Yahoo Tuning Groups Ultimate Backup tuning Let Pythagorus go--A Controversy.

the Turkish fellow on this list likes 41

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

robert thomas martin wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, > Graham Breed <gbreed@...> wrote:
> >
> > robert thomas martin wrote:
> > > In a certain sense the whole issue of microtuning revolves about
> how
> > > one tunes 3rds. If one accepts the idea that the Pythagorean
> thirds of
> > > 294 and 408 cents are just mathematical mumbo-jumbo and number
> juggling
> > > then what do we have left. What we have are the thirds of 267,
> 316, 386
> > > and 435 cents. Now the question arises. Which equal temperament
> is the
> > > best fit for these four thirds?
> >
> > What about 347 cents?
> >
> >
> > Graham
> > Many a medieval Arab and Persian music theorist has also wondered
> about this. I, myself, have carried out experiments with what is
> called the neutral third. It definitely has a distinctly neutral
> sound between major and minor. A wise man might say that if we wanted
> to include the middle eastern musicians in our world of music then we
> should adopt 31tet.
>
>

🔗robert thomas martin <robertthomasmartin@bigpond.com.au>

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> the Turkish fellow on this list likes 41
>
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria
<http://anaphoriasouth.blogspot.com/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
>
>
>
> robert thomas martin wrote:
> >
> > --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>,
> > Graham Breed <gbreed@> wrote:
> > >
> > > robert thomas martin wrote:
> > > > In a certain sense the whole issue of microtuning revolves
about
> > how
> > > > one tunes 3rds. If one accepts the idea that the Pythagorean
> > thirds of
> > > > 294 and 408 cents are just mathematical mumbo-jumbo and number
> > juggling
> > > > then what do we have left. What we have are the thirds of 267,
> > 316, 386
> > > > and 435 cents. Now the question arises. Which equal
temperament
> > is the
> > > > best fit for these four thirds?
> > >
> > > What about 347 cents?
> > >
> > >
> > > Graham
> > > Many a medieval Arab and Persian music theorist has also
wondered
> > about this. I, myself, have carried out experiments with what is
> > called the neutral third. It definitely has a distinctly neutral
> > sound between major and minor. A wise man might say that if we
wanted
> > to include the middle eastern musicians in our world of music
then we
> > should adopt 31tet.
> > OK. If we are going to have baseball bats at fifteen paces then
I'm going for 44tet. At least I'll have Charles Lucy for
backup.
Robert
> >
>

🔗George D. Secor <gdsecor@...>

🔗Andreas Sparschuh <a_sparschuh@...>

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@...> wrote:
on:
> --- In tuning@yahoogroups.com, "robert thomas martin" s

> > to include the middle eastern musicians in our world of music then
> > we should adopt 31tet.
>
> IMO, 31-ET significant outshines any EDO (equal division of the
> octave) of lesser number. After that, 34, 41, 46, 53, and 72 are
> the best competitors.
>
Hi George, RTM & others,
already I. Newton considerered 34,41,46,53....EDOs
that he obtained from:
http://www.research.att.com/~njas/sequences/A060528

from the corresponding scatterplot
http://www.research.att.com/~njas/sequences/graph?a=60528

he concluded from that alike already
http://en.wikipedia.org/wiki/Jing_Fang
that it had already been time in their lifetimes
to move from 12 instead 12 by that change:
http://mto.societymusictheory.org/issues/mto.93.0.3/mto.93.0.3.lindley7.gif

Even Schönberg -one of the alleged inventors of crude atonal 12-EDO-
confirmed 53 again in his famous statement:

http://www.plainsound.de/research/notation.pdf
Quote:
§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§
Die Obertonreihe ... enthält noch viele Probleme, die eine
Auseinandersetzung nötig machen werden. Und wenn wir diesen Problemen
augenblicklich noch entrinnen, so verdanken wir das fast
ausschließlich einem Kompromiß zwischen den natürlichen Intervallen
und unserer Unfähigkeit sie zu verwenden. Jenem Kompromiß, das sich
temperiertes System nennt, das einen auf eine unbestimmte Frist
geschlossenen Waffenstillstand darstellt. Diese Reduktion
der natürlichen Verhältnisse auf handliche wird aber die Entwicklung
auf die Dauer nicht aufhalten können; und das Ohr wird sich mit den
Problemen befassen müssen, weil es will.
Dann wird unsere Skala ebenso aufgehen in eine höhere Ordnung, wie die
Kirchentonarten in der Dur- und Molltonart aufgegangen sind. Ob dann
Viertel-, Achtel-, Drittel- oder (wie Busoni meint) Sechsteltöne
kommen, oder ob man direkt zu einer 53 tönigen Skala übergehen wird
... läßt sich nicht voraussagen. Vielleicht wird diese neue Teilung
der Oktave sogar
untemperiert sein und mit unserer Skala nur noch wenig gemeinsam haben."
Arnold Schoenberg: Harmonielehre, 3. Auflage, S. 22-24 (1922)
§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§

Translation:
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
"The overtone series still contains many problems that will have to
be faced. And if for the time being we still manage to escape those
problems, it is due to little else than a compromise
between the natural intervals and our inability to use them that
compromise which we call the tempered system, which amounts to an
indefinitely extended truce. This reduction of the
natural relations to manageable ones cannot permanently impede the
evolution of music; and the ear will have to attack the problems,
because it is so disposed. Then our scale will be
transformed into a higher order, as the church modes were transformed
into major and minor modes. Whether there will then be quarter tones,
eighth, third, or (as Busoni thinks) sixth tones, or whether we will
move directly to a 53-tone scale we cannot foretell. Perhaps this
new division of the octave will even be untempered and will not have
much left over in common with our scale."

Arnold Schoenberg: Theory of Harmony 3rd Edition, p. 25 (1922)
English translation by Roy E. Carter
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

That agrees with my own observation:
31 sounds worser in the 5ths than 12,
hence i personally do prefer
to agree with the above authors in their's preference of the:

http://en.wikipedia.org/wiki/53_equal_temperament
http://www.microtonal-synthesis.com/scale_53tet.htm
http://www.mythicalrecords.com/forum/viewtopic.php?p=287
http://archives.conlang.info/pho/voerfun/faenjhirkhian.html
http://www.msu.edu/~mannin44/Luke/music_theory.html
or the older alternative Philolaos predecessor
http://www.xs4all.nl/~huygensf/doc/scalesdir.txt
dyadic53tone9div.scl
53 from Philolaos tone-9-division 8:9=72:73:74:75:76:77:78:79:80:81
from:
/tuning/topicId_73974.html#73974

http://workshop-synesthetics.blogspot.com/2006/09/composing-by-numbers-summary-by-dorota.html
"LECTURE 3 XX CENTURY MUSIC

Towards atonality:
Tonal music is that in which a definite sense of key prevails, in
which all the notes are related to a central key note (a tonic):
changes of key center can be brought up by modulation
J.Cage: "the octave has no more reason to be divided into 5/6/7/9
equal intervals than to be devided into 36/59 parts. It's just a
matter of establishing limits"
C.Debussy was the first to use a scale different from traditional
scale: the whole tone scale, obtained by dividing the octave into 6
equal parts. Other possible divisions of the octave include 31 tone
scale (M. Mersenne designed a 31 tone keyboard) and 53 tone scale
(confirmed musical system in China in early 18th century)"

Yours sincerely
A.S.

