Ed7/3: Difference between revisions

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'''~~Ed7~~/3''' ~~means~~ '''~~Division of~~ the septimal minor tenth ([[7/3]]~~) into n~~ equal ~~parts'''~~.

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 numbero of [[equal]] steps.

== Properties ==

Division of 7/3 into equal parts ~~can be conceived of as to~~ directly ~~use~~ this interval as an equivalence~~, or not~~. 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 (and even the range of a ~~[https://en.wikipedia.org/wiki/~~Dastg%C4%81h-e_M%C4%81hur dastgah]) as well as a fairly trivial point to split the difference between the octave and the tritave (which is why ~~I have~~ 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 generated by a third or a fifth optionally with a period of a wolf fourth at most 560 cents wide) and, as is the twelfth, an alternative interval where ~~[[wikipedia: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 tetrads as the fundamental complete sonorities of a pseudo-traditional functional harmony due to their seventh degree being as structrally important as it is. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.

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}}) as well as 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 generated by a third or a fifth optionally with a period of a wolf fourth at most 560 cents wide) and, as is the twelfth, 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 tetrads as the fundamental complete sonorities of a pseudo-traditional functional harmony due to their seventh degree being as structrally 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.

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 branches of the Middletown family are named thus:

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Sort of unsurprisingly, though not so evidently, the pyrite tuning of edXs will turn out to divide a barely mistuned 5:2 of alomst exactly 45\34edo.

== Individual pages for ~~ED7~~/3s ==

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

{| class="wikitable center-all"

@@ Line 1: / Line 1: @@
-'''Ed7/3''' means '''Division of the septimal minor tenth ([[7/3]]) into n equal parts'''.
+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 numbero of [[equal]] steps.
 == Properties ==
-Division of 7/3 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. 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 (and even the range of a [https://en.wikipedia.org/wiki/Dastg%C4%81h-e_M%C4%81hur dastgah]) as well as a fairly trivial point to split the difference between the octave and the tritave (which is why I have 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 generated by a third or a fifth optionally with a period of a wolf fourth at most 560 cents wide) and, as is the twelfth, an alternative interval where [[wikipedia: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 tetrads as the fundamental complete sonorities of a pseudo-traditional functional harmony due to their seventh degree being as structrally important as it is. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.
+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}}) as well as 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 generated by a third or a fifth optionally with a period of a wolf fourth at most 560 cents wide) and, as is the twelfth, 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 tetrads as the fundamental complete sonorities of a pseudo-traditional functional harmony due to their seventh degree being as structrally 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.
+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 branches of the Middletown family are named thus:
@@ Line 24: / Line 24: @@
 Sort of unsurprisingly, though not so evidently, the pyrite tuning of edXs will turn out to divide a barely mistuned 5:2 of alomst exactly 45\34edo.
-== Individual pages for ED7/3s ==
+== Individual pages for ed7/3's ==
 {| class="wikitable center-all"