Re: [tuning] Two 11-of -79 tunings

Dear jl (I assume that would be John?),

I'm happy that you have listened to my improvisations of little worth. I'm
impressed that 79 MOS 159-tET can produce consistent 11-tones per octave
with less than 7 cents deviation. I wonder the possiblities...

I assume, by 11-U, you meant this scale:

0: 1/1 0.000 unison, perfect prime
1: 25/24 70.672 classic chromatic semitone, minor
chroma
2: 11/10 165.004 4/5-tone, Ptolemy's second
3: 15/13 247.741 tridecimal 5/4-tone
4: 11/9 347.408 undecimal neutral third
5: 13/10 454.214 tridecimal semi-diminished fourth
6: 18/13 563.382 tridecimal augmented fourth
7: 22/15 663.049 undecimal diminished fifth
8: 25/16 772.627 classic augmented fifth
9: 56/33 915.553
10: 11/6 1049.363 21/4-tone, undecimal neutral seventh
11: 2/1 1200.000 octave

I don't know if I got the 9th degree right. Perhaps 17/10 is the right
interval? Even so, the maximum difference is about 6 cents.

I am excited to hear about your work utilizing these scales. Please keep me
posted.

Cordially,
Oz.

----- Original Message -----
From: "J.Smith" <jsmith9624@sbcglobal.net>
To: <tuning@yahoogroups.com>
Sent: 28 Nisan 2006 Cuma 2:22
Subject: [tuning] Two 11-of -79 tunings

> Oz,
>
> I spent some time today listening to your impressive qanun
> compositions (improvisations?). Inspired, I went back to the posts
> about your 79-tone tuning -- more specifically, 79_MOS2.scl -- and
> selected 11 pitches to approximate an 11-EI* tuning (I have an 11-
> tone addiction, thanks to my trusty microtonal balalaika, elsewhere
> mentioned).
>
> 0: 0.0
> 7: 105.64591
> 14: 211.29182
> 22: 332.03
> 29: 437.67591
> 36: 543.32182
> 43: 648.96773
> 50: 762.3241
> 57: 867.97
> 65: 988.70819
> 72: 1094.35409
> 70: 1200.0
>
> In a similarly reckless mode, I will approximate 11-U:
>
> 0: 0.0
> 5: 75.46136
> 11: 166.015
> 17: 256.56864
> 23: 347.12228
> 30: 452.76818
> 37: 558.41409
> 44: 664.06
> 51: 777.41637
> 60: 913.24682
> 69: 1049.07728
> 79: 1200.0
>
> I already have two compositions started which use these tunings.
> I'll notify you when finished...I'd like to get your take on them.
>
> Thanks,
> jl
>
>
> (* Equal Interval)
>
>

> >
> > Dear jl (I assume that would be John?),
>
>
> Lol...Jon is the spelling my parents insisted on :-)
>

Alright then! Jon it is.

>
> > I'm happy that you have listened to my improvisations of little
> worth.
>
>
> "Little worth"...? I think not. Quite intricate and beautiful, I
> think.
>

You cause my poor self to experience great delight by such exquisitive
praises O Effendi.

SNIP

>
>
> Unless I'm greatly mistaken (someone please correct me if I am), the
> following ratios comprise 11-Utonality, and are the ratios I am
> using:
>
> 1/1 : 0.0
> 22/21 : 80.4
> 11/10 : 165.0
> 22/19 : 253.8
> 11/9 : 347.4
> 22/17 : 446.3
> 11/8 : 551.3
> 22/15 : 663.0
> 11/7 : 782.7
> 22/13 : 910.8
> 11/6 : 1049.4
> 2/1 : 1200.0
>

Ah. Now I see. They are U-tonal because all the numerators are the same
number.

> If I am understanding correctly, this is also 22-EDL, isn't it?
>
>

22-EDL reduced to and sorted within an octave. Originally, 22-EDL is this:

22/22
22/21
22/20
22/19
etc...
22/1

Cordially,
Oz.