21 good intervals

I used my Interval Calculator to work out all possible "good" (in harmony) intervals over a one octave range. There are 21 of them...

1/1, 9/8, 8/7, 7/6, 6/5, 5/4, 9/7, 4/3, 11/8, 7/5, 10/7, 3/2, 11/7, 8/5, 5/3, 12/7, 7/4, 9/5, 11/6, 13/7, 2/1.

I've tested them and they all sound okay.

So if you're tempering a scale temper the notes so that the greatest number of "good" intervals occur within a tolerance of +-6.775 cents (256/255).

John.

John,

The ones that come across to me from your list as very "original from 12TET but still quite concordant" are
7/6, 11/8, 12/7, 7/4, and 11/6. Out of those, my "modified Ptolemic 'Infinity' " scale uses 11/8, 7/4 and 11/6 as interval gaps.

Oddly enough these include most of the intervals I find as consonant. The other ones I find consonant not on your list include:
11/9 (1.2222)...true this sounds a bit more tense than 6/5 or 5/4...but not hugely so unlike, say, 17/14 or 21/17.
12/11 to 10/9 (they sound about the same and intervals in-between them actually sound fine to me...though 10/9 sounds a bit different than the rest it's not dramatic)
22/15 (this is an alternative to the usual 3/2 fifth with a slightly different, but not "wolfish" sound)

So do the rest of you have any intervals to add to (or debate as valid or invalid from) either
A) The "decently concordant interval" list John has made or
B) The "decently concordant and significantly different from 12TET" interval list I have made?

-Michael

--- In tuning@yahoogroups.com, "john777music" <jfos777@...> wrote:
>
> I used my Interval Calculator to work out all possible "good" (in harmony) intervals over a one octave range. There are 21 of them...
>
> 1/1, 9/8, 8/7, 7/6, 6/5, 5/4, 9/7, 4/3, 11/8, 7/5, 10/7, 3/2, 11/7, 8/5, 5/3, 12/7, 7/4, 9/5, 11/6, 13/7, 2/1.
>
> I've tested them and they all sound okay.

This has the entire 7-limit tonality diamond, and from the 11-limit diamond it misses 12/11, 11/10, 10/9, 11/9, 14/11, 16/11, 14/9, 18/11, 16/9, 20/11. Of these, 12/11, 10/9, 14/11, 16/11, 14/9, 16/9 are in effect present, as octave compliments (making them impossible to avoid.) Adding them in makes the interval list into the 11-limit diamond, minus 11/10, 20/11, 11/9, and 18/11 plus a lone 13-limit interval, 13/7.

If we allow 11/5 into consideration you'd want to add that to the list, so really all you'd end up doing would be to toss neutral thirds, and add a lonely 13/7. Why not just use the 11-limit diamond instead?