Yahoo Tuning Groups Ultimate Backup tuning CPS on a standard keyboard

Hi Aaron!
There is none off hand with the 1-3-5-7-9 double dekany coming in closest with 14 notes. there is also the stellate hexany at 13 notes also. Although when i was work exclusively in such animals i would tune up two hexanies opposite each other in the eikosany, The bewst of these (from memory) were hexanies like 5-7-9-11 because they are seperated by a 1-3 (things in the eikosany so often work that way). there is also the 1-5-7-11 hexany seperated by a 3-9 and being a big fan of the 1-3-7-9-11-15
eikosany (since it falls into a 22 tone scale so easily you have the 1-7-11-15
hexanies a 3-9 apart.

although for the most part i would use my centaur tuning http://anaphoria.com/centaur.html

>
> From: "Aaron K. Johnson" <akjmicro@comcast.net
>
> Tuners, (maybe Kraig Grady is the expert on this?):
>
> Are there any known precedents for 12-pitch-to-the-octave CPS's that would
> work on a standard keyboard...I'm interested in exploring them in a live
> improvisational setting.....
>
> Best,
> Aaron.
>

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

🔗Aaron K. Johnson <akjmicro@comcast.net>

On Sunday 28 December 2003 01:15 am, kraig grady wrote:
> Hi Aaron!
> There is none off hand with the 1-3-5-7-9 double dekany coming in closest
> with 14 notes. there is also the stellate hexany at 13 notes also. Although
> when i was work exclusively in such animals i would tune up two hexanies
> opposite each other in the eikosany, The bewst of these (from memory) were
> hexanies like 5-7-9-11 because they are seperated by a 1-3 (things in the
> eikosany so often work that way). there is also the 1-5-7-11 hexany
> seperated by a 3-9 and being a big fan of the 1-3-7-9-11-15 eikosany (since
> it falls into a 22 tone scale so easily you have the 1-7-11-15 hexanies a
> 3-9 apart.
>
> although for the most part i would use my centaur tuning
> http://anaphoria.com/centaur.html

Hi Kraig,

Yes...I've used Centaur more than once--nice tuning, and has also some useable
tempered sounding triads to boot (like the A major triad).

When I want to get more non-western, I like what you've done with the CPS
scales....for instance what did you use for that spacious beat-filled
textural drone-like mp3 sample from your new album?

By 'tuning hexanies opposite' I assume you mean 1-3-5-7, and 1-1/3-1/5-1/7 and
octave normalized, no?

And by 'seperated by 1-3' you mean 'a perfect fifth apart', correct?

I'm finding myself attracted to active, beating textures that I coud use to
slowly morph--you know, drone like things. Harmonics 12 thru 24 works, but I
want to keep exploring other options for the standard keyboard before giving
up and building stuff....

Best,
Aaron.

🔗kraig grady <kraiggrady@anaphoria.com>

> Hi Aaron!

>
> From: "Aaron K. Johnson" <akjmicro@comcast.net>
>
>
> When I want to get more non-western, I like what you've done with the CPS
> scales....for instance what did you use for that spacious beat-filled
> textural drone-like mp3 sample from your new album?

these are all from the scales of mt. meru of which I have only used the third one. The second one following the fibonacci series is pretty much unexxplored and would produce similar effects. I think it forms scales at 11 places but you can still take it up to 12 which mean you would have an alternate. So of the latter ones also form MOS at 12 But i can't figure it out right at this moment

>
>
> By 'tuning hexanies opposite' I assume you mean 1-3-5-7, and 1-1/3-1/5-1/7 and
> octave normalized, no?

in a hexany these two would come out the same. The ones i picked though occur on opposite sides of eikosanies

>
>
> And by 'seperated by 1-3' you mean 'a perfect fifth apart', correct?

yes i was just trying to show the different factors work each pair of hexanies are always seperated by the two factors not used in the hexany. If one wanted two 1-3-5-7 hexanies they occur a 9-11 apart. So i was just picking the ones that had a 3/2 either between 1-3 or 3-9. of of course you can always play with 13 limite hexanies a 3/2 apart which is virgin territory

>
>
> I'm finding myself attracted to active, beating textures that I coud use to
> slowly morph--you know, drone like things. Harmonics 12 thru 24 works, but I
> want to keep exploring other options for the standard keyboard before giving
> up and building stuff....

For beating material , mt meru is the way to go!!!

