Re: [tuning] Digest Number 1224

In Steve and Pauls thread Steve stated ...

>
> I love interval vectors, and they make me happy :)...

Is an interval vector like, LLsLLLs ?

> I can understand
> you reaction to the diatonic interval vector. When you compoare it to
> others though, you realize how special the set is! The interval vector
> tells us the interval content of a set, but also the common notes under
> transposition of that set. The diatonic Interval Vector shows us that there
> is a hierarchy among its transpositions. You can transpose the scale by a
> perfect fifth everytime and retain all tones but one.

I don't know quite what you mean here. Any transposable system shares all
but one note with its neighboring key. Perhaps you mean that the seven note
system is the only one that does it at the best approximation of 3/2 or
4/3? But there are other non-seven note systems that do this. One of the
many trees of transposable scales (which have real names that I'm still
learning) includes

L (L = 2)
L s (L ~ 3/2)
L s L (L ~ 4/3)
L s s L s (Ls ~ 4/3)
L s L L L s L (LLs ~ 4/3)
L s s L s L s L s s L s (LssLs ~ 4/3)

and we can do this forever. So if you are saying that the diatonic is
special because it is the only 7-note scale which transposes at the
fifth, then there are many systems which are unique because they
"are the only n-tone system that transposes at the Q" (substitute n
and Q as appropriate).

Thats somewhat in jest, I am a "small integer ratio" kinda guy, so
transposing at the 3/2 seems like a "good thing", nonetheless, it
doesn't pick "7" out of this tree more than "5" (pentatonic, also
quite popular), or 17 or 19 (the next choices on the way to forever).

Bob Valentine