Re: [tuning] Digest Number 1404

Joseph said :

> I am SERIOUS when I say that, based upon our discussions and my
> experimentation with that scale, I was SERIOUSLY considering that!
>
> I was thinking that it would replace 12-tET for me as a STANDARD, and
> I wouldn't need to do anything else... EVER.
>
> McLaren just has me questioning the wisdom of that... and it *was* a
> rather *drastic* thought, the more I think about it.
>

I've gone through the same sort of thing recently. I committed myself
towards "thirds" and felt that 31EDO would be the tuning for the rest
of my life. Now that I've rebuilt my tuning experiment ability, I've
decided that perfect fifths (and 3 prime offspring) are really cool,
and I'm getting interested in 17, 29, 41, and 53 as a result.

Which is okay, maybe one meantone and one schizmic(?) will be enough
for a lifetime...

except that there really are (an infinite number?) of different
approaches, too. I bought some 'random' CDs last night, a few early
music and a Thai collection. The Thai has some jangly pentatonics that
don't seem to match any of these approaches.

Lest I contribute to a tone that is perceived of this list being
anti-JI/RI, I just happen to like intervallic regularity and
transposablity at this point of my development. ED's give it to
me and ED2 is where I am now. It may well be that by the time I get to
a 14-o-o-131ED(22/3), that I'll be playing with a random collection of
just intervals, but thats a few years out.

Bob Valentine

> ----- Original Message -----
> From: Robert C Valentine <BVAL@IIL.INTEL.COM>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, June 10, 2001 10:57 PM
> Subject: Re: [tuning] Digest Number 1404
>
>
> ... It may well be that by the time I get to a
> 14-o-o-131ED(22/3), that I'll be playing with a
> random collection of just intervals, but thats
> a few years out.

This looked like a good tuning puzzle which I
couldn't resist... but my question is: which 14
pitches would you choose as a subset, Bob?

What I present below is what I first calculated,
and which I now realize is absolutely not what you're
talking about. But it seemed like an interesting
scale to me anyway, even if it isn't what you had in mind.

I calculated a meantone-like cycle of "5ths",
each of which is 22/3 (= 7 & 1/3) Semitones - which
equals 2^(80/131) - in size.

A symmetrical system representing 3^-7...3^7 would
yield a scale of 15 tones, so a 14-tone subset would
omit either 3^-7 or 3^7.

Here's the whole cycle:

"5th" Semitones

7 3.30
6 7.97
5 0.64
4 5.31
3 9.98
2 2.66
1 7.33
0 0.00
-1 4.67
-2 9.34
-3 2.02
-4 6.69
-5 11.36
-6 4.03
-7 8.70

So in scale form it would be either one of these:

11.36 11.36
9.98 9.98
9.34 9.34
8.70 7.97
7.97 7.33
7.33 6.69
6.69 5.31
5.31 4.67
4.67 4.03
4.03 3.30
2.66 2.66
2.02 2.02
0.64 0.64
0.00 0.00

Feedback welcome, especially regarding the true
tuning of Bob's scale.

-monz
http://www.monz.org
"All roads lead to n^0"

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