Masses of asses?

Would chords such as 0--23--35--49 or 0--23--35--58 in the 72-et be considered 9-limit asses? Using the approximations of the 72-et, or in fact in 225/224 planar temperament terms, these have 9-odd-limit intervals between each chord element. Would a survey of 72-et "asses" of this sort be of interest?

I posted the 8-tone scale consisting of the chords 0--23--35--49 and
7--30--42--65 to the list a while back, and am thinking of actually writing something in it.

>Would chords such as 0--23--35--49 or 0--23--35--58 in the 72-et
>be considered 9-limit asses? Using the approximations of the
>72-et, or in fact in 225/224 planar temperament terms, these have
>9-odd-limit intervals between each chord element.

That's one of Paul's "magic chords". I'd rather not call it an
ASS; prefer to keep these a feature of strict JI.

A while back I listened to these chords in 72-tET v. JI. I found
the difference to be nominal.

>Would a survey of 72-et "asses" of this sort be of interest?

Sure! Though we've had a lot of 73-tET lately. What about some
other temperaments (where results might offer more of a contrast
with strict JI)?

-Carl

> From: clumma <carl@lumma.org>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, January 13, 2002 8:00 PM
> Subject: [tuning] Re: Masses of asses?
>
>
> >Would a survey of 72-et "asses" of this sort be of interest?
>
> Sure! Though we've had a lot of 73-tET lately. What about some
> other temperaments (where results might offer more of a contrast
> with strict JI)?

I'm sure your finger slipped there ... you meant
"a lot of 72-tET", right?

-monz

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

In-Reply-To: <a1t8h7+3lub@eGroups.com>
gene wrote:

> Would chords such as 0--23--35--49 or 0--23--35--58 in the 72-et be
> considered 9-limit asses? Using the approximations of the 72-et, or in
> fact in 225/224 planar temperament terms, these have 9-odd-limit
> intervals between each chord element. Would a survey of 72-et "asses"
> of this sort be of interest?

I called these kind of things "pseudo-asses" before. The neutral triad is
a simple example. Strictly, for the middle "s" of "ass" to be correct,
they should be saturated. That is, no notes can be added within the
octave without introducing an interval with a higher odd limit.

There are so many of them in 72, I'm not sure what good it'd do to list
them all. Tempered lattices help to make them clear.

Graham

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

/tuning/topicId_32655.html#32663

> >Would chords such as 0--23--35--49 or 0--23--35--58 in the 72-et
> >be considered 9-limit asses? Using the approximations of the
> >72-et, or in fact in 225/224 planar temperament terms, these have
> >9-odd-limit intervals between each chord element.
>
> That's one of Paul's "magic chords". I'd rather not call it an
> ASS; prefer to keep these a feature of strict JI.
>
> A while back I listened to these chords in 72-tET v. JI. I found
> the difference to be nominal.
>
> >Would a survey of 72-et "asses" of this sort be of interest?
>
> Sure! Though we've had a lot of 73-tET lately. What about some
> other temperaments (where results might offer more of a contrast
> with strict JI)?
>
> -Carl

So, are the "magic chords" in 9-limit related to the "asses" of the
11 and 13-limit? Is it the same process, type of chord??

JP

>So, are the "magic chords" in 9-limit related to the "asses" of the
>11 and 13-limit? Is it the same process, type of chord??
>
>JP

Not really. Magic chords are only n-limit if you view some of
the dyads in them as approximations. ASSs are n-limit as they
stand. It is conceivable that viewing some of the intervals in
an ASS as approximations could even _increase_ their limit. I
think this is a case of two separate phenomena.

It all brings up the question of what makes a chord belong to an
n-limit. Until ASSs were discovered, the answer was easy: their
pitches could be represented as ratios sharing a numerary nexus
and having a maximum identity of n. This is Partch's definition.
ASSs make us ask if the real definition isn't: chords where all
the dyads between pitches can be expressed as ratios which, when
taken as pitches, would form an n-limit chord by Partch's
definition. n-adic harmonic entropy has the potential to replace
all this nonsense. . .

Does this help? Try playing with the chords in Gene's example,
and ASSs like 10:12:15:18.

-Carl

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

/tuning/topicId_32655.html#32686

> >So, are the "magic chords" in 9-limit related to the "asses" of
the
> >11 and 13-limit? Is it the same process, type of chord??
> >
> >JP
>
> Not really. Magic chords are only n-limit if you view some of
> the dyads in them as approximations. ASSs are n-limit as they
> stand.

****Hmmm. Thank's Carl, but that seems "odd" (and I don't
mean "limit"...) That would mean that "asses" are closer to Just
Intonation than the "magic chords," yes?? But they generally seemed
more "dissonant" if I recall... ?? Of course, I'm guessing that
you're also taking the *UTONAL* into account with this so, possibly
that explains it... ??

It is conceivable that viewing some of the intervals in
> an ASS as approximations could even _increase_ their limit. I
> think this is a case of two separate phenomena.
>
> It all brings up the question of what makes a chord belong to an
> n-limit. Until ASSs were discovered, the answer was easy: their
> pitches could be represented as ratios sharing a numerary nexus
> and having a maximum identity of n. This is Partch's definition.
> ASSs make us ask if the real definition isn't: chords where all
> the dyads between pitches can be expressed as ratios which, when
> taken as pitches, would form an n-limit chord by Partch's
> definition. n-adic harmonic entropy has the potential to replace
> all this nonsense. . .
>

****Oh... so this is a more "diadic" or "intervallic" interpretation
rather than just looking at the numbers of the ratios, yes??

> Does this help? Try playing with the chords in Gene's example,
> and ASSs like 10:12:15:18.
>
> -Carl

I'm hoping. I need to play with these again and get my asses into
gear, so to speak...

thanks!

JP

>>Not really. Magic chords are only n-limit if you view some of
>>the dyads in them as approximations. ASSs are n-limit as they
>>stand.
>
>****Hmmm. Thank's Carl, but that seems "odd" (and I don't
>mean "limit"...) That would mean that "asses" are closer to
>Just Intonation than the "magic chords," yes??

In a sense, yes.

>But they generally seemed more "dissonant" if I recall... ??

They won't be more or less dissonant as a rule. Try playing
some and see what you think.

>Of course, I'm guessing that you're also taking the *UTONAL*
>into account with this so, possibly that explains it... ??

The otonal/utonal distinction doesn't apply to ASSs. At least,
all the ASSs that have been discovered so far have a plane
of mirror symmetry right down the middle. Try making a "utonal"
version of 10:12:15:18 and you'll see what I mean.

