7-limit à la Turk

It was a cold and depressing night in East Texas, and this boy's
been working on something that's probably already been done before,
but I did come up with it myself anyhow. Long ago in a post about
the "C-Fb-G chord", I ended up with a 5-limit approximation of 53-
equal "Turkish" temperament.

And now, I have come up with 7-limit. The 4:5:6:7 chord could be
described as "D Gb A Ebbbb" and yes that's an E-quadruple flat.
That's using a "circle of fifths" notation. A more friendly
description would be "D F#- A C--", where the minus sign means the
pitch is lowered by one comma, or 1/53 of an octave. The numerical
expression would be "0 17 31 42".

So here's the tuning:

1/1 = D
81/80
64/63
21/20
135/128 = Eb
16/15 = D#
15/14
448/405
10/9
9/8 = E
256/225
8/7
75/64
32/27 = F
6/5
135/112
56/45
5/4 = Gb
81/64 = F#
32/25
21/16
320/243
4/3 = G
27/20
256/189
7/5
45/32 = Ab
64/45 = G#
10/7
189/128
40/27
3/2 = A
243/160
32/21
25/16
128/81 = Bb
8/5 = A#
45/28
224/135
5/3
27/16 = B
128/75
7/4
225/128
16/9 = C
9/5
405/224
28/15
15/8 = Db
243/128 = D
40/21
63/32
160/81
2/1 = D'

I swear I've seen this or something similar in the Scala files
somewhere. Whatever the case, I'm excited about the kind of music I
could write with this thing!

Correction:

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

> 16/9 = C
> 9/5
> 405/224
> 28/15
> 15/8 = Db
> 243/128 = D <------ this should be a C#
> 40/21
> 63/32
> 160/81
> 2/1 = D'

Also, I can't seem to get my real name in the From: part of the
post, but anyway y'all can call me Danny.

~Danny~

A late comment: I did the cents calculations on the scale, and it's not really
that close to 53-tet. I was able to work in the 7-limit intervals, but the
first few notes are tuned thusly:

D = 0
D+ = 21.50637
D++ = 27.26419
Ebd = 84.46712
Eb = 92.17872
D# = 111.7314
D#+ = 119.4428
Ep = 174.6921
Ed = 182.4038
E = 203.91

So there's a skip here and there. But the difference between, say, 7/4 and the
43nd degree of 53-tet, isn't too much.

=====
~DaW~ http://www.geocities.com/dawier

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--- In tuning@y..., "dawier" <dawier@y...> wrote:
> ... I ended up with a 5-limit approximation of 53-
> equal "Turkish" temperament.

Just for the record, there has never been a 53-equal Turkish
temperment.

Traditional Turkish music theory is an extension of mid-Eastern
theory; first studied by Al-Kindi, Farabi (Alfarabius), Ibn Sinâ
(Avicenna) et al; 'founded' by Safiuddin al Urmawi; perfected by
Abdulkadir Meragi and followed by Mehmed Çelebi of Ladik, Ahmed oğlu
Şükrullah etc.

With the exception of Kantemiroğlu (Demetrius Cantemir) who went 'his
own way', all theoricians followed this path leading back to Romans
and Ancient Greeks. The last remarkable author in the area was Şeyh
(Sheikh) Abdulbâkí Nâsır Dede, with his monumental book "Tedkík u
Tahkík".

All of the above mentioned authors explain the tone system as a non-
equal division of octave into 17 pitches (or pitch areas).

In the late XIX. and early XX. century, christian/arabic theorist
Mikhail Meshaqa of Lebanon (which was a Turkish terrain) influenced
the eastern music world with his 24-unequal division. His system is
officially taught in Arabic countries and Iran today. Turkish
musicologist Rauf Yektâ Bey also adopted his system with minor
changes to make it fit the Turkish practice and declared his 24-
unequal division. This sytem was modified by H.S. Arel and his
companion Dr. S. Ezgi, gradually becoming the standard system in
teaching.

Şefik Gürmeriç, pupil of Arel, started the "tradition" of explaining
the system as a whole tone divided into 9 'commas', hence octave
divided into 53 as a practical approach. Neither Yektâ, nor Arel-Ezgi
ever stated a 53-equal system.

Aside from those, Ekrem Karadeniz, pupil of great composer
Abdulkaadir Töre, formed his own 41-tone system identical to Partch's
43.

Again for the record, all of the above mentioned systems, except for
the classical 17 division, have failed explaining the ongoing Turkish
music practice. Especially the Arel-Ezgi system with its false
intervals and scales have never accorded with the performance and
tradition.

Regards,
Ertugrul

--- In tuning@y..., "ertugrulInanc" <ertugrulinanc@y...> wrote:
> All of the above mentioned authors explain the tone system as a non-
> equal division of octave into 17 pitches (or pitch areas).

