Paul,

My current model works like this:

pentachordal

(0 109 218 382 491 600 709 873 982 1091)

(1193 102 211 375 484 593 702 811 920 1084)

7 7 7 7 7 7 7 62 62 7

symmetrical

(0 109 218 382 491 600 709 818 982 1091)

(1193 102 211 320 484 593 702 811 920 1084)

7 7 7 62 7 7 7 7 62 7

So obviously, these two scales will come out

the same. But you've view -- and I remember

doing some listening experiments that back you

up (the low efficiency of the symmetrical

version was the other theory there) -- is that

the symmetrical version is not tetrachordal.

So what's going on here? Where's the error

in tetrachordality = similarity at transposition

by a 3:2?

-Carl

--- In tuning-math@y..., "clumma" <carl@l...> wrote:

> Paul,

>

> My current model works like this:

>

> pentachordal

> (0 109 218 382 491 600 709 873 982 1091)

> (1193 102 211 375 484 593 702 811 920 1084)

> 7 7 7 7 7 7 7 62 62 7

>

> symmetrical

> (0 109 218 382 491 600 709 818 982 1091)

> (1193 102 211 320 484 593 702 811 920 1084)

> 7 7 7 62 7 7 7 7 62 7

>

> So obviously, these two scales will come out

> the same. But you've view -- and I remember

> doing some listening experiments that back you

> up (the low efficiency of the symmetrical

> version was the other theory there) -- is that

> the symmetrical version is not tetrachordal.

>

> So what's going on here? Where's the error

> in tetrachordality = similarity at transposition

> by a 3:2?

An octave species is homotetrachordal if it has identical melodic

structure within two 4:3 spans, separated by either a 4:3 or a 3:2.

In the pentachordal scale, _all_ of the octave species are

homotetrachordal (some in more than one way). In the symmetrical

scale, _none_ of the octave species are homotetrachordal.

>>So obviously, these two scales will come out

>>the same. But you've view -- and I remember

>>doing some listening experiments that back you

>>up (the low efficiency of the symmetrical

>>version was the other theory there) -- is that

>>the symmetrical version is not tetrachordal.

>>

>>So what's going on here? Where's the error

>>in tetrachordality = similarity at transposition

>>by a 3:2?

>

>An octave species is homotetrachordal if it has identical melodic

>structure within two 4:3 spans, separated by either a 4:3 or a 3:2.

>In the pentachordal scale, _all_ of the octave species are

>homotetrachordal (some in more than one way). In the symmetrical

>scale, _none_ of the octave species are homotetrachordal.

That's the def. in your paper. But:

() I never understood how it reflects symmetry at the 3:2.

() "homotetrachordal" is a new term on me. Are there precise

defs. of homo- vs. omni- around? How did you choose these

prefixes?

() We agreed a bit ago that 'the number of notes that change

when a scale is transposed by 3:2 index its omnitetrachordality',

right? My current approach is just a re-scaling of this. So

do we want to revise this agreement?

-Carl

--- In tuning-math@y..., "clumma" <carl@l...> wrote:

> >>So obviously, these two scales will come out

> >>the same. But you've view -- and I remember

> >>doing some listening experiments that back you

> >>up (the low efficiency of the symmetrical

> >>version was the other theory there) -- is that

> >>the symmetrical version is not tetrachordal.

> >>

> >>So what's going on here? Where's the error

> >>in tetrachordality = similarity at transposition

> >>by a 3:2?

> >

> >An octave species is homotetrachordal if it has identical melodic

> >structure within two 4:3 spans, separated by either a 4:3 or a 3:2.

> >In the pentachordal scale, _all_ of the octave species are

> >homotetrachordal (some in more than one way). In the symmetrical

> >scale, _none_ of the octave species are homotetrachordal.

>

> That's the def. in your paper. But:

>

> () I never understood how it reflects symmetry at the 3:2.

4:3 more clearly than 3:2. However, you could look at 3:2 spans if

you wished, and still see a large gulf between the pentachordal and

symmetrical decatonic scales.

> () "homotetrachordal" is a new term on me. Are there precise

> defs. of homo- vs. omni- around?

Were those not precise enough for you?

> How did you choose these

> prefixes?

Homo = same -- two 4:3 spans that are the same

Omni = all -- all octave species are homotetrachordal.

> () We agreed a bit ago that 'the number of notes that change

> when a scale is transposed by 3:2 index its omnitetrachordality',

> right?

We did? I don't see transposition as coming into this -- rather, it's

a property of the _untransposed_ scale, heard in its full,

unmodulating glory.

> My current approach is just a re-scaling of this. So

> do we want to revise this agreement?

I guess so!!

>>That's the def. in your paper. But:

>>

>>() I never understood how it reflects symmetry at the 3:2.

>

>4:3 more clearly than 3:2. However, you could look at 3:2 spans

>if you wished, and still see a large gulf between the pentachordal

>and symmetrical decatonic scales.

I accept symmetry at 4:3 being tied to symmetry 3:2 in an octave-

equivalent universe. Just trying to see why we're getting

different results.

>> () "homotetrachordal" is a new term on me. Are there precise

>> defs. of homo- vs. omni- around?

>

> Were those not precise enough for you?

Never saw them!

>> How did you choose these prefixes?

>

> Homo = same -- two 4:3 spans that are the same

> Omni = all -- all octave species are homotetrachordal.

Aha! Now I've seen them!

>> () We agreed a bit ago that 'the number of notes that change

>> when a scale is transposed by 3:2 index its omnitetrachordality',

>> right?

>

>We did? I don't see transposition as coming into this -- rather,

>it's a property of the _untransposed_ scale, heard in its full,

>unmodulating glory.

You said something like "aren't we done? we just count the number

of notes that change...".

I always thought the basis for tetrachordality was that for any

note heard, it's 3:2 transposition was floating in the listener's

ear. Thus, if _that_ note is then played, it sounds natural (or,

you could say, it makes it easier to sing melodies). Also, there

was the anecdotal stories about folks at parties singing tunes

a 3:2 off. So that's an absolute pitch thing.

The interval pattern stuff (the L-L-s of conventional theory) is

a relative pitch thing... ?

-Carl

--- In tuning-math@y..., "clumma" <carl@l...> wrote:

> The interval pattern stuff (the L-L-s of conventional theory) is

> a relative pitch thing... ?

Not sure what you mean.

>>The interval pattern stuff (the L-L-s of conventional theory) is

>>a relative pitch thing... ?

>

>Not sure what you mean.

I'm trying to understand the psychoacoustical basis for the

version in your paper, and recent posts about ethnic scales

on the main list (x+x+y, etc.). And I'm trying to understand

the lack, if any, of a psychoacoustical basis for my stuff

(absolute pitches being transposed by a 3:2).

-Carl

--- In tuning-math@y..., "clumma" <carl@l...> wrote:

> >>The interval pattern stuff (the L-L-s of conventional theory) is

> >>a relative pitch thing... ?

> >

> >Not sure what you mean.

>

> I'm trying to understand the psychoacoustical basis for the

> version in your paper, and recent posts about ethnic scales

> on the main list (x+x+y, etc.).

You mean when I talk about tetrachordal (now homotetrachordal)

octave species of ethnic scales?

> And I'm trying to understand

> the lack, if any, of a psychoacoustical basis for my stuff

> (absolute pitches being transposed by a 3:2).

Psychoacoustic basis? Well, when you hear the step pattern repeated

at a 4:3 or a 3:2, it spells a more coherent tonal organization than

when you hear it repeated at some other interval. The patterns sound

more similar to one another in the first case, so the information

can be "compressed" more efficiently, if that makes any sense . . .