>>It all brings up the question of what makes a chord belong to an
>>n-limit. Until ASSs were discovered, the answer was easy: their
>>pitches could be represented as ratios sharing a numerary nexus
>>and having a maximum identity of n. This is Partch's definition.
>>ASSs make us ask if the real definition isn't: chords where all
>>the dyads between pitches can be expressed as ratios which, when
>>taken as pitches, would form an n-limit chord by Partch's
>>definition. n-adic harmonic entropy has the potential to replace
>>all this nonsense. . .
>
>****Oh... so this is a more "diadic" or "intervallic"
>interpretation rather than just looking at the numbers of the
>ratios, yes??

Well, it so happens that the diadic definition (the ASS-including
one) is a superset of the Partchian definition. All the Partchian
n-limit chords obey the diadic def. That's why the diadic def.
is so powerful. It can explain why the Partchian chords sound
good, and why the ASSs sound good.

-Carl

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

> The otonal/utonal distinction doesn't apply to ASSs. At least,
> all the ASSs that have been discovered so far have a plane
> of mirror symmetry right down the middle.

Not so -- right on the ASS page itself,

http://www.cix.co.uk/~gbreed/ass.htm ,

you'll find the pair of 15-limit asses 3:7:15:21 and 5:7:15:35, which
are mirror-images not of themselves, but of one another. Clearly one
is more otonal than the other.

> Not so -- right on the ASS page itself,
>
> http://www.cix.co.uk/~gbreed/ass.htm ,
>
>you'll find the pair of 15-limit asses 3:7:15:21 and 5:7:15:35,
>which are mirror-images not of themselves, but of one another.
>Clearly one is more otonal than the other.

Oh yeah, I forgot about that. That's when one of the variables
is rhubarb, or something.

-Carl

BTW these are commonly found as squares within the hexanies

clumma wrote:

> > Not so -- right on the ASS page itself,
> >
> > http://www.cix.co.uk/~gbreed/ass.htm ,
> >
> >you'll find the pair of 15-limit asses 3:7:15:21 and 5:7:15:35,
> >which are mirror-images not of themselves, but of one another.
> >Clearly one is more otonal than the other.
>
> Oh yeah, I forgot about that. That's when one of the variables
> is rhubarb, or something.
>
> -Carl
>
>

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

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

in fact you could view the hexany as 3 asses with the least amount of notes!

Kraig Grady wrote:

> BTW these are commonly found as squares within the hexanies
>
>

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

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:

> BTW these are commonly found as squares within the hexanies

Wouldn't the squares be 3:7:15:35, 5:7:15:21, and 5:7:15:21? Look
carefully . . .

> clumma wrote:
>
> > > Not so -- right on the ASS page itself,
> > >
> > > http://www.cix.co.uk/~gbreed/ass.htm ,
> > >
> > >you'll find the pair of 15-limit asses 3:7:15:21 and 5:7:15:35,
> > >which are mirror-images not of themselves, but of one another.
> > >Clearly one is more otonal than the other.
> >
> > Oh yeah, I forgot about that. That's when one of the variables
> > is rhubarb, or something.
> >
> > -Carl
> >
> >
>
> -- Kraig Grady
> North American Embassy of Anaphoria island
> http://www.anaphoria.com
>
> The Wandering Medicine Show
> Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:

> in fact you could view the hexany as 3 asses with the least amount
> of notes!

How so? I only see 2 asses in the [1.3.5.7] hexany, and they're both
15-limit asses.

Are not all squares asses ?

paulerlich wrote:

> --- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
>
> > in fact you could view the hexany as 3 asses with the least amount
> > of notes!
>
> How so? I only see 2 asses in the [1.3.5.7] hexany, and they're both
> 15-limit asses.
>
>
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-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

Paul!
well i hate to break a bubble but I noticed in helmholtz about 20 years ago in his description
of the seventh chord that it could be the intersection of two triads having common tones. Hence
such structures are already implied in his work. Chords of like structure are easily formed by
taking any 4 (or more ) tones in a row on your basic eikosany lattices.

paulerlich wrote:

> --- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
>
> > BTW these are commonly found as squares within the hexanies
>
> Wouldn't the squares be 3:7:15:35, 5:7:15:21, and 5:7:15:21? Look
> carefully . . .
>
> > clumma wrote:
> >
> > > > Not so -- right on the ASS page itself,
> > > >
> > > > http://www.cix.co.uk/~gbreed/ass.htm ,
> > > >
> > > >you'll find the pair of 15-limit asses 3:7:15:21 and 5:7:15:35,
> > > >which are mirror-images not of themselves, but of one another.
> > > >Clearly one is more otonal than the other.
> > >
> > > Oh yeah, I forgot about that. That's when one of the variables
> > > is rhubarb, or something.
> > >
> > > -Carl
>

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

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., "clumma" <carl@l...> wrote:
> >Would chords such as 0--23--35--49 or 0--23--35--58 in the 72-et
> >be considered 9-limit asses? Using the approximations of the
> >72-et, or in fact in 225/224 planar temperament terms, these have
> >9-odd-limit intervals between each chord element.
>
> That's one of Paul's "magic chords". I'd rather not call it an
> ASS; prefer to keep these a feature of strict JI.

ASSs are anomalous saturated suspensions. I understand "anomalous". It
is only anomalous relative to Partch. I understand "saturated". Every
dyad in the chord is "consonant", for some definition of consonant.
But what is the definition of "suspension", and are they all really
suspensions?

By the way, "magic" chords might now be confused with chords in
"MAGIC" temperament. Maybe we need an acronym for them like "ASS".
How about Theoretical Indispensably Tempered Saturations.

Sorry, I couldn't help myself. I'm still an adolescent at heart.
Thanks Roget. :-)

Perhaps a less strained acronym would be Necessarily Tempered
Saturated Suspension. NTSS.

> A while back I listened to these chords in 72-tET v. JI. I found
> the difference to be nominal.

Does this mean they sounded about the same? ASSs and magic? or 72-tET
and JI? Or all four?

Gene:
> >Would a survey of 72-et "asses" of this sort be of interest?

Yes. Provided you give the ratios for all the dyads in each chord, in
some readable form, and not just the 72-tET degree numbers.

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

> Perhaps a less strained acronym would be Necessarily Tempered
> Saturated Suspension. NTSS.

I was calling them "consonant", as in n-consonant. Is that too simple?

> Yes. Provided you give the ratios for all the dyads in each chord, in
> some readable form, and not just the 72-tET degree numbers.

You mean show all the approximations, etc? Sounds like a lot of work; why is it necessary?

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> > Perhaps a less strained acronym would be Necessarily Tempered
> > Saturated Suspension. NTSS.
>
> I was calling them "consonant", as in n-consonant. Is that too
simple?
>

That category would include both ASSs and NTSSs (pron. nutses)
wouldn't it? Maybe ASSs should be taken to include NTSSs and then we'd
need a new category of RASSs, being Rational ASSs?

