RE: [tuning] Harmonic Entropy for the Sophisticated Ear

Here is the harmonic entropy curve for s=0.6% (I used N=167, but could have
gone a little higher to get rid of weird inflection points):

http://www.egroups.com/files/tuning/perlich/

This represents the best ears listening to intervals in the best register. I
see this as a "limit" as to which diads could ever realistically be
considered consonant.

oops -- see http://www.egroups.com/files/tuning/perlich/ent_006.jpg

Paul!
I can't help but finding statements like this rather limiting. Pardon the pun. I don't
think the subjectivity of consonance can be so realistically considered.

"Paul H. Erlich" wrote:

> I
> see this as a "limit" as to which diads could ever realistically be
> considered consonant.

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com

I wrote,

>>I
>>see this as a "limit" as to which diads could ever realistically be
>>considered consonant.

Kraig wrote,

>I can't help but finding statements like this rather limiting. Pardon the
pun. I don't think the subjectivity of consonance can be so realistically
>considered.

I don't want to place impositions on anyone's music, I just want to put a
realistic bound (which agrees remarkably well with my experience, BTW) on
the applicability of JI to the consonance of diads. Beyond these ratios, for
example, one is no longer justified in assuming that a simpler ratio is more
concordant than a more complex one -- I'm just setting a "best possible"
limit to this kind of naive application of JI, and suggesting that one's
ears would be more important than the size of the numbers beyond this limit.

As a simple rule of thumb, I'd say that if the lower number in the ratio is
10 or more, one is highly unlikely to find any musical circumstances where
the diad is a local minimum of discordance; and when comparing two or more
ratios whose lower numbers are 10 or more, the size of the numbers is not
necessarily a guide to the relative concordance of the diads.

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

http://www.egroups.com/message/tuning/12361

> I don't want to place impositions on anyone's music, I just want to
put a realistic bound (which agrees remarkably well with my
experience, BTW) on the applicability of JI to the consonance of
diads. Beyond these ratios, for example, one is no longer justified
in assuming that a simpler ratio is more concordant than a more
complex one -- I'm just setting a "best possible" limit to this kind
of naive application of JI, and suggesting that one's ears would be
more important than the size of the numbers beyond this limit.
>
>As a simple rule of thumb, I'd say that if the lower number in the
ratio is 10 or more, one is highly unlikely to find any musical
circumstances where the diad is a local minimum of discordance; and
when comparing two or more ratios whose lower numbers are 10 or more,
the size of the numbers is not necessarily a guide to the relative
concordance of the diads.

Perhaps I am not understanding "Anaphorian" music correctly, but it
seems from what I am hearing that it really is not so much about
"simple consonance" as about a lot of other things... including
acoustical manifestations of "difference tones" and a lot of other
acoustical effects going on.

I hasten to add, by the way, that I have NEVER heard similar things
in ANY other (certainly in other acoustic) music to date!
____________ ___ ___ __ __ _
Joseph Pehrson

Paul!
I am just not understanding what is gained by placing "bounds". honestly. I can't help
remembering about the debate in Ancient Greece over over weather there should be a symbol for
nothing (as in a zero-o). they decided against it stating that nothingness didn't need a
symbol. This single act messed up western math until Fibonacci introduced the zero to the
west. Don't you think placing this 'Bounds" might have just this type of effect. Or do you
possibly see it as a foundation of a music along the lines of Hindemith

"Paul H. Erlich" wrote:

> I don't want to place impositions on anyone's music, I just want to put a
> realistic bound (which agrees remarkably well with my experience, BTW) on
> the applicability of JI to the consonance of diads.

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com

Kraig wrote,

>Or do you possibly see it as a foundation of a music along the lines of
Hindemith

Yes -- and as one foundation for a theory of music . . .