Re: [tuning] The Töre-Karadeniz system

Dear Danny, so sorry for my late reply:

> I think I'm going to seriously get into Turkish music now.

Splendid!

I also need to
> learn the language so I can fully understand pages like this:
>
http://www.turkmusikisi.com/nazariyat/sistemler/ekrem_karadeniz_sistemi.htm
>

It is regrettable that alternative theories for Turkish Maqam Music are not
yet translated to English.

> The page is on the theory of Abd�lkadir T�re and M. Ekrem Karadeniz, who
> came up with a scale using 41 pitches out of 106-EDO.

He gives the Turkish cent values in 10600-edo, but his relative frequencies
are these:

1
1.02
1.04
1.053
1.074
1.096
1.110

1.125
1.147
1.170
1.185
1.209
1.234

1.250
1.274
1.299
1.316

1.333
1.360
1.388
1.406
1.434
1.463
1.481

1.500
1.530
1.560
1.580
1.612
1.644
1.666

1.688
1.721
1.755

1.778
1.814
1.850
1.875
1.911
1.948
1.974
2.000

Yielding 1000-EDL something:

0: 1/1 C unison, perfect prime
1: 51/50 C) Db( 17th-partial chroma
2: 26/25 C)/ Db\
3: 1053/1000 C#\ Db
4: 537/500 C# Db/
5: 137/125 C#) D(
6: 111/100 D\
7: 9/8 D major whole tone
8: 1147/1000 D/
9: 117/100 D)/ Eb\
10: 237/200 D#\ Eb
11: 1209/1000 D#/ E(\
12: 617/500 D#) E(
13: 5/4 E\ major third
14: 637/500 E/ F(\
15: 1299/1000 E) F(
16: 329/250 E)/ F\
17: 1333/1000 F
18: 34/25 F) Gb(
19: 347/250 F)/ Gb\
20: 703/500 F#\ Gb
21: 717/500 F#/ G(\
22: 1463/1000 F#) G(
23: 1481/1000 G\
24: 3/2 G perfect fifth
25: 153/100 G) Ab(
26: 39/25 G)/ Ab\
27: 79/50 G#\ Ab
28: 403/250 G#/ A(\
29: 411/250 G#) A(
30: 833/500 A\
31: 211/125 A
32: 1721/1000 A) Bb(
33: 351/200 A)/ Bb\
34: 889/500 A#\ Bb
35: 907/500 A#/ B(\
36: 37/20 A#) B(
37: 15/8 B\ classic major seventh
38: 1911/1000 B/ C(\
39: 487/250 B) C(
40: 987/500 B)/ C\
41: 2/1 C octave

It's essentially
> 29-tone Pythagorean, three fifths up and 25 fifths down from Rast (middle
D,
> written as the G a fourth higher), with the three-comma gaps divided into
> halves, producing larger "commas" of 33.96 cents. This scale inspired the
> cosine temperament I keep talking about.
>
> It's also in the Scala archive as "turkish_41.scl", but with the pitches
> rounded up to the nearest cent.
>

The cycle of fifths for the relative frequencies is rather:

0: 0.000 cents 0.000 0 0 commas C
24: 701.955 cents 0.000 0 0 commas G
7: 701.955 cents 0.000 0 0 commas D
31: 702.468 cents 0.513 16 A
14: 712.860 cents 11.418 350 E/
38: 701.955 cents 11.418 350 B/
21: 702.861 cents 12.324 378 G(\
4: 699.539 cents 9.908 304 C#
28: 703.029 cents 10.982 337 A(\
11: 701.955 cents 10.982 337 E(\
35: 702.432 cents 11.459 352 B(\
18: 701.319 cents 10.823 332 F)
1: 701.955 cents 10.823 332 C)
25: 701.955 cents 10.823 332 G)
8: 701.200 cents 10.068 309 D/
32: 702.458 cents 10.572 324 A)
15: 712.985 cents 21.602 663 F(
39: 701.511 cents 21.157 649 C(
22: 704.323 cents 23.526 722 G(
5: 699.982 cents 21.552 661 D(
29: 701.955 cents 21.552 661 A(
12: 703.359 cents 22.956 705 E(
36: 701.019 cents 22.020 676 B(
19: 702.579 cents 22.644 695 Gb\
2: 700.291 cents 20.980 644 Db\
26: 701.955 cents 20.980 644 Ab\
9: 701.955 cents 20.980 644 Eb\
33: 701.955 cents 20.980 644 Bb\
16: 701.626 cents 20.651 634 F\
40: 701.955 cents 20.651 634 C\
23: 702.540 cents 21.236 652 G\
6: 700.786 cents 20.067 616 D\
30: 702.994 cents 21.106 648 A\
13: 702.648 cents 21.799 669 E\
37: 701.955 cents 21.799 669 B\
20: 701.647 cents 21.491 660 Gb
3: 699.491 cents 19.026 584 Db
27: 702.503 cents 19.574 601 Ab
10: 701.955 cents 19.574 601 Eb
34: 702.442 cents 20.061 616 Bb
17: 701.306 cents 19.412 596 F
41: 702.388 cents 19.845 609 C
Average absolute difference: 16.5692 cents
Root mean square difference: 18.0249 cents
Maximum absolute difference: 23.5257 cents
Maximum formal fifth difference: 11.0302 cents