> > Yes. Provided you give the ratios for all the dyads in each chord,
in
> > some readable form, and not just the 72-tET degree numbers.
>
> You mean show all the approximations, etc? Sounds like a lot of
work; why is it necessary?

It's the best way for me to tell if I've seen them before, or to
really understand what they are. I just glase over when I see lists of
72-tET degree numbers. I expect thois goes for others too. Letter
notation for the pitches would be good too, using maximum naturals
within the standard Blackjack key when they fit within Blackjack, and
some logical extension of it when they don't.

You would only have to write the code to do it once, rather than
require every one of your readers to do it themselves (or totally
ignore your post as is more likely). Miracle temperament should be a
useful intermediary in finding the approximate ratios.

Maybe a format like

C E G A D
4 :5
5 :6
8 :9
3 :4
2 : 3
3 : 4
2 : 3
3 : 5
5 : 9
4 : 9

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> Paul!
> well i hate to break a bubble but I noticed in helmholtz about
20 years ago in his description
> of the seventh chord that it could be the intersection of two triads
having common tones. Hence
> such structures are already implied in his work. Chords of like
structure are easily formed by
> taking any 4 (or more ) tones in a row on your basic eikosany
lattices.
>

Hi Kraig,

A square (or parallelogram) in the lattice would have to have _both_
diagonals to be an ASS. The second "S" in ASS stands for saturated.
For a chord to be considered n-limit saturated, _every_ dyad has to be
n-limit consonant. I think the minor seventh chord is the most
familiar such chord, being 9-limit saturated as follows.

[Choose Message Index then Expand Messages to see correct formatting
on the web]

A C E G
5 :6
4 :5
5 :6
2 : 3
2 : 3
5 : 9

A---E
\`/.\
C---G

DK!
thanks for clearing that up!

dkeenanuqnetau wrote:

>
>
> Hi Kraig,
>
> A square (or parallelogram) in the lattice would have to have _both_
> diagonals to be an ASS. The second "S" in ASS stands for saturated.
> For a chord to be considered n-limit saturated, _every_ dyad has to be
> n-limit consonant. I think the minor seventh chord is the most
> familiar such chord, being 9-limit saturated as follows.
>
> [Choose Message Index then Expand Messages to see correct formatting
> on the web]
>
> A C E G
> 5 :6
> 4 :5
> 5 :6
> 2 : 3
> 2 : 3
> 5 : 9
>
> A---E
> \`/.\
> C---G
>

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

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

>ASSs are anomalous saturated suspensions. I understand "anomalous".
>It is only anomalous relative to Partch. I understand "saturated".
>Every dyad in the chord is "consonant", for some definition of
>consonant.

That's what makes them n-limit. Technically, "saturated" means
you can't add any more pitches to the chord without raising n.

>But what is the definition of "suspension", and are they all
>really suspensions?

No, they're not. But you can't deny it makes for a good
acronym.

>By the way, "magic" chords might now be confused with chords in
>"MAGIC" temperament. Maybe we need an acronym for them like "ASS".
>How about Theoretical Indispensably Tempered Saturations.

;)

>>A while back I listened to these chords in 72-tET v. JI. I found
>>the difference to be nominal.
>
>Does this mean they sounded about the same? ASSs and magic? or
>72-tET and JI? Or all four?

72-tET and JI sounded about the same, concordance-wise, for both of
the chords in Gene's original post. ASSs are a completely different
topic.

>>>Would a survey of 72-et "asses" of this sort be of interest?
>
>Yes. Provided you give the ratios for all the dyads in each chord,
>in some readable form, and not just the 72-tET degree numbers.

For me, and probably most others, ratios are the clearest. If one
had to use degree numbers, 72-tET would be a very good choice. I
personally don't know Blackjack or Miracle-41 from a hole in the
wall, nor do I have any particular interest in changing this
situation. Applying diatonic note names may be familiar to some,
but would IMO be theoretically wrong and ultimately confusing.

-Carl

>>But what is the definition of "suspension", and are they all
>>really suspensions?
>
>No, they're not. But you can't deny it makes for a good
>acronym.

Well, if you define "suspension" to mean any concordant group
of notes that share a common subset with an otonal or utonal
chord, then yes, they are.

But this would be a bad definition, because the ASSs clearly
stand on their own as consonances, even in diatonic music. The
10:12:15:18 (or 12:14:18:21) minor 7th is consonant in jazz,
for example. I think a better def. of "suspension" is a subset
of the (diatonic) scale which is partially dissonant (and maybe,
but not necessarily, discordant to some degree).

-Carl

David and Paul!
If you are going to accept these as consonant units, then you can treat them as tetrads and
the latter case on graham page as a hexad which mean you can use the four elements to construct a
hexany and an eikosany.
The problem seems to be though that in each hexany you have two opposite tone which are the
same pitch. examples being in the 2 out of 4 -normally notated as 2)4-
3-7-9-21, 7x9=3x21 or 2)4 3-5-9-15, 3x15=5x9. one element being a composite leads to such
redundancy.
Anyway all each hexany in turn also seems to have one "dissonant" interval but if you omit one
of these you have some 4 tone chords examples which seems to have been overlooked ?
7 9 21 63
5 9 15 45
It is too late to tabulate them all using the process above

regardless although not of much use as hexanies they might be the most consonant (if we accept
this premise) 5 tone chords possible

dkeenanuqnetau wrote:

> Hi Kraig,
>
> A square (or parallelogram) in the lattice would have to have _both_
> diagonals to be an ASS. The second "S" in ASS stands for saturated.
> For a chord to be considered n-limit saturated, _every_ dyad has to be
> n-limit consonant. I think the minor seventh chord is the most
> familiar such chord, being 9-limit saturated as follows.

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

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

In-Reply-To: <a20iqk+tmh4@eGroups.com>
Dave Keenan:
> >>But what is the definition of "suspension", and are they all
> >>really suspensions?

Carl:
> >No, they're not. But you can't deny it makes for a good
> >acronym.

Carl again:
> Well, if you define "suspension" to mean any concordant group
> of notes that share a common subset with an otonal or utonal
> chord, then yes, they are.

I didn't know about suspended dissonances when I originally made up the
name. I was going to call them "anomalous saturated chords" and used
"suspension" as a synonym for "chord".

In fact, it isn't completely inappropriate. Each ASS is a subset of a
combined otonal and utonal chord. So you could use the ASS as an
intermediate chord in between the utonal and otonal. That's similar to
the way suspended fourths came about.

