Yahoo Tuning Groups Ultimate Backup tuning W.A. Mathieu (WAsRe: to Joe Pehrson(books)

In a message dated 2004:01:12 06:41:07 PM, paul-ewrites:

>--- In tuning@yahoogroups.com, "Joseph Pehrson" wrote:
>
>> It's also important to understand the relationship of the harmonic
>> series in this (maybe the book by Mathieu would help ... I own it
>>but still haven't read it... ! :)

tsk tsk... it's an enjoyable poetic book a la the reaaaally good fun
Beginner's Guide Books and the Introduction To... series from the UK (and much
better than the Dummy and Idiot and Klutz guides here in the US that try so hard
to be like or out-do the British guides...)

>It's a wonderful read, but I find many flaws in it.

Ditto. I actually argued with him over the phone back in 2000*! (One of
my pet peeves: that being he seems to think inharmonic scales are just
deviations from the JI model, etc.) I said he was stuck in his European-Arabic-Indian
musical background and his rather off-putting insistence that a practical
scale _must_ be singable or chantable. I quoted Hugo Ball at him just to get his
anthropocentric goat ("Noises ... are existentially more powerful than the
human voice.")

[*Kinda glad he didn't have a heartattack... or sumthin'. I've a bit o'
history of drivin' some teachers to nervous breakdowns...]

> Mathieu assumes that each mode of the diatonic scale (in 12-equal) is
heard as a
>different, idiosyncratically-shaped JI structure. And that "comma
>pumps" will be heard as JI progressions with one huge leap from one
>end of the lattice to another at some specific point in the
>progression. Both of these assumptions are highly unnecessary and
>misleading, I think, if one views temperament correctly.

Honestly I don't _fully_ understand the above, but I think the jist of it
all is also part of my arguement. Or rather my arguement is part of yours...

>Monz's Tonalsoft software is really going to help people in this
>department, and probably for many practical ends as well.

::does his imitation of sluggyfreelance.com's Kikki the Ferret:: "oh
shiney shiney..."
I just hope it's clunky-MacOS9-friendly ;)

>Not to mention that Mathieu allows the significance of meantone to
>completely fall through the cracks, fostering the tired old "JI vs.
>ET" mentality, where easily 1/3 of his book could -- and should --
>have been devoted to meantone examples (just about anything from 1480-
>1780 would fit the bill).

Yepyep, I am reaaally miffed he practically didn't even mention meantones
- and in specific you would think he would like the 16th/17th C. Italian
chromatic meantones and be totally ga-ga over the 17th C. French _temperaments
ordinaire_!
And he addresses dronality very well (but not as in-depth as I would like
or as far-ranging, i.e he is mainly concerned with augmented roots betraying
his largely EuroIndian music theory bias)... but hardly anything on
timbrality, i.e. tone-colour, _Klangfarbenmelodie_, etc.
IMHO tone-clusters are one of the last, true frontiers of chromaticism
and the beginnings of the next, timbrality and dronality. And Mathieu
practically dismisses secundal forms or doesn't consider it enough of musical importance
or interest.

But give the ol' guy credit: he at least wrote of the "Dark Side" of
music and has a whole chapter on symmetrical scales, modes of limited
transposition, lil section on equal temperaments beyond 12tET (mostly based on Blackwood
tho'), &, one of my fav subjects, the dissolution of tonality! HeHE!
And, aboveall, his writing style is memorable and witty... and that
counts BigTime in my book...

---|-----|--------|-------------|---------------------|
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)

"One taps into the core when one can leave the ego at the door..." - Jacky
Ligon

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

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, czhang23@a... wrote:

> > Mathieu assumes that each mode of the diatonic scale (in 12-
equal) is
> heard as a
> >different, idiosyncratically-shaped JI structure. And that "comma
> >pumps" will be heard as JI progressions with one huge leap from
one
> >end of the lattice to another at some specific point in the
> >progression. Both of these assumptions are highly unnecessary and
> >misleading, I think, if one views temperament correctly.
>
> Honestly I don't _fully_ understand the above, but I think the
jist of it
> all is also part of my arguement. Or rather my arguement is part of
yours...

What's the word he uses for these huge leaps, again? It's the same
idea as Monz's "bridging", though across a unison vector, not
necessarily across a xenharmonic bridge . . . but Mathieu paints it
as an almost cataclysmic musical event, while I see it as a non-event
brought on by the curved lattice of the temperament . . .