>
>
> Best,
> Aaron.
>

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

🔗Aaron K. Johnson <akjmicro@comcast.net>

Kraig---

I discovered an old McLaren post, and found 2 examples of a 12-tone CPS. I'm
sure there are more----

Below is the quote from the post:

#####################
" Another collapsed Wilson CPS formed by a set of generators most of which are
multiples of one another--in this case, 4 out of 8 from [1,2,3,4,5,6,7,8]:
0: 1/1 000.0000
1: 35/32 155.1396
2: 9/8 203.9100
3: 315/256 359.0498
4: 5/4 386.3139
5: 21/16 470.7811
6: 45/32 590.2239
7: 3/2 701.9553
8: 105/64 857.0950
9: 7/4 968.8264
10: 15/8 1088.269
11: 63/32 1172.736

For a change of pace, here's an oddball Wilson 4 out of 8--but NOT a
hebdomekontany. Because the first 8 integers are chosen as generators, most
of the generators are factors of other generators. As a result there are only
12 unique pitches rather than the usual 70. Wilson CPS 4,8 [1,2,3,4,5,6,7,8]:
1: 35/32 155.1396
2: 9/8 203.9100
3: 315/256 359.0498
4: 5/4 386.3139
5: 21/16 470.7811
6: 45/32 590.2239
7: 3/2 701.9553
8: 105/64 857.0950
9: 7/4 968.8264
10: 15/8 1088.269
11: 63/32 1172.736
12: 2/1 1200.000 "

Anyway, can you send me the "Mt. Meru" tuning as a .scl file? Or is it on your
site? I'll look.......

BTW, it appears you are wrong about 2,4 [1,3,5,7] and 2,4 [1,1/3,1/5,1/7]
coming out the same:
| 2,4 [1, 1/3, 1/5, 1/7] (utonal)
0: 1/1 0.000 unison, perfect prime
1: 16/15 111.731 minor diatonic semitone
2: 8/7 231.174 septimal whole tone
3: 4/3 498.045 perfect fourth
4: 32/21 729.219 wide fifth
5: 8/5 813.686 minor sixth
6: 64/35 1044.860 septimal neutral seventh
7: 2/1 1200.000 octave
| 2,4 [1, 3, 5, 7] (otonal)
0: 1/1 0.000 unison, perfect prime
1: 35/32 155.140 septimal neutral second
2: 5/4 386.314 major third
3: 21/16 470.781 narrow fourth
4: 3/2 701.955 perfect fifth
5: 7/4 968.826 harmonic seventh
6: 15/8 1088.269 classic major seventh
7: 2/1 1200.000 octave

or am I missing something? Yes, I know they are symmetrical about 1/1....is
that what you mean?

Best,
Aaron

On Sunday 28 December 2003 07:18 pm, kraig grady wrote:
> > Hi Aaron!
> >
> >
> >
> >
> > From: "Aaron K. Johnson" <akjmicro@comcast.net>
> >
> >
> > When I want to get more non-western, I like what you've done with the CPS
> > scales....for instance what did you use for that spacious beat-filled
> > textural drone-like mp3 sample from your new album?
>
> these are all from the scales of mt. meru of which I have only used the
> third one. The second one following the fibonacci series is pretty much
> unexxplored and would produce similar effects. I think it forms scales at
> 11 places but you can still take it up to 12 which mean you would have an
> alternate. So of the latter ones also form MOS at 12 But i can't figure it
> out right at this moment
>
> > By 'tuning hexanies opposite' I assume you mean 1-3-5-7, and
> > 1-1/3-1/5-1/7 and octave normalized, no?
>
> in a hexany these two would come out the same. The ones i picked though
> occur on opposite sides of eikosanies
>
> > And by 'seperated by 1-3' you mean 'a perfect fifth apart', correct?
>
> yes i was just trying to show the different factors work each pair of
> hexanies are always seperated by the two factors not used in the hexany. If
> one wanted two 1-3-5-7 hexanies they occur a 9-11 apart. So i was just
> picking the ones that had a 3/2 either between 1-3 or 3-9. of of course you
> can always play with 13 limite hexanies a 3/2 apart which is virgin
> territory
>
> > I'm finding myself attracted to active, beating textures that I coud use
> > to slowly morph--you know, drone like things. Harmonics 12 thru 24 works,
> > but I want to keep exploring other options for the standard keyboard
> > before giving up and building stuff....
>
> For beating material , mt meru is the way to go!!!
>
> > Best,
> > Aaron.
>
> -- -Kraig Grady
> North American Embassy of Anaphoria Island
> http://www.anaphoria.com
> The Wandering Medicine Show
> KXLU 88.9 FM WED 8-9PM PST
>
>
> You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - unsubscribe from the tuning group.
> tuning-nomail@yahoogroups.com - put your email message delivery on hold
> for the tuning group. tuning-digest@yahoogroups.com - change your
> subscription to daily digest mode. tuning-normal@yahoogroups.com - change
> your subscription to individual emails. tuning-help@yahoogroups.com -
> receive general help information.
>
>
>
> Yahoo! Groups Links
>
> To visit your group on the web, go to:
> /tuning/
>
> To unsubscribe from this group, send an email to:
> tuning-unsubscribe@yahoogroups.com
>
> Your use of Yahoo! Groups is subject to:
> http://docs.yahoo.com/info/terms/

