Oddball ET divisions and consonance vs. "natural-ness"

>The back and forth of this JI vs. ET vs. non-JI vs. non-JI/non-ET vs.

> non-octave battle is both exasperating and fascinating.

My two cents....
   7-note JI works because it represents the minimum of the dissonance curve for
the timber of most natural instruments (see Bill Sethares' page for an explanation of the dissonance formula)...IE where the overtones of each instrument become closest to matching the notes of the scale.

   Different cultures have instruments with different timbres and thus slightly different scales to fit them...what's a more consonant scale with one instrument may be less for another.

   But there are other phenomena at hand as well.  For example, JI does sound more natural than, say 10-TET even with pure sine waves, no harmonies (IE monophonically), NO overtones (when consonance is not involved).   It seems to me the mind looks to "compile" scales into simple functions IE does a regression of sorts...and the more the error
from that regression to more sense of discordance...even in monophonic music.

   But, at the same time, I've found scales in 33-TET of up to 9-notes that sound just as natural as 7 note JI.  And it seems the higher TET's are actually pretty good at approximating non-TET scales, especially those near numbers in the Fibonacci series IE 7TET, 12TET, 19TET, 33TET, and 54TET. 
    I don't quite get the point of going over 60TET because that appears to exceed the human resolution for frequency (at least to my ears).
----------------------------------------------------------------------------------------------------------------
    But, in general....I'm fascinated by the use of the higher TET's between 30 and 60 to make scales of over 7 notes sound fairly pure with most instruments.   I've found 9 notes per octave is the most that can be played within an octave in a melody with
sustain...but I'd love someone to show me a 10-note octave scale capable of consonant harmony. :-)

--- On Fri, 5/30/08, Kraig Grady <kraiggrady@...> wrote:
From: Kraig Grady <kraiggrady@...>
Subject: Re: [MMM] Re: Oddball ET divisions
To: MakeMicroMusic@yahoogroups.com
Date: Friday, May 30, 2008, 6:25 PM

on this page you describe Indonesian music as non harmonic which i tend

to disagree with in that difference tones seem to have some influence

(at least). I do not think there is any culture though that is based on

NOT doing something. What the something is that they go for is often

unsolved, in which simple ratio explain only a few.

The investigation into Phi where the desire was to find the most

dissonant merely lead to other type of phenomenon. So while i would

agree with Ricks premise of waves, there are also other 'patterns' that

humans and likewise the universe might serve as points of attraction.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_

_'''''''_ ^North/Western Hemisphere:

North American Embassy of Anaphoria Island <http://anaphoria. com/>

_'''''''_ ^South/Eastern Hemisphere:

Austronesian Outpost of Anaphoria <http://anaphoriasou th.blogspot. com/>

',',',',',', ',',',',' ,',',',', ',',',',' ,',',',', ',',',',' ,

Aaron Krister Johnson wrote:

>

> --- In MakeMicroMusic@ yahoogroups. com

> <mailto:MakeMicroMu sic%40yahoogroup s.com>, "Jacob"

> <tricesimoprimalist @...> wrote:

>

> Daniel wrote:

> > > Let me show you some calculations to find consonant intervals.

> >

>

> Jacob wrote:

> > Be not so quick to equate small-number- just with "consonance" , or

> even usefulness. But

> > that high horse belongs to other people.

>

> Jacob, I'm with you on this one; in fact, I just happened to have

> finished changing the http://untwelve. org/why.html

> <http://untwelve. org/why.html> page to get away

> from JI-centric thinking when I stumbled upon this response.

>

> I also think I'm skeptical of my skepticism: there is _something_ to

> the JI phenomenon, at least in the sense that non-tone-deaf singers

> for instance naturally find themselves anchoring to those 'points of

> stability'

>

> The back and forth of this JI vs. ET vs. non-JI vs. non-JI/non-ET vs.

> non-octave battle is both exasperating and fascinating. It sort of

> gives away how rich this subject really is. Or how incredibly weird

> and geeky we all are to be paying such close attention (or both?!)

>

> > Draw an isosceles right triangle. If those were string lengths, you

> now have a 600 cent

> > interval. Simple, no?

>

> Good one!

>

> -A.

>

>

[Non-text portions of this message have been removed]

I think you might have a hard time tuning 10 ET by ear.
also there is nothing to make me believe that consonance is a concern to many musical cultures.
Many seem more inclined to have the interval all have the same amount of tension in between them.
Many African and Indonesian scales have these properties. And in a way it allows much greater counterpuntal freedom.