> >Not to mention that Mathieu allows the significance of meantone to
> >completely fall through the cracks, fostering the tired old "JI
vs.
> >ET" mentality, where easily 1/3 of his book could -- and should --
> >have been devoted to meantone examples (just about anything from
1480-
> >1780 would fit the bill).
>
> Yepyep, I am reaaally miffed he practically didn't even mention
meantones
> - and in specific you would think he would like the 16th/17th C.
Italian
> chromatic meantones and be totally ga-ga over the 17th C. French
_temperaments
> ordinaire_!

Well, the latter have exactly the same "topology" as 12-equal, but
the former do not, and a single example of meantone and how it "eats"
81:80 would have added so much to this book . . . but instead he
jumps directly from JI to 12-equal/well, straight from no eating to
all the commas he mentions getting eaten, without stopping at the
extremely important (historically) middle ground.

> And he addresses dronality very well (but not as in-depth as I
would like
> or as far-ranging, i.e he is mainly concerned with augmented roots
betraying
> his largely EuroIndian music theory bias)

What do you mean by augmented roots?

> But give the ol' guy credit: he at least wrote of the "Dark
Side" of
> music and has a whole chapter on symmetrical scales, modes of
limited
> transposition,

Well, these can be viewed much like the diatonic scale in that they
depend on only one comma getting eaten: for diatonic it's 81:80, for
diminished it's 648:625, for diminished it's 128:125, for 10-note
mode of limited transposition, it's 2048:2045. In fact each of these
implies its own temperament, just as 81:80 implies meantone. But he
just views these symmetrical scales as 'artificial' products of 12-
equal -- frown.

🔗wallyesterpaulrus <paul@stretch-music.com>

🔗czhang23@aol.com

In a message dated 2004:01:12 11:02:02 PM, paul-e writes:

>What's the word he uses for these huge leaps, again? It's the same
>idea as Monz's "bridging", though across a unison vector, not
>necessarily across a xenharmonic bridge . . . but Mathieu paints it
>as an almost cataclysmic musical event, while I see it as a non-event
>brought on by the curved lattice of the temperament . . .

Great Diesis. Horrible useless neologistic term, I totally agree...
Always reminds me of the Grim Reaper ;) Ta-fuckin'-Da! The GRRREAAAAT DIE*US....
::ok _I_ woke up on the wrong side - wait I woke up not only on the wrong
side of bed, I woke up the floor and it wasn't even my bed...::

>> >Not to mention that Mathieu allows the significance of meantone to
>> >completely fall through the cracks, fostering the tired old "JI vs.
>> >ET" mentality, where easily 1/3 of his book could -- and should --
>> >have been devoted to meantone examples (just about anything from
>>1480- 1780 would fit the bill).
>
>> Yepyep, I am reaaally miffed he practically didn't even mention
>>meantones - and in specific you would think he would like the 16th/17th C.
>>Italian chromatic meantones and be totally ga-ga over the 17th C. French
>>_temperaments ordinaire_!
>
>Well, the latter have exactly the same "topology" as 12-equal, but
>the former do not, and a single example of meantone and how it "eats"
>81:80 would have added so much to this book . . . but instead he
>jumps directly from JI to 12-equal/well, straight from no eating to
>all the commas he mentions getting eaten, without stopping at the
>extremely important (historically) middle ground.

I chalk it up to both his bias and his tendency to be a tad lil ADD...
kinda reminds me of both McLaren and Warren Burt when they get all worked up -
whether happy as chimp diggin inna termite hill or pissed like a rhino on a
highway island...
but ain't we all at times, lah?

>> And he addresses dronality very well (but not as in-depth as I
>>would like or as far-ranging, i.e he is mainly concerned with augmented
roots
>>betraying his largely EuroIndian music theory bias)
>
>What do you mean by augmented roots?