D D D
F# G G
E E E
B B C

> But this would be a bad definition, because the ASSs clearly
> stand on their own as consonances, even in diatonic music.

Ah, that's what makes them anomalous!

Graham

In-Reply-To: <3C441CD5.5D331556@anaphoria.com>
Kraig wrote:

> If you are going to accept these as consonant units, then you can
> treat them as tetrads and
> the latter case on graham page as a hexad which mean you can use the
> four elements to construct a
> hexany and an eikosany.

Asses are all subsets of an Euler genus, so they may well also be (subsets
of) a CPS. Do you have a general method for this?

> The problem seems to be though that in each hexany you have two
> opposite tone which are the
> same pitch. examples being in the 2 out of 4 -normally notated as 2)4-
> 3-7-9-21, 7x9=3x21 or 2)4 3-5-9-15, 3x15=5x9. one element being a
> composite leads to such
> redundancy.

Why is this a problem?

> Anyway all each hexany in turn also seems to have one "dissonant"
> interval but if you omit one
> of these you have some 4 tone chords examples which seems to have been
> overlooked ?
> 7 9 21 63
> 5 9 15 45
> It is too late to tabulate them all using the process above

Both of these are utonal subsets, so there's nothing anomalous about them.
The first is 1/(1:3:7:9) and the other 1/(1:3:5:9)

> regardless although not of much use as hexanies they might be the most
> consonant (if we accept
> this premise) 5 tone chords possible

Wouldn't the conventional 9-limit chords have this status?

Graham

graham@microtonal.co.uk wrote:

>
>
> Asses are all subsets of an Euler genus, so they may well also be (subsets
> of) a CPS. Do you have a general method for this?

taking the two out of 4 sets

>
>
> > The problem seems to be though that in each hexany you have two
> > opposite tone which are the
> > same pitch. examples being in the 2 out of 4 -normally notated as 2)4-
> > 3-7-9-21, 7x9=3x21 or 2)4 3-5-9-15, 3x15=5x9. one element being a
> > composite leads to such
> > redundancy.
>
> Why is this a problem?
> it lacks the acoustical cues to hear it as such
>
> Both of these are utonal subsets, so there's nothing anomalous about them.
> The first is 1/(1:3:7:9) and the other 1/(1:3:5:9)

yes one should not do math at 3 in the morning. anyway was surprised no one thought of using them
in hexanies.

>
>
> > regardless although not of much use as hexanies they might be the most
> > consonant (if we accept
> > this premise) 5 tone chords possible
>
> Wouldn't the conventional 9-limit chords have this status?

these being related to these class of objects

>
>
> Graham
>

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

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

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

/tuning/topicId_32655.html#32723

> >>But what is the definition of "suspension", and are they all
> >>really suspensions?
> >
> >No, they're not. But you can't deny it makes for a good
> >acronym.
>
> Well, if you define "suspension" to mean any concordant group
> of notes that share a common subset with an otonal or utonal
> chord, then yes, they are.
>
> But this would be a bad definition, because the ASSs clearly
> stand on their own as consonances, even in diatonic music. The
> 10:12:15:18 (or 12:14:18:21) minor 7th is consonant in jazz,
> for example. I think a better def. of "suspension" is a subset
> of the (diatonic) scale which is partially dissonant (and maybe,
> but not necessarily, discordant to some degree).
>
> -Carl

Hello Carl!

Well, of course, that's the *traditional* definition of
a "suspension..." If the "suspensions" in ASSes aren't really that
at all, it would argue for a different "S-word," no?

"Substratum" is a "foundation or groundwork for something" (Webster)

Maybe something like "substrate...." etc.. It's related
to "subset..." Or something else...

JP

--- In tuning@y..., graham@m... wrote:

/tuning/topicId_32655.html#32730

> In-Reply-To: <a20iqk+tmh4@e...>
> Dave Keenan:
> > >>But what is the definition of "suspension", and are they all
> > >>really suspensions?
>
> Carl:
> > >No, they're not. But you can't deny it makes for a good
> > >acronym.
>
> Carl again:
> > Well, if you define "suspension" to mean any concordant group
> > of notes that share a common subset with an otonal or utonal
> > chord, then yes, they are.
>
> I didn't know about suspended dissonances when I originally made up
the
> name. I was going to call them "anomalous saturated chords" and
used
> "suspension" as a synonym for "chord".
>
> In fact, it isn't completely inappropriate. Each ASS is a subset
of a
> combined otonal and utonal chord. So you could use the ASS as an
> intermediate chord in between the utonal and otonal. That's
similar to
> the way suspended fourths came about.
>
> D D D
> F# G G
> E E E
> B B C
>
> > But this would be a bad definition, because the ASSs clearly
> > stand on their own as consonances, even in diatonic music.
>
> Ah, that's what makes them anomalous!
>
>
> Graham

"Substrate" is the word. You might use "solution," but that would
seem like some kind of *answer* to something...

JP

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:

> Maybe something like "substrate...." etc.. It's related
> to "subset..." Or something else...

They tend to be tonally ambiguous, so you could call it an ambiguous substrate subset. I have no idea what that means, but I don't like the other acronym much either since they aren't anomalous, it doesn't much matter if they are saturated and I don't see what suspensions have to do with it. In any case we need a word which covers more than RI and which makes no assumptions about saturation.

>That category would include both ASSs and NTSSs (pron. nutses)
>wouldn't it? Maybe ASSs should be taken to include NTSSs and then
>we'd need a new category of RASSs, being Rational ASSs?

I think we should keep ASSs what they are (recent reflection has
shown all three letters to be theoretically appropriate, with
the possible but trivial exception of the third one).

As far as these other acronyms... whew. Though magic chords
could be confused with chords in MAGIC temperament. Therefore, I
suggest the acronym SSS, for Super-Saturated Suspensions. In
chemistry, a solution is super-saturated when it contains a higher
concentration of the disolved compound at the given temperature
than is allowed. You get it to the high concentration at a higher
temperature, and then slowly lower the temperature, being careful
to avoid any shocks to the system. The slightest jolt will
collapse the whole business into slush. I think the analogy
between temperature and temperament is good here.

-Carl

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

> As far as these other acronyms... whew. Though magic chords
> could be confused with chords in MAGIC temperament. Therefore, I
> suggest the acronym SSS, for Super-Saturated Suspensions.

Sounds like an escaping gas.

>>As far as these other acronyms... whew. Though magic chords
>>could be confused with chords in MAGIC temperament. Therefore, I
>>suggest the acronym SSS, for Super-Saturated Suspensions.
>
>Sounds like an escaping gas.

You have to say the letters.

You don't mean to say you were pronouncing the ASS acronym,
do you? :)

-C.

