Reply to Keenan Pepper

Keenan Pepper wrote:

>On a related thought, I think the limit of a piece should be split into two
>categories, tuning limit and consonance limit. Tuning limit is the regular,
>familiar concept of the highest prime number appearing in a ratio, but
>consonance limit is the highest odd multiple that can appear in a final
>chord, all the more complex intervals needing to be resolved. Thus in
>7-limit 5-consonant music, 7-limit ratios and chords would appear, but they
>would always resolve to 5-limit consonances.

I agree, and I beat you to it, Keenan -- these are the definitions of
"prime-limit" and "odd-limit" I contributed to the Tuning Dictionary
http://www.ixpres.com/interval/dict/index.htm:
http://www.ixpres.com/interval/dict/limit.htm

>I'd just like to comment that not enough distinction is being made between
>dissonance, which can be used, desired, and even focused on, and plain
>out-of-tune-ness, which I would only ever use for beats, as in the
beginning
>of http://www.xs4all.nl/~huygensf/midi/beatgen.mid
>I've experimented with various dissonant intervals (especially the 7/5
>tritone) in just and tempered, and the dissonance, or pull to the
>resolution, is incariably sharpened. The fact that they are in tune adds
the
>extra capacity to linger tantalizingly of them before finally resolving,
>without the pain.

But Keenan, wouldn't the out-of-tuneness of intervals at a certain odd-limit
(say 7) help to project the logic piece if the piece is in that odd-limit
(say 5)? Wouldn't you think the piece could more easily slip into a 7-limit
of consonance if the 7-limit intervals were all very much in tune?

In my opinion, since resolutions operate melodically as well as
harmonically, one should allow melodic considerations to determine the best
tuning for the dissonant intervals, rather than tuning them to a just
interval standard beyond the consonance limit of the composition.