Partch's Claim That 12EDO Is "5-Limit":

Partch's Claim That 12EDO Is "5-Limit":

I was reading Partch's Genesis yesterday, and his claim
that 12EDO is "5-limit" is nonsense. I looked up all of the
just intervals on Kyle Gann's online table that are the
closest to the 12EDO intervals (1,2,3,4,5,6,7,8,9,10,11
semitones), and there are ratios with factors of 7,11,17,
and 121.

What gives? Thanks.

--
Bill Flavell

On 3/22/06, Bill Flavell <bill_flavell@email.com> wrote:
> Partch's Claim That 12EDO Is "5-Limit":
>
> I was reading Partch's Genesis yesterday, and his claim
> that 12EDO is "5-limit" is nonsense. I looked up all of the
> just intervals on Kyle Gann's online table that are the
> closest to the 12EDO intervals (1,2,3,4,5,6,7,8,9,10,11
> semitones), and there are ratios with factors of 7,11,17,
> and 121.
>
> What gives? Thanks.

Partch meant that when you hear, for example, a 12edo major third,
your ear hears it as implying 5/4, rather than 14/11 or 19/15 or
infinitely many other ratios, because although 5/4 is 14 cents off, it
is a simpler, more powerful relationship that dominates the other
possibilities. In these terms none of the 12edo intervals represents a
simple 7-limit consonance. 12edo contains consistent and _distinct_
approximations for all the 5-limit intervals, but not 7-limit (for
example 7/6 and 6/5 are confounded).

Note that Partch was opposed to all forms of temperament, and he
definitely would not have equated 12edo with 5-limit JI.

Keenan

--- In tuning@yahoogroups.com, "Bill Flavell" <bill_flavell@...> wrote:
>
> Partch's Claim That 12EDO Is "5-Limit":
>
> I was reading Partch's Genesis yesterday, and his claim
> that 12EDO is "5-limit" is nonsense.

It's not nonsense, it's a judgment call. The highest limit 12 does a
halfway decent job for is 5. However, it's consistent through the
7-limit (in fact, the 9 odd limit.)

I looked up all of the
> just intervals on Kyle Gann's online table that are the
> closest to the 12EDO intervals (1,2,3,4,5,6,7,8,9,10,11
> semitones), and there are ratios with factors of 7,11,17,
> and 121.
>
> What gives? Thanks.

You are ignoring what the limit business means; there will always be
intervals for any et it approximates arbitarily well. The question is,
how does it deal with *every* odd prime less than or equal to a given
one?

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:

> In these terms none of the 12edo intervals represents a
> simple 7-limit consonance.

But it gets arbirarily close to 7-limit intervals. The 400 cent
interval, aka the cube root of 2, is very close indeed to 63/50. Three
63/50s in a row is sharper than an octave by the landscape comma,
250047/250000. If we were in 612edo and not 12edo, that's probably how
we would interpret the interval.