> I notice that the accidental symbol chart is incomplete: there's a
reversed
> flat and half-sharp for Irha (1� commas) and the normal flat and symbol
used
> by Arel and Ezgi for a five-comma sharp for Bakiye (4 commas); then it
shows
> a flat with an arrow attached to the stem for the five-comma flat, but no
> symbol for a five-comma sharp!
>

That table is mishandled by whoever wrote that article. The correct one is
here:

K - comma..............77/76.........22.63 cents......K# 1
R - small diesis.........51/50.........34.28 cents......K# 1.5
S - large diesis.........31/30..........56.77 cents.....K# 2.5
B - limma...............20/19..........88.8 cents......K# 4
C - apotome............16/15.........111.73 cents.....K# 5
M - minor whole tone..10/9..........182.40 cents.....K# 8
T - major whole tone...9/8...........203.91 cents....K# 9

Four types of sharps:

a) R sharp (3 steps of 106-tET), K# 1.5
b) S sharp (6 steps of 106-tET), K# 3
c) B sharp (8 steps of 106-tET), K# 4
d) C sharp (11 steps of 106-tET), K# 5.5

Four types of flats:

a) K flat (2 steps of 106-tET), K# 1
b) S flat (4 steps of 106-tET), K# 2
c) B flat (7 steps of 106-tET), K# 3.5
d) C flat (10 steps of 106-tET), K# 5

A bit complicated, no?

> He also expresses the Rast makam in JI terms: 1/1 9/8 5/4 4/3 3/2 27/16
15/8
> 2/1, with 16/9 replacing 15/8 in the descending scale.
>

5/3, not 27/16. He used the Pythagorean major sixth when delineating the
Pythagorean major scale.

> The website also discusses other theorists (free registration is required
to
> view many pages; Nazariyat is the Turkish word for music theory).
>

We had a laugh with academician Recep Uslu the other day concerning this
very subject. He joked that I should say something to those who claimed that
Nazariyat and music theory were different concepts. It appears that my
argumentative skills are quite popular around.

> So since I'm doing that, any suggestions and other ideas are appreciated,
> especially from Ozan. ;)
>
> ~Danny~
>
>

Cordially,
Ozan

Oops. It would have been EDL if 1000 was found on the numerator of the
ratios, right?

----- Original Message -----
From: "Mohajeri Shahin" <shahinm@kayson-ir.com>
To: <tuning@yahoogroups.com>
Sent: 03 Haziran 2006 Cumartesi 9:29
Subject: RE: [tuning] The T�re-Karadeniz system

> Dear ozan
> This is 1000-ADO and not 1000-EDL (-;
>
>
>

I find it eclectic Danny. The extended Arel-Ezgi type of classification for
Maqamat - not to mention the 24-tone tuning - does great harm to Turkish
Music theory in my not so humble opinion.

> I forgot to ask: what's your opinion of the book T�rk M�s�k�si Nazariyat�
ve
> Us�lleri by �smail Hakk� �zkan? ~DaW~
>

> >
> > It is regrettable that alternative theories for Turkish Maqam Music are
> > not
> > yet translated to English.
>
> I'm trying to learn Turkish myself, so maybe I can help. (And later on,
> translate into Spanish and whatever else.)
>

That would be excellent. I shall make myself available for assistance toward
such a project when the time comes.

>
> I thought at first he was just rounding to the nearest thousandth--but he
> has 5/4 for Segah, and 8192/6561 and 2^(17/53) are closer to 1.249 than
> 1.250. Maybe he was rounding but sneaked 5/4 and 15/8 in for segah and
> Irak/Evc respectively.
>

He must have aimed the Rast scale which he equates with Zarlino's diatonical
gamut.