Could you give examples of these?

> In the late XIX. and early XX. century, christian/arabic theorist
> Mikhail Meshaqa of Lebanon (which was a Turkish terrain) influenced
> the eastern music world with his 24-unequal division.

And this?

> Aside from those, Ekrem Karadeniz, pupil of great composer
> Abdulkaadir Töre, formed his own 41-tone system identical to Partch's
> 43.

Identical to Genesis Minus? I'd like to see it!

--- In tuning@y..., "ertugrulInanc" <ertugrulinanc@y...> wrote:
> --- In tuning@y..., "dawier" <dawier@y...> wrote:
> > ... I ended up with a 5-limit approximation of 53-
> > equal "Turkish" temperament.
>
> Just for the record, there has never been a 53-equal Turkish
> temperment.
>
> Traditional Turkish music theory is an extension of mid-Eastern
> theory; first studied by Al-Kindi, Farabi (Alfarabius), Ibn Sinâ
> (Avicenna) et al; 'founded' by Safiuddin al Urmawi; perfected by
> Abdulkadir Meragi and followed by Mehmed Çelebi of Ladik, Ahmed
oðlu
> Þükrullah etc.
>
> With the exception of Kantemiroðlu (Demetrius Cantemir) who
went 'his
> own way', all theoricians followed this path leading back to Romans
> and Ancient Greeks. The last remarkable author in the area was Þeyh
> (Sheikh) Abdulbâkí Nâsýr Dede, with his monumental book "Tedkík u
> Tahkík".
>
> All of the above mentioned authors explain the tone system as a non-
> equal division of octave into 17 pitches (or pitch areas).
>
> In the late XIX. and early XX. century, christian/arabic theorist
> Mikhail Meshaqa of Lebanon (which was a Turkish terrain) influenced
> the eastern music world with his 24-unequal division. His system is
> officially taught in Arabic countries and Iran today. Turkish
> musicologist Rauf Yektâ Bey also adopted his system with minor
> changes to make it fit the Turkish practice and declared his 24-
> unequal division. This sytem was modified by H.S. Arel and his
> companion Dr. S. Ezgi, gradually becoming the standard system in
> teaching.
>
> Þefik Gürmeriç, pupil of Arel, started the "tradition" of
explaining
> the system as a whole tone divided into 9 'commas', hence octave
> divided into 53 as a practical approach. Neither Yektâ, nor Arel-
Ezgi
> ever stated a 53-equal system.
>
> Aside from those, Ekrem Karadeniz, pupil of great composer
> Abdulkaadir Töre, formed his own 41-tone system identical to
Partch's
> 43.
>
> Again for the record, all of the above mentioned systems, except
for
> the classical 17 division, have failed explaining the ongoing
Turkish
> music practice. Especially the Arel-Ezgi system with its false
> intervals and scales have never accorded with the performance and
> tradition.
>
> Regards,
> Ertugrul

this is great. what would be invaluable, in addressing previous
discussions on this and for other reasons, would be details -- lots
of details. both on the above systems, and on any relevant
measurements of traditional performance practice. the more details,
the better.

thanks,
paul

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "ertugrulInanc" <ertugrulinanc@y...> wrote:
> > All of the above mentioned authors explain the tone system as a
non-
> > equal division of octave into 17 pitches (or pitch areas).
>
> Could you give examples of these?

I don't have the sources handy but fortunately I have some 'secondary
sources'.

Abdulkadir Meragi, who is cited to have done the most important
contribution to the system founded by Safiyyuddin, tells us
the "monochord method", ie formation of the fundamental scale by
dividing a sounding string, in several of his books: Makásıdu'l-Elhân
("Bab" 2), Câmi'u'l-Elhân ("Bab" 2)

For 'occidental' references to Safiyyuddin and Meragi see the
following:

Amnon Shiloah, "The Theory of Music in Arabic Writings (c.900-1900):
Descriptive Catalogue of Manuscripts of Europe and the USA", München
1979

Owen Wright, "The Modal System of Arab and Persian Music", Oxford
University Press 1978

I have only one of the fundamental sources at the moment:
Kantemiroğlu, who I said "went his own way".

He does not mention any intervallic ratios but refers to the frets of
Tanbur, which was a concrete example for his readers. He forms a
diatonic scale of -what he calls- fundamental pitches and defines two
secondary pitches 'related to' five of them; one secondary pitch
related to the each of the remaining two, thus having 17 intervals
per octave.

> > In the late XIX. and early XX. century, christian/arabic theorist
> > Mikhail Meshaqa of Lebanon (which was a Turkish terrain)
influenced
> > the eastern music world with his 24-unequal division.
>
> And this?

Rauf Yektâ must have mentioned the relation in the declaration of the
1930 congress of Cairo (which he attended). However, you may need to
check & compare his and Mehaqa's writings (none of which can I access
for now).