🔗Torsten Anders <torstenanders@...>

🔗Carl Lumma <carl@...>

🔗Graham Breed <gbreed@...>

Andreas Sparschuh wrote:

> Hi George, RTM & others,
> already I. Newton considerered 34,41,46,53....EDOs
> that he obtained from:
> http://www.research.att.com/~njas/sequences/A060528

How do you know? We talked about Newton before and I don't remember anybody coming up with references. What was he interested in?

> he concluded from that alike already
> http://en.wikipedia.org/wiki/Jing_Fang
> that it had already been time in their lifetimes > to move from 12 instead 12 by that change: > http://mto.societymusictheory.org/issues/mto.93.0.3/mto.93.0.3.lindley7.gif

The Jing Fang page is informative, anyway. That MTO picture is the same one we had all along.

> Even Schï¿½nberg -one of the alleged inventors of crude atonal 12-EDO-
> confirmed 53 again in his famous statement:
> > http://www.plainsound.de/research/notation.pdf
<snip>
> > That agrees with my own observation:
> 31 sounds worser in the 5ths than 12, > hence i personally do prefer
> to agree with the above authors in their's preference of the:
> > http://en.wikipedia.org/wiki/53_equal_temperament

That's a good page, but it lacks a citation for Newton.

<snip>
> http://workshop-synesthetics.blogspot.com/2006/09/composing-by-numbers-summary-by-dorota.html
> "LECTURE 3 ï¿½ XX CENTURY MUSIC

(Doesn't load)

> Towards atonality:
> Tonal music is that in which a definite sense of key prevails, in
> which all the notes are related to a central key note (a tonic):
> changes of key center can be brought up by modulation
> J.Cage: "the octave has no more reason to be divided into 5/6/7/9
> equal intervals than to be devided into 36/59 parts. It's just a
> matter of establishing limits"
> C.Debussy was the first to use a scale different from traditional
> scale: the whole tone scale, obtained by dividing the octave into 6
> equal parts. Other possible divisions of the octave include 31 tone
> scale (M. Mersenne designed a 31 tone keyboard) and 53 tone scale
> (confirmed musical system in China in early 18th century)"

18th Century? The only Chinese reference for 53 in Wikipedia is the theoretical one from Jing Fang in the Han Dynasty.

Graham

🔗Herman Miller <hmiller@...>

Graham Breed wrote:
> robert thomas martin wrote:
>> In a certain sense the whole issue of microtuning revolves about how >> one tunes 3rds. If one accepts the idea that the Pythagorean thirds of >> 294 and 408 cents are just mathematical mumbo-jumbo and number juggling >> then what do we have left. What we have are the thirds of 267, 316, 386 >> and 435 cents. Now the question arises. Which equal temperament is the >> best fit for these four thirds?
(As integer ratios: 7/6, 6/5, 5/4, and 9/7)

The answer is likely to depend on how you measure the "best fit". Take for example the largest deviation in cents, since that's easily calculated in a spreadsheet. (You can download OpenOffice for free if you don't have one.) E.g. the deviations for 12-ET are 33 cents (300-267), 16 cents (316-300), 14 cents (400-386), and 35 cents (435-400), and the largest of these is 35 cents. Quite a substantial deviation, but it's better than any ET with a smaller number of steps. Then if you go down the list of ETs with more steps per octave that have a better fit by this measure, you get:

16-ET (33.13 cents)
18-ET (31.58 cents)
19-ET (14.24 cents)
22-ET (11.63 cents)
31-ET (9.28 cents)
41-ET (6.31 cents)
49-ET (5.73 cents)
50-ET (3.64 cents)
72-ET (2.98 cents)
99-ET (1.57 cents)
149-ET (1.55 cents)
171-ET (0.35 cents)

> What about 347 cents?
(11/9)

Not to mention 289 cents, 418 cents, and even 298 cents. (13/11, 14/11, and 19/16).

🔗robert thomas martin <robertthomasmartin@...>

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>
> Graham Breed wrote:
> > robert thomas martin wrote:
> >> In a certain sense the whole issue of microtuning revolves about
how
> >> one tunes 3rds. If one accepts the idea that the Pythagorean
thirds of
> >> 294 and 408 cents are just mathematical mumbo-jumbo and number
juggling
> >> then what do we have left. What we have are the thirds of 267,
316, 386
> >> and 435 cents. Now the question arises. Which equal temperament
is the
> >> best fit for these four thirds?
> (As integer ratios: 7/6, 6/5, 5/4, and 9/7)
>
> The answer is likely to depend on how you measure the "best fit".
Take
> for example the largest deviation in cents, since that's easily
> calculated in a spreadsheet. (You can download OpenOffice for free
if
> you don't have one.) E.g. the deviations for 12-ET are 33 cents
> (300-267), 16 cents (316-300), 14 cents (400-386), and 35 cents
> (435-400), and the largest of these is 35 cents. Quite a
substantial
> deviation, but it's better than any ET with a smaller number of
steps.
> Then if you go down the list of ETs with more steps per octave that
have
> a better fit by this measure, you get:
>
> 16-ET (33.13 cents)
> 18-ET (31.58 cents)
> 19-ET (14.24 cents)
> 22-ET (11.63 cents)
> 31-ET (9.28 cents)
> 41-ET (6.31 cents)
> 49-ET (5.73 cents)
> 50-ET (3.64 cents)
> 72-ET (2.98 cents)
> 99-ET (1.57 cents)
> 149-ET (1.55 cents)
> 171-ET (0.35 cents)
>
> > What about 347 cents?
> (11/9)
>
> Not to mention 289 cents, 418 cents, and even 298 cents. (13/11,
14/11,
> and 19/16).
>
From Robert: Any move away from 12tet is going to be expensive. I
think that 22tet is the most economical model to adopt because
musicians would have to put up with nine extra notes just to gain a
few cents with the purity of thirds if they adopted 31tet.Robert.

