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.

Division of 7/3 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed7/3 scales have a perceptually important [[Pseudo-octave|false octave]], with various degrees of accuracy.  

The structural utility of 7/3 (or another tenth) 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}}).

{{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".

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]]".

The branches of the Middletown family are named thus:

* 4&5: Montrose (between 5\4edo and 4\3edo in particular, MOS generated by [pseudo] octaves belong to this branch)

The family of interlaced [[octatonic scale]]-based temperaments in the "Middletown valley" is called Vesuvius (i.e. the volcano east of Naples).

* 4&7: Saptimpun (10 1/2)

* 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]].

| [[27ed7/3|27]]

[[Category:Ed7/3's| ]]

[[Category:Lists of scales]]

{{todo|inline=1|cleanup|explain edonoi|text=Most people do not think 7/3 sounds like an equivalence, so there must be some other reason why people are dividing it — some property ''other than'' equivalence that makes people want to divide it. Please add to this page an explanation of what that reason is... The page also needs a general overall cleanup.}}