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:

> Are not all squares asses ?

3:7:15:35 is not an ass.

3:5:21:35 is not an ass.

5:7:15:21 is not an ass.

Can you find a square that _is_ an ass?

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:

> Paul!
> well i hate to break a bubble but I noticed in helmholtz about
> 20 years ago in his description
> of the seventh chord that it could be the intersection of two
>triads having common tones.

What bubble is being broken?

> Hence
> such structures are already implied in his work.

And in the work of many Baroque composers.

> Chords of like structure are easily formed by
> taking any 4 (or more ) tones in a row on your basic eikosany
>lattices.

Can you give an example? Which lattice might I want to look at to see
this?

--- In tuning@y..., "clumma" <carl@l...> wrote:
> >>But what is the definition of "suspension", and are they all
> >>really suspensions?
> >
> >No, they're not. But you can't deny it makes for a good
> >acronym.
>
> Well, if you define "suspension" to mean any concordant group
> of notes that share a common subset with an otonal or utonal
> chord, then yes, they are.
>
> But this would be a bad definition, because the ASSs clearly
> stand on their own as consonances, even in diatonic music. The
> 10:12:15:18 (or 12:14:18:21) minor 7th is consonant in jazz,
> for example. I think a better def. of "suspension" is a subset
> of the (diatonic) scale which is partially dissonant (and maybe,
> but not necessarily, discordant to some degree).
>
> -Carl

I think we're being sent on a wild goose chase here. Correct me if
I'm wrong, but I think Graham used the term "suspension" to evoke the
_chemistry_ sense of "saturated suspension". This has absolutely
nothing with the _musical_ term "suspension" and I don't think we
should look for parallels there.

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> David and Paul!
> If you are going to accept these as consonant units, then you
>can treat them as tetrads and
> the latter case on graham page as a hexad
> which mean you can use the four elements to construct a
> hexany and an eikosany.

Never thought of this! Dave, how does this idea strike you?

> Anyway all each hexany in turn also seems to have
one "dissonant" interval but if you omit one
> of these you have some 4 tone chords examples which seems to have
been overlooked ?

> 7 9 21 63

This is 1/(9:7:3:1), merely a subset of the 9-limit Utonal pentad.
Hence it's not saturated.

> 5 9 15 45

This is 1/(9:5:3:1), merely a subset of the 9-limit Utonal pentad.
Hence it's not saturated.

Thanks for looking, though -- I love this kind of collaborative
research!

>>If you are going to accept these as consonant units, then you
>>can treat them as tetrads and the latter case on graham page
>>as a hexad which mean you can use the four elements to
>>construct a hexany and an eikosany.
>
>Never thought of this! Dave, how does this idea strike you?

Sounds like a killer idea, but won't the CPS collapse due to
redundant points? Let's see,

12:14:18:21

14*12 18*14 21*18
18*12 21*14
21*12

168 252 378
216 294
252

Hmm. -C.

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> > David and Paul!
> > If you are going to accept these as consonant units, then you
> >can treat them as tetrads and
> > the latter case on graham page as a hexad
> > which mean you can use the four elements to construct a
> > hexany and an eikosany.
>
> Never thought of this! Dave, how does this idea strike you?

Without examining it further ... Brilliant!

> > Anyway all each hexany in turn also seems to have
> one "dissonant" interval but if you omit one
> > of these you have some 4 tone chords examples which seems to have
> been overlooked ?
>
> > 7 9 21 63
>
> This is 1/(9:7:3:1), merely a subset of the 9-limit Utonal pentad.
> Hence it's not saturated.
>
> > 5 9 15 45
>
> This is 1/(9:5:3:1), merely a subset of the 9-limit Utonal pentad.
> Hence it's not saturated.

That's my fault. I didn't define saturated properly. From Monz's
dictionary: "a chord to which no note may be added without increasing
the chord's odd limit is said to be saturated."

So although a saturated chord must have all dyads consonant, a chord
can have all dyads consonant without being saturated. What do we call
these? Consonant? Complete? I've been using "fully-pairwise-consonant"
but that's a mouthful.

Kraig wrote,

> >>If you are going to accept these as consonant units, then you
> >>can treat them as tetrads and the latter case on graham page
> >>as a hexad which mean you can use the four elements to
> >>construct a hexany and an eikosany.

I wrote,

> >Never thought of this! Dave, how does this idea strike you?

Carl wrote,

> Sounds like a killer idea, but won't the CPS collapse due to
> redundant points?

That's what Kraig was saying. I guess you didn't read his post, but
only my reply to it? You shouldn't do that, lest you contribute to
the feeling that 'cliques' exist on this list :)

>That's what Kraig was saying. I guess you didn't read his post, but
>only my reply to it? You shouldn't do that, lest you contribute to
>the feeling that 'cliques' exist on this list :)

No, I read Kraig's post, I just couldn't decipher that out of it.

I don't exclude posts by author. When I'm on the list, I usually
read close to 100% of posts, sometimes excluding a few by subject.
In these cases, I usually exclude the whole thread, or start with
an apology when I enter it.

On the other hand, you recently replied to one of my posts
apparently without reading Graham's or Dave K.'s replies.

In general, you reply to more people than I, which has gone a
long way toward breaking down barriers on this list.

-Carl

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

> So although a saturated chord must have all dyads consonant, a
chord
> can have all dyads consonant without being saturated. What do we
call
> these? Consonant? Complete?

Incomplete o-limit (where o is an odd number)

> I've been using "fully-pairwise-consonant"
> but that's a mouthful.

How about just pairwise consonant?

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

> On the other hand, you recently replied to one of my posts
> apparently without reading Graham's or Dave K.'s replies.

I've read everything. Is there anything in particular you'd like me
to reply to?

Paul!
yes i woke up at 3 in the morning and thought that these could be used as set for hexanies. I
saw the harmonic tetrad in the hexanies but missed the two subharmonic ones due to that grogginess
one has at such times. It would be worth looking at the 7 eikosanies possible out of the
3:5:9:15:25:45:75 set or the the 1)7- 7)7 CPS 's.
Sorry i missed the properties at first look as i saw one aspect of them only at first.
what can we do with them? there must be something!

paulerlich wrote:

>
>
> Thanks for looking, though -- I love this kind of collaborative
> research!
>

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

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., "paulerlich" <paul@s...> wrote:

> How about just pairwise consonant?

I've been saying just consonant, or o-consonant when I need the limit. Is there any reason not to?

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:

> It would be worth looking at the 7 eikosanies possible out of the
> 3:5:9:15:25:45:75 set

Perhaps -- unfortunately I believe a 25-limit standard of consonance
(within which this is an ASS) has very little to do with anything I
can perceive.

