Yahoo Tuning Groups Ultimate Backup tuning scales formed by alternating thirds/dual generators

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

> this is discussed and is the basis of the 17 tone scale here
> http://anaphoria.com/genus.PDF

Another way of getting to virtually the same scale is to start with 5-
limit JI and then treat the schisma or 32805:32768 as a unison
(either through temperament or otherwise). Helmholtz wrote and
experimented a lot in this direction so I associate schemes tied with
32805:32768 with his name in my 'Middle' Path paper (as opposed to
the technical term "Skhismatic"). As I tried to explain there
(incompletely perhaps), this (along with octave-equivalence) implies
a series of scales with 12, 17, 29, 41, 53 . . . notes. The 17-note
scale is nearly identical with this one.

> in passing conversation i asked him about dual+ generators and he
said
> he found the results of a single generator was more workable and it
is
> quite easy to produce the same type of material..

This is a perfect example, since as we both know, the Helmholtz or
Skhismatic system can be generated by the 3:2-ratio interval
or "fifth" (with the period equal to the 2:1-ratio interval
or "octave"), as long as the schisma or 32805:32768 is being
neglected.

However, the two points of view of this scale don't have to be in
competition with one another and can provide complementary ways to
view it, as they do for the diatonic scale.

Meanwhile, for all we know, it's certainly conceivable that there can
be musical pitch systems which are best understood in terms of
alternating generators, and can't be explained otherwise In terms the
growth of flowers/plants, which can be understood as parallel to
musical scales if a full circle is equated with the octave, see this
page, especially the bottom:

http://maven.smith.edu/~phyllo/About/Classification.html

Spiral phyllotaxis corresponds to the MOS (single-generator), octave-
period scale systems Erv Wilson has written about, and multijugate
phyllotaxis corresponds to the maybe-MOS scales like augmented (e.g.
L-s-L-s-L-s), diminished (e.g. s-L-s-L-s-L-s-L), pajara/srutal (e.g.
s-s-s-s-L-s-s-s-s-L), and other such scale systems where the period
is a fraction of an octave. But see the bottom of the page where it
says "Other Phyllotactic Patterns". There is some evidence that some
plants grow in neither of these ways, nor in a way corresponding to
an "equal division of the octave", but rather according to a
repeating sequence of at least 2 different generator angles (sizes).
The example depicted at the bottom alternates generators that would
correspond to 581.17 cents and 183.73 cents if an interval of
equivalence of exactly 1200 cents is assumed. This produces scales
like:

0
146.07
329.80
475.87
581.17
764.90
910.97
1094.70
1200

with step sizes of
146.0700
183.7300
146.0700
105.3000
183.7300
146.0700
183.7300
105.3000

or a MLMsLMLs pattern of steps.

🔗Carl Lumma <clumma@yahoo.com>

> http://maven.smith.edu/~phyllo/About/Classification.html
>
> Spiral phyllotaxis corresponds to the MOS (single-generator),
> octave-period scale systems Erv Wilson has written about, and
> multijugate phyllotaxis corresponds to the maybe-MOS scales
> like augmented (e.g. L-s-L-s-L-s), diminished
> (e.g. s-L-s-L-s-L-s-L), pajara/srutal (e.g. s-s-s-s-L-s-s-s-s-L),
> and other such scale systems where the period is a fraction of
> an octave. But see the bottom of the page where it says "Other
> Phyllotactic Patterns". There is some evidence that some plants
> grow in neither of these ways, nor in a way corresponding to an
> "equal division of the octave", but rather according to a
> repeating sequence of at least 2 different generator angles
> (sizes). The example depicted at the bottom alternates
> generators that would correspond to 581.17 cents and 183.73
> cents if an interval of equivalence of exactly 1200 cents is
> assumed. This produces scales like:
>
> 0
> 146.07
> 329.80
> 475.87
> 581.17
> 764.90
> 910.97
> 1094.70
> 1200
>
> with step sizes of
> 146.0700
> 183.7300
> 146.0700
> 105.3000
> 183.7300
> 146.0700
> 183.7300
> 105.3000
>
> or a MLMsLMLs pattern of steps.

Whoa!

