159edo: Difference between revisions
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| Fifth = 93\159 (701.75¢) (→ [[53edo|31\53]]) | | Fifth = 93\159 (701.75¢) (→ [[53edo|31\53]]) | ||
| Major 2nd = 27\159 (204¢) | | Major 2nd = 27\159 (204¢) | ||
| | | Semitones = 15:12 (113¢ : 91¢) | ||
| | | Consistency = 17 | ||
}} | }} | ||
The '''159 equal divisions of the octave''' ('''159edo'''), or the '''159(-tone) equal temperament''' ('''159tet''', '''159et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 159 [[equal]] parts of about 7.55 [[cent]]s each, a size close to [[243/242]], the rastma. | The '''159 equal divisions of the octave''' ('''159edo'''), or the '''159(-tone) equal temperament''' ('''159tet''', '''159et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 159 [[equal]] parts of about 7.55 [[cent]]s each, a size close to [[243/242]], the rastma. | ||
== 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 a step-size so small as to have individual steps blend completely into one another. Thus, it can be said that 159edo falls in what can perhaps be considered the ideal range for a Mega-EDO in terms of possible musical functionality outside of pitch bends. | 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 a step-size so small as to have individual steps blend completely into one another. Thus, it can be said that 159edo falls in what can perhaps be considered the ideal range for a Mega-EDO in terms of possible musical functionality outside of pitch bends. | ||
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== Music == | == Music == | ||
The songs below are written in approximations of 159edo that differ from the actual 159edo by only fractions of a [[cent]]. | The songs below are written in approximations of 159edo that differ from the actual 159edo by only fractions of a [[cent]]. | ||
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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. | ||