Oops, augmented tonics, the cornerstone to basic dronality... small
critical diff AFAIK, eh? ;)

>> But give the ol' guy credit: he at least wrote of the "Dark
>>Side" of music and has a whole chapter on symmetrical scales, modes of
>>limited transposition,
>
>Well, these can be viewed much like the diatonic scale in that they
>depend on only one comma getting eaten: for diatonic it's 81:80, for
>diminished it's 648:625, for diminished it's 128:125

In a message dated 2004:01:12 11:12:00 PM, paul-e quickly amends:

>for *augmented* it's 128:125. for 10-note

>mode of limited transposition, it's 2048:2045. In fact each of these
>implies its own temperament, just as 81:80 implies meantone. But he
>just views these symmetrical scales as 'artificial' products of 12-
>equal -- frown.

Like I said at least he included these things that are quite fun, 12tET,
"mutant" 12EDO or other EDO, or "JI approximation" of ET symmetrical scales
(ever try one of these type chromatic scales in JI? fun fun fun & somehow even
funner on a fretted _and_ prepared string instrument.... *mwaHaHa!*(musical mad
scientist googolplexgigglabyte-fit!)*

---|-----|--------|-------------|---------------------|
Hanuman Zhang, musical mad scientist

"What strange risk of hearing can bring sound to music - a hearing whose
obligation awakens a sensibility so new that it is forever a unique, new-born,
anti-death surprise, created now and now and now. .. a hearing whose moment
in time is always daybreak." - Lucia Dlugoszewski

🔗alternativetuning <alternativetuning@yahoo.com>

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, czhang23@a... wrote:
>
> In a message dated 2004:01:12 11:02:02 PM, paul-e writes:
>
> >What's the word he uses for these huge leaps, again? It's the same
> >idea as Monz's "bridging", though across a unison vector, not
> >necessarily across a xenharmonic bridge . . . but Mathieu paints
it
> >as an almost cataclysmic musical event, while I see it as a non-
event
> >brought on by the curved lattice of the temperament . . .
>
> Great Diesis. Horrible useless neologistic term, I totally
agree...
> Always reminds me of the Grim Reaper ;) Ta-fuckin'-Da! The
GRRREAAAAT DIE*US....
> ::ok _I_ woke up on the wrong side - wait I woke up not only on
the wrong
> side of bed, I woke up the floor and it wasn't even my bed...::

You can always call it by its other name, the 'minor diesis'. The 5-
limit intervals for which the name 'diesis' is used in SCALA and
Monz's ET page, obviously cobbled together from at least two
different theorists' naming systems, include:

minimal diesis: 20000/19683 (27.66 cents in JI, .4 cents wider than
septimal comma)

small diesis: 3125/3072 (29.61 cents in JI)

minor/great diesis: 128/125 (41.06 cents in JI)

maximal diesis: 250/243 (49.17 cents in JI)

major diesis: 648/625 (62.57 cents in JI)

> >> And he addresses dronality very well (but not as in-depth as
I
> >>would like or as far-ranging, i.e he is mainly concerned with
augmented
> roots
> >>betraying his largely EuroIndian music theory bias)
> >
> >What do you mean by augmented roots?
>
> Oops, augmented tonics, the cornerstone to basic dronality...
small
> critical diff AFAIK, eh? ;)

Hmm . . . I still don't know what you mean. "Augmented tonics"?

> Like I said at least he included these things that are quite
fun, 12tET,
> "mutant" 12EDO or other EDO, or "JI approximation" of ET
symmetrical scales
> (ever try one of these type chromatic scales in JI?

I'd be happy to provide some JI "pre-image" periodicity blocks for
these scales, if you're interested . . .

🔗czhang23@aol.com

In a mess dated 2004:01:14 08:32:46 AM, paulE kwootz mee & writes:

>> Great Diesis. [...]
>
>You can always call it by its other name, the 'minor diesis'.

That's IMHO the most common understandable one.

> The 5-limit intervals for which the name 'diesis' is used in SCALA and
>Monz's ET page, obviously cobbled together from at least two
>different theorists' naming systems, include:
>
>minimal diesis: 20000/19683 (27.66 cents in JI, .4 cents wider than
>septimal comma)
>
>small diesis: 3125/3072 (29.61 cents in JI)
>
>minor/great diesis: 128/125 (41.06 cents in JI)
>
>maximal diesis: 250/243 (49.17 cents in JI)
>
>major diesis: 648/625 (62.57 cents in JI)

Ah, thanx for the thoroughness in adding the cents values... that helps
me a lot in "visualizing" the whole deal...