--
OCEAN, n. A body of water occupying about two-thirds of a world made
for man -- who has no gills. -Ambrose Bierce 'The Devils Dictionary'

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:

/tuning/topicId_50494.html#50532

> >
>
> Hi Aaron!
> There is none off hand with the 1-3-5-7-9 double dekany coming in
closest with 14 notes. there is also the stellate hexany at 13 notes
also. Although when i was work exclusively in such animals i would
tune up two hexanies opposite each other in the eikosany, The bewst
of these (from memory) were hexanies like 5-7-9-11 because they are
seperated by a 1-3 (things in the eikosany so often work that way).
there is also the 1-5-7-11 hexany seperated by a 3-9 and being a big
fan of the 1-3-7-9-11-15
> eikosany (since it falls into a 22 tone scale so easily you have
the 1-7-11-15
> hexanies a 3-9 apart.
>
> although for the most part i would use my centaur tuning
http://anaphoria.com/centaur.html
>

***I believe there is a "Stellated Hexany" scale in the Scala archive
that uses 12 notes per octave. I used it for my piece _Violahexy._
However, I am not at home at the moment, so I don't have recourse to
specific details...

J. Pehrson

🔗kraig grady <kraiggrady@anaphoria.com>

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Aaron K. Johnson" <akjmicro@c...>
wrote:
>
> Kraig---
>
> I discovered an old McLaren post,

[...]

> BTW, it appears you are wrong about 2,4 [1,3,5,7] and 2,4
[1,1/3,1/5,1/7]
> coming out the same:
> | 2,4 [1, 1/3, 1/5, 1/7] (utonal)
> 0: 1/1 0.000 unison, perfect prime
> 1: 16/15 111.731 minor diatonic semitone
> 2: 8/7 231.174 septimal whole tone
> 3: 4/3 498.045 perfect fourth
> 4: 32/21 729.219 wide fifth
> 5: 8/5 813.686 minor sixth
> 6: 64/35 1044.860 septimal neutral seventh
> 7: 2/1 1200.000 octave
> | 2,4 [1, 3, 5, 7] (otonal)
> 0: 1/1 0.000 unison, perfect prime
> 1: 35/32 155.140 septimal neutral second
> 2: 5/4 386.314 major third
> 3: 21/16 470.781 narrow fourth
> 4: 3/2 701.955 perfect fifth
> 5: 7/4 968.826 harmonic seventh
> 6: 15/8 1088.269 classic major seventh
> 7: 2/1 1200.000 octave
>
> or am I missing something?

Aaron, any post should stand or fall on its own merit, but when in
doubt, especially when it concerns Wilson's constructs, it's fairly
safe to assume Kraig is right and McLaren is wrong.

Hexanies only have six pitches to the octave,
not seven! And yes, the two come out the same -- depending on how you
calculate them, they may be transpositions (or modes) of one another,
or absolutely the same -- CPSs are not defined with respect to a
fixed tonal center the way Partch diamonds, etc. are. -- so really I
would unequivocally say "yes, they're the same".

I have a 'Gentle Introduction to CPSs' up somewhere . . .

🔗Carl Lumma <ekin@lumma.org>

>> BTW, it appears you are wrong about 2,4 [1,3,5,7] and
>> 2,4 [1,1/3,1/5,1/7] coming out the same:
>>
>> | 2,4 [1, 1/3, 1/5, 1/7] (utonal)
>> 0: 1/1 0.000 unison, perfect prime
>> 1: 16/15 111.731 minor diatonic semitone
>> 2: 8/7 231.174 septimal whole tone
>> 3: 4/3 498.045 perfect fourth
>> 4: 32/21 729.219 wide fifth
>> 5: 8/5 813.686 minor sixth
>> 6: 64/35 1044.860 septimal neutral seventh
>> 7: 2/1 1200.000 octave
>> | 2,4 [1, 3, 5, 7] (otonal)
>> 0: 1/1 0.000 unison, perfect prime
>> 1: 35/32 155.140 septimal neutral second
>> 2: 5/4 386.314 major third
>> 3: 21/16 470.781 narrow fourth
>> 4: 3/2 701.955 perfect fifth
>> 5: 7/4 968.826 harmonic seventh
>> 6: 15/8 1088.269 classic major seventh
>> 7: 2/1 1200.000 octave
>>
>> or am I missing something?
>
>Hexanies only have six pitches to the octave,
>not seven!

These have 6 -- don't count the octave twice!

>And yes, the two come out the same -- depending on how you
>calculate them, they may be transpositions (or modes) of one
>another,

Indeed; the above appears to be Scala output.

There's another McLaren post about otonal vs. utonal hexanies.
Hexanies are symmetrical about the o/u thang, so whenever you
see "otonal hexany" be on your guard.

