The Tuning Debate: AEU, Yarman-79, and Alternative Frameworks

The Arel-Ezgi-Uzdilek system divides the octave into 53 equal Holdrian commas, selects roughly 24 perdeler from that grid, and assigns each one a fixed position. It is the standard taught in Turkish conservatories, printed in published notation, and assumed in nearly every makam textbook since the mid-20th century. It has also been disputed for nearly as long as it has existed.

The AEU consensus and its limits

Established The mathematics of the 53-comma division are sound — 53 stacked pure fifths very nearly close the circle, producing a comma of approximately 22.64 cents that closely approximates Pythagorean intervals. The problem is not the math. The problem is the claim that this grid faithfully describes what performers do.

Attested Signell observed in 1977 that master performers routinely deviate from AEU's predicted pitches, particularly on the neutral seconds and thirds that give makams like Uşşak and Segâh their character. These deviations are not errors to be corrected but expressive choices the notation cannot capture.

Karadeniz's 41-interval alternative

Attested The first sustained internal critique came from M. Ekrem Karadeniz (1904–1981), who corresponded directly with Arel and Ezgi around 1950 before ultimately rejecting their framework. His treatise Türk Mûsikîsinin Nazariye ve Esasları, completed in 1965 and published in 1983, proposed an alternative 41-interval system derived from the tuning practices of Abdülkadir Töre rather than from 53 equal commas.

Attested Karadeniz's central argument was that AEU's equal divisions do not reflect how musicians actually tune their instruments. Where AEU treats every comma as mathematically identical, Karadeniz insisted on a system grounded in observed practice rather than theoretical symmetry. His framework gained some academic attention but never displaced AEU in conservatory teaching.

Yarman's 79-tone proposal

Attested The most technically detailed modern alternative comes from Ozan Yarman, whose 2008 doctoral dissertation at Istanbul Technical University proposed a 79-tone tuning system as a superset that better accommodates the intervals performers actually produce. Yarman's approach was empirical: he analyzed recordings of master musicians — including neyzen Niyazi Sayın and tanburî Necdet Yaşar — and documented neutral-second-sized intervals that fall between AEU's fixed comma positions.

Attested The 79-tone system does not replace the 53-comma framework so much as embed it within a finer mesh. It preserves backward compatibility with AEU notation while adding the resolution needed to distinguish intervals that AEU conflates. The trade-off is complexity: 79 tones per octave is substantially harder to teach, notate, and implement than 24 named perdeler from a 53-division grid.

Practice Yarman himself teaches at Istanbul Technical University's Turkish Music State Conservatory — the same institution that has taught AEU for decades. The debate continues from inside the system, not only from outside it.

What computational analysis reveals

Attested The strongest evidence in the debate comes not from alternative tuning proposals but from empirical pitch measurement. Can Akkoc's 2002 study in the Journal of New Music Research applied spectral analysis to recordings of master performers and found that they do not target fixed pitch positions at all. Instead, each perde functions as a probability distribution — a zone of attraction rather than a point on a grid.

Attested Barış Bozkurt's computational work (2008, 2010) confirmed and extended Akkoc's findings across larger corpora. His automatic pitch analysis method, applied to hundreds of recordings, produced pitch histograms showing that performers cluster around characteristic frequency regions but with measurable variance that no fixed temperament — whether 53-tone, 79-tone, or 41-tone — can fully predict.

Attested These studies shift the debate from "which grid is correct?" to "is any fixed grid the right model?" The answer, based on the evidence, is that theoretical grids are useful approximations — maps that describe the territory — but no single grid captures the flexible, context-dependent intonation that distinguishes a living makam tradition from a mechanical reproduction.

The Persian parallel

Attested The Persian dastgah system avoids this debate entirely by never committing to a fixed temperament. Hormoz Farhat uses approximate cent values in his analyses, explicitly acknowledging that perdeler in dastgah music are zones rather than points. The concept of moteghayyer — pitches that shift depending on melodic direction and modal context — is built into the theoretical framework itself rather than existing as an embarrassing deviation from it.

Practice This is not to say Persian theory is "better" — it simply models flexibility differently. AEU's precision makes it possible to publish scores, build electronic instruments, and teach large conservatory classes. Farhat's approach preserves the flexibility but at the cost of the notational precision that institutional music education requires.

Why the debate matters for learners

Practice For students of makam music, the tuning debate is not an academic curiosity. It shapes what you hear and how you practice:

• Learn AEU as vocabulary, not gospel. The 24 perdeler and their comma values give you a shared language for discussing intervals. They do not give you permission to stop listening.

• Trust your ear over the chart. When a master performer's Segâh sounds different from the AEU-predicted 17 commas, the performer is not wrong — the chart is incomplete.

• Understand why the debate is unresolved. AEU survives because it is institutionally entrenched, pedagogically simple, and "good enough" for most purposes. Its challengers survive because they are empirically closer to what performers do. Neither side has a decisive advantage.

• Use the grid as a starting point. The comma system gives you a reference framework. Recordings of master performers give you the actual music. The distance between the two is where artistry lives.

Where to go from here

The AEU system's history and structure: Arel-Ezgi-Uzdilek. The mathematics: Holdrian Commas. The computational evidence in depth: Theory-Practice Gap. Three pitch systems compared: 53-TET vs 24-TET vs Just Intonation. Practical implications: Practical Tuning Methods.