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| '''Ed7/3''' means '''Division of the septimal minor tenth ([[7/3]]) into n equal parts'''.
| | #REDIRECT [[User:Moremajorthanmajor/Ed7/3]] |
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| == Properties ==
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| 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) and, as is the twelfth, an alternative interval where [[wikipedia:Inversion_(music)#Counterpoint|invertible counterpoint]] has classically occurred. 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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| Incidentally, one way to treat 7/3 as an equivalence is the use of the 3:4:5:(7) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to [[5/1]], here it takes two [[28/15]] to get to 7/2 (tempering out the comma 225/224). So, doing this yields 15, 19, and 34 note MOS 2/1 apart. While the notes are rather farther apart, the scheme is uncannily similar to meantone. "Macrobichromatic" might be a practically perfect term for it if it hasn't been named yet.
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| The branches of the Middletown family are named thus:
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| * 3&6: Tritetrachordal
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| * 4&5: Montrose (between 5\4edo and 4\3edo in particular, MOS generated by [pseudo] octaves belong to this branch)
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| * 2&7: Terra Rubra
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| The family of interlaced octatonic scale based temperaments in the "Middletown valley" is called Vesuvius (i. e. the volcano east of Naples).
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| The Middlebury temperament falls in the "Middletown valley", but its enneatonic scales are "generator-remainder".
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| The temperaments neighboring Middletown proper are named thus:
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| * 5&6: Rosablanca
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| * 4&7: Saptimpun (10 1/2)
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| * 5&7: 8bittone (Old Middetown)
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| 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.
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| == Individual pages for ED7/3s ==
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| * [[8ed7/3]]
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| * [[9ed7/3]]
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| * [[15ed7/3]]
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| * [[16ed7/3]]
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| * [[17ed7/3]]
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| * [[19ed7/3]]
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| * [[30ed7/3]]
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| * [[34ed7/3]]
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| * [[38ed7/3]]
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| * [[49ed7/3]]
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| * [[53ed7/3]]
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| * [[68ed7/3]]
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| * [[98ed7/3]]
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| * [[106ed7/3]]
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| [[Category:Ed7/3| ]] <!-- main article -->
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| [[Category:Equal-step tuning]]
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