Re: Gene's Tuning

--- In MakeMicroMusic@y..., "jacky_ligon" <jacky_ligon@y...> wrote:

> > You now have nine of your cherished 12:14:18:21 chords,
essentially
> just! Also, there are nine 100-cent steps -- familiar semitones!
>
> Gene is a very *creative* and industrious fellow indeed.

Yes he is, but this isn't his tuning -- I wonder how that confusion
came about.

> This reminds me of my tranposing ETs by Phi:
>
> Cents Consecutive Ratio
> 0.000
> 50.929 50.929
> 133.333 82.405 1.618
> 184.262 50.929 0.618
> 266.667 82.405 1.618
> 317.595 50.929 0.618
> 400.000 82.405 1.618
> 450.929 50.929 0.618
> 533.333 82.405 1.618
> 584.262 50.929 0.618
> 666.667 82.405 1.618
> 717.595 50.929 0.618
> 800.000 82.405 1.618
> 850.929 50.929 0.618
> 933.333 82.405 1.618
> 984.262 50.929 0.618
> 1066.667 82.405 1.618
> 1117.595 50.929 0.618
> 1200.000 82.405 1.618
>
>
> Jacky Ligon

What you have here is very close to the 18-tone MOS of Gene's
Ennealimmal temperament.

--- In MakeMicroMusic@y..., "jacky_ligon" <jacky_ligon@y...> wrote:

> > What you have here is very close to the 18-tone MOS of Gene's
> > Ennealimmal temperament.
>
> This is a neologism and tuning which I'm wholely unfamiliar with.

I assume you understand MOS, yes?

The interval 27/25 is called the "large limma". Gene noticed that it
equals 1/9 octave almost exactly. So 1/9 octave is used as the period
of repetition. The MOS proceeds by a generator of 49 cents. If you
iterate this generator once, you have the 18-tone scale I mentioned
above (virtually identical to your phi-based one). If you iterate it
four times, so that there are 5 notes in each period of repetition,
you get a 45-tone scale. In this scale, there are eighteen 4:5:6:7
tetrads, and eighteen 1/(7:6:5:4) tetrads, and the intervals in these
chords are all within 0.2 cent of JI. Astounding accuracy. The scale
is also wonderful in the 11-limit.

The full 45-tone scale will simply be the pitches

0
35.333
49
84.333
98

repeated over and over again at an interval of 133.333 cents.

Sorry if that was too technical for this list -- future queries
should be directed either to the main tuning list (where I've tried
to talk to you lately, Jacky) or to

tuning-math@yahoogroups.com