🔗Gene Ward Smith <gwsmith@svpal.org>

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

> Another way of getting to virtually the same scale is to start with 5-
> limit JI and then treat the schisma or 32805:32768 as a unison
> (either through temperament or otherwise). Helmholtz wrote and
> experimented a lot in this direction so I associate schemes tied with
> 32805:32768 with his name in my 'Middle' Path paper (as opposed to
> the technical term "Skhismatic"). As I tried to explain there
> (incompletely perhaps), this (along with octave-equivalence) implies
> a series of scales with 12, 17, 29, 41, 53 . . . notes. The 17-note
> scale is nearly identical with this one.

In terms of 5-limit scales with circles of thirds, which therefore are
analogous to Meantone[7] (the diatonic scale) the most obvious are
Diaschismic[10] and Schismatic[17].

Diaschismic[10] could be defined as what you get when you tune Paul's
decatonic scale to 34-et and not 22-et, and with 10 notes rather than
17, has more of a chance of really being grasped as a scale. Schismatic
[17] has been suggested as an alternate world historical path for
Western harmony, but I don't buy the theory it would evolve to 17 equal
r even 22, so it would in my view have lead to a very different
development.

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Justin . <justinasia@yahoo.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Ozan Yarman <ozanyarman@superonline.com>

Traditionally, the tuning involves the Pythagorean ratios of Safiyuddin Urmawi of Baghdad who lived during the Mongol invasion which dethroned the caliphate. This 3-limit system has been extended to 24-pitches by Rauf Yekta a century ago and adopted by Arel-Ezgi in Turkey not much after that. The difference between these are, Yekta started his scale from perde yegah which he notated as D (Re) due to the frequently preferred Mansur Ney producing this pitch (actually the pitch an octave below that written) according to the standard diapason, while Arel-Ezgi used the exact same system, except that they preferred to start with C (Do), which they called Kaba-Chargah. By doing so, they had to redefine the whole system starting from this very tone and consequently they had chosen the Pythagorean diatonic major scale as default, although it was by no means appropriate for Maqam Music at that time.

Little did any one of them realize that the system of Key Transposition required perde rast, or the first note produced from the second partial of the Ney (since the first harmonic is hard to produce), to be the first degree for the tonality of the entire Maqamat. Therefore, the relative frequency of perde rast should have been accepted as 1/1, which should have been `Do` and notated as C on the staff for all Ahenks just as it was done for Clarinets and Trumpets for centuries.

They also violated the `sacred` code of the apotome by breaking the chain of fifths that brought forth the sharps (#) and flats (b). Instead of #, the sharps started to get a curious symbol resembling a TV-antenna, which remains as an element of utter consternation.

Decades ago, due to the standard tuning of the Tanbur and its incorporation in Maqam Music ensembles, the diapason has been transposed up by a perfect fifth to Bolahenk (actually the octave complement of it, which is Nisfiye) instead of Mansur. This was done by denoting 440 Hz as Re instead of the international standard La. The result was that the entire repertory is now sung a fourth lower than written with the same note names! To add insult to injury, this is once more transposed a fourth lower nowadays in order that some may sing from the regularly preferred Kiz Ahenk, as Bolahenk Nisfiye is way too high.

The pitches of Maqam Music are better understood as pitch-clusters. This has been ascertained by Can Akkoc, Ph. D. in his analyses of the records of Maqam Music masters.

The Arabs solved the mess by agreeing to a 24-tET, or near 24-tET solution as proposed by Mushaqa (where perde rast is correctly notated) which they may admit is not quite exact.

Cordially,
Ozan Yarman

----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 24 Eylül 2005 Cumartesi 2:52
Subject: [tuning] Re: Arab tuning

--- In tuning@yahoogroups.com, "Justin ." <justinasia@y...> wrote:
>
> > > Schismatic
> > > [17] has been suggested as an alternate world
> > historical path for
> > > Western harmony,
> >
> > It's also been put forth, essentially, as the
> > Medieval Arabic tuning
> > system.
>
> What is this tuning? Is it still used today?

It's basically Pythagorean, with perhaps the fifth flattened very
slightly by 1/8 to 1/10 schisma. 53, 118 or 171 are typical
schismatic equal temperaments. As for how generally it is used,
particularly in a scale of 17 tones, I don't know. The Indian system
of srutis may implicitly use it with 22 tones, Helmholtz used it
with 24, and so forth.

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Justin . <justinasia@yahoo.com>

🔗Ozan Yarman <ozanyarman@superonline.com>

Hi Justin! To my knowledge, fretted instruments like the Tanbur comprise 30-40 pitches out of a possible hundred for Maqam Music. I also believe there are indeed regional instruments in North Africa, Arabian peninsula, North India, etc... which are prepared to playing particular maqams our of possible hundreds.

