Holdrian comma

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The Holdrian comma, also called Holder's comma, and sometimes the Arabian comma, is a small musical interval of 22.6415 cents, equal to one step of 53 equal temperament, or . The name comma is misleading, since this interval is an irrational number and does not describe the compromise between intervals of any tuning system; it assumes this name because it is an approximation of the syntonic comma, which was widely used as a measurement of tuning in William Holder's time.

[edit] History

Nicholas Mercator applied logarithms to determine that was nearly equivalent to a syntonic comma (a feature of the prevalent meantone temperament tuning system of the time). He also considered that an "artificial comma" of might be useful, because it could be practically approximated by a cycle of 53 just fifths. William Holder, for whom this interval is named, favoured this unit because the intervals of 53 equal temperament are closer to just intonation than that of 55.

[edit] Arabian comma

The name "Arabian comma" may be inaccurate; the comma has been employed mainly in Turkish music theory by Kemal Ilerici, and by the Turkish composer Erol Sayan. The name of the comma is "Holder kommasi" in Turkish.

For instance, the rāst maqām row (equivalent to the Western major scale) may be considered in terms of Holdrian commas:

        c d e f g a b c'
commas:  9 8 5 9 9 8 5

But in contrast, nahawand (a Western minor scale):

        c d eb f g ab bb c'
commas:  9 4  9 9 4  9  9

has between d-e, e-f, g-a, a-b, and b-c' medium seconds, which cannot be precisely described by Holdrian commas, since it lies somewhere between 8 and 9 commas.

[edit] References

• Holder, William, A Treatise on the Natural Grounds, and Principles of Harmony, facsimile of the 1694 edition, Broude Brothers, New York, 1967. (Original pp. 103-106.)
• Habib Hassan Touma (1996). The Music of the Arabs, trans. Laurie Schwartz. Portland, Oregon: Amadeus Press. ISBN 0-931340-88-8.