Ed7/3: Difference between revisions
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== Properties == | == Properties == | ||
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. | ||
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}}). | |||
It also 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]] temperament family being 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. | |||
Incidentally, [[Pseudo-traditional harmonic functions of enneatonic scale_degrees|enneatonic scales]], especially those equivalent at e.g. 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 (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. "Macrobichromatic" might be a practically perfect term for it if it hasn't been named yet. | |||
The Middlebury temperament falls in the "Middletown valley", but its enneatonic scales are "generator-remainder". | The branches of the [[Middletown family]] are named thus: | ||
* 3&6: [[Tritetrachordal]] | |||
* 4&5: [[Montrose]] (between 5\4edo and 4\3edo in particular, MOS generated by [pseudo] octaves belong to this branch) | |||
* 2&7: [[Terra rubra|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 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) | ||
* 5&7: 8bittone (Old Middetown) | * 5&7: [[8bittone]] (Old Middetown) | ||
The [[pyrite]] tuning of [[edX]]s will turn out to divide a barely mistuned [[5/2]] of almost exactly 45\[[34edo]]. | |||
== Individual pages for ed7/3's == | == Individual pages for ed7/3's == | ||