🔗Paul Poletti <paul@...>

--- In tuning@yahoogroups.com, "robert thomas martin"
<robertthomasmartin@...> wrote:
>
> In a certain sense the whole issue of microtuning revolves about how
> one tunes 3rds. If one accepts the idea that the Pythagorean thirds of
> 294 and 408 cents are just mathematical mumbo-jumbo and number juggling
> then what do we have left. What we have are the thirds of 267, 316, 386
> and 435 cents. Now the question arises. Which equal temperament is the
> best fit for these four thirds?
>
I don't check the list often, and admittedly I don't have time to read
the whole thread, so excuse me if these points have already been
raised. But from the limited amount of messages I did read, it seemed
as though this thread degenerated almost instantly into arguing about
which EDO would be better. I have two point to raise.

First, we can't forget the neutral third of 347.4 cents, because it is
a real acoustical consonance, being 9/11. It is quite possible to tune
this interval by ear alone, and once you cop to it, it rings as true
as any of the other alternative consonances that traditional western
music ignores. There is also a fairly wide-spread use of this interval
in a lot of folk traditions.

Secondly, this whole approach seems to me to represent a mentality of
the 19th century. Any fixed system is only required when talking about
acoustical instruments. If we are talking about electronic
instruments, the obvious answer is to adopt no particular fixed
system, but rather to develop systems of infinitely flexible control.
In other words, first decide what the musical end is and then design a
control system which allows the intonation to serve that purpose.
Limiting oneself to a scheme which is so large as to be unwieldy in
order to attempt to cover all bases will simultaneously excluding some
possibilities is an antiquated mindset. This would represent a great
paradigm shift, and I realize it will cause many to loose their own
particular intellectual "raison d'etre" when they no longer have this
or that system to sing the praises of, but technology has finally
freed us from the bottleneck that has always kept microtonal music
from truly spreading its wings. Why should we keep wearing these
chains just because we have become so accustomed to bearing their weight?

Ciao,

🔗robert thomas martin <robertthomasmartin@...>

--- In tuning@yahoogroups.com, "Paul Poletti" <paul@...> wrote:
>
> --- In tuning@yahoogroups.com, "robert thomas martin"
> <robertthomasmartin@> wrote:
> >
> > In a certain sense the whole issue of microtuning revolves about
how
> > one tunes 3rds. If one accepts the idea that the Pythagorean
thirds of
> > 294 and 408 cents are just mathematical mumbo-jumbo and number
juggling
> > then what do we have left. What we have are the thirds of 267,
316, 386
> > and 435 cents. Now the question arises. Which equal temperament
is the
> > best fit for these four thirds?
> >
> I don't check the list often, and admittedly I don't have time to
read
> the whole thread, so excuse me if these points have already been
> raised. But from the limited amount of messages I did read, it
seemed
> as though this thread degenerated almost instantly into arguing
about
> which EDO would be better. I have two point to raise.
>
> First, we can't forget the neutral third of 347.4 cents, because it
is
> a real acoustical consonance, being 9/11. It is quite possible to
tune
> this interval by ear alone, and once you cop to it, it rings as true
> as any of the other alternative consonances that traditional western
> music ignores. There is also a fairly wide-spread use of this
interval
> in a lot of folk traditions.
>
> Secondly, this whole approach seems to me to represent a mentality
of
> the 19th century. Any fixed system is only required when talking
about
> acoustical instruments. If we are talking about electronic
> instruments, the obvious answer is to adopt no particular fixed
> system, but rather to develop systems of infinitely flexible
control.
> In other words, first decide what the musical end is and then
design a
> control system which allows the intonation to serve that purpose.
> Limiting oneself to a scheme which is so large as to be unwieldy in
> order to attempt to cover all bases will simultaneously excluding
some
> possibilities is an antiquated mindset. This would represent a great
> paradigm shift, and I realize it will cause many to loose their own
> particular intellectual "raison d'etre" when they no longer have
this
> or that system to sing the praises of, but technology has finally
> freed us from the bottleneck that has always kept microtonal music
> from truly spreading its wings. Why should we keep wearing these
> chains just because we have become so accustomed to bearing their
weight?
>
> Ciao,
>
> P
>
I can only say that according to my own experimental findings that
the neutral third works very well when it is associated with
Pythagorean systems which contain 294 and 408cents. It doesn't work
very well in systems with 316 and 386. This would suggest that
Pythagorism leads to 24tet and Just and Septimal lead to 22tet. Since
the 22tet keyboard design fits onto a 24tet keyboard design then a
24tet microtunable keyboard would please most of the people most of
the time.
Robert.

🔗Paul Poletti <paul@...>

--- In tuning@yahoogroups.com, "robert thomas martin"
<robertthomasmartin@...> wrote:
>

> >
> I can only say that according to my own experimental findings that
> the neutral third works very well when it is associated with
> Pythagorean systems which contain 294 and 408cents. It doesn't work
> very well in systems with 316 and 386.

My point exactly. As long as your mind is stuck in thinking in
"systems", you are straightjacketing your creativity. Meanwhile,
musicians who play "systemless" instruments, like the violin, without
giving a thought to whether or not "it works" continue doing what
they've been doing for centuries, i.e., mixing the "neutral" third
with pure major and minor thirds. Or Pythagorean. Or whatever. Real
freedom, not the illusion of such.

As I said before, for the first time in history, modern technology can
finally allow the mechanical musician (keyboard player) to catch up
with "primitive" technology, but first they must slough off the
intellectual trimmings and trappings of 2000 years of conceiving of
their gamut as a collection of discrete pitches, no matter how large.

But I suppose this particular list really ought to be called "the
extended discrete pitch set" list, as it seems as 99% of the
discussion is precisely about that.

;-)

Free your mind, and your music will follow.