Since the two above scales are perfect octave inversions of
one another, they clearly have the same shape on the lattice,
merely reflected about the 1/1. That said, they are obviously
different in pitch space, so one could combine them into a
12-note, 'double hexany' scale.

-Carl

🔗Aaron K. Johnson <akjmicro@comcast.net>

On Tuesday 30 December 2003 04:42 pm, Carl Lumma wrote:
> >> BTW, it appears you are wrong about 2,4 [1,3,5,7] and
> >>
> >> 2,4 [1,1/3,1/5,1/7] coming out the same:
> >> | 2,4 [1, 1/3, 1/5, 1/7] (utonal)
> >>
> >> 0: 1/1 0.000 unison, perfect prime
> >> 1: 16/15 111.731 minor diatonic semitone
> >> 2: 8/7 231.174 septimal whole tone
> >> 3: 4/3 498.045 perfect fourth
> >> 4: 32/21 729.219 wide fifth
> >> 5: 8/5 813.686 minor sixth
> >> 6: 64/35 1044.860 septimal neutral seventh
> >> 7: 2/1 1200.000 octave
> >>
> >> | 2,4 [1, 3, 5, 7] (otonal)
> >>
> >> 0: 1/1 0.000 unison, perfect prime
> >> 1: 35/32 155.140 septimal neutral second
> >> 2: 5/4 386.314 major third
> >> 3: 21/16 470.781 narrow fourth
> >> 4: 3/2 701.955 perfect fifth
> >> 5: 7/4 968.826 harmonic seventh
> >> 6: 15/8 1088.269 classic major seventh
> >> 7: 2/1 1200.000 octave
> >>
> >> or am I missing something?
> >
> >Hexanies only have six pitches to the octave,
> >not seven!
>
> These have 6 -- don't count the octave twice!

Yeah, but I also realized that this is Scala output--one should 'delete 0' to
make a theoretically correct CPS.

I have to say that I'm with McLaren when it comes down to whether something is
usable or not is more important to me than it be theoretically correct....

But yes, one should know the definition of a true CPS anyway. And it is nice
that getting rid of 1/1 makes the scale 'less gravitational'.

> >And yes, the two come out the same -- depending on how you
> >calculate them, they may be transpositions (or modes) of one
> >another,
>
> Indeed; the above appears to be Scala output.
>
> There's another McLaren post about otonal vs. utonal hexanies.
> Hexanies are symmetrical about the o/u thang, so whenever you
> see "otonal hexany" be on your guard.

Who cares if they are symmetrical? They are different pitches, no?

> Since the two above scales are perfect octave inversions of
> one another, they clearly have the same shape on the lattice,
> merely reflected about the 1/1. That said, they are obviously
> different in pitch space, so one could combine them into a
> 12-note, 'double hexany' scale.

Yes, that's what I'm interested in....

I don't get why anyone would care if they are 'the same shape' if they are a
different set of pitches, and thus have a different musical effect.

Another example of theory trumping musical reality. Yuck.

It seems that all this disagreement comes from the semantics of the word
'same'. Some people here contend that a thing is the 'same' if is the
reflection of another pitch set. Clearly, it is not. Is 4/3 the same sound as
3/2?

Arguing about these kinds of things is an utter waste of time, IMO. Searching
for musically interesting structures that are usble on a standard 12
keyboard, OTOH.....that's a worthwhile search!

Best,
Aaron.

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> BTW, it appears you are wrong about 2,4 [1,3,5,7] and
> >> 2,4 [1,1/3,1/5,1/7] coming out the same:
> >>
> >> | 2,4 [1, 1/3, 1/5, 1/7] (utonal)
> >> 0: 1/1 0.000 unison, perfect prime
> >> 1: 16/15 111.731 minor diatonic semitone
> >> 2: 8/7 231.174 septimal whole tone
> >> 3: 4/3 498.045 perfect fourth
> >> 4: 32/21 729.219 wide fifth
> >> 5: 8/5 813.686 minor sixth
> >> 6: 64/35 1044.860 septimal neutral seventh
> >> 7: 2/1 1200.000 octave
> >> | 2,4 [1, 3, 5, 7] (otonal)
> >> 0: 1/1 0.000 unison, perfect prime
> >> 1: 35/32 155.140 septimal neutral second
> >> 2: 5/4 386.314 major third
> >> 3: 21/16 470.781 narrow fourth
> >> 4: 3/2 701.955 perfect fifth
> >> 5: 7/4 968.826 harmonic seventh
> >> 6: 15/8 1088.269 classic major seventh
> >> 7: 2/1 1200.000 octave
> >>
> >> or am I missing something?
> >
> >Hexanies only have six pitches to the octave,
> >not seven!
>
> These have 6 -- don't count the octave twice!