>>On the other hand, you recently replied to one of my posts
>>apparently without reading Graham's or Dave K.'s replies.
>
>I've read everything. Is there anything in particular you'd
>like me to reply to?

No, thanks (sincerely). I was referring to the ASS thing,
where Graham seemed to indicate that he was trying to use
the musical meaning of "suspension" and I had already pointed
out the possible correspondence to chemistry.

-Carl

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> > How about just pairwise consonant?
>
> I've been saying just consonant, or o-consonant when I need the
limit. Is there any reason not to?

I guess not. But there's a reason not to use "consonant" at all for
this, and that's that consonance is a perceptual property and people
are gonna disagree like hell about which chords sound consonant. Maybe
better to use some term derived from graph theory, but it seems that
"complete" already has a different meaning for chords than it does in
graph theory. Sigh.

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

> I was referring to the ASS thing,
> where Graham seemed to indicate that he was trying to use
> the musical meaning of "suspension" and I had already pointed
> out the possible correspondence to chemistry.

I repeated your point and ignored Graham's only because I hadn't read
them YET, and after I read them, I didn't feel I had anything to
revise.

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> --- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> > --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> >
> > > How about just pairwise consonant?
> >
> > I've been saying just consonant, or o-consonant when I need the
> limit. Is there any reason not to?
>
> I guess not. But there's a reason not to use "consonant" at all for
> this, and that's that consonance is a perceptual property and
people
> are gonna disagree like hell about which chords sound consonant.

In particular, our experiments on the harmonic entropy list seem to
indicate that otonal consonance limit is more important than pairwise
consonance limit.

>>I was referring to the ASS thing, where Graham seemed to
>>indicate that he was trying to use the musical meaning
>>of "suspension" and I had already pointed out the possible
>>correspondence to chemistry.
>
>I repeated your point and ignored Graham's only because I
>hadn't read them YET, and after I read them, I didn't feel
>I had anything to revise.

No bad, no bad. I also was not going to comment. -C.

> From: paulerlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Tuesday, January 15, 2002 4:08 PM
> Subject: [tuning] Re: Masses of asses?
>
>
> In particular, our experiments on the harmonic entropy
> list seem to indicate that otonal consonance limit is
> more important than pairwise consonance limit.

Hmmm ... that's something that I've always intuitively
believed, despite my grudging acceptance of Partch's dualism.

Looking forward to the abstracted synopsis on this list,
when the dust at harmonic_entropy settles down.

-monz

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

--- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > From: paulerlich <paul@s...>
> > To: <tuning@y...>
> > Sent: Tuesday, January 15, 2002 4:08 PM
> > Subject: [tuning] Re: Masses of asses?
> >
> >
> > In particular, our experiments on the harmonic entropy
> > list seem to indicate that otonal consonance limit is
> > more important than pairwise consonance limit.
>
>
> Hmmm ... that's something that I've always intuitively
> believed, despite my grudging acceptance of Partch's dualism.
>
> Looking forward to the abstracted synopsis on this list,
> when the dust at harmonic_entropy settles down.

I don't know what you mean. The harmonic entropy list is so quiet,
it's nearly dead!

Paul!
Hmmm. as this is listed on graham page http://www.cix.co.uk/~gbreed/ass.htm
i thought this limit was already accepted as a chord . was this graham or someone elses choice and
not yours?

paulerlich wrote:

> --- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
>
> > It would be worth looking at the 7 eikosanies possible out of the
> > 3:5:9:15:25:45:75 set
>
> Perhaps -- unfortunately I believe a 25-limit standard of consonance
> (within which this is an ASS) has very little to do with anything I
> can perceive.
>

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

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:

> Paul!
> Hmmm. as this is listed on graham page
http://www.cix.co.uk/~gbreed/ass.htm
> i thought this limit was already accepted as a chord. was this
graham or someone elses choice and
> not yours?

I don't object to the fact that Graham put all the examples of asses
through some rather high odd limits up on his page -- they're of
theoretical interest if nothing else. Personally, I agree with Partch
that somewhere between 11 and 25, the ear gives up (for dyads, which
is the issue here -- certainly higher limits are relevant for big
otonal chords -- but pairwise consonance is the context of the ASS
stuff).

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

> I guess not. But there's a reason not to use "consonant" at all for
> this, and that's that consonance is a perceptual property and people
> are gonna disagree like hell about which chords sound consonant.

If you use "o-consonant" it is a Humpty Dumpty definition--consonance is whatever I define it to be at this particular moment.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:

/tuning/topicId_32655.html#32747

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > Maybe something like "substrate...." etc.. It's related
> > to "subset..." Or something else...
>
> They tend to be tonally ambiguous, so you could call it an
ambiguous substrate subset. I have no idea what that means, but I
don't like the other acronym much either since they aren't anomalous,
it doesn't much matter if they are saturated and I don't see what
suspensions have to do with it. In any case we need a word which
covers more than RI and which makes no assumptions about saturation.

Hi Gene!

Thank you for "refining" this... I like this. Maybe "ambiguous
substrate subset" could cover our ASSes, so to speak....

JP

--- In tuning@y..., "paulerlich" <paul@s...> wrote:

/tuning/topicId_32655.html#32753

> --- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
>
> > Are not all squares asses ?
>
> 3:7:15:35 is not an ass.
>
> 3:5:21:35 is not an ass.
>
> 5:7:15:21 is not an ass.
>
> Can you find a square that _is_ an ass?

Perhaps Kraig was speaking "metaphorically..." :)

JP

--- In tuning@y..., "paulerlich" <paul@s...> wrote:

/tuning/topicId_32655.html#32758

> --- In tuning@y..., "clumma" <carl@l...> wrote:
> > >>But what is the definition of "suspension", and are they all
> > >>really suspensions?
> > >
> > >No, they're not. But you can't deny it makes for a good
> > >acronym.
> >
> > Well, if you define "suspension" to mean any concordant group
> > of notes that share a common subset with an otonal or utonal
> > chord, then yes, they are.
> >
> > But this would be a bad definition, because the ASSs clearly
> > stand on their own as consonances, even in diatonic music. The
> > 10:12:15:18 (or 12:14:18:21) minor 7th is consonant in jazz,
> > for example. I think a better def. of "suspension" is a subset
> > of the (diatonic) scale which is partially dissonant (and maybe,
> > but not necessarily, discordant to some degree).
> >
> > -Carl
>
> I think we're being sent on a wild goose chase here. Correct me if
> I'm wrong, but I think Graham used the term "suspension" to evoke
the
> _chemistry_ sense of "saturated suspension". This has absolutely
> nothing with the _musical_ term "suspension" and I don't think we
> should look for parallels there.