Ciao,

🔗robert thomas martin <robertthomasmartin@...>

--- In tuning@yahoogroups.com, "Paul Poletti" <paul@...> wrote:
>
> --- In tuning@yahoogroups.com, "robert thomas martin"
> <robertthomasmartin@> wrote:
> >
>
> > >
> > I can only say that according to my own experimental findings
that
> > the neutral third works very well when it is associated with
> > Pythagorean systems which contain 294 and 408cents. It doesn't
work
> > very well in systems with 316 and 386.
>
> My point exactly. As long as your mind is stuck in thinking in
> "systems", you are straightjacketing your creativity. Meanwhile,
> musicians who play "systemless" instruments, like the violin,
without
> giving a thought to whether or not "it works" continue doing what
> they've been doing for centuries, i.e., mixing the "neutral" third
> with pure major and minor thirds. Or Pythagorean. Or whatever. Real
> freedom, not the illusion of such.
>
> As I said before, for the first time in history, modern technology
can
> finally allow the mechanical musician (keyboard player) to catch up
> with "primitive" technology, but first they must slough off the
> intellectual trimmings and trappings of 2000 years of conceiving of
> their gamut as a collection of discrete pitches, no matter how
large.
>
> But I suppose this particular list really ought to be called "the
> extended discrete pitch set" list, as it seems as 99% of the
> discussion is precisely about that.
>
> ;-)
>
> Free your mind, and your music will follow.
>
> Ciao,
>
> P
>
From Robert. I am not sure if you are criticising me or the rest of
the world. I am concerned with designing methodologies which enable
musicologists to approach different tets with a consistent approach.
Each tet has probably got something to offer the musical world. If
all the tets between 5 and 24 are assumed to be valid then a
microtunable 24tet keyboard can cater to this need.

🔗Charles Lucy <lucy@...>

I concur with your sentiments, Paul, and in a "primitive technology" society there is no practical choice, except to do it "by ear".

Our technology is evolving in a way in which "arts" and "engineering/sciences" are now merging into a more "wholistic" (horrible newage word) form, where each discipline can benefit from developments across the traditional (and artificial) arts/sciences divide.

If one wished to fret an instrument, or set the tuning of a keyboard, it was necessary to agree on some "formula" so that players could be "in tune" with eachother.

If musicians wish to play with eachother, they need to agree some "ground" rules. e.g. what the predominant pitch should be (say A=440).

The progress of music technology is somewhat like language in that it is constantly evolving, and recently in music this is happening at a accelerating rate.

On this list we are individuals who are a small part of that evolution, and the list is very useful in the way in which those interested can exchange ideas fairly efficiently.

I remember as a teenager visiting Haifa, and having my first experience of attempted to "jam" with an Arab musician playing some sort of oud, and with whom I had no common language.

I could hear that he was playing around what I judged to be a minor key from a pitch that matched the E on my 12tET guitar.

So I tried to improvise around the chord of E minor, only to hear that none of the other notes that he was playing matched what I attempted.

This was just two instruments, which made me realise that the difficulty would be even greater if we were to add more participants to the "jam".

So we have reached a situation now where we can clearly see that there are many different "competing/co-operating" paradigms for tuning; JI, edos, meantones, septimal, malvina, breed, LucyTuning, etc.

Each model has its own advocates, and heresies, and the participants can learn from the experiences of the others and choose (as you say) which "extended discrete pitch set" they would like to play with.

I enjoy the diversity, and appreciate having my ears stretched.

Long may the tuning or ("extended discrete pitch set") list continue!

On 11 May 2008, at 09:46, Paul Poletti wrote:

> --- In tuning@yahoogroups.com, "robert thomas martin"
> <robertthomasmartin@...> wrote:
> >
>
> > >
> > I can only say that according to my own experimental findings that
> > the neutral third works very well when it is associated with
> > Pythagorean systems which contain 294 and 408cents. It doesn't work
> > very well in systems with 316 and 386.
>
> My point exactly. As long as your mind is stuck in thinking in
> "systems", you are straightjacketing your creativity. Meanwhile,
> musicians who play "systemless" instruments, like the violin, without
> giving a thought to whether or not "it works" continue doing what
> they've been doing for centuries, i.e., mixing the "neutral" third
> with pure major and minor thirds. Or Pythagorean. Or whatever. Real
> freedom, not the illusion of such.
>
> As I said before, for the first time in history, modern technology can
> finally allow the mechanical musician (keyboard player) to catch up
> with "primitive" technology, but first they must slough off the
> intellectual trimmings and trappings of 2000 years of conceiving of
> their gamut as a collection of discrete pitches, no matter how large.
>
> But I suppose this particular list really ought to be called "the
> extended discrete pitch set" list, as it seems as 99% of the
> discussion is precisely about that.
>
> ;-)
>
> Free your mind, and your music will follow.
>
> Ciao,
>
> P
>
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

🔗Paul Poletti <paul@...>

--- In tuning@yahoogroups.com, "robert thomas martin"
<robertthomasmartin@...> wrote:
>

> From Robert. I am not sure if you are criticising me or the rest of
> the world. I am concerned with designing methodologies which enable
> musicologists to approach different tets with a consistent approach.
> Each tet has probably got something to offer the musical world. If
> all the tets between 5 and 24 are assumed to be valid then a
> microtunable 24tet keyboard can cater to this need.
>
I'm not criticizing anybody, I'm just trying to encourage people to
think beyond their normal habits of thought, to try to begin to get
ready make the quantum leap that will come soon enough, I fear. Like
it or not, technology is careening toward dissolving the interface,
i.e. direct neural connection between man and machine. When this
happens, we will no longer be subject to the limitations of fingers
and buttons, really the only thing holding us back now (well, there is
MIDI as well). Then it will only be our intellectual limitations which
restrict us to "systems". I suppose some sort of structure is always
needed, but it can just as well be a fluid structure of shifting
relationships rather than a rigid structure of discrete components.
What this will be like or sound like I cannot begin to imagine. But
I'm trying nonetheless.

Ciao,

🔗Kraig Grady <kraiggrady@...>

But i think people use more tones than they think. a string quartet will constantly change what it does depending on what the music dictates. In ex. just thirds in calmer places, raised ones in more energetic passages. different things at cadences, etc.. Maybe we need to be conscious of this, but then maybe it might distract from the task at hand.

I do not share any such optimistic view though. The great mask of the next dark age will be the technology. Hence no one will bother to realize the more toys does not equal more evolved. Microtones it self still needs to be aware of it possibility to becoming a reactionary endeavor. It preoccupation with triads of which there only appears to be one
( think of the basic religion of the culture ) mixed with ETs ( platonic view of the state) makes me wonder. How little or infrequently has it ventured beyond a Partch. At one point i thought the more people doing microtones the better, the more i think now it will degenerate into the new emperor clothes of academic serialism, or on the other end, an exotic spice to banal former musics.