Try again Carl. These have 7, or 8 if you count the octave as well as
the unison. The first note is numbered 0! Neither note 0 nor note 7
belong in either of these hexanies. Transposition is arbitrary, but
it's most common to transpose so that one of the 6 notes is labeled
1/1.

> There's another McLaren post about otonal vs. utonal hexanies.

Yes, I know he's written erroneous material about this before.

🔗Carl Lumma <ekin@lumma.org>

[Paul]
>> >> BTW, it appears you are wrong about 2,4 [1,3,5,7] and
>> >> 2,4 [1,1/3,1/5,1/7] coming out the same:
>> >>
>> >> | 2,4 [1, 1/3, 1/5, 1/7] (utonal)
>> >> 0: 1/1 0.000 unison, perfect prime
>> >> 1: 16/15 111.731 minor diatonic semitone
>> >> 2: 8/7 231.174 septimal whole tone
>> >> 3: 4/3 498.045 perfect fourth
>> >> 4: 32/21 729.219 wide fifth
>> >> 5: 8/5 813.686 minor sixth
>> >> 6: 64/35 1044.860 septimal neutral seventh
>> >> 7: 2/1 1200.000 octave
>> >> | 2,4 [1, 3, 5, 7] (otonal)
>> >> 0: 1/1 0.000 unison, perfect prime
>> >> 1: 35/32 155.140 septimal neutral second
>> >> 2: 5/4 386.314 major third
>> >> 3: 21/16 470.781 narrow fourth
>> >> 4: 3/2 701.955 perfect fifth
>> >> 5: 7/4 968.826 harmonic seventh
>> >> 6: 15/8 1088.269 classic major seventh
>> >> 7: 2/1 1200.000 octave
>> >>
>> >> or am I missing something?
>> >
>> >Hexanies only have six pitches to the octave,
>> >not seven!
>>
>> These have 6 -- don't count the octave twice!
>
>Try again Carl. These have 7, or 8 if you count the octave as well
>as the unison.

Mea culpa!

[Manuel/MMM...]
>You need to do "delete 0" after making the CPS. It's in the help,
>but I'll improve the dialog to prevent that people forget this.

Looks like that's what Brian missed. The correct output is
then...

0: 1/1 0.000 unison, perfect prime
1: 7/6 266.871 septimal minor third
2: 5/4 386.314 major third
3: 35/24 653.185 septimal semi-diminished fifth
4: 5/3 884.359 major sixth, BP sixth
5: 7/4 968.826 harmonic seventh
6: 2/1 1200.000 octave

...for either 2|4 [1 3 5 7] or [1 1/3 1/5 1/7].

[Aaron]
>I have to say that I'm with McLaren when it comes down to whether
>something is usable or not is more important to me than it be
>theoretically correct....

I think it's important not to make false attributions. If a scale
sounds a certain way but isn't a CPS, one shouldn't call it a CPS.

>Who cares if they are symmetrical? They are different pitches, no?
//
>I don't get why anyone would care if they are 'the same shape' if
>they are a different set of pitches, and thus have a different
>musical effect.

Because then they are simply transpositions of one another, and
the variable is the interval that separates them. Why pick this
particular interval?

>Arguing about these kinds of things is an utter waste of time, IMO.
>Searching for musically interesting structures that are usble on a
>standard 12 keyboard, OTOH.....that's a worthwhile search!

Uh oh -- looks like McLaren's gotten to you. How does one conduct
such a search? Trying all possible 12-tone scales is clearly
impossible. Thus, some theoretical help is needed.

-Carl

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Aaron K. Johnson" <akjmicro@c...>
wrote:

> > There's another McLaren post about otonal vs. utonal hexanies.
> > Hexanies are symmetrical about the o/u thang, so whenever you
> > see "otonal hexany" be on your guard.
>
> Who cares if they are symmetrical? They are different pitches, no?

No. It's a mistake to treat, for example, "3*5" as the pitch 15/8 or
15/1, and "1/3*1/5" as the pitch 16/15 or 8/15 or 1/15, relative to a
common fixed 1/1. The generating factors of a CPS are only there to
give you the right intervallic relationships between the tones, not
to set a pitch level relative to a given tonic (which is against the
whole point) or to another CPS. But as you say, a misunderstanding of
a theoretical concept can often be as creatively fruitful as its
successful application.

> I don't get why anyone would care if they are 'the same shape' if
they are a
> different set of pitches, and thus have a different musical effect.

How can you say they have a different musical effect? Do you really
have such a strong degree of absolute pitch that transposing
something to a different key gives it a different musical effect for
you?

> Another example of theory trumping musical reality. Yuck.

Hmm . . . what do you have against keeping good theoretical concepts
straight, and then doing whatever you want in musical practice?

> It seems that all this disagreement comes from the semantics of the
word
> 'same'. Some people here contend that a thing is the 'same' if is
the
> reflection of another pitch set. Clearly, it is not. Is 4/3 the
same sound as
> 3/2?

