Yahoo Tuning Groups Ultimate Backup tuning The T�re-Karadeniz system

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

The page is on the theory of Abdï¿½lkadir Tï¿½re and M. Ekrem Karadeniz, who came up with a scale using 41 pitches out of 106-EDO. 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.

I notice that the accidental symbol chart is incomplete: there's a reversed flat and half-sharp for Irha (1ï¿½ 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!

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.

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

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

~Danny~

🔗Daniel A. Wier <dawiertx@sbcglobal.net>

Ozan Yarman wrote,

> Dear Danny, so sorry for my late reply:

Aw, no biggie.

>> >> 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.

I'm trying to learn Turkish myself, so maybe I can help. (And later on, translate into Spanish and whatever else.)

> 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

[snip]

> Yielding 1000-EDL something:
>
> 0: 1/1 C unison, perfect prime
> 1: 51/50 C) Db( 17th-partial chroma
> 2: 26/25 C)/ Db\

> 13: 5/4 E\ major third

> 24: 3/2 G perfect fifth

> 37: 15/8 B\ classic major seventh

> 41: 2/1 C octave

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.

>> I notice that the accidental symbol chart is incomplete: there's a
> reversed
>> flat and half-sharp for Irha (1ï¿½ 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?

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.

>> 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.

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.)

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.

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.

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

~Danny~

🔗Daniel A. Wier <dawiertx@sbcglobal.net>

Ozan wrote (and again, sorry for the delay; I got busy):

>> 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.

[see my reply below]

>> 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 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~

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

🔗Daniel A. Wier <dawiertx@sbcglobal.net>

Gene Ward Smith wrote:

> 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.
>
> 665 does indeed have nearly perfect fifths. Since however the fifths
> of 612 are a mere 0.00578 cents flat, it has nearly perfect fifths
> also. In other words, you've reached the point of diminished returns
> here, and having a fifth 0.00011 cents sharp instead is unlikely to
> help you. How, exactly, would you use the fact?

I could've gone either way; I just felt like using 665 for the purposes of this project. I'm really using JI, and it's easier for me to think in terms in parts of a comma on a fretboard than in cents.

🔗Daniel A. Wier <dawiertx@sbcglobal.net>

Ozan Yarman wrote:

> 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.

I'd have to think that a JI scale wouldn't be complete without 9/8 and 16/9. 28/25 and 25/24 could be used as alternatives, or "allophones" again, if the standard ratios for a 9-comma major second and 44-comma minor seventh would create too much roughness in a given harmonic environment. But I have yet to compose or improvise anything with such a situation. (I haven't written very much JI music yet.)

Same goes for 15/14 vs. 16/15, 14/13 vs. 13/12, 11/10 vs. 12/11, 45/32 vs. 7/5, and so on. (But I still need a better term for "allophone", a term I borrowed from linguistics, since I'm still developing my own JI theoretical language.)

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.

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

Actually for me it's 1/3 of a comma, or 4 schismas, or 1200 ï¿½ 4/665 = 7.218 cents. An even stricter tolerance would be 1/4 or a comma, 3 schismas, or 5.414 cents.

~Danny~