> > Aside from those, Ekrem Karadeniz, pupil of great composer
> > Abdulkaadir Töre, formed his own 41-tone system identical to
Partch's
> > 43.
>
> Identical to Genesis Minus? I'd like to see it!

Well, the resemblance is not so far. The basic factor that leads
writers think of these two similar is the close amount of intervals.
Karadeniz also tends to form a JI-like system of 'pure' intervals but
one cannot claim that he insisted on that. On the other hand, we know
that Karadeniz bought the Genesis and got it read to himself (because
he was blind).

Hth,
Ertugrul

ertugrulInanc wrote:

> > > In the late XIX. and early XX. century, christian/arabic theorist
> > > Mikhail Meshaqa of Lebanon (which was a Turkish terrain)
> influenced
> > > the eastern music world with his 24-unequal division.
> >
> > And this?
>
> Rauf Yekt� must have mentioned the relation in the declaration of the
> 1930 congress of Cairo (which he attended). However, you may need to
> check & compare his and Mehaqa's writings (none of which can I access
> for now).

I have Habib Hassan Touma's "Basics of Ratio in Arab Music" here. He
definitely says that Mishaqa (who must be the sam as your Meshaqa)
specified an equal division. The diagram that's supposed to show this
would actually give quartertones between 48.8 and 52.1 cents, I think.
That looks like a mathematician's attempt to simplify an equal scale for
practical tuning, rather than a musician's unequal scale.

This is what I make the first octave:

48.8 48.8
97.9 49.1
147.4 49.5
197.2 49.8
247.3 50.1
297.7 50.4
348.4 50.7
399.4 51.0
450.6 51.2
502.1 51.4
553.7 51.6
605.5 51.8
657.4 51.9
709.5 52.0
761.6 52.1
813.7 52.1
865.8 52.1
917.7 52.0
969.6 51.8
1021.2 51.6
1072.6 51.4
1123.6 51.0
1174.1 50.6
1224.2 50.1

Graham

--- In tuning@y..., graham@m... wrote:
> ertugrulInanc wrote:
>
> > > > In the late XIX. and early XX. century, christian/arabic
theorist
> > > > Mikhail Meshaqa of Lebanon (which was a Turkish terrain)
> > influenced
> > > > the eastern music world with his 24-unequal division.
> > >
> > > And this?
> >
> > Rauf Yektâ must have mentioned the relation in the declaration of
the
> > 1930 congress of Cairo (which he attended). However, you may need
to
> > check & compare his and Mehaqa's writings (none of which can I
access
> > for now).
>
> I have Habib Hassan Touma's "Basics of Ratio in Arab Music" here.
He
> definitely says that Mishaqa (who must be the sam as your Meshaqa)
> specified an equal division. The diagram that's supposed to show
this
> would actually give quartertones between 48.8 and 52.1 cents, I
think.
> That looks like a mathematician's attempt to simplify an equal
scale for
> practical tuning, rather than a musician's unequal scale.
>
> This is what I make the first octave:
>
> 48.8 48.8
> 97.9 49.1
> 147.4 49.5
> 197.2 49.8
> 247.3 50.1
> 297.7 50.4
> 348.4 50.7
> 399.4 51.0
> 450.6 51.2
> 502.1 51.4
> 553.7 51.6
> 605.5 51.8
> 657.4 51.9
> 709.5 52.0
> 761.6 52.1
> 813.7 52.1
> 865.8 52.1
> 917.7 52.0
> 969.6 51.8
> 1021.2 51.6
> 1072.6 51.4
> 1123.6 51.0
> 1174.1 50.6
> 1224.2 50.1
>
>
> Graham

what do you mean by saying that's what you make to be the first
octave? do you mean Mishaqa completely avoided the ratio 2/1, or that
Touma did??

In-Reply-To: <a9ffr0+33vg@eGroups.com>
emotionaljourney22 wrote:

> what do you mean by saying that's what you make to be the first
> octave? do you mean Mishaqa completely avoided the ratio 2/1, or that
> Touma did??

Touma gives a geometrical construction from Mishaqa which produces the
fret spacings for 24 frets to the octave. It happens that a cumulative
error makes the octave quite sharp.

Graham

--- In tuning@y..., graham@m... wrote:
> In-Reply-To: <a9ffr0+33vg@e...>
> emotionaljourney22 wrote:
>
> > what do you mean by saying that's what you make to be the first
> > octave? do you mean Mishaqa completely avoided the ratio 2/1, or
that
> > Touma did??
>
> Touma gives a geometrical construction from Mishaqa which produces
the
> fret spacings for 24 frets to the octave. It happens that a
cumulative
> error makes the octave quite sharp.
>
>
> Graham

maybe the user was then supposed to move the bridge to make a good
octave, as was the case in Europe with the Rule of 18?