That's not reflection. 4/3 vs. 3/4 would be reflection. But as to 4/3
vs. 3/2 --

Either:

Each is only a single pitch, but one is a major second lower than the
other. If transposing something by a major second makes a big
difference to you, fine -- it doesn't to me.

Or:

Each is a dyad (in which case some of us would have written '4:3'
and '3:2', but one corresponds to the 2nd and 3rd members of a
harmonic (or subharmonic) series, while the other corresponds to the
3rd and 4th members of a harmonic (or subharmonic) series.

> Arguing about these kinds of things is an utter waste of time, IMO.
Searching
> for musically interesting structures that are usble on a standard
12
> keyboard, OTOH.....that's a worthwhile search!

Well then, let the search continue! I will help you to the extent
that I can. But I don't think this dismissive attitude is helpful, as
it can lead to you lose sight of possibilities that truly do sound
different -- for example, two hexanies configured in other, equally
valid both theoretically and musically, ways relative to one another.

Keep your mind and ears open,
Paul

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Carl Lumma <ekin@lumma.org>

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "Aaron K. Johnson" <akjmicro@c...>

/tuning/topicId_50494.html#50720

> Arguing about these kinds of things is an utter waste of time, IMO.
Searching
> for musically interesting structures that are usble on a standard
12
> keyboard, OTOH.....that's a worthwhile search!
>
> Best,
> Aaron.

***Hi Aaron,

When I get back from Michigan, I'll post the 12-note hexany-derived
scale that I used for my Viola and electronic piece _Violahexy_. It
will be interesting to discover where it deviates from "hexany
orthodoxy..."

And, yes, for all the doubters, I consider the use of *one* performer
and electronics a *very* viable, teachable and personal way to convey
the mysteries of microtonality and I will continue to create pieces
in this format.

Joseph Pehrson

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> ***Hi Aaron,
>
> When I get back from Michigan, I'll post the 12-note hexany-derived
> scale that I used for my Viola and electronic piece _Violahexy_.
It
> will be interesting to discover where it deviates from "hexany
> orthodoxy..."

No need to -- Google helped me find it right away, even faster than
searching the archives:

/tuning/topicId_20628.html#20628

As Kraig pointed out, the stellated hexany normally has 13 pitches,
not 12. The lattice of the stellated hexany is an octahedron (the
hexany itself) with a tetrahedron protruding from each of its 8 faces.

If I lattice your _Violahexy_ scale in the 7-limit lattice, though, I
get this (as always, if you're viewing this on the Web, click
on "Reply" to see it correctly):

35/32----105/64
,'/ \`. ,'/ \`.
5/4-/---\15/8-/---\45/32
/|\/ \/|\/ \/|\
/ |/\ /\|/\ /\| \
/ 7/4------21/16-----63/32\
/,' `.\ /,' `.\ /,' `.\
1/1-------3/2-------9/8------27/16

Very different -- this structure actually contains *two* hexanies
(not just one) which share 2 notes in common, and then there are 2
additional pitches forming additional consonances. This is one of the
great multiplicity of 12-note scales with 2 hexanies that I was
referring to in my original reply to Aaron J.

🔗Carl Lumma <ekin@lumma.org>

🔗Paul Erlich <paul@stretch-music.com>

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_50494.html#50864

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
>
> > ***Hi Aaron,
> >
> > When I get back from Michigan, I'll post the 12-note hexany-
derived
> > scale that I used for my Viola and electronic piece _Violahexy_.
> It
> > will be interesting to discover where it deviates from "hexany
> > orthodoxy..."
>
> No need to -- Google helped me find it right away, even faster than
> searching the archives:
>
> /tuning/topicId_20628.html#20628
>

***Wow! Fast work, Paul!

> As Kraig pointed out, the stellated hexany normally has 13 pitches,
> not 12. The lattice of the stellated hexany is an octahedron (the
> hexany itself) with a tetrahedron protruding from each of its 8
faces.
>
> If I lattice your _Violahexy_ scale in the 7-limit lattice, though,
I
> get this (as always, if you're viewing this on the Web, click
> on "Reply" to see it correctly):
>
>
> 35/32----105/64
> ,'/ \`. ,'/ \`.
> 5/4-/---\15/8-/---\45/32
> /|\/ \/|\/ \/|\
> / |/\ /\|/\ /\| \
> / 7/4------21/16-----63/32\
> /,' `.\ /,' `.\ /,' `.\
> 1/1-------3/2-------9/8------27/16
>
> Very different -- this structure actually contains *two* hexanies
> (not just one) which share 2 notes in common, and then there are 2
> additional pitches forming additional consonances. This is one of
the
> great multiplicity of 12-note scales with 2 hexanies that I was
> referring to in my original reply to Aaron J.

