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In [[music theory]] and [[musical tuning]] the '''Holdrian comma''', also called '''Holder's comma''', and sometimes the '''Arabian comma''',<ref name="Touma">[[Habib Hassan Touma]] (1996). ''The Music of the Arabs'', p.23. trans. Laurie Schwartz. Portland, Oregon: Amadeus Press. ISBN 0-931340-88-8.</ref> is a small [[interval (music)|musical interval]] of approximately 22.6415 [[cent (music)|cents]],<ref name="Touma"/> equal to one step of [[53 equal temperament]], or <math>\sqrt[53]{2}</math> ({{Audio|Holdrian comma on C.mid|play}}). The name [[comma (music)|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]] (21.51 cents)({{Audio|Syntonic comma on C.mid|play}}), which was widely used as a measurement of tuning in [[William Holder]]'s time. | |||
'''Mercator's comma''' is a name often used for a closely related interval because of its association with [[Nicholas Mercator]]. One of these intervals was first described by Ching-Fang in 45 BCE.<ref name="Touma"/> | |||
== Mercator's comma and the Holdrian comma ==<!--[[Mercator's comma]] redirects here--> | |||
Mercator applied logarithms to determine that <math>\sqrt[55]{2}</math> (≈ 21.8182 cents) was nearly equivalent to a syntonic comma of ≈ 21.5063 cents (a feature of the prevalent sixth-comma [[meantone temperament]] tuning system of the time). He also considered that an "artificial comma" of <math>\sqrt[53]{2}</math> might be useful, because 31 octaves could be practically approximated by a cycle of 53 [[just fifth]]s. [[William Holder]], for whom the Holdrian comma is named, favored this latter unit because the intervals of 53 equal temperament are closer to [[just intonation]] than that of 55. Thus '''Mercator's comma''' and the Holdrian comma are two distinct but related intervals. | |||
== 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 this comma is "Holder koması" in Turkish. | |||
For instance, the [[makam]] ''rast'' (similar 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 | |||
while in contrast, the makam ''nihavend'' (similar to the Western [[minor scale]]): | |||
c d e{{music|b}} f g a{{music|b}} b{{music|b}} c' | |||
commas: 9 4 9 9 4 9 9 | |||
has [[medium second]]s between d–e, e–f, g–a, a–b, and b–c', a medium second being somewhere in between 8 and 9 commas.<ref name="Touma"/> | |||
==References== | |||
{{reflist}} | |||
==Further reading== | |||
*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.) | |||
==External links== | |||
*Monzo, Joe (2005). [http://www.tonalsoft.com/enc/m/mercator-comma.aspx "Mercator's Comma"], ''Tonalsoft''. | |||
{{Intervals|state=expanded}} | |||
{{DEFAULTSORT:Holdrian Comma}} | |||
[[Category:Commas]] | |||
Revision as of 19:42, 8 May 2013
In music theory and musical tuning the Holdrian comma, also called Holder's comma, and sometimes the Arabian comma,[1] is a small musical interval of approximately 22.6415 cents,[1] equal to one step of 53 equal temperament, or (My name: Lindsey Gavin
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My age: 28
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![{\displaystyle {\sqrt[{53}]{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/002e1680d9bd3711d8ab535f101f4a3992f1bed8)
Mercator's comma is a name often used for a closely related interval because of its association with Nicholas Mercator. One of these intervals was first described by Ching-Fang in 45 BCE.[1]
Mercator's comma and the Holdrian comma
Mercator applied logarithms to determine that (≈ 21.8182 cents) was nearly equivalent to a syntonic comma of ≈ 21.5063 cents (a feature of the prevalent sixth-comma meantone temperament tuning system of the time). He also considered that an "artificial comma" of might be useful, because 31 octaves could be practically approximated by a cycle of 53 just fifths. William Holder, for whom the Holdrian comma is named, favored this latter unit because the intervals of 53 equal temperament are closer to just intonation than that of 55. Thus Mercator's comma and the Holdrian comma are two distinct but related intervals.
![{\displaystyle {\sqrt[{55}]{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6996e93d3031bc959b8f8401eb38918ae395dd9c)
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 this comma is "Holder koması" in Turkish.
For instance, the makam rast (similar 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
while in contrast, the makam nihavend (similar to the Western minor scale):
c d eTemplate:Music f g aTemplate:Music bTemplate:Music c' commas: 9 4 9 9 4 9 9
has medium seconds between d–e, e–f, g–a, a–b, and b–c', a medium second being somewhere in between 8 and 9 commas.[1]
References
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Further reading
- 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.)
External links
- Monzo, Joe (2005). "Mercator's Comma", Tonalsoft.
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- ↑ 1.0 1.1 1.2 1.3 Habib Hassan Touma (1996). The Music of the Arabs, p.23. trans. Laurie Schwartz. Portland, Oregon: Amadeus Press. ISBN 0-931340-88-8.