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Miras-ı Saz

Lesson 1 / 19 · Fundamentals

Koma (comma)

The small unit used to measure intervals in makam music; a whole tone (tanini) is counted as 9 commas. The Arel-Ezgi-Uzdilek theory builds its pitches from Pythagorean ratios (the Pythagorean comma, about 23.5 cents); dividing the octave into 53 equal parts (the Holder comma, about 22.6 cents) matches this system within less than 1 cent and is what is used in practice, including on this site.

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Lesson notes

Related concepts

  • Interval: The difference in pitch between two notes. In makam music, intervals are named by their number of commas: bakiye (4), küçük mücenneb (5), büyük mücenneb (8), tanini (9) and artık ikili, the augmented second (12–13 commas).
  • Holder koması (Holdrian comma): One of the 53 equal parts of the octave, about 22.6 cents; named after the 17th-century English theorist William Holder. In the 53-equal division, 4, 5, 8 and 9 Holdrian commas match AEÜ’s Pythagorean bakiye, küçük mücenneb, büyük mücenneb and tanini intervals within less than 1 cent, which is why “comma” in teaching usually means this unit. The sounds on this site are also calculated with the 53-equal division.
  • Pisagor koması (Pythagorean comma): The amount by which twelve pure fifths (3/2) stacked on top of each other exceed seven octaves; its ratio is 531441/524288, about 23.5 cents. In Arel-Ezgi-Uzdilek theory the comma is this interval: the bakiye, küçük mücenneb, büyük mücenneb and tanini intervals are built from Pythagorean ratios and counted as 4, 5, 8 and 9 commas. These counts are approximate; the bakiye (256/243, about 90 cents), for example, is not exactly 4 Pythagorean commas.
  • Tanini: A nine-comma interval, that is, a whole tone; abbreviated T. The interval between Rast and Dügah, and between Çargah and Neva, is a tanini.
  • Arel-Ezgi-Uzdilek system: The theory and notation system named after H. Sadettin Arel, Suphi Ezgi and Salih Murat Uzdilek, developed in the first half of the 20th century. It builds a 24-pitch system based on Pythagorean ratios; the pitches are notated on a 53-comma scale. It is the system most widely used in teaching today. Abbreviated AEÜ.