12 eşit sese ilk matematiksel yaklaşımlar


12-ton Eşit Taksimata matematiksel ilk yaklaşanlar Çinliler deniyor. 1584’te Zhu Zaiyu 12 eşit ses teorisini kaleme alıyor, yarım yüzyıl sonra Marin Mersenne aynı minvalde bir nazariyat kitabı yazıyor. Bir başka iddiaya göre (Barbour: Tuning & Temperament, 1951), 1533’te Giovanni Maria Lafranco Eşit Temperamanı tarif ediyor. Vincenzo Galilei (1581) zamanından başlayarak destanlı telli çalgılara (19/18 oranıyla başlayan) eşit yarım sesler yerleştirilmeye çalışılıyor. Eşit Temperamanın Avrupa’da klavyelere uygulanması ise çok daha sonra, 19. YY’ın ortalarına sarkacaktır.

Letter to Karl Signell on ITU TMDK Congress (11.20.2009)


Dear Karl,

My lengthy and well-studied critique against Nail Yavuzoğlu’s attempt at maqam theory and his utterings in that regard is not just a “complaint” . It is a serious work aimed at bringing down the many fallacies propounded under the guise of factuality. I would have expected you, of all people, not to have underestimated my erudite efforts in that direction, especially toward the unmasking of so much fraud.

Secondly, I believe you are being quite unfair towards the sincere undertaking by Prof. Dr. Lale Berköz, who has concerned herself (even as an outsider) with the quotidian problems of Turkish Classical/Art/Folk musics so much so that she spearheaded this much required event. I don’t see the current administration concerning itself with the outrageously glaring defects of AEU theory which continues to hinder the tradition, do you?

Admittedly, such unfortunate occurences as egotistic sabotages and admission of irrelevant papers that had nothing whatsoever to do with the spirit of the congress undermined Prof. Berköz’s honest intentions, not to mention the fact that her successors have failed to carry the flag after her departure… but isn’t this the way things are with the Turkish bureaucratic academia in general?

The committee responsible for the final report have made the conclusions of the congress (making use of my very own words) quite clear:

“It has been established on the basis of frequency measurements and analyses, that dividing the octave into 24 unequal parts is not a model suitable to express all the intervals of Turkish (Maqam) Music. However, the fact that this tuning has laid the foundation for the discussion of new tunings has been accepted by the scientists partaking in this congress.”

It is not the fault of Lale Berköz or any officer of the late administration in ITU TMDK if this clause is being neglected today.

To continue with the final report:


Solutions as a result of all that followed have been determined to be

1. To reflect the tone-system models that have been developed in conformity with the main theme of this congress to practices in our education and art institutions after evaluating them at broader platforms.

2. Taking Rast as the main maqam instead of Çargah, as defined in “Arel-Ezgi-Uzdilek”, and accepting that scale (as primary).

3. The acceptance of the A4/La = 440 Hz international diapason, which is a requisite of having adopted the Western staff notation,

4. The standardization of scores,

5. Continuity of history and the invigoration of tradition,

6. To regard the solutions to the (discussed) problems with a unified approach that incorporates the common rudiments of Turkish (Maqam) music.

Undoubtedly, there have been other worthwhile suggestions proposed in this congress. It has been understood that wide-ranging research and perspectives are essential and that the need for organizing discussive platforms, panels and briefings on tuning systems has become apparent. This congress held by ITU TMDK is an important step toward the solution of the (discussed) problems. ITU TMDK will continue to pioneer and support detailed and original work on this subject in accordance with contemporary developments.


I don’t need to point out that the (hearsay?) danger of forcing Nail’s theoretical attempt down the throats of every musician studying at ITU TMDK is a gross adulteration of the purposes and conclusions of the congress.

So, do you still deem the conclusions pointless and the congress a sham? That would be a shame. The shame is rather on the current administration, in fact, for failing to uphold the results spelled out by the committee, and failing to maintain its credibility toward the expectations of honest scientists and theorists who partook in the congress.

