159edo: Difference between revisions
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'''159edo''' is the '''159 equal division of the octave''' into equal parts of 7.547 [[cent|cents]] each. | '''159edo''' is the '''159 equal division of the octave''' into equal parts of 7.547 [[cent|cents]] each. | ||
= Theory = | == Theory == | ||
As the step size of 159edo is simultaneously above the average peak [http://musictheory.zentral.zone/huntsystem2.html#2 JND] of human pitch perception and small enough to be well within the margin of error between Just 5-limit intervals and their [[12edo]] counterparts, 159edo offers a decent balance between allowing the possibility of seamless modulation to keys that are not in the same series of fifths, and not having so many steps as to have individual steps blend completely into one another. Furthermore, the septimal kleisma, [[225/224]], maps to a single step in 159edo- a third the size of the tempered version of [[81/80]]- which allows not only for the septimal kleisma to be easily accounted for in notation systems, but also for easy distinctions between certain fairly important intervals such as [[25/16]] and [[14/9]] that are tempered out in other EDOs. As a bonus, 159edo is [[consistent]] up to the 17 odd-limit- though it proves to be inconsistent in the 19-limit. | As the step size of 159edo is simultaneously above the average peak [http://musictheory.zentral.zone/huntsystem2.html#2 JND] of human pitch perception and small enough to be well within the margin of error between Just 5-limit intervals and their [[12edo]] counterparts, 159edo offers a decent balance between allowing the possibility of seamless modulation to keys that are not in the same series of fifths, and not having so many steps as to have individual steps blend completely into one another. Furthermore, the septimal kleisma, [[225/224]], maps to a single step in 159edo- a third the size of the tempered version of [[81/80]]- which allows not only for the septimal kleisma to be easily accounted for in notation systems, but also for easy distinctions between certain fairly important intervals such as [[25/16]] and [[14/9]] that are tempered out in other EDOs. As a bonus, 159edo is [[consistent]] up to the 17 odd-limit- though it proves to be inconsistent in the 19-limit. | ||
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: ''See also: [[Table of 159edo Intervals]]'' | : ''See also: [[Table of 159edo Intervals]]'' | ||
== Just approximation == | === Just approximation === | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
! colspan="2" | | ! colspan="2" | | ||
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= Articles = | == Articles == | ||
* [http://www.ozanyarman.com/files/doctorate_thesis.pdf ''79-Tone Tuning & Theory for Turkish Maqam Music''] - Ozan Yarman's dissertation | * [http://www.ozanyarman.com/files/doctorate_thesis.pdf ''79-Tone Tuning & Theory for Turkish Maqam Music''] - Ozan Yarman's dissertation | ||
* [http://www.ozanyarman.com/files/34ten79a.pdf ''Search For A Theoretical Model Conforming To Turkish Maqam Music Practice: A Selection Of Fixed-Pitch Settings From 34-tone Equal Temperament To The 79-tone Tuning''] - also by Ozan Yarman, gives a summary. | * [http://www.ozanyarman.com/files/34ten79a.pdf ''Search For A Theoretical Model Conforming To Turkish Maqam Music Practice: A Selection Of Fixed-Pitch Settings From 34-tone Equal Temperament To The 79-tone Tuning''] - also by Ozan Yarman, gives a summary. | ||