7L 3s (4/1-equivalent): Difference between revisions

(29 intermediate revisions by 4 users not shown)

Line 1:

~~'''7L 3s<4/1>''' (sometimes called '''diaquadic''') refers to a non-octave [[~~MOS scale]] family with a period of a [[4/1]] and which has 7 large and 3 small steps. These scales are in some ways a double octave clone of [[5L 2s|diatonic scale]]s because they are generated from perfect fifths and have the [[7edo]]/[[7ed4]] 685-cent flat fifth and [[5edo]]/10ed4's 720-cent sharp fifth at the ends of the tuning spectrum. However, ~3/2 is now the chroma-negative rather than chroma-positive generator, equalized and collapsed tunings are now swapped (equalized is 720-cent fifth and collapsed is 685-cent fifth), and the basic tuning is now the 705-cent gentle fifth from [[17edo]]/[[17ed4]] instead of 12edo's fifth. Diaquadic scales are also more widely spaced than diatonic scales, closer melodically to an octave-period pentatonic scale.

~~== Modes ==~~

These scales are in some ways a double octave clone of [[5L 2s|diatonic scale]]s because they are generated from perfect fifths and have the [[7edo]]/[[7ed4]] 685{{c}} flat fifth and [[5edo]]/10ed4's 720{{c}} sharp fifth at the ends of the tuning spectrum. However, ~3/2 is now the chroma-negative rather than chroma-positive generator, equalized and collapsed tunings are now swapped (equalized is 720{{c}} fifth and collapsed is 685{{c}} fifth), and the basic tuning is now the 705-cent gentle fifth from [[17edo]]/[[17ed4]] instead of 12edo's fifth. Diaquadic scales are also more widely spaced than diatonic scales, closer melodically to an octave-period pentatonic scale.

~~The darker modes contain both major triads~~ and ~~augmented triads on~~ the ~~root~~, and the ~~brighter modes contain both minor and diminished triads on~~ the ~~root~~.

* LLLsLLsLLs 9|0

== Scale properties ==

* LLsLLLsLLs 8|1

* LLsLLsLLLs 7|2

* LLsLLsLLsL 6|3

=== Intervals ===

* LsLLLsLLsL 5|4

* LsLLsLLLsL 4|5

* LsLLsLLsLL 3|6

=== Generator chain ===

* sLLLsLLsLL 2|7

* sLLsLLLsLL 1|8

* sLLsLLsLLL 0|9

=== Modes ===

== Scale tree ==

{{MOS tuning spectrum

| 5/3 = Quarchy is around here

| 3/1 = Tetrominant is around here

| 4/1 = Meanquad is around here

}}

== Temperaments ==

There are two major rank-2 temperament interpretations of diaquadic, corresponding to double octave clones of [[meantone]] and [[archy]].

=== Meanquad ===

''Main article: [[Meanquad]]''

* [[Subgroup]]: 4.5.6

* [[Comma list]]: [[81/80]]

* [[~~Val~~]]s: 7, 31, 38, 24, 17, 10, 69, 45, 55, 11[-5], 52, 41, 13[+5], 27[+5]

* {{Mapping|legend=1|1 0 1|0 4 1}}

* [[Support]]ing ETs: 7, 31, 38, 24, 17, 10, 69, 45, 55, 11[-5], 52, 41, 13[+5], 27[+5]

* [[CTE tuning]]: ~[[3/2]] = 697.214

==== Tetrominant ====

* [[Subgroup]]: 4.5.6.7

* [[Comma list]]: [[36/35], [[64/63]]

* [[Comma list]]: [[36/35]], [[64/63]]

* [[~~Val~~]]s: 7, 17, 24, 10, 31, 41, 27[+5], 38[+7], 55[+7], 58[+5, +7], 65[+5, +7], 44[+5], 75[+5, +7]

* {{Mapping|legend=1|1 0 1 2|0 4 1 -2}}

* [[Support]]ing ETs: 7, 17, 24, 10, 31, 41, 27[+5], 38[+7], 55[+7], 58[+5, +7], 65[+5, +7], 44[+5], 75[+5, +7]

* [[CTE tuning]]: ~[[3/2]] = 699.622

=== Quarchy ===

* [[Subgroup]]: 4.6.7

* [[Comma list]]: [[64/63]]