>> >> And he addresses dronality very well (but not as in-depth as
> > >>I would like or as far-ranging, i.e he is mainly concerned with
>>augmented roots betraying his largely EuroIndian music theory bias)
>
>> >What do you mean by augmented roots?
>
>> Oops, augmented tonics
>
>Hmm . . . I still don't know what you mean. "Augmented tonics"?

;) *gigglafit!* like code-switching 'cept this _can be_ mode-switching,
i.e. figuring 'tween a low C tonic (root) and its neighboring C# (augmented
tonic/root) in dronality. ::ok too much caffeine & nicotine...and ran outta psych
meds & money::

>> Like I said at least he included these things that are quite
>>fun, 12tET, "mutant" 12EDO or other EDO, or "JI approximation" of ET
>>symmetrical scales (ever try one of these type chromatic scales in JI?
>
>I'd be happy to provide some JI "pre-image" periodicity blocks for
>these scales, if you're interested . . .

WoWzA! And didn't even ask. Considerin' the times ya have quite often
come up with answers to questions I haven't even asked yet... ya have ESP or what?
I am esp'ly keen on augmented chromatics (&, naturally, _asymmetric_
scales, "tumbling strains" and tone-clusters/tone-masses - are also big favs with
me... heterophony exploded/exploding in another words, does that make
sense?)... and oh I haven't gotten too far into periodicity blocks in my online
studies ::chagrin::

--- º°`°º ø,¸¸,ø º°`°º ø,¸¸,ø º°`°º ø,¸¸,ø º°`°º º°`°º ø,¸~->

Hanuman "Mister Sinister" Zhang, Sloth-Style Gungfu Typist

"One thing foreigners, computers, and poets have in common
is that they make unexpected linguistic associations." --- Jasia Reichardt

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, czhang23@a... wrote:
>
> In a mess dated 2004:01:14 08:32:46 AM, paulE kwootz mee & writes:
>
> >> Great Diesis. [...]
> >
> >You can always call it by its other name, the 'minor diesis'.
>
> That's IMHO the most common understandable one.
>
> > The 5-limit intervals for which the name 'diesis' is used in
SCALA and
> >Monz's ET page, obviously cobbled together from at least two
> >different theorists' naming systems, include:
> >
> >minimal diesis: 20000/19683 (27.66 cents in JI, .4 cents wider
than
> >septimal comma)
> >
> >small diesis: 3125/3072 (29.61 cents in JI)
> >
> >minor/great diesis: 128/125 (41.06 cents in JI)
> >
> >maximal diesis: 250/243 (49.17 cents in JI)
> >
> >major diesis: 648/625 (62.57 cents in JI)
>
> Ah, thanx for the thoroughness in adding the cents values...
that helps
> me a lot in "visualizing" the whole deal...

The first graph on this page:

http://sonic-arts.org/dict/bingo.htm

should help in "visualizing" the 'whole deal' in other ways . . .

> >> >> And he addresses dronality very well (but not as in-depth
as
> > > >>I would like or as far-ranging, i.e he is mainly concerned
with
> >>augmented roots betraying his largely EuroIndian music theory
bias)
> >
> >> >What do you mean by augmented roots?
> >
> >> Oops, augmented tonics
> >
> >Hmm . . . I still don't know what you mean. "Augmented tonics"?
>
> ;) *gigglafit!* like code-switching 'cept this _can be_ mode-
switching,
> i.e. figuring 'tween a low C tonic (root) and its neighboring C#
(augmented
> tonic/root) in dronality.

Hmm . . . I don't remember Mathieu talking about this, let alone
being 'mainly concerned' about this . . . If you have the book
available, can you provide a few telling quotes?

> >> Like I said at least he included these things that are quite
> >>fun, 12tET, "mutant" 12EDO or other EDO, or "JI approximation"
of ET
> >>symmetrical scales (ever try one of these type chromatic scales
in JI?
> >
> >I'd be happy to provide some JI "pre-image" periodicity blocks for
> >these scales, if you're interested . . .
>
> WoWzA! And didn't even ask. Considerin' the times ya have quite
often
> come up with answers to questions I haven't even asked yet... ya
have ESP or what?

Is that a yes?

Perhaps Gene could help here . . . Gene, how about a list of all the
possible Fokker-block detemperings of Diminished[8], Augmented[6],
Augmented[9] = Tcherepnin, and Diaschismic[10]?

