correction

I wrote...

>>Even in 12-tET, a minor sixth alone can be heard as a dissonance,
>>in sharp contrast to a major third. Triadic harmony will tend to
>>clarify the meaning of the minor sixth to the point where it can
>>no longer be considered dissonant.
>
>Gee, I don't know about this one... Harmonizing a melody with sixths, for
>example?

Sorry, I mis-read you. You said "no longer be". So we are in agreement.

C.

Oops - it wasn't 1994, it was 1991.

> My recollection is, Moog was calling it the "multiply sensitive keyboard".
>
> He demonstrated it to myself and Peter Otto up in Buffalo when we
> brought him to the North American New Music Festival in 1994.

When I said L+s before, I was thinking of 7 note scales. For 10
note scales, I think the neutral third is 2L+s. That's right, isn't
it?

I wrote,

>But if you want to consider this scale as a strict index of 5L 2s,
then L=5&s=0, as 20e sits on the (5e) diagonal border

But for 20e, it should have read L=4&s=0. So:

> L=5&s=0) would require a spelling of:
>
> L,,L,s'L,L,,L,,s''

should have read:

L,Ls'LL,L,s''

Dan

In my post I said:

> I don't where the high third comes from. My point here is only that string
> players are not as likely to be influenced by keyboards as are singers.
> That's _all. The question of the "high third" is relevant here (as far as I
> know).

I meant "is irrelevant here (as far as I know)."

Sorry I missed it. I hope it wasn't a problem.

Jerry

whoops, the graphs would have n dimensions rather that n + 1, because for a
scale of n notes, we need consider only n - 1 intervals.

jason

Whoops. Typo. Make that Eaton's emulation of the 7th partial
harmonic rather than the 72nd partial harmonic. The latter is better
emulated by La Monte Young...

J. Pehrson

----- Original Message -----
From: "jpehrson2" <jpehrson@rcn.com>
To: <tuning@yahoogroups.com>
Sent: Thursday, June 20, 2002 11:02 AM
Subject: [tuning] correction

> Whoops. Typo. Make that Eaton's emulation of the 7th partial
> harmonic rather than the 72nd partial harmonic. The latter is better
> emulated by La Monte Young...

A 9/8?

* David Beardsley
* http://biink.com
* http://mp3.com/davidbeardsley

--- In tuning@y..., David Beardsley <davidbeardsley@b...> wrote:

/tuning/topicId_808.html#38018

>
> ----- Original Message -----
> From: "jpehrson2" <jpehrson@r...>
> To: <tuning@y...>
> Sent: Thursday, June 20, 2002 11:02 AM
> Subject: [tuning] correction
>
>
> > Whoops. Typo. Make that Eaton's emulation of the 7th partial
> > harmonic rather than the 72nd partial harmonic. The latter is
better
> > emulated by La Monte Young...
>
> A 9/8?
>
> * David Beardsley
> * http://biink.com
> * http://mp3.com/davidbeardsley

Hi David...

Is *that* what it "reduces down" to?? How you do that??

JP

----- Original Message -----
From: "jpehrson2" <jpehrson@rcn.com>

> --- In tuning@y..., David Beardsley <davidbeardsley@b...> wrote:
>
> /tuning/topicId_808.html#38018
>
> >
> > ----- Original Message -----
> > From: "jpehrson2" <jpehrson@r...>
> > To: <tuning@y...>
> > Sent: Thursday, June 20, 2002 11:02 AM
> > Subject: [tuning] correction
> >
> >
> > > Whoops. Typo. Make that Eaton's emulation of the 7th partial
> > > harmonic rather than the 72nd partial harmonic. The latter is
> better
> > > emulated by La Monte Young...
> >
> > A 9/8?
> >
> > * David Beardsley
> > * http://biink.com
> > * http://mp3.com/davidbeardsley
>
>
> Hi David...
>
> Is *that* what it "reduces down" to?? How you do that??

74th harmonic is 74/64.

74 / 2 = 36
64 / 2 = 32, which gives us 36/32

36 / 2 = 18
32 / 2 = 16, which gives us 18/16

18 / 2 = 9
8 / 2 = 8, which gives us 9/8.

And.....9/8 happens to be very important to at least the
Dream House chord, which is a symertrical microtonal cluster
around 1/1, between the 7th and 9th harmonics over 6:7:9.

I'm simplifying GREATLY, but I hope I'm making sense.
For a clearer and more concise explanation, I refer you to Kyle Gann's
article in the Sound and Light book.

Now if you used a higher prime harmonic....that's really what
La Monte is known for!

* David Beardsley
* http://biink.com
* http://mp3.com/davidbeardsley

--- In tuning@y..., David Beardsley <davidbeardsley@b...> wrote:

/tuning/topicId_808.html#38020

>
> 18 / 2 = 9
> 8 / 2 = 8, which gives us 9/8.
>
> And.....9/8 happens to be very important to at least the
> Dream House chord, which is a symertrical microtonal cluster
> around 1/1, between the 7th and 9th harmonics over 6:7:9.
>

***Thanks, David!

JP

--- In tuning@y..., "alternativetuning" <alternativetuning@y...>

/tuning/topicId_unknown.html#38079

wrote:
> > > > * David Beardsley wrote:
> > 74th harmonic is 74/64.
> >
>
> Yes.
>
>
> > 74 / 2 = 36
>
>
> No. 74 / 2 = 37, a prime number, ratio doesn't reduce to 9/8
>
> Gabor
>

***David! Look at that division. You had me fooled for a minute! :)

Joe

----- Original Message -----
From: "jpehrson2" <jpehrson@rcn.com>

> --- In tuning@y..., "alternativetuning" <alternativetuning@y...>
>
> /tuning/topicId_unknown.html#38079
>
> wrote:
> > > > > * David Beardsley wrote:
> > > 74th harmonic is 74/64.
> > >
> >
> > Yes.
> >
> >
> > > 74 / 2 = 36
> >
> >
> > No. 74 / 2 = 37, a prime number, ratio doesn't reduce to 9/8
> >
> > Gabor
> >
>
> ***David! Look at that division. You had me fooled for a minute! :)

Hm.....now we know why I don't spend a lot of time following those
endless discussions about math. ;)

* David Beardsley
* http://biink.com
* http://mp3.com/davidbeardsley