial of the fifth member of the otonal series, since the partial in
...

Yes I see, that's true, thanks Paul.

>That's exactly right, and I've brought this up here on the list many times,
>to point to the glaring inadequacies of the "coinciding partials"
>explanation of consonance.

Glad I got the argument right then!

Well, I can test it with FTS 1.10 when I get there by
actually counting the beats for all the partials for chords of as
many notes as one likes - not part. computing intensive to do that
as time for computation will be about linear in the number of notes.

Sounds like we should actually expect it to figure out the otonal one as
_less_ consonant when using Helmholtz method. We'll see,...

>Or even with an _arbitrary_ inharmonic timbre with a given spectrum in cents
>-- the argument runs as above, but now you'll have _three_ distances between
>partials to add, and that distance will be spanned in _three_ different
>ways

Yes, I see.

>tetrad. For example, everyone gave 4:5:6:7 a much more favorable rating than
>1/7:1/6:1/5:1/4, even though the two chords contain exactly the same
...

I've listened to your samples, thanks. Yes, I agree, at that pitch.

Indeed, at any fixed pitch I expect.

So I thought I'd try them at random pitches as well, to see if I do any better
than major / minor, which I still can't get completely out of context (can't do
4/3 and 6/5 even).

However, I can't do that yet - for me the consonance / otherwise of this chord
is overwhelmed by the absolute pitch timbre of its notes, when completely
out of any context.

Sometimes in the random chord quiz, I hear the otonal chord, then hear
the next chord shifted in pitch by a smallish amount, and I immediately
say "utonal" on the basis of the kind of overal timbre of the chord,
and in fact it is the "otonal" one again with the pitch timbres all changed.
(I can tell if an otonal and a utonal one are played one after another at
the same pitch.)

Tried adding a few more pitches to make, say, a seven note otonal chord
from the harmonic series, and compare it with a utonal one, and it still
doesn't work for me.

So I'm not a very good subject for experiments in this area unfortunately!

However I agree with the conclusion that the otonal chord is more
consonant than the utonal one even with this small chord of four
notes.

It is just that for me, pitch timbres can easily overwhelm
the comparatively smaller effect of consonance of otonal and utonal chords.
which makes it a bit less clear to hear, at least, when the chords
are presented in isolation.

But I can tell the difference between major and minor triad played
as a melody at any absolute pitch, if you add just a few extra melodic
notes immediately after it.

E.g. in just intonation 12 t, I can immediately distinguish degrees
0 4 7 9 7 4 from 0 3 7 9 7 3 in nearly all random transpositions
(all except about one or two out of ten)
but often get muddled between 0 4 7 and 0 3 7

Even between 0 3 and 0 5 (minor third and fourth).

Indeed, 0 4 7 9 7 and 0 3 7 9 7 also confuse me, so it
isn't the actual pitches so much as the need to have a bit
of a melodic line to make some intervalic sense out of them.

Adding one extra note makes all the difference!

But I think I'm getting there - beginning to anticipate what the chord is
going to turn out to be before the end of the melodic line...

I wonder, might the extra consonance of the otonal chord, and relative
somewhat dissonance, or "sadness / tenderness" of a minor chord somehow play
a stronger role when it is in the context of a piece of music, or even, used
as a melodic line, than it does in an isolated chord?

Robert

Robert wrote,

>pitch timbres

You keep referring to this, but I don't understand. What do you mean by
"pitch timbres"?

>I wonder, might the extra consonance of the otonal chord, and relative
>somewhat dissonance, or "sadness / tenderness" of a minor chord somehow
play
>a stronger role when it is in the context of a piece of music,

Maybe.

>or even, used
>as a melodic line,

I doubt that that's true in general -- it's only in the West since the
advent of tonal music (1600's) that the minor mode has been considered
"sad".