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > Perhaps Gene could help here . . . Gene, how about a list of all
> the
> > possible Fokker-block detemperings of Diminished[8], Augmented
[6],
> > Augmented[9] = Tcherepnin, and Diaschismic[10]?
>
> Could you remind me of this at some point in time? I want to do
> temperings of 12 note Fokker blocks first.

OK. For now, I will produce a limited array of 'centered' examples
for Hanuman Zhang:

Diminished: unison vectors 648/625 and 9/8

cents numerator denominator
0 1 1
133.24 27 25
315.64 6 5
386.31 5 4
631.28 36 25
701.96 3 2
884.36 5 3
1017.6 9 5

cents numerator denominator
0 1 1
70.672 25 24
315.64 6 5
386.31 5 4
568.72 25 18
701.96 3 2
884.36 5 3
1017.6 9 5

cents numerator denominator
0 1 1
182.4 10 9
315.64 6 5
498.04 4 3
631.28 36 25
813.69 8 5
884.36 5 3
1129.3 48 25

cents numerator denominator
0 1 1
182.4 10 9
315.64 6 5
498.04 4 3
568.72 25 18
813.69 8 5
884.36 5 3
1066.8 50 27

Augmented: unison vectors 128/125 and (9/8 or 10/9)

cents numerator denominator
0 1 1
315.64 6 5
386.31 5 4
701.96 3 2
813.69 8 5
1088.3 15 8

cents numerator denominator
0 1 1
315.64 6 5
386.31 5 4
701.96 3 2
813.69 8 5
1129.3 48 25

cents numerator denominator
0 1 1
111.73 16 15
386.31 5 4
498.04 4 3
813.69 8 5
884.36 5 3

cents numerator denominator
0 1 1
70.672 25 24
386.31 5 4
498.04 4 3
813.69 8 5
884.36 5 3

Tcherepnin: unison vectors 128/125 and 135/128 (any other poss's?)

cents numerator denominator
0 1 1
111.73 16 15
315.64 6 5
386.31 5 4
498.04 4 3
701.96 3 2
813.69 8 5
884.36 5 3
1088.3 15 8

Messaien: unison vectors 2048/2025 and 25/24 (any other poss's?)

cents numerator denominator
0 1 1
111.73 16 15
203.91 9 8
386.31 5 4
498.04 4 3
590.22 45 32
701.96 3 2
813.69 8 5
996.09 16 9
1088.3 15 8

cents numerator denominator
0 1 1
111.73 16 15
203.91 9 8
386.31 5 4
498.04 4 3
609.78 64 45
701.96 3 2
813.69 8 5
996.09 16 9
1088.3 15 8

🔗czhang23@aol.com

In a message dated 2004:01:15 01:51:13 PM, paul-E writes:

>Hmm . . . I don't remember Mathieu talking about this [dronality], let alone
>being 'mainly concerned' about this . . . If you have the book
>available, can you provide a few telling quotes?

Okay a bit o' exaggeration on the "mainly concerned with" bit... but he
uses dronality to illustrate the "Great Diesis" quite alot... and in other
contexts to illustrate, Indian-like/Jazz-like, uses of modes, transpositions of
modes and tonal ambiguity, etc. So waaay too much to even quote. And again he
is rather insistent on the singability of these things or at least playing them
on guitar or piano.

>> >> Like I said at least he included these things that are quite
>> >>fun, 12tET, "mutant" 12EDO or other EDO, or "JI approximation"
>of ET symmetrical scales (ever try one of these type chromatic scales
>in JI?
>
>> >I'd be happy to provide some JI "pre-image" periodicity blocks for
>> >these scales, if you're interested . . .
>
>> WoWzA! And didn't even ask. Considerin' the times ya have quite
>>often come up with answers to questions I haven't even asked yet... ya
>>have ESP or what?
>
>Is that a yes?

Yepyep :)

>Perhaps Gene could help here . . . Gene, how about a list of all the
>possible Fokker-block detemperings of Diminished[8], Augmented[6],
>Augmented[9] = Tcherepnin, and Diaschismic[10]?

:)
(:

---|-----|--------|-------------|---------------------|
Hanuman Zhang, musical mad scientist: "Nah, I don't wanna take over the
world, just the sound spectrum to make it my home."