When visual artist first worked with new materials, of course there was a stage where they tried to do what paint did, then they realized that the material itself, it properties leads to it own unique applications and possibilities.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Paul Poletti wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, > "robert thomas martin"
> <robertthomasmartin@...> wrote:
> >
>
> > From Robert. I am not sure if you are criticising me or the rest of
> > the world. I am concerned with designing methodologies which enable
> > musicologists to approach different tets with a consistent approach.
> > Each tet has probably got something to offer the musical world. If
> > all the tets between 5 and 24 are assumed to be valid then a
> > microtunable 24tet keyboard can cater to this need.
> >
> I'm not criticizing anybody, I'm just trying to encourage people to
> think beyond their normal habits of thought, to try to begin to get
> ready make the quantum leap that will come soon enough, I fear. Like
> it or not, technology is careening toward dissolving the interface,
> i.e. direct neural connection between man and machine. When this
> happens, we will no longer be subject to the limitations of fingers
> and buttons, really the only thing holding us back now (well, there is
> MIDI as well). Then it will only be our intellectual limitations which
> restrict us to "systems". I suppose some sort of structure is always
> needed, but it can just as well be a fluid structure of shifting
> relationships rather than a rigid structure of discrete components.
> What this will be like or sound like I cannot begin to imagine. But
> I'm trying nonetheless.
>
> Ciao,
>
> P
>
>

🔗Killian/O'Callaghan Residence <gottharddanae@...>

🔗robert thomas martin <robertthomasmartin@...>

--- In tuning@yahoogroups.com, "Paul Poletti" <paul@...> wrote:
>
> --- In tuning@yahoogroups.com, "robert thomas martin"
> <robertthomasmartin@> wrote:
> >
>
> > From Robert. I am not sure if you are criticising me or the
rest of
> > the world. I am concerned with designing methodologies which
enable
> > musicologists to approach different tets with a consistent
approach.
> > Each tet has probably got something to offer the musical world.
If
> > all the tets between 5 and 24 are assumed to be valid then a
> > microtunable 24tet keyboard can cater to this need.
> >
> I'm not criticizing anybody, I'm just trying to encourage people to
> think beyond their normal habits of thought, to try to begin to get
> ready make the quantum leap that will come soon enough, I fear. Like
> it or not, technology is careening toward dissolving the interface,
> i.e. direct neural connection between man and machine. When this
> happens, we will no longer be subject to the limitations of fingers
> and buttons, really the only thing holding us back now (well, there
is
> MIDI as well). Then it will only be our intellectual limitations
which
> restrict us to "systems". I suppose some sort of structure is always
> needed, but it can just as well be a fluid structure of shifting
> relationships rather than a rigid structure of discrete components.
> What this will be like or sound like I cannot begin to imagine. But
> I'm trying nonetheless.
>
> Ciao,
>
> P
>

Ok. But until the great fluidlty descends upon us I think that we
should try to maintain the musical civilisation which we have in our
possession. We need to make everything easier for the younger
generations so that they may stand on our shoulders. From Robert.

🔗Cameron Bobro <misterbobro@...>

--- In tuning@yahoogroups.com, "robert thomas
>martin" <robertthomasmartin@...> wrote:

> I can only say that according to my own experimental findings
>that
> the neutral third works very well when it is associated with
> Pythagorean systems which contain 294 and 408cents. It doesn't work
> very well in systems with 316 and 386.

Different strokes for different folks, of course, but to me it seems
very much otherwise. I think the "middle" and "other" thirds work
very well with 6/5 and 5/4, and combining various thirds is a quick
and simple way to get all kinds of euphonious chords which can also
break out of the do-mi(me)-sol framework. For tunings where melodic
intervals are very important, I find that middle thirds in
conjunction with 6/5 and 5/4 tend to kind of just happen along the
way, anyway. Integration of Just "classics" also seems to take the
poison out of many chords could otherwise be pretty hairy, with
apparently diminshed or augmented fifths etc.

For example, the interval 22/15, at approx. 663 cents, is very active
and probably would be considered dissonant by just about anybody. As
the product of 11/9 and 6/5, it is suddenly softer, try it yourself.
Trying different versions and inversions, this exuberant interval
can find itself transformed as part of a noble and even quite pretty
harmony, 5/3 split into an 11/9 and and 15/11. Spicy, but not sour
(to my ears).

And of course, if you're thinking of taller chords in terms of higher
partials, you're going to get middle thirds quite quickly, whether
you want them or not (in octave-reduced terms, between 9/8 and 11/8,
so you'll also have a 27/22 if you've got a 3/2 off the 9/8, and so
on).

I did a little improvisation to illustrate some of these kinds of
chords. The second part has a motoric and repetitive bass line in
order to demonstrate, hopefully, that there can be quite a bit of
percieved harmonic movement using ambiguously rooted harmonies, even
if the bass is droning away. This is in reference to some recent
discussions here about ambiguity of roots in "microtonal" harmonies.

http://abumbrislumen.googlepages.com/DimAugVerb.mp3

>This would suggest that
> Pythagorism leads to 24tet

I think a string of fifths is going to suggest 53 equal, not 24.
53 pure fifths octave-reduced differs from 53-equal by a maximum
of, lessee, 3.5 cents, and an average of two cents or so. 24 pure
fifths is going to be way off from 24-equal, more like two 12-equals
offset by an eighth-tone or something along those lines.

>and Just and Septimal lead to 22tet.

Just just leads to mo' Just, or "Rational Intonation", in my opinion,
being infinite in nature, and I hopefully won't find myself being
led to 22-equal for any reason because the sound is very much not to
my taste. To each their own of course. If by "Just" you mean 6/5 and
5/4 triads, that actually leads to all kinds of possibilities, for
better or for worse. By the way, I haven't used a literal equal
division of the octave, other than for notation, for several years.
Literally equal divisions, for me, would do nothing but create more
work in synthesis, detuning for a less sterile sound. Why use a ruler
then go over the line to make it look like it was brushed rather than
using a brush in the first place? take care,

-Cameron Bobro

🔗ozanyarman@...

Hi Cameron,

I see you have an admiration for maqamic intervals. I liked your improvisation. Would you be interested in trying out:

9:8
16:13
4:3
19:13

which is a pretty rugged Saba flavour?

Oz.

