Yahoo Tuning Groups Ultimate Backup tuning Minimum/Desired Criteria for a Melody-Centric Tuning?

1. One lesson learned from the 12EDO tuning system is that
any EDO tuning system allows total melodic freedom in the
sense that ANY INTRVAL CLASS IS SOUNDABLE FROM
ANY PITCH CLASS IN EITHER IT'S ASCENDING OR
DESCENDING FORM. This is a very important quality of
EDO tunings, and I haven't heard it mentioned in relation
to why anybody should abandon working in 12EDO. All
the arguments I've seen seem to focus on the quality of
individual intervals in isolation rather than general
properties of the tunings.

2. Another lesson learned from 12EDO is that EDO tunings
also allow for the sounding of the inversion of any melody/interval
string within that tuning. I consider this a minimum criteria
for a tuning for anybody who is interested in writing melody-centric
music.

3. Since I have come to the conclusion that the best way
to generate/evaluate melodies is by creating all-interval-class/
all-contour melodies using the Morse-Thue sequence as
a contour choice ordering "template", it should be realized
that the EDO tunings are superior in this department also.
But my next project is to start testing one of my 12-tone
symmetrical just tunings to see if an all-interval-class/
all-contour melody using the Morse-Thue contour choice
ordering algorithm is possible or not in that general class
of tunings.

Bill Flavell

🔗Keenan Pepper <keenanpepper@gmail.com>

On 3/6/06, Bill Flavell <bill_flavell@email.com> wrote:
>
> 1. One lesson learned from the 12EDO tuning system is that
> any EDO tuning system allows total melodic freedom in the
> sense that ANY INTRVAL CLASS IS SOUNDABLE FROM
> ANY PITCH CLASS IN EITHER IT'S ASCENDING OR
> DESCENDING FORM. This is a very important quality of
> EDO tunings, and I haven't heard it mentioned in relation
> to why anybody should abandon working in 12EDO. All
> the arguments I've seen seem to focus on the quality of
> individual intervals in isolation rather than general
> properties of the tunings.
>
> 2. Another lesson learned from 12EDO is that EDO tunings
> also allow for the sounding of the inversion of any melody/interval
> string within that tuning. I consider this a minimum criteria
> for a tuning for anybody who is interested in writing melody-centric
> music.
>
> 3. Since I have come to the conclusion that the best way
> to generate/evaluate melodies is by creating all-interval-class/
> all-contour melodies using the Morse-Thue sequence as
> a contour choice ordering "template", it should be realized
> that the EDO tunings are superior in this department also.
> But my next project is to start testing one of my 12-tone
> symmetrical just tunings to see if an all-interval-class/
> all-contour melody using the Morse-Thue contour choice
> ordering algorithm is possible or not in that general class
> of tunings.
>
>
> Bill Flavell

These seem to be the standard arguments for equal temperament and
against JI, which have been stated many times before. Why don't you
take a good EDO, like 19 or 22 or even 5, and actually write some
music in it? I look forward to hearing your compositions.

Keenan

🔗Hudson Lacerda <hfmlacerda@yahoo.com.br>

Bill Flavell escreveu:
> 3. Since I have come to the conclusion that the best way
> to generate/evaluate melodies is by creating all-interval-class/
> all-contour melodies using the Morse-Thue sequence as
> a contour choice ordering "template", it should be realized
> that the EDO tunings are superior in this department also.

What is that method to `generate/evaluate' melodies based on Morse-Thue sequence? How does it works?

> But my next project is to start testing one of my 12-tone > symmetrical just tunings to see if an all-interval-class/
> all-contour melody using the Morse-Thue contour choice
> ordering algorithm is possible or not in that general class
> of tunings.

The difficult part of assymetrical scales (I mean to have different ratios for each interval class) is that they are not easy to deal in a rational (a la Descartes) way. I would like to apply pitch-set theory to such scales, but in general this doesn't correspond to the actual musical effect of the pitch relations. Other approaches are needed to use such scales.

Hudson Lacerda

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🔗Bill Flavell <bill_flavell@email.com>

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...>
wrote:
>
> These seem to be the standard arguments for equal temperament and
> against JI, which have been stated many times before.

Well, I'm not against JI per se, but I'm only interested in exploring
symmetrical JI tunings now, after 20 years of studying 12EDO pitch
class set theory! :)

> Why don't you
> take a good EDO, like 19 or 22 or even 5, and actually write some
> music in it? I look forward to hearing your compositions.

Thanks you very much for the suggestion, but I don't have access to
even 12EDO compositional facilities right now, let alone JI! :)

Bill Flavell

🔗Hudson Lacerda <hfmlacerda@yahoo.com.br>

Bill Flavell escreveu:
> [...] I'm only interested in exploring > symmetrical JI tunings now, after 20 years of studying 12EDO pitch > class set theory! :)

Hi Bill.