Arabs have simplified the whole deal by adopting 24-tET, Turks and Syrians 24-Pythagorean. I am not sure about Persians, but suspect that their system is resemblant of the Hindustani Sangeet which is also based on 22 pseudo-obscure srutis per octave.

Neither 24-EQ nor 24-Pyth do justice to Maqam Music pitches in my opinion. One needs as dense a system as 193-tET in order to correctly represent the meantone-pythagorean hybrid nature of this genre at every degree of 12 semitones per octave with all the intonational flavours.

Cordially,
Ozan
----- Original Message -----
From: Justin .
To: tuning@yahoogroups.com
Sent: 25 Eylül 2005 Pazar 12:16
Subject: Re: [tuning] Re: Arab tuning

Thank you for putting me on to Maqam music. In case
any of you are interested I found a very nce website
with lots of audio samples of the different scales
http://www.maqamworld.com/index.html
There are so many scales with different tunings that I
am confused as to how many pitches they might have in
total. And whether the freted instuments can play
every note of all the scales or whether there are
different instruments for the different families of
scales (maybe regional?) Maybe some of you know the
answers?
Best wishes
Justin.

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🔗Carl Lumma <clumma@yahoo.com>

> Thank you for putting me on to Maqam music. In case
> any of you are interested I found a very nce website
> with lots of audio samples of the different scales
> http://www.maqamworld.com/index.html
> There are so many scales with different tunings that I
> am confused as to how many pitches they might have in
> total. And whether the freted instuments can play
> every note of all the scales or whether there are
> different instruments for the different families of
> scales (maybe regional?) Maybe some of you know the
> answers?
> Best wishes
> Justin.

Hi Justin (and all),

You might like...
http://www.oriental-vision.com/realvideo/Adib-ISDN.rm

He's an ud maker, and, really, I don't know much about
maqam music, but I have some ud recordings (including
a very nice one by Munir Bashir) and this is some of
the most amazing playing I've heard.

-Carl

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
> [gws:]
> > Schismatic
> > [17] has been suggested as an alternate world historical path for
> > Western harmony,
> [pe:]
> It's also been put forth, essentially, as the Medieval Arabic
tuning
> system.
> [gws:]
> > > but I don't buy the theory it would evolve to 17 equal
> > > r even 22,
> > [pe:]
> > Whose theory is that? 17-equal is hardly schismatic, and 22-equal
most
> > certainly isn't at all.
> [gws:]
> I thought George claimed that could have plausibly happened. George?

Margo Schulter and I speculated about an alternate historical path
for *western Europe* beginning around the 13th century, but in a
superpythagorean rather than a schismic framework. Following the
idea that the requirements for effective melody (i.e., small
semitones via wide fifths) might have taken precedence over consonant
harmony (i.e., more consonant triads via narrow fifths), we concluded
that a tempered 6:7:9 would have eventually become the most consonant
tonic triad in a septimal non-5 harmonic system, with 11 (as
6:7:9:11, e.g.) entering the picture as harmonic development
progressed. This would have resulted in a closed system of either 17
or 22 tones. In our alternate path we chose 17 over 22 for several
reasons: its melodic properties, a fifth less heavily tempered, our
desire to maintain non-5 harmony, and the possibility of interpreting
neutral intervals as ratios of 13 (as well as 11). In this there are
striking parallels (as well as notable differences) with the
development of 5-limit harmony in a meantone framework (as explained
in my neo-medieval paper, which should appear some day in
Xenharmonikon 18). For example, for the 17-division we expressed a
preference for a well-temperament over 17-ET, but had we chosen the
22-division, it would have probably been 22-equal, in which an
interval of 4 degrees is very close to a super-meantone 2nd (midway
between 8:9 and 7:8), making 22 analogous to 31.

In our private discussion we wondered whether this might have any
relationship to Turkish or Arabic tuning. Perhaps others would like
to comment.

--George

scales formed by alternating thirds/dual generators

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗Carl Lumma <clumma@yahoo.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Justin . <justinasia@yahoo.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Ozan Yarman <ozanyarman@superonline.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Justin . <justinasia@yahoo.com>

🔗Ozan Yarman <ozanyarman@superonline.com>

🔗Carl Lumma <clumma@yahoo.com>

🔗George D. Secor <gdsecor@yahoo.com>