13 tones equal tempered

Last week the topic of 13 tones equal tempered scales had three scales suggested. I tried them and I like them: 3121222 3131212 2141212. Will someone suggest what notes to combine together to make chords or at least two notes together to play harmonies? I have used the scale of 2212231. I never found very nice chords or two notes together to play harmonically with my scale. My microtonal instrument is a "steel guitar" of a homemade type. I can retune each string in thirds or whatever works for the scale I am playing. Does anyone have some suggestion on what tones go together with 13 tet? Alita Morrison

>Does anyone have some suggestion on what tones go together with 13 tet?

13-tet is a very dissonant tuning, notable for its lack of reasonable
3-limit ratios (perfect 5ths and 4ths). If you are looking for some
nice dissonances, simply improvising in this scale will make great
results (there is no need to consciously avoid tonality as in 12-tet).

I gather that you are looking for consonant relationships, however.

1 = 19/18
2 = 10/9
3 = 7/6
4 = 5/4
5 = wolf 4/3
6 = 11/8
7 = wolf 3/2
8 = wolf 3/2
9 = 8/5 or 13/8
10 = 12/7
11 = 9/5
12 = 15/8
13 = 2/1

Above is one possible just interpretation of 13-tet. Of these
intervals, the most consonant are probably the 3-step minor third,
followed by the 4-step major third, and the 11-step minor seventh.

As for triads... the best to my ear is 4:5:9 (13-tet degrees
0-4-15). You can form a quasi 10:12:15 with degrees 0-3-7 (same
pattern as a minor triad in 12-tet!), and a quasi 12:14:21 with
degrees 0-3-11. All this depends on the timbre used, naturally.
You'll have to experiment.

One approach would be to really exploit "voicings". In a tuning
this dissonant, you need to use your octaves! Don't be afraid to
consider 6:7:12 a triad, to consider 6:12:7 a different triad, etc.

>Last week the topic of 13 tones equal tempered scales had three
>scales suggested. I tried them and I like them: 3121222 3131212
>2141212.

You might also like to try my 10-tone scale 2112112111. Get a
hold of Xenharmonikon 13, too, if you can. It has two good articles
on 13-tet harmonic practice. Chalmers suggests an 8-tone scale
2212212...

-Carl

I wrote...
>Chalmers suggests an 8-tone scale 2212212...

Whoops! The last 1 got chopped off somehow. The 8-tone scale is 22122121.
It's a 5L+3s MOS.

-Carl