Dekany in 4D (Excel)

It's at
http://dkeenan.com/Music/DekanyRotation.xls

This time I've added some sliders so you can go quickly to some set of
angles and animate from there. Also you can reverse the animation so if you
think you see something interesting go past, you can back up to have
another look at it. The way this all works is less than ideal, but hey
Excel wasn't really intended for this at all.

I s'pose you want a different colour for each of the 10 kinds of dyads now?

-- Dave Keenan
http://dkeenan.com

--- In tuning@egroups.com, David C Keenan <D.KEENAN@U...> wrote:

http://www.egroups.com/message/tuning/14912

> It's at
> http://dkeenan.com/Music/DekanyRotation.xls
>

Wow. This is really wild!

JP

David Finnamore wrote...

>Thanks, Kraig, that does help clear things up a bit. But it's
>unrealistic and unnecesary in this society to require everyone to
>travel to California and sit at the feet of the guru.

Who's requiring?

>If all teachers had that attitude we'd still all be sitting around
>camp fires sharpening stones.

What's to say Erv would not prefer that? I doubt he would, but
I don't know for sure...

-Carl

>I think it is an exageration to say that any CPS has no preferred tonal
>center. All consonant dyads are not equally consonant and otonal chords
>are not equal to utonal.

True, but there is more to tonality than consonance. In fact I think
it's an abuse of the term to call CPSs atonal. I think what has been
meant in the past, with comparisons to the diamond, etc., is the way
the common tones are distributed between the chords.

>But still it's an extraordinary acheivement to get as close to atonal
>as this, in JI.

Not especially. It's quite easy to use the diamond atonally. Or, one
could use a bunch of chords distant from eachother on the lattice. The
cool thing about CPS is the number of consonant chords you can use, from
a small number of notes, without boring the hell out of people by having
them always hear a single common frequency as in the diamond.

>I think that complete atonality can only be obtained by using all the
>notes from some equal temperament (equal division of the octave).

I disagree, even if we take atonality to mean a lack of consonance. One
central theme of the list seems to be that the brain is hard-wired for
JI... it will always hear some intervals as more consonant than others, ET
or otherwise.

> 5*7
> ,'/ \`.
>1*5-/---\-3*5-------5*9
> |\/ \/| /|\
> |/\ /\| / | \
>1*7-------3*7-------7*9 \
> `.\ /,' /,' `.\
> 1*3-------1*9-------3*9
>
>It seems clear to me that some notes will have a much stronger pull than
>others because they are involved in more consonances that are simple and
>otonal.

Which ones are those?

-Carl

Dave Keenan wrote...

>>>It seems clear to me that some notes will have a much stronger pull than
>>>others because they are involved in more consonances that are simple and
>>>otonal.
>>
>>Which ones are those?
>
>1*3, 1*5, 1*7, 1*9. When one recognises the extra "degenerate"
>(non-dispentachoron) consonances, 1*3 looks like a clear winner to me,
>which is why I called it "C" in:
>
> Fx
> ,'/ \`.
>A -/---\- E ------- B
>|\/ \/|\ /|\
>|/\ /\| \ / | \
>D#------- A#------- E# \
> `.\ /,' `.\ /,' `.\
> C ------- G ------- D
>
>The "degenerate" edges shown this time.

I'm not sure why the fuss over degenerate edges, and I don't
see how "C" participates in any more consonances than "G", nor
do I feel that counting consonances has anything to do with
a perceived key center. If we did consider this a tonal scale,
and assumed some random tune, then perhaps we could say that
Fx, B, and E# are weekest, since they can't be the :2 of a 3:2.

-Carl

Carl Lumma wrote,

>I'm not sure why the fuss over degenerate edges

Because they ruin the structural properties that the CPS is supposed to
have!

>and I don't
>see how "C" participates in any more consonances than "G"

Remember, this is 9-limit, so C participates in a 7:9 and a 1:9, while G
doesn't.

>nor
>do I feel that counting consonances has anything to do with
>a perceived key center.

It has a little to do with it. In Partch's world it has everything to do
with it (and it is in only in Partch's world that the hexany is "atonal" and
the diamond is "tonal").

>If we did consider this a tonal scale,
>and assumed some random tune, then perhaps we could say that
>Fx, B, and E# are weekest, since they can't be the :2 of a 3:2.

I agree with that analysis, and I'm sure Dave would too. However, Partch
wouldn't, since he sees the "fifth" of a minor chord as its tonal center,
and the "seventh" of a half-diminished seventh chord (tuned 1/7:1/6:1/5:1/4)
as its tonal center. It just goes to show how dualism taken to its logical
conclusion (as Partch did) leads to results that conflict with common
musical experience.

>>I'm not sure why the fuss over degenerate edges
>
>Because they ruin the structural properties that the CPS is supposed to
>have!

Nonsense. We don't have to use the extra consonances, and even if we do,
the CPS is still intact.

>>If we did consider this a tonal scale, and assumed some random tune, then
>>perhaps we could say that Fx, B, and E# are weekest, since they can't be
>>the :2 of a 3:2.
>
>I agree with that analysis, and I'm sure Dave would too. However, Partch
>wouldn't, since he sees the "fifth" of a minor chord as its tonal center,
>and the "seventh" of a half-diminished seventh chord (tuned 1/7:1/6:1/5:1/4)
>as its tonal center. It just goes to show how dualism taken to its logical
>conclusion (as Partch did) leads to results that conflict with common
>musical experience.

Sure.

-Carl

I wrote,

>>Because they ruin the structural properties that the CPS is supposed to
>>have!

Carl wrote,

>Nonsense. We don't have to use the extra consonances, and even if we do,
>the CPS is still intact.

Well, by that argument, Kraig Grady would have no grounds for objecting to
Dave Keenan's microtempering of CPSs.

Paul!
It's is a free country they can do anything they want!

"Paul H. Erlich" wrote:

> I wrote,
>
> >>Because they ruin the structural properties that the CPS is supposed to
> >>have!
>
> Carl wrote,
>
> >Nonsense. We don't have to use the extra consonances, and even if we do,
> >the CPS is still intact.
>
> Well, by that argument, Kraig Grady would have no grounds for objecting to
> Dave Keenan's microtempering of CPSs.
>
>

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

>>>Because they ruin the structural properties that the CPS is supposed to
>>>have!
>
>>Nonsense. We don't have to use the extra consonances, and even if we do,
>>the CPS is still intact.
>
>Well, by that argument, Kraig Grady would have no grounds for objecting to
>Dave Keenan's microtempering of CPSs.

Correct. For the person who is interested in only the CPS structure,
however, microtempering is un-desirable.

-Carl