Have you thought about some extension/adaptation of pitch class sets theory for irregular scales?

Hudson Lacerda

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🔗Keenan Pepper <keenanpepper@gmail.com>

On 3/7/06, Bill Flavell <bill_flavell@email.com> wrote:
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...>
> wrote:
> >
> > These seem to be the standard arguments for equal temperament and
> > against JI, which have been stated many times before.
>
> Well, I'm not against JI per se, but I'm only interested in exploring
> symmetrical JI tunings now, after 20 years of studying 12EDO pitch
> class set theory! :)

Yes it is against JI! You said:

"ANY INTRVAL CLASS IS SOUNDABLE FROM ANY PITCH CLASS IN EITHER IT'S
ASCENDING OR DESCENDING FORM"

That is not possible in JI with a finite number of notes.

> > Why don't you
> > take a good EDO, like 19 or 22 or even 5, and actually write some
> > music in it? I look forward to hearing your compositions.
>
> Thanks you very much for the suggestion, but I don't have access to
> even 12EDO compositional facilities right now, let alone JI! :)

You can just send me the note numbers or whatever and I'd be happy to
make it into a MIDI file or synthesized rendering.

Keenan

🔗Bill Flavell <bill_flavell@email.com>

Thanks for the response, Hudson! :)

Bill Flavell

--- In tuning@yahoogroups.com, Hudson Lacerda <hfmlacerda@...> wrote:
>
> Bill Flavell escreveu:
> > 3. Since I have come to the conclusion that the best way
> > to generate/evaluate melodies is by creating all-interval-class/
> > all-contour melodies using the Morse-Thue sequence as
> > a contour choice ordering "template", it should be realized
> > that the EDO tunings are superior in this department also.
>
> What is that method to `generate/evaluate' melodies based on Morse-
Thue
> sequence? How does it works?
>
> > But my next project is to start testing one of my 12-tone
> > symmetrical just tunings to see if an all-interval-class/
> > all-contour melody using the Morse-Thue contour choice
> > ordering algorithm is possible or not in that general class
> > of tunings.
>
> The difficult part of assymetrical scales (I mean to have different
> ratios for each interval class) is that they are not easy to deal
in a
> rational (a la Descartes) way. I would like to apply pitch-set
theory to
> such scales, but in general this doesn't correspond to the actual
> musical effect of the pitch relations. Other approaches are needed
to
> use such scales.
>
> Hudson Lacerda
>
> --
> '----------------------------------------------------------------
---.
> Hudson Lacerda <http://geocities.yahoo.com.br/hfmlacerda/>
> *Não deixe seu voto sumir! http://www.votoseguro.org/
> *Apóie o Manifesto:
http://www.votoseguro.com/alertaprofessores/
>
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option=com_wrapper&Itemid=182
> .----------------------------------------------------------------
---'
> --
>
>
>
> _______________________________________________________
> Yahoo! Acesso Grátis - Internet rápida e grátis. Instale o discador
agora!
> http://br.acesso.yahoo.com
>

🔗Bill Flavell <bill_flavell@email.com>

--- In tuning@yahoogroups.com, Hudson Lacerda <hfmlacerda@...> wrote:
>
> Hi Bill.
>
> Have you thought about some extension/adaptation of pitch class
sets
> theory for irregular scales?

No, Hudson, by definition 12EDO pitch class set theory is only valid
for either the 12EDO tuning or a 12-tone subsection of a larger-than-
12-pitch-class EDO tuning, if my understanding is correct.

Each different EDO tuning requires a separate calculation of the
structurally unique subscales contained in that tuning.

I'm not sure if a pitch class set theory of a symmetrical just
intonation tuning would be possible or not, but I'll think about it
and post something later.

Bill Flavell

🔗Bill Flavell <bill_flavell@email.com>

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...>
wrote:
>
> Yes it is against JI! You said:
>
> "ANY INTRVAL CLASS IS SOUNDABLE FROM ANY PITCH CLASS IN EITHER IT'S
> ASCENDING OR DESCENDING FORM"
>
> That is not possible in JI with a finite number of notes.

Right! That's strictly a characteristic of an EDO tuning.

> > > Why don't you
> > > take a good EDO, like 19 or 22 or even 5, and actually write
some
> > > music in it? I look forward to hearing your compositions.
> >
> > Thanks you very much for the suggestion, but I don't have access
to
> > even 12EDO compositional facilities right now, let alone JI! :)
>
> You can just send me the note numbers or whatever and I'd be happy
to
> make it into a MIDI file or synthesized rendering.

Thank you very much for the offer, Keenan, and I'll start thinking of
what I could do along those lines in the future, and e-mail you
privately about that! :)

Bill Flavell

🔗Hudson Lacerda <hfmlacerda@yahoo.com.br>

Bill Flavell escreveu:
[...]
> No, Hudson, by definition 12EDO pitch class set theory is only valid > for either the 12EDO tuning or a 12-tone subsection of a larger-than-
> 12-pitch-class EDO tuning, if my understanding is correct.