On May 19, 2008, at 1:04 AM, Cameron Bobro wrote:

> --- In tuning@yahoogroups.com, "robert thomas
>> martin" <robertthomasmartin@...> wrote:
>
>> I can only say that according to my own experimental findings
>> that
>> the neutral third works very well when it is associated with
>> Pythagorean systems which contain 294 and 408cents. It doesn't work
>> very well in systems with 316 and 386.
>
> Different strokes for different folks, of course, but to me it seems
> very much otherwise. I think the "middle" and "other" thirds work
> very well with 6/5 and 5/4, and combining various thirds is a quick
> and simple way to get all kinds of euphonious chords which can also
> break out of the do-mi(me)-sol framework. For tunings where melodic
> intervals are very important, I find that middle thirds in
> conjunction with 6/5 and 5/4 tend to kind of just happen along the
> way, anyway. Integration of Just "classics" also seems to take the
> poison out of many chords could otherwise be pretty hairy, with
> apparently diminshed or augmented fifths etc.
>
> For example, the interval 22/15, at approx. 663 cents, is very active
> and probably would be considered dissonant by just about anybody. As
> the product of 11/9 and 6/5, it is suddenly softer, try it yourself.
> Trying different versions and inversions, this exuberant interval
> can find itself transformed as part of a noble and even quite pretty
> harmony, 5/3 split into an 11/9 and and 15/11. Spicy, but not sour
> (to my ears).
>
> And of course, if you're thinking of taller chords in terms of higher
> partials, you're going to get middle thirds quite quickly, whether
> you want them or not (in octave-reduced terms, between 9/8 and 11/8,
> so you'll also have a 27/22 if you've got a 3/2 off the 9/8, and so
> on).
>
> I did a little improvisation to illustrate some of these kinds of
> chords. The second part has a motoric and repetitive bass line in
> order to demonstrate, hopefully, that there can be quite a bit of
> percieved harmonic movement using ambiguously rooted harmonies, even
> if the bass is droning away. This is in reference to some recent
> discussions here about ambiguity of roots in "microtonal" harmonies.
>
> http://abumbrislumen.googlepages.com/DimAugVerb.mp3
>
>> This would suggest that
>> Pythagorism leads to 24tet
>
> I think a string of fifths is going to suggest 53 equal, not 24.
> 53 pure fifths octave-reduced differs from 53-equal by a maximum
> of, lessee, 3.5 cents, and an average of two cents or so. 24 pure
> fifths is going to be way off from 24-equal, more like two 12-equals
> offset by an eighth-tone or something along those lines.
>
>> and Just and Septimal lead to 22tet.
>
> Just just leads to mo' Just, or "Rational Intonation", in my opinion,
> being infinite in nature, and I hopefully won't find myself being
> led to 22-equal for any reason because the sound is very much not to
> my taste. To each their own of course. If by "Just" you mean 6/5 and
> 5/4 triads, that actually leads to all kinds of possibilities, for
> better or for worse. By the way, I haven't used a literal equal
> division of the octave, other than for notation, for several years.
> Literally equal divisions, for me, would do nothing but create more
> work in synthesis, detuning for a less sterile sound. Why use a ruler
> then go over the line to make it look like it was brushed rather than
> using a brush in the first place? take care,
>
> -Cameron Bobro

🔗robert thomas martin <robertthomasmartin@...>

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...>
wrote:
>
> --- In tuning@yahoogroups.com, "robert thomas
> >martin" <robertthomasmartin@> wrote:
>
> > I can only say that according to my own experimental findings
> >that
> > the neutral third works very well when it is associated with
> > Pythagorean systems which contain 294 and 408cents. It doesn't
work
> > very well in systems with 316 and 386.
>
> Different strokes for different folks, of course, but to me it
seems
> very much otherwise. I think the "middle" and "other" thirds work
> very well with 6/5 and 5/4, and combining various thirds is a quick
> and simple way to get all kinds of euphonious chords which can also
> break out of the do-mi(me)-sol framework. For tunings where melodic
> intervals are very important, I find that middle thirds in
> conjunction with 6/5 and 5/4 tend to kind of just happen along the
> way, anyway. Integration of Just "classics" also seems to take the
> poison out of many chords could otherwise be pretty hairy, with
> apparently diminshed or augmented fifths etc.
>
> For example, the interval 22/15, at approx. 663 cents, is very
active
> and probably would be considered dissonant by just about anybody.
As
> the product of 11/9 and 6/5, it is suddenly softer, try it
yourself.
> Trying different versions and inversions, this exuberant interval
> can find itself transformed as part of a noble and even quite
pretty
> harmony, 5/3 split into an 11/9 and and 15/11. Spicy, but not sour
> (to my ears).
>
> And of course, if you're thinking of taller chords in terms of
higher
> partials, you're going to get middle thirds quite quickly, whether
> you want them or not (in octave-reduced terms, between 9/8 and
11/8,
> so you'll also have a 27/22 if you've got a 3/2 off the 9/8, and so
> on).
>
> I did a little improvisation to illustrate some of these kinds of
> chords. The second part has a motoric and repetitive bass line in
> order to demonstrate, hopefully, that there can be quite a bit of
> percieved harmonic movement using ambiguously rooted harmonies,
even
> if the bass is droning away. This is in reference to some recent
> discussions here about ambiguity of roots in "microtonal"
harmonies.
>
> http://abumbrislumen.googlepages.com/DimAugVerb.mp3
>
> >This would suggest that
> > Pythagorism leads to 24tet
>
> I think a string of fifths is going to suggest 53 equal, not 24.
> 53 pure fifths octave-reduced differs from 53-equal by a maximum
> of, lessee, 3.5 cents, and an average of two cents or so. 24 pure
> fifths is going to be way off from 24-equal, more like two 12-
equals
> offset by an eighth-tone or something along those lines.
>
> >and Just and Septimal lead to 22tet.
>
> Just just leads to mo' Just, or "Rational Intonation", in my
opinion,
> being infinite in nature, and I hopefully won't find myself being
> led to 22-equal for any reason because the sound is very much not
to
> my taste. To each their own of course. If by "Just" you mean 6/5
and
> 5/4 triads, that actually leads to all kinds of possibilities, for
> better or for worse. By the way, I haven't used a literal equal
> division of the octave, other than for notation, for several years.
> Literally equal divisions, for me, would do nothing but create more
> work in synthesis, detuning for a less sterile sound. Why use a
ruler
> then go over the line to make it look like it was brushed rather
than
> using a brush in the first place? take care,
>
> -Cameron Bobro
>
From Robert. Try 0-126-252-378-663-789-915-1200cents if you like
663cents so much.

🔗Cameron Bobro <misterbobro@...>

🔗robert thomas martin <robertthomasmartin@...>

🔗Cameron Bobro <misterbobro@...>

Sure- here's one that has a chain of 663 cent like you proposed, but
with each split as 11/9 and 6/5.

0: 1/1 0.000 unison, perfect prime
1: 242/225 126.098
2: 11/9 347.408 undecimal neutral third
3: 2662/2025 473.506
4: 22/15 663.049 undecimal diminished fifth
5: 5324/3375 789.148
6: 242/135 1010.457
7: 2/1 1200.000 octave

hang on, let's see... going to do "compare scale" in the Scala
archive...well as happens sometimes when I pick some harmony just by
noodling around to find what sounds sweet to me, then roll it out in
a logical fashion, this one is very close to a mode of one of Erv
Wilson's scales (in this case, golden horogram number 11, transposed
to the second tone).

