Good chords in 22EDO within 7.2 cents accuracy

I posted this earlier but it never got through, second try.
I was using a +/-6.776 cents (256/255) accuracy in my analysis of the good dyads in EDOs 4 to 24. Gene pointed out that the Perfect Fifth is only 7.1 cents out of tune in 22EDO so I tweaked my program to use a 7.2 cents tolerance instead of 6.776 cents. 3/2 and 4/3 are now *in*. If the keys in 22EDO are named 1 to 22 then the octave is 23. Here are the good intervals (within 7.2 cents accuracy) that occur in 22EDO.

1 = 1/1, 6 = 7/6, 8 = 5/4, 9 = 9/7, 10 = 4/3, 11 = 11/8, 14 = 3/2, 16 = 8/5, 18 = 12/7, 23 = 2/1.

Here are the good chords (an octave or less wide) that occur in 22EDO where every dyad in each chord corresponds to one of the good dyads listed above (within 7.2 cents accuracy).

1, 6, 11, 16
1, 6, 11
1, 6, 14, 23
1, 6, 14
1, 6, 16, 23
1, 6, 16
1, 6, 23
1, 8, 16, 23
1, 8, 16
1, 8, 18, 23
1, 8, 18
1, 8, 23
1, 9, 14
1, 9, 16
1, 9, 18
1, 10, 18, 23
1, 10, 18
1, 10, 23
1, 11, 16
1, 11, 18
1, 14, 23
1, 16, 23
1, 18, 23

There are 6 good tetrads and 17 good triads. I doubt if any other EDO less than 25 would come close. Of course all these chords will work in all keys.

John.

>"Here are the good chords (an octave or less wide) that occur in 22EDO
where every dyad in each chord corresponds to one of the good dyads
listed above (within 7.2 cents accuracy).

1, 6, 11, 16
1, 6, 11....."

This kind of implies the idea to make a scale with all the above chords IE

1,6,8,9,10,11,14,16,18,23
...a 10-note scale

Or...what scale do you all think would capture the greatest number of John's chords on a "chords per note" basis?

Sorry John, I had missed this post. I didn't realize that you were now
in the habit of analyzing things outside of the 256/255 range. If you
are now willing to do so, or if you're in general willing to
experiment with different tolerance values in your model, then I
apologize and concede my criticism on this point.

-Mike

On Fri, Apr 1, 2011 at 2:01 PM, john777music <jfos777@...> wrote:
>
> I posted this earlier but it never got through, second try.
> I was using a +/-6.776 cents (256/255) accuracy in my analysis of the good dyads in EDOs 4 to 24. Gene pointed out that the Perfect Fifth is only 7.1 cents out of tune in 22EDO so I tweaked my program to use a 7.2 cents tolerance instead of 6.776 cents. 3/2 and 4/3 are now *in*. If the keys in 22EDO are named 1 to 22 then the octave is 23. Here are the good intervals (within 7.2 cents accuracy) that occur in 22EDO.
>
> 1 = 1/1, 6 = 7/6, 8 = 5/4, 9 = 9/7, 10 = 4/3, 11 = 11/8, 14 = 3/2, 16 = 8/5, 18 = 12/7, 23 = 2/1.
>
> Here are the good chords (an octave or less wide) that occur in 22EDO where every dyad in each chord corresponds to one of the good dyads listed above (within 7.2 cents accuracy).
>
> 1, 6, 11, 16
> 1, 6, 11
> 1, 6, 14, 23
> 1, 6, 14
> 1, 6, 16, 23
> 1, 6, 16
> 1, 6, 23
> 1, 8, 16, 23
> 1, 8, 16
> 1, 8, 18, 23
> 1, 8, 18
> 1, 8, 23
> 1, 9, 14
> 1, 9, 16
> 1, 9, 18
> 1, 10, 18, 23
> 1, 10, 18
> 1, 10, 23
> 1, 11, 16
> 1, 11, 18
> 1, 14, 23
> 1, 16, 23
> 1, 18, 23
>
> There are 6 good tetrads and 17 good triads. I doubt if any other EDO less than 25 would come close. Of course all these chords will work in all keys.
>
> John.