> >
> > That table is mishandled by whoever wrote that article. The correct one
> > is
> > here:
> >
> > K - comma..............77/76.........22.63 cents......K# 1
> > R - small diesis.........51/50.........34.28 cents......K# 1.5
> > S - large diesis.........31/30..........56.77 cents.....K# 2.5
> > B - limma...............20/19..........88.8 cents......K# 4
> > C - apotome............16/15.........111.73 cents.....K# 5
> > M - minor whole tone..10/9..........182.40 cents.....K# 8
> > T - major whole tone...9/8...........203.91 cents....K# 9
> >
> > Four types of sharps:
> >
> > a) R sharp (3 steps of 106-tET), K# 1.5
> > b) S sharp (6 steps of 106-tET), K# 3
> > c) B sharp (8 steps of 106-tET), K# 4
> > d) C sharp (11 steps of 106-tET), K# 5.5
> >
> > Four types of flats:
> >
> > a) K flat (2 steps of 106-tET), K# 1
> > b) S flat (4 steps of 106-tET), K# 2
> > c) B flat (7 steps of 106-tET), K# 3.5
> > d) C flat (10 steps of 106-tET), K# 5
> >
> > A bit complicated, no?
>
> Yeah, but I know his tuning isn't an equal temperament, so it's a matter
of
> counting steps up or down rather than exact intervals.
>

No wonder his theory was not a favourite among Turkish Maqam Music circles.

> > 5/3, not 27/16. He used the Pythagorean major sixth when delineating the
> > Pythagorean major scale.
>
> I misread; that's the Do-Re-Mi major scale actually. He uses Ptolemy and
> Zarlino's JI major. (But Rast would still have 5/4 and 15/8.)
>

Indeed! However, I insist that Rast uses 27/16 more than 5/3.

> Now why exactly did Karadeniz use half-commas? I'm thinking maybe he
wanted
> a better approximation of Al-Farabi's intervals, since 53-tET doesn't
> represent 18/17, 162/149, 54/49, 81/68 or 27/22 all that well.
>

Moreover, he seems to have desired 12/11 and 11/10.

> Also, on an unrelated note, I'm going back to 53-tone Pythagorean (*not*
> equal temperament) as a rough but adequate approximation of 13-limit JI,
and
> vice versa. But this is for my own work, not as an interpretation of
> Turkish, Arab, Greek, Iranian or Indian music. I'm in the process of
reading
> Genesis of a Music, and I've turned into a bit of a Partchista. I still
wish
> he hadn't have stopped at 11 limit.
>

Why don't you adopt my 79-tone tuning? I go all the way to 17-limit.

> (I'm also reading Augusto Novaro's Sistema Natural. I'm still fairly new
to
> microtonalism, remember.)
>
> ~Danny~
>
>

Cordially,
Oz.

Danny,

Notwithstanding, I meant to imply that you could use 79 MOS 159-tET as a
"skeleton-scale". Would you not rather a 28/25 instead of 9/8 and 25/14
instead of 16/9? I represent these ratios excellently.

I admit I consider 15/14, 14/13 and 13/12 allophones also, and swap them on
a chosen degree.

And we do seem to be aware of the same aural tolerance limitation of about
7-8 cents.

Cordially,
Oz.

----------------------------------------------------------------------------
--------

> Why don't you adopt my 79-tone tuning? I go all the way to 17-limit.

I'm actually using 53-tone as a guide for fretless string instruments
(violin, oud, bass). I spent this morning making myself a chart of 31-limit
JI intervals. Each is expressed in 665-tET; a Pythagorean comma is divided
into thirteen equal parts. You can also use 612-tET, which is a better
approximation of 11-limit, but 665-tET has near-perfect fifths and fourths.

Intervals of up to 13-limit fit in the 53-tone Pythagorean "skeleton scale"
fairly well, with exceptions such as 15/11 and 22/15. Intervals using the
prime 17 tend to lie in-between degrees, and are best thought of in
half-commas.

I want to use 53-tone for fixed-pitch purposes since the kind of music I
write needs stronger fifths and fourths, and I don't have to be that precise
with other JI intervals. 9/8 is halfway between the 13th and 14th degrees of
your scale, and I need pure major seconds and 16/9 minor sevenths.

About 12/11 and 11/10: I represent them as "allophones" of a 7-comma neutral
second. The interval 2^/3^22, approximately 156.99 cents, lies in between
these two JI intervals (150.64 and 165.00 respectively). 11/10 would be an
alternative for 12/11, which is closer to Pythagorean and within my "safe
range" of 4 steps in 665-tET or about 7.22 cents.

~Danny~

About 37/53 of a syntonic comma actually... or roughly 4 septimal schismas,
if you will.

----- Original Message -----
From: "Daniel A. Wier" <dawiertx@sbcglobal.net>
To: <tuning@yahoogroups.com>
Sent: 13 Haziran 2006 Sal� 21:08
Subject: Re: [tuning] The T�re-Karadeniz system

I wrote:

> The reason for my use of pure Pythagorean as a reference, and because I'm
> used to thinking of things as a circle/spiral of fifths. But I also like
> to
> describe things in parts of a comma, thus my use of 665-EDO as a
> measurement
> since it divides the syntonic comma into 12 parts. Your 79-tone scale uses
> steps of 2/3 of a comma, or 8 schismas.

Actually more like 8 1/3 of these "Pythagorean schismas" or whatever you
call them.