🔗czhang23@aol.com

In a message dated 2004:01:15 04:45:31 PM, paul-E writes:

>> > Perhaps Gene could help here . . . Gene, how about a list of all
>>> the possible Fokker-block detemperings of Diminished[8], Augmented
>>[6], Augmented[9] = Tcherepnin, and Diaschismic[10]?
>
Gene:
>> Could you remind me of this at some point in time? I want to do
>> temperings of 12 note Fokker blocks first.
>
Paul:
>OK. For now, I will produce a limited array of 'centered' examples
>for Hanuman Zhang:

Thanx and the data confirms a suspicion/intuition that I have had for
some time (well, recently) ... I think I finally got a good grasp and foot-in' of
what augmented means in microtonal scales - & not just some
microtonally-inflected simulations of 12tET aug. modes - thanx to Herman Miller's website and
this info)

Also this has me thinkin' that the ancient Chinese pentatonic scales were
partly intuitive versions of augmented scales... which possibly influenced
and inspired the augmented _inharmonic_ scales in South East Asia (i.e. Thailand
and Indonesia).
And it seems - at cursory glance - that the Japanese and Koreans went in
another direction: closer to diminished scales.

BTW this augmented scale is practically an exact _qin_/_ch'in_ tuning/mode
that I like a lot (just add an interval close to 8:7 {232 cents} & a stretched
octave at 1220 or so cents and you would have one complete archaic heptatonic
qin tuning:)

> cents numerator denominator
>
> 0 1 1
> 315.64 6 5
> 386.31 5 4
> 701.96 3 2
> 813.69 8 5
> 1129.3 48 25

---|-----|--------|-------------|---------------------|
Hanuman Zhang, musical mad scientist: "Nah, I don't wanna take over the
world, just the sound spectrum to make it my home."

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, czhang23@a... wrote:
>
> In a message dated 2004:01:15 04:45:31 PM, paul-E writes:
>
> >> > Perhaps Gene could help here . . . Gene, how about a list of
all
> >>> the possible Fokker-block detemperings of Diminished[8],
Augmented
> >>[6], Augmented[9] = Tcherepnin, and Diaschismic[10]?
> >
> Gene:
> >> Could you remind me of this at some point in time? I want to do
> >> temperings of 12 note Fokker blocks first.
> >
> Paul:
> >OK. For now, I will produce a limited array of 'centered' examples
> >for Hanuman Zhang:
>
> Thanx and the data confirms a suspicion/intuition that I have
had for
> some time (well, recently) ... I think I finally got a good grasp
and foot-in' of
> what augmented means in microtonal scales - & not just some
> microtonally-inflected simulations of 12tET aug. modes - thanx to
Herman Miller's website and
> this info)

Have you seen these:

/tuning/files/Erlich/augmented.gif
/tuning/files/Erlich/augmented2.gif

> Also this has me thinkin' that the ancient Chinese pentatonic
scales were
> partly intuitive versions of augmented scales...

Can you give some examples of such scales?

> which possibly influenced
> and inspired the augmented _inharmonic_ scales in South East Asia >
(i.e. Thailand
> and Indonesia).

Same question.

Have you seen:

/tuning/files/Erlich/pelogic.gif
/tuning/files/Erlich/pelogic2.gif

You might also want to look at

/tuning/files/Erlich/dicot.gif
/tuning/files/Erlich/dicot2.gif

and maybe even

/tuning/files/Erlich/beep.gif
/tuning/files/Erlich/beep2.gif

> And it seems - at cursory glance - that the Japanese and
Koreans went in
> another direction: closer to diminished scales.

Well, it seems to me that Japanese scales are more often pentatonics,
and some of the most 'characteristic' ones are periodicity blocks
with unison vectors 135/128 and 10/9 . . . but which ones look like
diminished scales to you?

Also, see:

/tuning/files/Erlich/diminished.gif
/tuning/files/Erlich/diminished2.gi
f

> BTW this augmented scale is practically an exact _qin_/_ch'in_
tuning/mode
> that I like a lot (just add an interval close to 8:7 {232 cents} &
a stretched
> octave at 1220 or so cents and you would have one complete archaic
heptatonic
> qin tuning:)

My last post was all 5-limit . . . should we move on to 7-limit?