***This is *exactly* what I said, and truly I believe the
term "suspension" is absolutely out of place for *any* of these if
you're talking about *music* where the term is *absolutely* and
*specifically* defined!

Huh?

JP

Thanks Joe for noticing:) !

jpehrson2 wrote:

> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> /tuning/topicId_32655.html#32753
>
> > --- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> >
> > > Are not all squares asses ?
> >
> > 3:7:15:35 is not an ass.
> >
> > 3:5:21:35 is not an ass.
> >
> > 5:7:15:21 is not an ass.
> >
> > Can you find a square that _is_ an ass?
>
> Perhaps Kraig was speaking "metaphorically..." :)
>
> JP
>

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

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_32655.html#32796

>
> > From: paulerlich <paul@s...>
> > To: <tuning@y...>
> > Sent: Tuesday, January 15, 2002 4:08 PM
> > Subject: [tuning] Re: Masses of asses?
> >
> >
> > In particular, our experiments on the harmonic entropy
> > list seem to indicate that otonal consonance limit is
> > more important than pairwise consonance limit.
>
>
> Hmmm ... that's something that I've always intuitively
> believed, despite my grudging acceptance of Partch's dualism.
>
> Looking forward to the abstracted synopsis on this list,
> when the dust at harmonic_entropy settles down.
>
>
>
> -monz
>

As I recall, this is something that Paul and I were discussing way
back when he generated all his tetrads for the "Tuning Lab" page,
probably more than a year ago.

The idea was that the tetrads formed by consonant *diads,* if I
remember correctly, weren't "behaving" as they should always in terms
of consonance, and it was only when we invoked an *otonal* model that
we could make sense of the classifications.

At least that's how *I* remember things.

These tests and the Tuning Lab is at the following URL:

http://artists.mp3s.com/artists/140/tuning_lab.html

JP

--- In tuning@y..., "paulerlich" <paul@s...> wrote:

/tuning/topicId_32655.html#32797

> --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >
> > > From: paulerlich <paul@s...>
> > > To: <tuning@y...>
> > > Sent: Tuesday, January 15, 2002 4:08 PM
> > > Subject: [tuning] Re: Masses of asses?
> > >
> > >
> > > In particular, our experiments on the harmonic entropy
> > > list seem to indicate that otonal consonance limit is
> > > more important than pairwise consonance limit.
> >
> >
> > Hmmm ... that's something that I've always intuitively
> > believed, despite my grudging acceptance of Partch's dualism.
> >
> > Looking forward to the abstracted synopsis on this list,
> > when the dust at harmonic_entropy settles down.
>
> I don't know what you mean. The harmonic entropy list is so quiet,
> it's nearly dead!

Wasn't there at one point a discussion of possibly combining it
with "Tuning-math??"

JP

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:

/tuning/topicId_32655.html#32815

> Thanks Joe for noticing:) !
>
> jpehrson2 wrote:
>
> > --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> >
> > /tuning/topicId_32655.html#32753
> >
> > > --- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> > >
> > > > Are not all squares asses ?
> > >
> > > 3:7:15:35 is not an ass.
> > >
> > > 3:5:21:35 is not an ass.
> > >
> > > 5:7:15:21 is not an ass.
> > >
> > > Can you find a square that _is_ an ass?
> >
> > Perhaps Kraig was speaking "metaphorically..." :)
> >
> > JP
> >

I thought it was funny.. but then I tend to be a *words* person...

JP

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:

> Wasn't there at one point a discussion of possibly combining it
> with "Tuning-math??"

I've never figured out why it isn't.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > Wasn't there at one point a discussion of possibly combining it
> > with "Tuning-math??"
>
> I've never figured out why it isn't.

One suggestion, in case anyone involved hadn't thought about it:
unless someone (like Paul, who started the forum) has the entire
thing as single posts or digests, get Robert Walker to archive it.
You guys have probably done a lot worth saving, and unless you simply
leave the forum 'hanging' there, you won't have the data in the
archives.

Makes sense to combine, but keep all that work...

Cheers,
Jon

>One suggestion, in case anyone involved hadn't thought about it:
>unless someone (like Paul, who started the forum) has the entire
>thing as single posts or digests, get Robert Walker to archive it.
>You guys have probably done a lot worth saving,

You bet we have!

>and unless you simply leave the forum 'hanging' there, you won't
>have the data in the archives.

The rumors of its death have been greatly exaggerated. I don't
see anything wrong with it, myself.

>Makes sense to combine, but keep all that work...

I argued long ago to combine it with tuning-math. For reasons of
ideal posting volume (vs. threads getting shut out in the
boisterous lattice-searching place that tuning-math has since
become), I could still see the combination, but I've come to
realize that harmonic entropy deserves its own place -- I'd say
it's a tit-for-tat situation, best left in the hands of the
moderator. I don't know what I'd do in his shoes, actually.

-Carl

In-Reply-To: <3C4440A9.21050ECC@anaphoria.com>
Me:
> > Asses are all subsets of an Euler genus, so they may well also be
> > (subsets
> > of) a CPS. Do you have a general method for this?

Kraig:
> taking the two out of 4 sets

Two out of what 4? 2)1.3.3.7 and 2)1.3.3.5 seem to do it in the 9-limit,
but where's the extra note? It isn't particularly efficient to use
combinations of 4 intervals to get a 4 note chord, either. You could call
them 1)3.7.9.21 and 1)3.5.9.15 instead.

Graham

In-Reply-To: <3C44D4A0.6F40DC3F@anaphoria.com>
Kraig wrote:

> Hmmm. as this is listed on graham page
> http://www.cix.co.uk/~gbreed/ass.htm
> i thought this limit was already accepted as a chord . was this graham
> or someone elses choice and
> not yours?

Can you make that <http://x31eq.com/ass.htm> because I might
pull the plug on the CIX site one day.

Nothing on there implies consonance in real music. I was working with the
specific, mathematically precise definition of odd-limit intervals, and
showing how some chords can only contain such intervals without belonging
to the relevant o- or utonality. I wasn't even sure about 7-limit
consonance then, it was merely a question of filling in a gap in Partch's
theory.

I wanted to go as high as anybody could possibly want me to, which meant I
had to consider the 15-limit because that behaves differently to lower
ones. After that, it was very easy to add the 17- and 19-limit examples,
because they're the same as the 9-limit ones but with more zeros. I
jumped to the 25-limit because I thought it might make a difference being
within the 5-limit, as people tuning to 5-limit systems could still try it
out.

Graham

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:

/tuning/topicId_32655.html#32825

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > Wasn't there at one point a discussion of possibly combining it
> > with "Tuning-math??"
>
> I've never figured out why it isn't.

