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| == Chords and harmonies == | | == Chords and harmonies == |
| {{main|Pseudo-traditional harmonic functions of enneatonic scale degrees}}
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| [[:Category:9-tone scales|Enneatonic scale]]s, especially those equivalent at 7/3, can sensibly take [[tetrad]]s as the fundamental complete sonorities of a pseudo-traditional functional harmony due to their seventh degree being as structurally important as it is. Many, though not all, of these scales have a perceptually important [[Pseudo-octave|pseudo (false) octave]], with various degrees of accuracy. | | [[:Category:9-tone scales|Enneatonic scale]]s, especially those equivalent at 7/3, can sensibly take [[tetrad]]s as the fundamental complete sonorities of a pseudo-traditional functional harmony due to their seventh degree being as structurally important as it is. Many, though not all, of these scales have a perceptually important [[Pseudo-octave|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. [[Joseph Ruhf]] named this scheme "macrobichromatic". | | 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]]. |
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| == Middletown ==
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| {{idiosyncratic terms}}
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| 7/3 provides a fairly trivial point to split the difference between the [[octave]] and the [[tritave]], which is why Ruhf has named the region of intervals between 6 and 7 degrees of [[5edo]] the "[[Middletown valley]]".
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| The proper [[Middletown family|Middletown temperament family]] is based on an [[enneatonic]] scale [[generator|generated]] by a third or a fifth optionally with a [[period]] of a [[Wolf interval|wolf]] fourth at most 560 [[cents]] wide) and, as is the twelfth (tritave), an alternative interval where {{w|Inversion (music) #Counterpoint|invertible counterpoint}} has classically occurred.
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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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| The [[pyrite]] tuning of [[edX]]s will turn out to divide a barely mistuned [[5/2]] of almost exactly 45\[[34edo]].
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| == Individual pages for ed7/3's == | | == Individual pages for ed7/3's == |
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| | [[98ed7/3|98]] | | | [[98ed7/3|98]] |
| | [[99ed7/3|99]] | | | [[99ed7/3|99]] |
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| {| class="wikitable center-all mw-collapsible mw-collapsed"
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| |+ style=white-space:nowrap | 100…199
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| |} | | |} |
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