Re: 12 eq (Dante)

Dante wrote,

>>>Most ET intervals require
>>>relatively high number ratio approximations

I wrote,

>>I don't know what you mean by "require", but shouldn't the only
>>requirement is that our ears can really make out the ratios you're
>>using? I would say that under most circumstances, most 12-ET intervals
>>require relatively low number ratio approximations: the minor third is
>>6:5, the major third is 5:4, the perfect fourth is 4:3, their
inversions
>>similarly, and the tritone is quite often 7:5 or 10:7.

Dante wrote,

>Surely it is easy to hear 5/4 and 400c as two different intervals.

Of course!

>>400c is
closely approximated by 635/504 (399.99943c). This is a 127 limit(!)
ratio.

It's also approximated by tons of other ratios that are too complex to
make out as having any JI character. What I was saying is that the
character of 400 cents is more influenced by 5:4 than by any other ratio
(9:7 is important in some contexts).

>Within a tonal context, we do read 400c as 5/4, but 400c still has a
sound
>of its own. Weather that sound fits within any discernable musical
system
>>as< itself is another question. I doubt if it could to any human ears
(at
>least at this stage of our aural evolution. Who knows what the next few
>thousand years may bring!)

Evolution happens because of survival of the fittest. What kind of
eugenics program do you forsee that will wipe out those with poor aural
resolution? (Sorry, didn't mean to get smart, I just hate these kinds of
statements.)

>But I would say that anyone who argues for an
>independent function for et intervals (as opposed to their being read
by
>our ears as low number ratios) would have to answer this.

I say most of them are read as low number ratios. Does that mean I don't
have to answer? (Again, sorry if I sound rude, but I'm really concerned
I'm not getting the jist of your arguments here.)

Dante wrote,

>>>so the question of perception
>>>of ET intervals can be considered as identical with that of the
>>perception
>>>of higher number ratios.

I wrote,

>>Yes, both will tend to be heard in terms of simpler ratios (this is
>>quite related to my last post!).

Dante wrote,

>I think this has alot to do with context. To my ear, gamelan scales do
not
>sound like mistuned low integer ratios.

Well, ignoring the very important fact of the inharmonic partials of
most gamelan instruments, you have to admit that gamelan intervals can
be approximated just as well as ET intervals, or any other non-just
intervals, by higher number ratios. That must have some bearing on what
you were claiming above about the questions of perception being
identical. Are you now saying they're not identical? (Once again, I
apologize if I seem like I'm being unnecessarily argumentative. But to
be honest, I got the sense that your last post, which was a reply to me,
had elements of changing the terms of the discussion to gain some sort
of advantage. I had to defend myself, but if I totally misread you, I
sincerely apologize.)