There's a certain sound of Just plus not-Just-that-is-somehow-"other
Just", laced together. I don't know how to describe it it in words.
To each their own of course.

-Cameron Bobro

🔗robert thomas martin <robertthomasmartin@...>

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...>
wrote:
>
> --- In tuning@yahoogroups.com, "robert thomas
> martin" <robertthomasmartin@> wrote:
> >
> > --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@>
> > wrote:
> > >
> > > --- In tuning@yahoogroups.com, "robert thomas
> > > martin" <robertthomasmartin@> wrote:
> > >
> > > > Try 0-126-252-378-663-789-915-1200cents if you like
> > > > 663cents so much.
> > >
> > >
> > > That's a generator of 663, with a period of a pure octave.
Where
> > are
> > > the middle thirds? The combination of middle thirds with other
> > thirds
> > > is the point; in the example I gave, 11/9 and 6/5. I believe
> that
> > I
> > > was quite clear in saying that the 663 cents in itself isn't
the
> > > goal- in fact I'm certain that this was clear, because Ozan
> > > immediately offered another harmony of the same kind and
> principle,
> > a
> > > 16/13 combined with a 19/16. Another example would be, say, a 5/
> 4
> > on
> > > top of a middle third, resulting in the appearance of an
> > > "augmented" "fifth". Of course it's not necessarily a "fifth"
at
> > all.
> > >
> > > -Cameron Bobro
> > >
> > From Robert. Would you be able to supply one or more heptatonic
> > scales (in cents) which illustrate your ideas? Or else, a 12-note
> > tuning table which I can program into my sound device? I don't
> quite
> > understand what you are talking about. Sorry.
> >
>
> Sure- here's one that has a chain of 663 cent like you proposed,
but
> with each split as 11/9 and 6/5.
>
> 0: 1/1 0.000 unison, perfect prime
> 1: 242/225 126.098
> 2: 11/9 347.408 undecimal neutral third
> 3: 2662/2025 473.506
> 4: 22/15 663.049 undecimal diminished fifth
> 5: 5324/3375 789.148
> 6: 242/135 1010.457
> 7: 2/1 1200.000 octave
>
> hang on, let's see... going to do "compare scale" in the Scala
> archive...well as happens sometimes when I pick some harmony just
by
> noodling around to find what sounds sweet to me, then roll it out
in
> a logical fashion, this one is very close to a mode of one of Erv
> Wilson's scales (in this case, golden horogram number 11,
transposed
> to the second tone).
>
> There's a certain sound of Just plus not-Just-that-is-somehow-
"other
> Just", laced together. I don't know how to describe it it in words.
> To each their own of course.
>
> -Cameron Bobro
>
From Robert. I've had a closer look and listen to your supplied
scale. It appears to be consistently mapped onto a I-IIm-V chord
progression. For example, C-E-G becomes 0-347-663 and D-F-A becomes
126-474-789 and G-B-D becomes 663-1010-126. Some of the readers will
no doubt realise that they can substitute lots of other possibilities
onto the I-IIm-V and I-IV-V progressions.

🔗robert thomas martin <robertthomasmartin@...>

--- In tuning@yahoogroups.com, "robert thomas martin"
<robertthomasmartin@...> wrote:
>
> --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@>
> wrote:
> >
> > --- In tuning@yahoogroups.com, "robert thomas
> > martin" <robertthomasmartin@> wrote:
> > >
> > > --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@>
> > > wrote:
> > > >
> > > > --- In tuning@yahoogroups.com, "robert thomas
> > > > martin" <robertthomasmartin@> wrote:
> > > >
> > > > > Try 0-126-252-378-663-789-915-1200cents if you like
> > > > > 663cents so much.
> > > >
> > > >
> > > > That's a generator of 663, with a period of a pure octave.
> Where
> > > are
> > > > the middle thirds? The combination of middle thirds with
other
> > > thirds
> > > > is the point; in the example I gave, 11/9 and 6/5. I believe
> > that
> > > I
> > > > was quite clear in saying that the 663 cents in itself isn't
> the
> > > > goal- in fact I'm certain that this was clear, because Ozan
> > > > immediately offered another harmony of the same kind and
> > principle,
> > > a
> > > > 16/13 combined with a 19/16. Another example would be, say, a
5/
> > 4
> > > on
> > > > top of a middle third, resulting in the appearance of an
> > > > "augmented" "fifth". Of course it's not necessarily a "fifth"
> at
> > > all.
> > > >
> > > > -Cameron Bobro
> > > >
> > > From Robert. Would you be able to supply one or more
heptatonic
> > > scales (in cents) which illustrate your ideas? Or else, a 12-
note
> > > tuning table which I can program into my sound device? I don't
> > quite
> > > understand what you are talking about. Sorry.
> > >
> >
> > Sure- here's one that has a chain of 663 cent like you proposed,
> but
> > with each split as 11/9 and 6/5.
> >
> > 0: 1/1 0.000 unison, perfect prime
> > 1: 242/225 126.098
> > 2: 11/9 347.408 undecimal neutral third
> > 3: 2662/2025 473.506
> > 4: 22/15 663.049 undecimal diminished fifth
> > 5: 5324/3375 789.148
> > 6: 242/135 1010.457
> > 7: 2/1 1200.000 octave
> >
> > hang on, let's see... going to do "compare scale" in the Scala
> > archive...well as happens sometimes when I pick some harmony just
> by
> > noodling around to find what sounds sweet to me, then roll it out
> in
> > a logical fashion, this one is very close to a mode of one of Erv
> > Wilson's scales (in this case, golden horogram number 11,
> transposed
> > to the second tone).
> >
> > There's a certain sound of Just plus not-Just-that-is-somehow-
> "other
> > Just", laced together. I don't know how to describe it it in
words.
> > To each their own of course.
> >
> > -Cameron Bobro
> >
> From Robert. I've had a closer look and listen to your supplied
> scale. It appears to be consistently mapped onto a I-IIm-V chord
> progression. For example, C-E-G becomes 0-347-663 and D-F-A becomes
> 126-474-789 and G-B-D becomes 663-1010-126. Some of the readers
will
> no doubt realise that they can substitute lots of other
possibilities
> onto the I-IIm-V and I-IV-V progressions.
>
More from Robert. If you have a Kurzweil (or similar) and if you
treat your scale as being built from the 0-347-663 chord then when
applied to a I-IV-V progression a 12-note tuning table can be
constructed for playing standard midi files. This tuning table would
be: C=0, C#=1137, D=126, Eb=157, E=347, F=284, F#=474, G=663, Ab=694,
A=789, Bb=821, B=1010 and C'=1200. This is an application of the
universal 3-note chord algorithm previously posted.