Paul, is there some way to "concatenate" lists, or maybe just make
a "grand summary" of the Harmonic Entropy list and post it to "Tuning
Math..."

Of course you'd have to "blow away" the Harmonic Entropy group unless
there's some way of saving the messages... Perhaps that would be
problematic.

Or maybe just a note saying the discussions would continue over on
Tuning-Math...

There are too many "inactive" lists, in *my* opinion.

JP

--- In tuning@y..., "jonszanto" <JSZANTO@A...> wrote:

/tuning/topicId_32655.html#32826

> --- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> > --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> >
> > > Wasn't there at one point a discussion of possibly combining it
> > > with "Tuning-math??"
> >
> > I've never figured out why it isn't.
>
> One suggestion, in case anyone involved hadn't thought about it:
> unless someone (like Paul, who started the forum) has the entire
> thing as single posts or digests, get Robert Walker to archive it.
> You guys have probably done a lot worth saving, and unless you
simply
> leave the forum 'hanging' there, you won't have the data in the
> archives.
>
> Makes sense to combine, but keep all that work...
>
> Cheers,
> Jon

Jon, I think that's the solution...

JP

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

/tuning/topicId_32655.html#32827

> >One suggestion, in case anyone involved hadn't thought about it:
> >unless someone (like Paul, who started the forum) has the entire
> >thing as single posts or digests, get Robert Walker to archive it.
> >You guys have probably done a lot worth saving,
>
> You bet we have!
>
> >and unless you simply leave the forum 'hanging' there, you won't
> >have the data in the archives.
>
> The rumors of its death have been greatly exaggerated. I don't
> see anything wrong with it, myself.
>
> >Makes sense to combine, but keep all that work...
>
> I argued long ago to combine it with tuning-math. For reasons of
> ideal posting volume (vs. threads getting shut out in the
> boisterous lattice-searching place that tuning-math has since
> become), I could still see the combination, but I've come to
> realize that harmonic entropy deserves its own place -- I'd say
> it's a tit-for-tat situation, best left in the hands of the
> moderator. I don't know what I'd do in his shoes, actually.
>
> -Carl

But, Carl, I thought Paul just said there were very few postings over
there??

JP

Graham!
You asked me how i did it not that the results were good . In fact i noticed why they weren't
but i was looking at you list of 4 note chords and taking the combination of 2 out of four and
multiplying them.
ex. 3:5:9:15

3x5
3x9
3x15
5x9
5x15
9x15

that would be a hexany and it didn't pan out as such a fascinating structure reaches a musical
dead end. The only musical application i can think of is possibly as a point of "incomplete
cadence as the consonance is low but lack the finality of the ot or utonality tetrads. Can you see
another use!

graham@microtonal.co.uk wrote:

> In-Reply-To: <3C4440A9.21050ECC@anaphoria.com>
> Me:
> > > Asses are all subsets of an Euler genus, so they may well also be
> > > (subsets
> > > of) a CPS. Do you have a general method for this?
>
> Kraig:
> > taking the two out of 4 sets
>
> Two out of what 4? 2)1.3.3.7 and 2)1.3.3.5 seem to do it in the 9-limit,
> but where's the extra note? It isn't particularly efficient to use
> combinations of 4 intervals to get a 4 note chord, either. You could call
> them 1)3.7.9.21 and 1)3.5.9.15 instead.
>
> Graham
>

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

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

> From: jpehrson2 <jpehrson@rcn.com>
> To: <tuning@yahoogroups.com>
> Sent: Wednesday, January 16, 2002 6:20 AM
> Subject: [tuning] too many lists
>
>
> Paul, is there some way to "concatenate" lists, or maybe just make
> a "grand summary" of the Harmonic Entropy list and post it to "Tuning
> Math..."
>
> Of course you'd have to "blow away" the Harmonic Entropy group unless
> there's some way of saving the messages... Perhaps that would be
> problematic.
>
> Or maybe just a note saying the discussions would continue over on
> Tuning-Math...
>
> There are too many "inactive" lists, in *my* opinion.

I originally agreed with you about not wanting the big list to
split up, but now that it's happened, I disagree with what you
say here. I think it's good that each focus-area has its own
Yahoo Group, and see no reason not to simply let dormant ones
lie dormant until interest picks up again.

I think that, with all the many tuning lists there are now,
inactivity is a *good* thing! Gives an opportunity to pay
attention to the activity that's happening on just a handful
of them. But then when there is an occassional post on one
of the less-active lists, it still stays archived nicely in
it most topic-relevant place.

-monz

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

>>I argued long ago to combine it with tuning-math. For reasons of
>>ideal posting volume (vs. threads getting shut out in the
>>boisterous lattice-searching place that tuning-math has since
>>become), I could still see the combination, but I've come to
>>realize that harmonic entropy deserves its own place -- I'd say
>>it's a tit-for-tat situation, best left in the hands of the
>>moderator. I don't know what I'd do in his shoes, actually.
>>
>> -Carl
>
>
>But, Carl, I thought Paul just said there were very few postings
>over there??
>
> JP

You mean you have an opinion, and you're not even a member (you
certainly were a part of the tetrads listening test)? Shame on
you!

There have been 580 no-nonsense messages, over a period of
almost 18 months (oldest of all splinter lists!). We have 40
members, which makes it the 4th biggest splinter list.

-Carl

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

> I'd say
> it's a tit-for-tat situation, best left in the hands of the
> moderator. I don't know what I'd do in his shoes, actually.
>
> -Carl

I don't see any reasonable way of combining the two lists.

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

/tuning/topicId_32655.html#32846

> >>I argued long ago to combine it with tuning-math. For reasons of
> >>ideal posting volume (vs. threads getting shut out in the
> >>boisterous lattice-searching place that tuning-math has since
> >>become), I could still see the combination, but I've come to
> >>realize that harmonic entropy deserves its own place -- I'd say
> >>it's a tit-for-tat situation, best left in the hands of the
> >>moderator. I don't know what I'd do in his shoes, actually.
> >>
> >> -Carl
> >
> >
> >But, Carl, I thought Paul just said there were very few postings
> >over there??
> >
> > JP
>
> You mean you have an opinion, and you're not even a member (you
> certainly were a part of the tetrads listening test)? Shame on
> you!
>

I'm a member of Harmonic Entropy, Carl! Otherwise I wouldn't have
said anything. I was following it for a while at the beginning, but
then when it got slow for a while neglected it...

Well, maybe you *should* "let it be..." It seems it "heats up" from
time to time.

Maybe somebody could mention here on the "big list" when developments
are going on over there, as they do for Tuning Math, so we
could "tune* our attention over there as necessary.

(I believe this also *has* been done, but only very infrequently...)

JP