RE: [tuning] Crunchiness

Keenan wrote,

>A good
>example is the 3-7 square chord, 1/1:21/16:3/2:7/4. Every interval is
>7-odd-limit consonant except the 21/16, which is so close to 4/3 as to be
>quite dissonant, giving this chord the melancholy sound common to all
>crunchy chords. This is completely lost in 12-eq because the best
>approximation to 21/16 is the perfect fourth. 1/1:9/8:7/6:3/2:7/4 is also
>very crunchy because every interval is 9-odd-limit consonant except the
>28/27, a very narrow interval of 63 cents or a thirdtone. This chord is
>recognizable in 12-eq as min7(9), but just doesn't have the same bite. I
>think the characteristic sound of these chords stems from the statement of
>two pitches that would be consonant on their own but are not with each
>other, like when two arguments both make sense but are mutually
conflicting.

Awesome, Keenan. Crunchy chords would be the next category after saturated
chords (see http://www.cix.co.uk/~gbreed/ass.htm) in a classification of JI
chords. Read that link and tell me what a crunchy rhubarb would be :)

>My goal is to find a cruchy chord in which the harmonic entropy of the
>crunchy interval is more than the sum of all the other entropies combined.
>Such a chord would be as crunchy as ice cold raw green pepper, proven to be
>the most crunchy food.

Unlike the other calculations I've been doing, that would depend sensitively
on what order Farey (or whatever) series I use, since the higher the order,
the higher the whole curve.