***This scale really produces a nice lattice, though, doesn't it?
Nothing is off to the side or into "outer space... " :)

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

/tuning/topicId_50494.html#50916

>> > No need to -- Google helped me find it right away, even faster
than
> > searching the archives:
> >
> > /tuning/topicId_20628.html#20628
> >
>
>
> > As Kraig pointed out, the stellated hexany normally has 13
pitches,
> > not 12. The lattice of the stellated hexany is an octahedron (the
> > hexany itself) with a tetrahedron protruding from each of its 8
> faces.
> >
> > If I lattice your _Violahexy_ scale in the 7-limit lattice,
though,
> I
> > get this (as always, if you're viewing this on the Web, click
> > on "Reply" to see it correctly):
> >
> >
> > 35/32----105/64
> > ,'/ \`. ,'/ \`.
> > 5/4-/---\15/8-/---\45/32
> > /|\/ \/|\/ \/|\
> > / |/\ /\|/\ /\| \
> > / 7/4------21/16-----63/32\
> > /,' `.\ /,' `.\ /,' `.\
> > 1/1-------3/2-------9/8------27/16
> >
> > Very different -- this structure actually contains *two* hexanies
> > (not just one) which share 2 notes in common, and then there are
2
> > additional pitches forming additional consonances. This is one of
> the
> > great multiplicity of 12-note scales with 2 hexanies that I was
> > referring to in my original reply to Aaron J.
>

***Oh... just as a point of clarification then. It's correct to say
that the _Violahexy_ scale is *not* a stellated hexany but, instead,
*two* hexanies with a two pitch "fudge factor..." ??

Thanks!

Joseph

🔗Carl Lumma <ekin@lumma.org>

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_50494.html#50864
>
>
> > --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
> wrote:
> >
> > > ***Hi Aaron,
> > >
> > > When I get back from Michigan, I'll post the 12-note hexany-
> derived
> > > scale that I used for my Viola and electronic piece
_Violahexy_.
> > It
> > > will be interesting to discover where it deviates from "hexany
> > > orthodoxy..."
> >
> > No need to -- Google helped me find it right away, even faster
than
> > searching the archives:
> >
> > /tuning/topicId_20628.html#20628
> >
>
> ***Wow! Fast work, Paul!
>
>
>
> > As Kraig pointed out, the stellated hexany normally has 13
pitches,
> > not 12. The lattice of the stellated hexany is an octahedron (the
> > hexany itself) with a tetrahedron protruding from each of its 8
> faces.
> >
> > If I lattice your _Violahexy_ scale in the 7-limit lattice,
though,
> I
> > get this (as always, if you're viewing this on the Web, click
> > on "Reply" to see it correctly):
> >
> >
> > 35/32----105/64
> > ,'/ \`. ,'/ \`.
> > 5/4-/---\15/8-/---\45/32
> > /|\/ \/|\/ \/|\
> > / |/\ /\|/\ /\| \
> > / 7/4------21/16-----63/32\
> > /,' `.\ /,' `.\ /,' `.\
> > 1/1-------3/2-------9/8------27/16
> >
> > Very different -- this structure actually contains *two* hexanies
> > (not just one) which share 2 notes in common, and then there are
2
> > additional pitches forming additional consonances. This is one of
> the
> > great multiplicity of 12-note scales with 2 hexanies that I was
> > referring to in my original reply to Aaron J.
>
>
> ***This scale really produces a nice lattice, though, doesn't it?
> Nothing is off to the side or into "outer space... " :)
>
> JP

Yup -- it's also very 'otonally oriented' with 3 otonal tetrads
(4:5:6:7s) but only 1 utonal tetrad (1/7:1/6:1/5:1/4).

🔗Carl Lumma <ekin@lumma.org>

🔗Paul Erlich <paul@stretch-music.com>

🔗czhang23@aol.com

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗wallyesterpaulrus <paul@stretch-music.com>

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

/tuning/topicId_50494.html#50940

> >> >
> >> > 35/32----105/64
> >> > ,'/ \`. ,'/ \`.
> >> > 5/4-/---\15/8-/---\45/32
> >> > /|\/ \/|\/ \/|\
> >> > / |/\ /\|/\ /\| \
> >> > / 7/4------21/16-----63/32\
> >> > /,' `.\ /,' `.\ /,' `.\
> >> > 1/1-------3/2-------9/8------27/16
> >
> >
> >***Oh... just as a point of clarification then. It's correct to
say
> >that the _Violahexy_ scale is *not* a stellated hexany but,
instead,
> >*two* hexanies with a two pitch "fudge factor..." ??
>
> Howabout: "a connected structure with two hexanies plus two
> additional tones"?
>
> -Carl

***That sounds pretty goooood... to me.. I'd better stop calling it
a "stellated hexany scale" all over the place...

Curiously, though... the "1/1" seems to be one of the "additional"
pitches...

