Ed7/3: Difference between revisions

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.  

== 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.  

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 family|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.  

=== Chords and harmonies ===

{{main|Pseudo-traditional harmonic functions of enneatonic scale_degrees}}

Incidentally, 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]]".

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