Ed7/3: Difference between revisions

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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".

~~== Middletown ==~~

~~{{idiosyncratic terms}}~~

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 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:~~

* 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

~~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:~~

* 5&6: Rosablanca

* 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]].~~

== Individual pages for ed7/3's ==

@@ Line 13: / Line 13: @@
 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".
-== Middletown ==
-{{idiosyncratic terms}}
-/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 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:
-* 3&amp;6: Tritetrachordal
-* 4&amp;5: Montrose (between 5\4edo and 4\3edo in particular, MOS generated by [pseudo] octaves belong to this branch)
-* 2&amp;7: 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:
-* 5&amp;6: Rosablanca
-* 4&amp;7: Saptimpun (10 1/2)
-* 5&amp;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 ==