Isn't that a bit weird that it comes out that way? Or is than in
keeping with the "nature" of hexanies...

thanks!

🔗wallyesterpaulrus <paul@stretch-music.com>

🔗Carl Lumma <ekin@lumma.org>

🔗czhang23@aol.com

In a message dated 2004:01:06 10:44:21 AM, ekin@lumma.org writes:

>>> Howabout: "a connected structure with two hexanies plus two
>>> additional tones"?

ok, here's a _professional a la gonzo_ linguamangler's buncha attempts:

- augmented double hexany

- double loaded hex

---|-----|--------|-------------|---------------------|
Hanuman Zhang, musical mad scientist
"Space is a practiced place." -- Michel de Certeau
"Space is the Place for the Human Race." -- William S. Burroughs

"... simple, chaotic, anarchic and menacing.... This is what people of today
have lost and need most - the ability to experience permanent bodily and
mental ecstasy, to be a receiving station for messages howling by on the ether from
other worlds and nonhuman entities, those peculiar short-wave messages which
come in static-free in the secret pleasure center in the brain." - Slava Ranko
(Donald L. Philippi)

The German word for "noise" _Geräusch_ is derived from _rauschen_ "the
sound of the wind," related to _Rausch_ "ecstasy, intoxication" hinting at some
of the possible aesthetic, bodily effects of noise in music. In Japanese
Romaji: _uchu_ = "universe"... _uchoten_ = "ecstasty," "rapture"..._uchujin_ =
[space] alien!

"When you're trying to do something you should feel absolutely alone, like a
spark in the blackness of the universe."-Xenakis

"For twenty-five centuries, Western knowledge has tried to look upon the
world. It has failed to understand that the world is not for the beholding. It
is for the hearing. It is not legible, but audible. ... Music is a herald,
for change is inscribed in noise faster than it transforms society. ...
Listening to music is listening to all noise, realizing that its appropriation and
control is a reflection of power, that is essentially political." - Jacques
Attali, _Noise: The Political Economy of Music_

"The sky and its stars make music in you." - Dendera, Egypt wall
inscription

"Sound as an isolated object of reproduction, call it our collective memory
bank... Any sound can be you." - DJ Spooky that Subliminal Kid (a.k.a. Paul D.
Miller)

"Overhead, without any fuss, the stars were going out."
--Arthur C. Clarke, _The Nine Billion Names of God_

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

/tuning/topicId_50494.html#51092

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
>
> > Curiously, though... the "1/1" seems to be one of
the "additional"
> > pitches...
> >
> > Isn't that a bit weird that it comes out that way? Or is than in
> > keeping with the "nature" of hexanies...
>
> I would say that, when dealing with anything short of full-fledged
> tonality (perhaps in some varieties we don't yet know about), and
> *especially* when dealing with CPS scales like hexanies, the choice
> of which note to label "1/1" is arbitrary. What matters is what
> intervals and chords are available in the scale, and that doesn't
> change even if you choose to label a different note as "1/1" (and
of
> course calculate the other pitch-ratios accordingly, by applying
the
> same transposition to them as you did to get the new "1/1" to
> be "1/1") . . .

***TX!

CPS on a standard keyboard

🔗Aaron K. Johnson <akjmicro@comcast.net>

🔗Dave Keenan <d.keenan@bigpond.net.au>

🔗kraig grady <kraiggrady@anaphoria.com>

🔗Aaron K. Johnson <akjmicro@comcast.net>

🔗kraig grady <kraiggrady@anaphoria.com>

🔗Aaron K. Johnson <akjmicro@comcast.net>

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗kraig grady <kraiggrady@anaphoria.com>

🔗Paul Erlich <paul@stretch-music.com>

🔗Carl Lumma <ekin@lumma.org>

🔗Aaron K. Johnson <akjmicro@comcast.net>

🔗Paul Erlich <paul@stretch-music.com>

🔗Carl Lumma <ekin@lumma.org>

🔗Paul Erlich <paul@stretch-music.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Carl Lumma <ekin@lumma.org>

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗Paul Erlich <paul@stretch-music.com>

🔗Carl Lumma <ekin@lumma.org>

🔗Paul Erlich <paul@stretch-music.com>

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗Carl Lumma <ekin@lumma.org>

🔗Paul Erlich <paul@stretch-music.com>

🔗Carl Lumma <ekin@lumma.org>

🔗Paul Erlich <paul@stretch-music.com>

🔗czhang23@aol.com

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗wallyesterpaulrus <paul@stretch-music.com>

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗wallyesterpaulrus <paul@stretch-music.com>

🔗Carl Lumma <ekin@lumma.org>

🔗czhang23@aol.com

🔗Joseph Pehrson <jpehrson@rcn.com>