🔗Cameron Bobro <misterbobro@...>

--- In tuning@yahoogroups.com, "robert thomas
martin" <robertthomasmartin@...> wrote:
>
> --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@>
> wrote:
> >
> > --- In tuning@yahoogroups.com, "robert thomas
> > martin" <robertthomasmartin@> wrote:
> > >
> > > --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@>
> > > wrote:
> > > >
> > > > --- In tuning@yahoogroups.com, "robert thomas
> > > > martin" <robertthomasmartin@> wrote:
> > > >
> > > > > Try 0-126-252-378-663-789-915-1200cents if you like
> > > > > 663cents so much.
> > > >
> > > >
> > > > That's a generator of 663, with a period of a pure octave.
> Where
> > > are
> > > > the middle thirds? The combination of middle thirds with
other
> > > thirds
> > > > is the point; in the example I gave, 11/9 and 6/5. I
believe
> > that
> > > I
> > > > was quite clear in saying that the 663 cents in itself isn't
> the
> > > > goal- in fact I'm certain that this was clear, because Ozan
> > > > immediately offered another harmony of the same kind and
> > principle,
> > > a
> > > > 16/13 combined with a 19/16. Another example would be, say,
a 5/
> > 4
> > > on
> > > > top of a middle third, resulting in the appearance of an
> > > > "augmented" "fifth". Of course it's not necessarily a
"fifth"
> at
> > > all.
> > > >
> > > > -Cameron Bobro
> > > >
> > > From Robert. Would you be able to supply one or more
heptatonic
> > > scales (in cents) which illustrate your ideas? Or else, a 12-
note
> > > tuning table which I can program into my sound device? I don't
> > quite
> > > understand what you are talking about. Sorry.
> > >
> >
> > Sure- here's one that has a chain of 663 cent like you proposed,
> but
> > with each split as 11/9 and 6/5.
> >
> > 0: 1/1 0.000 unison, perfect prime
> > 1: 242/225 126.098
> > 2: 11/9 347.408 undecimal neutral third
> > 3: 2662/2025 473.506
> > 4: 22/15 663.049 undecimal diminished fifth
> > 5: 5324/3375 789.148
> > 6: 242/135 1010.457
> > 7: 2/1 1200.000 octave
> >
> > hang on, let's see... going to do "compare scale" in the Scala
> > archive...well as happens sometimes when I pick some harmony
just
> by
> > noodling around to find what sounds sweet to me, then roll it
out
> in
> > a logical fashion, this one is very close to a mode of one of
Erv
> > Wilson's scales (in this case, golden horogram number 11,
> transposed
> > to the second tone).
> >
> > There's a certain sound of Just plus not-Just-that-is-somehow-
> "other
> > Just", laced together. I don't know how to describe it it in
>words.
> > To each their own of course.
> >
> > -Cameron Bobro
> >
> From Robert. I've had a closer look and listen to your supplied
> scale. It appears to be consistently mapped onto a I-IIm-V chord
> progression. For example, C-E-G becomes 0-347-663 and D-F-A
becomes
> 126-474-789 and G-B-D becomes 663-1010-126. Some of the readers
>will
> no doubt realise that they can substitute lots of other
possibilities
> onto the I-IIm-V and I-IV-V progressions.

This is fundamentally incorrect. But it is a good example of "how to
make microtonal music more difficult", and a classic example of one
of things that drag microtonal music down and make it sound hmmm...
what's the word... bad.

Chord numbers like I, ii, etc., come from functional harmony. Now,
you can probably train yourself to hear the lowest tone of any
roughly triad-shaped harmony as the root. But even in "common
practice" music, where at first glance this might seem to be
identical to hearing the "real" root, this is known to be bogus.

Look at the history of the 6-4 voicing, the second inversion.

Take what's got to be the most blatantly rooted triad of all:

0-386-702 (cents)

let's call it C-E-G.

There are probably dozens of different explanations as to "why" C is
percieved as the root, but I've never come across anything suggesting
that, given the concept of "root" at all, C is not the root of a
first position C Major triad. In orchestration, you might cocievably
have a situation where the E is played fortissimo by the brass and
C and G are whispered sotto voce by a blockflute and a comb-and-
tissue-paper, and in composition you might have G hammered out 96
times in a row while C and E appear once, or things like that, but
when we're listening to a C Major first-position triad, and we
believe in roots at all, C is the root.

Now drop the fifth into the bass, so it's now G-C-E. There is now a
sixth above the lowest note, and a fourth, hence "6-4". (C-E-G is "5-
3"). The intervals are now 0-498-386, but it's still obviously a C
major, right?

Well, listen to it and sing with it some, and it should be clear why
there are long traditions, customs, and "rules" about the second
inversion in tonal music. Descriptions vary- something like "less
stable than first position", "somewhat dissonant" all the way to "it
sounds like a suspension that wants to resolve, with G as the root".
Only in "musical set theory", or in uneducated common-practice-stylee
chit-chat, would anyone claim that C-E-G and G-C-E are the "same".

In the vast body of Western tonal harmony you'll find the second
inversion far more often in cadences (it's even called a "cadential"
voicing) and areas of modulation than elsewhere.

Pre-Rameau, before the idea of "roots" was "established" and things
were so oriented to voice-leading and ear-o-ry, I bet this bad boy
almost always held the G, with the C and E moving in parallel to B
and D. If Margot Schulter is around, she'll know the exact dates and
stats on these things.

So anyway: right from the git-go, in the most simple and
straightforward tonal situation of all, we already have "but..."'s
and footnotes about the I, for crying out loud. We didn't even have
to look at vii° or whatever.

Now we start using microtunes and different tunings. If a simple
matter of voicing already has at least some tonal impact on the most
"rooted" chord of them all, it's as plain as day that when we start
using all kinds of intervals in different inversions we're going to
have ambiguous roots, indeterminate roots, whatever. Sooner or later
we will be using chords that aren't nearly as evenly spaced as a
major 3d + minor 3d, and the "root position" of such chords, or even
the very existence of a "root position", is going to be a matter of
debate.

And this is going to happen even in a roughly diatonic and triad
environment, which is just one possibility, not the only possibility.

It should be obvious that you can't shoehorn "microtonal" music into
I-IV-V, not if you assume that those numbers have any real meaning
whatsover. At the very least there must be a lot of qualifying.

Good luck with your new Yahoo group.

-Cameron Bobro

Let Pythagorus go--A Controversy.

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