* [[~~Val~~]]s: 10, 17, 7, 27, 37, 44, 13, 24, 47, 11[+7], 23, 57, 16, 41

* {{Mapping|legend=1|1 2 0|0 1 -2}}

* [[Support]]ing ETs: 10, 17, 7, 27, 37, 44, 13, 24, 47, 11[+7], 23, 57, 16, 41

* [[CTE tuning]]: ~[[3/2]] = 709.595

@@ Line 1: / Line 1: @@
 {{Infobox MOS}}
-'''7L 3s<4/1>''' (sometimes called '''diaquadic''') refers to a non-octave [[MOS scale]] family with a period of a [[4/1]] and which has 7 large and 3 small steps. These scales are in some ways a double octave clone of [[5L 2s|diatonic scale]]s because they are generated from perfect fifths and have the [[7edo]]/[[7ed4]] 685-cent flat fifth and [[5edo]]/10ed4's 720-cent sharp fifth at the ends of the tuning spectrum. However, ~3/2 is now the chroma-negative rather than chroma-positive generator, equalized and collapsed tunings are now swapped (equalized is 720-cent fifth and collapsed is 685-cent fifth), and the basic tuning is now the 705-cent gentle fifth from [[17edo]]/[[17ed4]] instead of 12edo's fifth. Diaquadic scales are also more widely spaced than diatonic scales, closer melodically to an octave-period pentatonic scale.
+{{MOS intro}}
-== Modes ==
+These scales are in some ways a double octave clone of [[5L 2s|diatonic scale]]s because they are generated from perfect fifths and have the [[7edo]]/[[7ed4]] 685{{c}} flat fifth and [[5edo]]/10ed4's 720{{c}} sharp fifth at the ends of the tuning spectrum. However, ~3/2 is now the chroma-negative rather than chroma-positive generator, equalized and collapsed tunings are now swapped (equalized is 720{{c}} fifth and collapsed is 685{{c}} fifth), and the basic tuning is now the 705-cent gentle fifth from [[17edo]]/[[17ed4]] instead of 12edo's fifth. Diaquadic scales are also more widely spaced than diatonic scales, closer melodically to an octave-period pentatonic scale.
-The darker modes contain both major triads and augmented triads on the root, and the brighter modes contain both minor and diminished triads on the root.
-* LLLsLLsLLs 9|0
+== Scale properties ==
-* LLsLLLsLLs 8|1
+{{TAMNAMS use}}
-* LLsLLsLLLs 7|2
-* LLsLLsLLsL 6|3
+=== Intervals ===
-* LsLLLsLLsL 5|4
+{{MOS intervals}}
-* LsLLsLLLsL 4|5
-* LsLLsLLsLL 3|6
+=== Generator chain ===
-* sLLLsLLsLL 2|7
+{{MOS genchain}}
-* sLLsLLLsLL 1|8
-* sLLsLLsLLL 0|9
+=== Modes ===
+{{MOS mode degrees}}
+== Scale tree ==
+{{MOS tuning spectrum
+| 5/3 = Quarchy is around here
+| 3/1 = Tetrominant is around here
+| 4/1 = Meanquad is around here
+}}
 == Temperaments ==
 There are two major rank-2 temperament interpretations of diaquadic, corresponding to double octave clones of [[meantone]] and [[archy]].
 === Meanquad ===
 ''Main article: [[Meanquad]]''
 * [[Subgroup]]: 4.5.6
 * [[Comma list]]: [[81/80]]
-* [[Val]]s: 7, 31, 38, 24, 17, 10, 69, 45, 55, 11[-5], 52, 41, 13[+5], 27[+5]
+* {{Mapping|legend=1|1 0 1|0 4 1}}
+* [[Support]]ing ETs: 7, 31, 38, 24, 17, 10, 69, 45, 55, 11[-5], 52, 41, 13[+5], 27[+5]
 * [[CTE tuning]]: ~[[3/2]] = 697.214
 ==== Tetrominant ====
 * [[Subgroup]]: 4.5.6.7
-* [[Comma list]]: [[36/35], [[64/63]]
+* [[Comma list]]: [[36/35]], [[64/63]]
-* [[Val]]s: 7, 17, 24, 10, 31, 41, 27[+5], 38[+7], 55[+7], 58[+5, +7], 65[+5, +7], 44[+5], 75[+5, +7]
+* {{Mapping|legend=1|1 0 1 2|0 4 1 -2}}
+* [[Support]]ing ETs: 7, 17, 24, 10, 31, 41, 27[+5], 38[+7], 55[+7], 58[+5, +7], 65[+5, +7], 44[+5], 75[+5, +7]
 * [[CTE tuning]]: ~[[3/2]] = 699.622
 === Quarchy ===
 * [[Subgroup]]: 4.6.7
 * [[Comma list]]: [[64/63]]
-* [[Val]]s: 10, 17, 7, 27, 37, 44, 13, 24, 47, 11[+7], 23, 57, 16, 41
+* {{Mapping|legend=1|1 2 0|0 1 -2}}
+* [[Support]]ing ETs: 10, 17, 7, 27, 37, 44, 13, 24, 47, 11[+7], 23, 57, 16, 41
 * [[CTE tuning]]: ~[[3/2]] = 709.595