The tuning and timbre question is interesting though and hard to tell which came first. It appears that modification and development over time with western instruments has been toward making them sound good in 12ET. Which is one reason the path of using these to explore other systems is problematic.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Michael Sheiman wrote:
>
> >The back and forth of this JI vs. ET vs. non-JI vs. non-JI/non-ET vs.
>
> > non-octave battle is both exasperating and fascinating.
>
> My two cents....
>    7-note JI works because it represents the minimum of the > dissonance curve for
> the timber of most natural instruments (see Bill Sethares' page for an > explanation of the dissonance formula)...IE where the overtones of > each instrument become closest to matching the notes of the scale.
>
>    Different cultures have instruments with different > timbres and thus slightly different scales to fit them...what's a more > consonant scale with one instrument may be less for another.
>
>    But there are other phenomena at hand as well.  For > example, JI does sound more natural than, say 10-TET even with pure > sine waves, no harmonies (IE monophonically), NO overtones (when > consonance is not involved).   It seems to me the mind looks > to "compile" scales into simple functions IE does a regression of > sorts...and the more the error
> from that regression to more sense of discordance...even in monophonic > music.
>
>    But, at the same time, I've found scales in 33-TET of up > to 9-notes that sound just as natural as 7 note JI.  And it seems > the higher TET's are actually pretty good at approximating non-TET > scales, especially those near numbers in the Fibonacci series IE 7TET, > 12TET, 19TET, 33TET, and 54TET. 
>     I don't quite get the point of going over 60TET > because that appears to exceed the human resolution for frequency (at > least to my ears).
> ----------------------------------------------------------
>     But, in general....I'm fascinated by the use of the > higher TET's between 30 and 60 to make scales of over 7 notes sound > fairly pure with most instruments.   I've found 9 notes per > octave is the most that can be played within an octave in a melody with
> sustain...but I'd love someone to show me a 10-note octave scale > capable of consonant harmony. :-)
>
> --- On Fri, 5/30/08, Kraig Grady <kraiggrady@... > <mailto:kraiggrady%40anaphoria.com>> wrote:
> From: Kraig Grady <kraiggrady@... > <mailto:kraiggrady%40anaphoria.com>>
> Subject: Re: [MMM] Re: Oddball ET divisions
> To: MakeMicroMusic@yahoogroups.com > <mailto:MakeMicroMusic%40yahoogroups.com>
> Date: Friday, May 30, 2008, 6:25 PM
>
> on this page you describe Indonesian music as non harmonic which i tend
>
> to disagree with in that difference tones seem to have some influence
>
> (at least). I do not think there is any culture though that is based on
>
> NOT doing something. What the something is that they go for is often
>
> unsolved, in which simple ratio explain only a few.
>
> The investigation into Phi where the desire was to find the most
>
> dissonant merely lead to other type of phenomenon. So while i would
>
> agree with Ricks premise of waves, there are also other 'patterns' that
>
> humans and likewise the universe might serve as points of attraction.
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
>
> _'''''''_ ^North/Western Hemisphere:
>
> North American Embassy of Anaphoria Island <http://anaphoria. com/>
>
> _'''''''_ ^South/Eastern Hemisphere:
>
> Austronesian Outpost of Anaphoria <http://anaphoriasou th.blogspot. > com/>
>
> ',',',',',', ',',',',' ,',',',', ',',',',' ,',',',', ',',',',' ,
>
> Aaron Krister Johnson wrote:
>
> >
>
> > --- In MakeMicroMusic@ yahoogroups. com
>
> > <mailto:MakeMicroMu sic%40yahoogroup s.com>, "Jacob"
>
> > <tricesimoprimalist @...> wrote:
>
> >
>
> > Daniel wrote:
>
> > > > Let me show you some calculations to find consonant > intervals.
>
> > >
>
> >
>
> > Jacob wrote:
>
> > > Be not so quick to equate small-number- just with > "consonance" , or
>
> > even usefulness. But
>
> > > that high horse belongs to other people.
>
> >
>
> > Jacob, I'm with you on this one; in fact, I just happened to have
>
> > finished changing the http://untwelve. org/why.html
>
> > <http://untwelve. org/why.html> page to get away
>
> > from JI-centric thinking when I stumbled upon this response.
>
> >
>
> > I also think I'm skeptical of my skepticism: there is _something_ to
>
> > the JI phenomenon, at least in the sense that non-tone-deaf singers
>
> > for instance naturally find themselves anchoring to those 'points of
>
> > stability'
>
> >
>
> > The back and forth of this JI vs. ET vs. non-JI vs. non-JI/non-ET vs.
>
> > non-octave battle is both exasperating and fascinating. It sort of
>
> > gives away how rich this subject really is. Or how incredibly weird
>
> > and geeky we all are to be paying such close attention (or both?!)
>
> >
>
> > > Draw an isosceles right triangle. If those were string > lengths, you
>
> > now have a 600 cent
>
> > > interval. Simple, no?
>
> >
>
> > Good one!
>
> >
>
> > -A.
>
> >
>
> >
>
>
>
>
>
>
>
>
>
>
>
> [Non-text portions of this message have been removed]
>
>