JI theory

Hi group.

I've now read Partch's 'Genesis', Fokker's 'Just Intonation', and a
good deal of Chalmers' 'Divisions of the Tetrachord'. I perused
Johnston's article "Scalar Order as a Compositional Device" and made
a futile attempt to read Helmholtz...
The idea of combining Partch's O- and Utonalities with Fokker's
melodic groupings- melodic sets created by mixing harmonics and
subharmonics of different pitches- fascinates me, but I wonder if
there is some possible system to it that I don't know about.

I've also familiarized myself with the theories of Koffka and
Wertheimer re Gestalt, e.g., the laws of Pragnanz, good continuation,
common fate; and with George A. Miller's concept of 'The Magical
Number 7 +/- 2.' It seems to me both of these ways of explaining
perception have a huge bearing on what is thought to be beautiful in
music. I also suspect most microtonalists don't consider these.

I think that, when presented with too many pitches, the brain will
attempt to simplify the set by defining some in terms of others. So
that, given:

1/1 9/8 6/5 5/4 7/5 3/2 8/5 7/4 9/5

There's no way to treat each pitch as a separate item, so they'll
tend to be grouped according to tonality, even if melodic movement
doesn't follow the same logic, at least to a certain point.

What sorts of broader schemes are there for harmonic relations in
JI? I'm thinking of common-tone modulations in particular; I've
heard some that intrigue me, and I can hear some logic, but I don't
know enough about it to know where to start in my own experiments.
I have a cheap Yamaha keyboard hooked to WinXP with Scala, which
seems to be all I need, but trying to map all the pitches I might
want to include is daunting. Perhaps there is a useful system for
switching between different scales in the memory banks that could
provide the kind of variety I want.

Does Meyer's 'Emotion and Meaning in Music' approach any of this
stuff?

Gestalt illustrations:
http://www.ethnomusic.ucla.edu/courses/276/gestalt.htm

Miller:
http://www.well.com/user/smalin/miller.html

Later.
-Chuckk

hi Chuckk,

--- In tuning@yahoogroups.com, "touchedchuckk" <BadMuthaHubbard@h...>
wrote:

> I've also familiarized myself with the theories of
> Koffka and Wertheimer re Gestalt, e.g., the laws of
> Pragnanz, good continuation, common fate; and with
> George A. Miller's concept of 'The Magical Number 7 +/- 2.'
> It seems to me both of these ways of explaining
> perception have a huge bearing on what is thought
> to be beautiful in music. I also suspect most
> microtonalists don't consider these.

i'm not familiar with the first batch of names,
but many of us have indeed taken into consideration
the Miller Limit when constructing scales.

> I think that, when presented with too many pitches, the
> brain will attempt to simplify the set by defining some
> in terms of others. So that, given:
>
> 1/1 9/8 6/5 5/4 7/5 3/2 8/5 7/4 9/5
>
> There's no way to treat each pitch as a separate item,
> so they'll tend to be grouped according to tonality, even
> if melodic movement doesn't follow the same logic, at
> least to a certain point.

this sounds a lot like what i mean by "finity".

http://tonalsoft.com/enc/index2.htm?finity.htm

i came up with that in 1998 and haven't considered it
deeply since then ... so there's still a lot of detail
in my theory of finity that needs to be filled in.

-monz

--- In tuning@yahoogroups.com, "touchedchuckk" <BadMuthaHubbard@h...>

/tuning/topicId_55976.html#55976

>
> 1/1 9/8 6/5 5/4 7/5 3/2 8/5 7/4 9/5
>
> There's no way to treat each pitch as a separate item, so they'll
> tend to be grouped according to tonality, even if melodic movement
> doesn't follow the same logic, at least to a certain point.
>
>
> What sorts of broader schemes are there for harmonic relations in
> JI? I'm thinking of common-tone modulations in particular; I've
> heard some that intrigue me, and I can hear some logic, but I don't
> know enough about it to know where to start in my own experiments.

***Well, of course modulation in JI becomes tricky, since there is an
additional accumulation of accidentals as one moves away from the
1/1. This we see in Ben Johnston's work.

Paul Erlich has done quite a bit of work thinking about and relating
consonances. One of the practical derivatives has been
the "Blackjack" scale, which is a scale of 21 notes very close to JI
(within 3 cents, for the most part). However, many of the basic
pitches relate to each other by JI intervals, and it is possible to
plot "common tone" harmony with the use of a "Blackjack lattice"
which shows, visually, the near-JI connections.

So, this kind of thing has been going on with this list...

J. Pehrson