Reply to Glen Peterson

>"For triads or higher-ads - the roughness of Otonal chords is the same as
>that of Utonal chords because they have the same intervals, but the
>tonalness of Otonal chords is much greater, because they imply a much
>simpler set of harmonics over a fundamental."

>Also, difference tones from Otonal dyads are generally consonant, while
>Utonal dyads often produce dissonant ones.

Absolutely! Roughness, tonalness, and difference tones are the three major
pyschoacoustical phenomena responsible for the preference for small-integer
ratios. The simple complexity formulae we've been throwing around can only
model one of these at a time. Sethares carefully models roughness, harmonic
entropy models tonalness, and a model such as Grady's focuses on difference
tones. Note that with sine waves or inharmonic timbres, roughness only
applies to intervals less than a minor third and difference tones are very clear.

>I was thinking about a "fifth" up and a "fourth" down as being the same. It
>makes sense that in actual music, the intervals are heard differently. I
>have also been wondering if I even consider "fourths and fifths" to be
>consonant or dissonant. They are almost neither.

If a fifth is not consonant, what is?

[Glen Peterson:]
>I have also been wondering if I even consider "fourths and fifths" to
be consonant or dissonant. They are almost neither.

[Paul Erlich:]
> If a fifth is not consonant, what is?

I think this is (well at least _may_ be...) fairly easy to see from a
sort of gustatory angle, where "fourths and fifths" (assuming that
means 4/3s & 3/2s or some _very_ near cousins!) occupy some
indeterminate zone between (overtly) 'sweet' and 'sour.'

Dan

>The simple complexity formulae we've been throwing around can only model one
>of these at a time. Sethares carefully models roughness, harmonic entropy
>models tonalness, and a model such as Grady's focuses on difference tones.

Sorry, but which is Grady's? I must have missed it.

>Note that with sine waves or inharmonic timbres, roughness only applies to
>intervals less than a minor third and difference tones are very clear.

With inharmonic timbres roughness doesn't apply?

-C.

I wrote,

>>The simple complexity formulae we've been throwing around can only model
one
>>of these at a time. Sethares carefully models roughness, harmonic entropy
>>models tonalness, and a model such as Grady's focuses on difference tones.

Carl Lumma wrote,

>Sorry, but which is Grady's? I must have missed it.

He posted it a few weeks ago. My vague recollection is that he just adds the
numbers, and if the difference tone is distinct, he adds that number too.

>>Note that with sine waves or inharmonic timbres, roughness only applies to
>>intervals less than a minor third and difference tones are very clear.

>With inharmonic timbres roughness doesn't apply?

It does, but it doesn't favor small-integer ratios. That's the thrust of
Sethares' work.

Carl!
I have experimented with some various models with the following the
one that
seem to work the best. Taking the spacing of the chord, you then add the
harmonics without any octave reduction and the first order difference tones
omitting any repeats of harmonics. It is a formula in progress and would
appreciate your feed back as to Lullaby at
http://www.anaphoria.com/tun.per.html . It is arrange from con. to dis.
based on
the this formula so we have something to try with our EARS and the more
EARS the
better!

Carl Lumma wrote:

> From: Carl Lumma <clumma@nni.com>
>
> >The simple complexity formulae we've been throwing around can only model one
> >of these at a time. Sethares carefully models roughness, harmonic entropy
> >models tonalness, and a model such as Grady's focuses on difference tones.
>
> Sorry, but which is Grady's? I must have missed it.
>
> >Note that with sine waves or inharmonic timbres, roughness only applies to
> >intervals less than a minor third and difference tones are very clear.
>
> With inharmonic timbres roughness doesn't apply?
>
> -C.
> .

-- Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com

>> studies have shown that subjects perceive a melodic octave
>> with sine waves
>> to be most in-tune at about 1210 cents in the middle

>What Studies?

I've seen this over and over again but I don't have the references handy.
But the best evidence is to try it yourself. 1200-cent octaves played
melodically with sine waves sound like very sharp major sevenths to me. I
wouldn't trust glass organs to be sinusoidal enough to demonstrate this --
the finger will probably contribute enough second harmonic to destroy the
effect completely.

>> In all, if your carillon is truly producing sine waves, I
>> suspect you will
>> find it rather unmusical, a poor demonstration of JI, and
>> probably rather
>> annoying to the ear.

>Someone should slap you for this! I would hope that the point of this list
>is to ENCOURAGE each other to experiment, theorize, and dream about tuning
>and microtonal instruments. Your comment has the opposite effect on me.

I apologize. That was not my intent. I was basing this comment on my own
experience with sine waves. I was hoping Darren Burgess would be encouraged
to try other timbres. I did not mean to be discouraging.

>On another note, you mentioned my otonal/utonal chords. Here are the
>primary ones I was using:

>Otonal:

>9/5, 9/7, 9/8, 3/2
>16/9, 8/5, 4/3, 8/7
>7/4, 14/9, 7/5, 7/6
>12/7, 3/2, 1/1, 6/5
>5/3, 10/7, 5/4, 10/9

>Utonal:

>9/5, 8/5, 7/5, 6/5
>16/9, 14/9, 4/3, 10/9
>7/4, 3/2, 5/4, 9/8
>12/7, 10/7, 9/7, 8/7
>5/3, 2/1, 4/3, 7/6

You seem to have otonal and utonal switched! (I suspect you just made a typo
this one time, though). Anyway, are all your pitches really between 1/1 and
2/1? After you confirm this, I will try these chords myself on the synth and
get back to you. Also, can you tell me what intervals, if any, you find
dissonant on your glass organ?

Glen, can you tell me whether your reversal of otonal and utonal was a
one-time typo, or did it apply to our previous discussions as well?

-Paul

> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
>
> Glen, can you tell me whether your reversal of otonal and utonal was a
> one-time typo, or did it apply to our previous discussions as well?

I just goofed in that email, not regarding our previous discussion.
Otonalities are the ones that share a common factor in the denominator while
the numerator varies, Utonalities are the opposite. The Harmonic Series is
all Otonalities. When people talk about "sub-harmonics" I assume they are
talking about Utonalities.

---
Glen Peterson
30 Elm Street North Andover, MA 01845
(978) 975-1527
http://www.OrganicDesign.org/Glen/Instruments