Re: [tuning] Re: BASIC: What was temperament again? (was: True nature of the blackjack scale (in 7-limit) . . . and more epimores)

Paul Erlich schrieb:
>

> Hi Klaus. I meant the diatonic scale of Western musical practice,
> since the advent of 5-limit harmony in the late 15th century. All
> _practical_ tuning systems for this music have tempered out the
> 81:80. There is no difference between 9/8 and 10/9, not only
> physically in these tunings, but also conceptually in the music
> itself, that is, 99% of the common-practice and Renaissance
> repertoire. This point has been made exceptionally well by Daniel
> Wolf here in the past.

Oh, you meant a *tempered* 5-limit scale! (I should have seen that,
since the context was really about tempering. It's just that I like
those unequal harmonic steps too much.)

What are the language regulations for "5-limit harmony", explained
for a pedant? Is it, as I believe, shorthand for "some scale that
happens to be consistent up to and including the 5th harmonic"? Or
is the presence of the 5th harmonic or a 5-limit interval in the
scale (while everything else may have been fiddled with) reason
enough to call the whole thing "5-limit"? (An answer to this, and
I'll stop nagging...)

Klaus

--- In tuning@y..., klaus schmirler <KSchmir@z...> wrote:
>
> What are the language regulations for "5-limit harmony", explained
> for a pedant?

The term "limit" comes from Harry Partch. He primarily meant, "all
intervals using ratios with odd numbers up to and including 5 are
considered consonant; other ratios are considered dissonant". Others
after Harry Partch have tended to use "limit" to refer to the highest
_prime_ number in a tuning system, rather than the highest _odd_
number in a consonant chord. But this is a departure from Partch's
primary usage. When the question is one of verticality, I think the
odd specification makes a lot more sense than the prime one (since
you can approximate _any_ interval with arbitrary accuracy using 5-
prime-limit ratios -- thus the prime limit doesn't really tell you
anything about the kind of harmonic sounds a composer may wish to
use). Hope that answers your question.

>(An answer to this, and
> I'll stop nagging...)

Please, keep nagging . . . I love it!