One does not need limit to 12EDO. Pitch class set theory can be applied to any EDO. There are some details specific for each *scale*, but the *theory* itself can be used unchanged.

I worked on a software called MUSAS which can deal with mod<N> pitch sets operations like transposition, inversion, sub/supersets, invariance, interval vectors, index vectors, symmetry axis, operations on rows...

> > Each different EDO tuning requires a separate calculation of the > structurally unique subscales contained in that tuning.

Such kind of database (prime forms list) out of mod12 is not still implemented in MUSAS.

> > I'm not sure if a pitch class set theory of a symmetrical just > intonation tuning would be possible or not, but I'll think about it > and post something later.

OK.

> > > Bill Flavell

Cheers,
Hudson

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🔗Gene Ward Smith <genewardsmith@coolgoose.com>

--- In tuning@yahoogroups.com, Hudson Lacerda <hfmlacerda@...> wrote:

> Such kind of database (prime forms list) out of mod12 is not still
> implemented in MUSAS.

The number of possible prime forms for N edo is N!. For 12, that is
already an intractible 479001600. For 72, it's 6.12 x 10^103. So
listing all of them, something which would only be relevant in any
case for serial composition, is not a reasonable requirement. A far
better starting point I think is chords, but even here it's a problem.
There are 12 choose 4, or 495, four-note chords in 12edo, but 72
choose 4, or
1028790, in 72edo.

🔗Hudson Lacerda <hfmlacerda@yahoo.com.br>

Gene Ward Smith escreveu:
> --- In tuning@yahoogroups.com, Hudson Lacerda <hfmlacerda@...> wrote:
> > >>Such kind of database (prime forms list) out of mod12 is not still >>implemented in MUSAS.
> > > The number of possible prime forms for N edo is N!. For 12, that is
> already an intractible 479001600. For 72, it's 6.12 x 10^103. So
> listing all of them, something which would only be relevant in any
> case for serial composition, is not a reasonable requirement. A far
> better starting point I think is chords, but even here it's a problem.
> There are 12 choose 4, or 495, four-note chords in 12edo, but 72
> choose 4, or
> 1028790, in 72edo.

These are not the prime forms (as described by Allen Forte and others), but all subsets. They are reduced into prime forms using transposition and inversion operators. Thus, all major and minor chords (like [0,4,7] and [0,3,7]) are reduced to only one prime form (0,3,7). In mod12 (12EDO), there are few more than 700 prime forms.

Hudson

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🔗Gene Ward Smith <genewardsmith@coolgoose.com>

--- In tuning@yahoogroups.com, Hudson Lacerda <hfmlacerda@...> wrote:

> These are not the prime forms (as described by Allen Forte and others),
> but all subsets.

Sorry, I didn't realize you were talking about Forte's theory, I thought
we were enumerating tone rows. Does anyone know the number of Forte
prime forms for the smaller edos?

🔗Bill Flavell <bill_flavell@email.com>

Thanks very much for that information, Hudson! :)

I wasn't aware of it.

Bill Flavell

--- In tuning@yahoogroups.com, Hudson Lacerda <hfmlacerda@...> wrote:
>
> One does not need limit to 12EDO. Pitch class set theory can be
applied
> to any EDO. There are some details specific for each *scale*, but
the
> *theory* itself can be used unchanged.
>
> I worked on a software called MUSAS which can deal with mod<N>
pitch
> sets operations like transposition, inversion, sub/supersets,
> invariance, interval vectors, index vectors, symmetry axis,
operations
> on rows...
>
> >
> > Each different EDO tuning requires a separate calculation of the
> > structurally unique subscales contained in that tuning.
>
> Such kind of database (prime forms list) out of mod12 is not still
> implemented in MUSAS.
>
> >
> > I'm not sure if a pitch class set theory of a symmetrical just
> > intonation tuning would be possible or not, but I'll think about
it
> > and post something later.
>
> OK.
>
> >
> >
> > Bill Flavell
>
> Cheers,
> Hudson
>
> --
> '----------------------------------------------------------------
---.
> Hudson Lacerda <http://geocities.yahoo.com.br/hfmlacerda/>
> *Não deixe seu voto sumir! http://www.votoseguro.org/
> *Apóie o Manifesto:
http://www.votoseguro.com/alertaprofessores/
>
> == THE WAR IN IRAQ COSTS ==
> http://nationalpriorities.org/index.php?
option=com_wrapper&Itemid=182
> .----------------------------------------------------------------
---'
> --
>
>
>
> _______________________________________________________
> Yahoo! Acesso Grátis - Internet rápida e grátis. Instale o discador
agora!
> http://br.acesso.yahoo.com
>