Ed7/3: Difference between revisions
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The '''equal division of 7/3''' ('''ed7/3''') is a [[tuning]] obtained by dividing the [[7/3|septimal minor tenth (7/3)]] in a certain number of [[equal]] steps. | The '''equal division of 7/3''' ('''ed7/3''') is a [[tuning]] obtained by dividing the [[7/3|septimal minor tenth (7/3)]] in a certain number of [[equal]] steps. | ||
== | == Applications == | ||
Division of 7/3 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. The question of equivalence has not even been posed yet. | Division of 7/3 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. The question of equivalence has not even been posed yet. | ||
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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{{citation needed}} (and even the range of a {{w|Dastg%C4%81h-e_M%C4%81hur|dastgah}}{{citation needed}}). | 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{{citation needed}} (and even the range of a {{w|Dastg%C4%81h-e_M%C4%81hur|dastgah}}{{citation needed}}). | ||
== Chords and harmonies == | |||
{{main|Pseudo-traditional harmonic functions of enneatonic scale_degrees}} | |||
[[: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. | |||
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, | |||
== Middletown == | |||
7/3 provides a fairly trivial point to split the difference between the [[octave]] and the [[tritave]], which is why [[Joseph Ruhf]] has named the region of intervals between 6 and 7 degrees of [[5edo]] the "[[Middletown valley]]". | |||
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. | |||
The branches of the Middletown family are named thus: | The branches of the Middletown family are named thus: | ||
* 3&6: Tritetrachordal | * 3&6: Tritetrachordal | ||
* 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) | ||
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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). | The family of interlaced [[octatonic scale]]-based temperaments in the "Middletown valley" is called Vesuvius (i.e. the volcano east of Naples). | ||
The Middlebury temperament falls in the "Middletown valley", but its enneatonic scales are | The Middlebury temperament falls in the "Middletown valley", but its enneatonic scales are "[[generator-remainder]]". | ||
The temperaments neighboring Middletown proper are named thus: | 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) | ||
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== Individual pages for ed7/3's == | == Individual pages for ed7/3's == | ||
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