Ed7/3: Difference between revisions
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'''EdX''' | '''EdX''' means '''Division of a tenth interval into n equal parts'''. | ||
<font style="font-size: 19.5px;">Division of a tenth (e. g. 7/3) into n equal parts</font> | |||
Division of [[7/3]] into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. The utility of 7:3 or another tenth as a base though, is apparent by being the absolute widest range most generally used in popular songs (and even the range of a [https://en.wikipedia.org/wiki/Dastg%C4%81h-e_M%C4%81hur dastgah]) as well as a fairly trivial point to split the difference between the octave and the tritave (which is why I have named the region of intervals between 6 and 7 degrees of 5edo the "Middletown valley", the proper Middletown temperament family being based on an enneatonic scale generated by a third or a fifth optionally with a period of a [[wolf]] fourth at most 560 cents wide). Incidentally [[Pseudo-traditional harmonic functions of enneatonic scale_degrees|enneatonic scales]], especially those equivalent at e. g. 7:3, can sensibly take tetrads as the fundamental complete sonorities of a pseudo-traditional functional harmony due to their seventh degree being as structrally important as it is. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy. | Division of [[7/3]] into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. The utility of 7:3 or another tenth as a base though, is apparent by being the absolute widest range most generally used in popular songs (and even the range of a [https://en.wikipedia.org/wiki/Dastg%C4%81h-e_M%C4%81hur dastgah]) as well as a fairly trivial point to split the difference between the octave and the tritave (which is why I have named the region of intervals between 6 and 7 degrees of 5edo the "Middletown valley", the proper Middletown temperament family being based on an enneatonic scale generated by a third or a fifth optionally with a period of a [[wolf]] fourth at most 560 cents wide). Incidentally [[Pseudo-traditional harmonic functions of enneatonic scale_degrees|enneatonic scales]], especially those equivalent at e. g. 7:3, can sensibly take tetrads as the fundamental complete sonorities of a pseudo-traditional functional harmony due to their seventh degree being as structrally important as it is. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy. | ||
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* 4&5: Montrose (between 5/4edo and 4/3edo in particular, MOS generated by [pseudo] octaves belong to this branch) | * 4&5: Montrose (between 5/4edo and 4/3edo in particular, MOS generated by [pseudo] octaves belong to this branch) | ||
* 2&7: Terra Rubra | * 2&7: Terra Rubra | ||
The family of interlaced octatonic scale based temperaments in the "Middletown valley" is called Vesuvius (i. e. the volcano east of Naples). | |||
The temperaments neighboring Middletown proper are named thus: | |||
* 5&6: Rosablanca | * 5&6: Rosablanca | ||
* 4&7: Saptimpun (10 1/2) | * 4&7: Saptimpun (10 1/2) | ||
* 5&7: 8bittone | * 5&7: 8bittone | ||
Sort of unsurprisingly, though not so evidently, the pyrite tuning of edXs will turn out to divide a barely mistuned 5:2 of alomst exactly 45/34edo. | |||
* [[8edX]] | * [[8edX]] | ||
* [[9edX]] | * [[9edX]] | ||
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* [[17edX]] | * [[17edX]] | ||
* [[19edX]] | * [[19edX]] | ||
[[Category:EdX| ]] <!-- main article --> | [[Category:EdX| ]] <!-- main article --> | ||
[[Category:ed7/3]] | [[Category:ed7/3]] | ||
[[Category:Equal-step tuning]] | |||