Dr. Ozan Yarman

“Mujannab zone” ratios


The neutral thirds of Maqam music are more diversified than the ratio 11:9 can encompass. As far as I can tell, middle second intervals roam the “mujannab zone” between 14:13 and 11:10. This is a region 37 cents wide. Then again, it is possible to broaden the zone and take 15:14 and 10:9 as the extremes. In that case, we acquire a zone that is 63 cents wide!

I conjecture that high prime-limit and relatively simple integer ratios such as 14:13, 27:25, 13:12, 12:11, 35:32, 11:10, 54:49 are at play. Then again, instead of middle seconds, we might be looking at neutral thirds, in which case, the performer could be searching for 17:14, 39:32, 11:9, 27:22, 16:13, 21:17 and 31:25.

So many ratios imply the necessity to temper pitches and represent diverse middle seconds as well as neutral thirds with few, yet, variegated microtones that are reasonably spaced apart. That is how I arrived at 79 MOS 159-tET. Check out page 95 of my doctorate dissertation. There, you will see how the 79-tone tuning approximates many such RI intervals.

Yavuzoğlu48’e göre makamlar


Nail Yavuzoğlu’nun 48 eşit perdeli önerisine göre, sent değerinde müteakip aralıklarla makam dizileri:

Uşşak [150+150+200] + [200+100+200+200]
Hüseyni [175+125+200+200] + [150+150+200] yahut [100+200+200]
Rast [200+175+125+200] + [200+175+125] yahut [200+100+200]
Segah [125+200] + [200+175+125] yahut [200+100+200]
Nigar [200+200+100] + [200+200+100+200]
Kürdi [100+200+200] + [200+100+200+200]
Neva [175+125+200] + [200+175+125+200]
Hicaz [125+275+100] + [200+175+125+200]
Hümayun [125+275+100] + [200+100+200+200]
Karcığar [150+150+200] + [150+250+100+200]
Suzinak [200+175+125+200] + [125+275+100] yahut [150+250+100]
Mahur-Acemaşiran [200+200+100+200] + [200+200+100]
Nihavend [200+100+200+200] + [100+200+200] yahut [125+275+100]
Nikriz [200+125+275+100] + [200+175+125] yahut [200+100+200]
Neveser [200+125+275+100] + [125+275+100]
Buselik [200+100+200+200] + [100+200+200] yahut [150+150+200]
Hisar [175+125+200+200] + [125+275+100]
Uzzal [125+275+100+200] + [150+150+200]
Zirguleli Hicaz, Suzidil, Evcara, Şedaraban, Zirguleli Suznak, Hicazkar
[125+275+100+200] + [125+275+100]
                           yahut [100+200+200] (sadece Hicazkar’da…)
Kürdili Hicazkar [100+200+200+200] + [125+275+100] yahut [150+150+200]
Çargah [150+250+100+200] + [125+175+100]
Ferahnak [125+200] + [200+175+125] yahut [200+100+200]
Müstear [200+125] + [200+175+125] yahut [200+100+200]
Nişabur [200+100] + [200+175+125] yahut [200+100+200]
Hüzzam [125+200] + [150+250+100]
Saba [150+150] + [150+250+100+200] + [125+175+100]
Sünbüle [100+200] + [150+250+100+200] + [125+175+100]
Şevkefza [200+200+100+200] + [150+250+100+200] + [125+175+100]
Bestenigar [125+200] + [150+150] + [150+250+100+200] + [125+175+100]
Irak [125+200] + [150+150+200] + [200+100+200+200]
Araban [150+150+200] + [125+275+100] + [200+100+200+200]
Revnaknüma [125+275+100+125+100] + [200+175+125] yahut [200+100+200]
Yegah [200+175+125+200] + [175+125+200] + [200+175+125+200]
                                      yahut [150+150+200] + [200+100+200+200]