5L 7s: Difference between revisions

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5L 7s represents the chromatic scales of [[Pythagorean tuning|Pythagorean]]/[[~~Schismatic family|~~schismic]] and [[superpyth]], the former being [[Rothenberg propriety|proper]] but the latter improper until expanded by 5 more notes, producing ~~superpyth~~[17]. Such scales are characterized by having a small step ([[diatonic semitone]]) that is smaller than the [[chroma]] ([[chromatic semitone]]), the reverse of [[7L 5s]].

5L 7s represents the chromatic scales of [[Pythagorean tuning|Pythagorean]]/[[schismic]] and [[superpyth]], the former being [[Rothenberg propriety|proper]] but the latter improper until expanded by 5 more notes, producing Superpyth[17]. Such scales are characterized by having a small step ([[diatonic semitone]]) that is smaller than the [[chroma]] ([[chromatic semitone]]), the reverse of [[7L 5s]].

The two distinct harmonic entropy minima are, on the one hand, scales very close to Pythagorean ~~such that [[64/63]] is not tempered out, such as~~ the schismatic ~~temperaments known as Helmholtz and Garibaldi~~, and on the other hand, th simpler and less accurate temperament known as ~~[[archy]]~~ in which 64/63 is tempered out.

The two distinct harmonic entropy minima are, on the one hand, scales very close to Pythagorean tuning or the schismatic temperament, and on the other hand, the simpler and less accurate temperament known as superpyth in which 64/63 is tempered out.

==Intervals==

== Scale properties ==

=== Intervals ===

== Modes ==

=== Generator chain ===

=== Modes ===

=== Proposed ~~Names~~ ===

=== Proposed names ===

The modes are named by [[Eliora]] after Chinese zodiac animals. 5L 7s is the opposite mos to [[7L 5s]], named after a Western concept, Gregorian months, therefore this mos scale has Eastern nomenclature. Furthermore, 12edo (equalized tuning of this MOS) was independently discovered in China.

{{MOS modes|Mode Names= Rat; Ox; Tiger; Rabbit; Dragon; Snake; Horse; Goat; Monkey; Rooster; Dog; Pig}}

{{MOS modes

| Mode Names=

Rat $

Ox $

Tiger $

Rabbit $

Dragon $

Snake $

Horse $

Goat $

Monkey $

Rooster $

Dog $

Pig $

}}

== Scales ==

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== Scale tree ==

{{~~Scale tree~~|~~Comments=~~6/5: [[Photia]], ↑ [[grackle]];

{{MOS tuning spectrum

5/4: [[Helmholtz]], [[Pythagorean tuning]] (701.~~955¢~~);

| 6/5 = [[Photia]], ↑ [[grackle]]

9/7: [[Garibaldi]] / [[cassandra]];

| 5/4 = [[Helmholtz (temperament)|Helmholtz]], [[Pythagorean tuning]] (701.955{{c}})

4/3: Garibaldi / [[andromeda]];

| 9/7 = [[Garibaldi]] / [[cassandra]]

11/8: [[Kwai]];

| 4/3 = Garibaldi / [[andromeda]]

10/7: [[Undecental]], argent tuning (702.~~944¢~~);

| 11/8 = [[Kwai]]

3/2: [[Edson]];

| 10/7 = [[Undecental]], argent tuning (702.944{{c}})

13/8: [[Polypyth]], golden neogothic (704.~~096¢~~);

| 3/2 = [[Edson]]

5/3: [[Leapday]];

| 13/8 = [[Polypyth]], golden neogothic (704.096{{c}})

12/7: [[Leapweek]];

| 5/3 = [[Leapday]]

7/3: [[Supra]];

| 12/7 = [[Leapweek]]

13/5: Golden supra (708.~~054¢~~);

| 7/3 = [[Supra]]

8/3: [[Quasisuper]] / [[quasisupra]];

| 13/5 = Golden supra (708.054{{c}})

3/1: [[Suprapyth]];

| 8/3 = [[Quasisuper]] / [[quasisupra]]

7/2: [[Superpyth]];

| 3/1 = [[Suprapyth]]

6/1: ↓ [[Oceanfront]] / [[ultrapyth]]

| 7/2 = [[Superpyth]]

| 6/1 = ↓ [[Oceanfront]] / [[ultrapyth]]

}}

[[Category:12-tone scales]]

[[Category:P-chromatic| ]]

[[Category:Chromatic scales]]

@@ Line 1: / Line 1: @@
 {{Infobox MOS}}
 {{MOS intro|Other Names=p-chromatic}}
-L 7s represents the chromatic scales of [[Pythagorean tuning|Pythagorean]]/[[Schismatic family|schismic]] and [[superpyth]], the former being [[Rothenberg propriety|proper]] but the latter improper until expanded by 5 more notes, producing superpyth[17]. Such scales are characterized by having a small step ([[diatonic semitone]]) that is smaller than the [[chroma]] ([[chromatic semitone]]), the reverse of [[7L 5s]].
+L 7s represents the chromatic scales of [[Pythagorean tuning|Pythagorean]]/[[schismic]] and [[superpyth]], the former being [[Rothenberg propriety|proper]] but the latter improper until expanded by 5 more notes, producing Superpyth[17]. Such scales are characterized by having a small step ([[diatonic semitone]]) that is smaller than the [[chroma]] ([[chromatic semitone]]), the reverse of [[7L 5s]].
-The two distinct harmonic entropy minima are, on the one hand, scales very close to Pythagorean such that [[64/63]] is not tempered out, such as the schismatic temperaments known as Helmholtz and Garibaldi, and on the other hand, th simpler and less accurate temperament known as [[archy]] in which 64/63 is tempered out.
+The two distinct harmonic entropy minima are, on the one hand, scales very close to Pythagorean tuning or the schismatic temperament, and on the other hand, the simpler and less accurate temperament known as superpyth in which 64/63 is tempered out.
-==Intervals==
+== Scale properties ==
+{{TAMNAMS use}}
+=== Intervals ===
 {{MOS intervals}}
-== Modes ==
+=== Generator chain ===
+{{MOS genchain}}
+=== Modes ===
 {{MOS mode degrees}}
-=== Proposed Names ===
+=== Proposed names ===
 The modes are named by [[Eliora]] after Chinese zodiac animals. 5L 7s is the opposite mos to [[7L 5s]], named after a Western concept, Gregorian months, therefore this mos scale has Eastern nomenclature. Furthermore, 12edo (equalized tuning of this MOS) was independently discovered in China.
-{{MOS modes|Mode Names= Rat; Ox; Tiger; Rabbit; Dragon; Snake; Horse; Goat; Monkey; Rooster; Dog; Pig}}
+{{MOS modes
+| Mode Names=
+Rat $
+Ox $
+Tiger $
+Rabbit $
+Dragon $
+Snake $
+Horse $
+Goat $
+Monkey $
+Rooster $
+Dog $
+Pig $
+}}
 == Scales ==
@@ Line 25: / Line 47: @@
 == Scale tree ==
-{{Scale tree|Comments=6/5: [[Photia]], ↑ [[grackle]];
+{{MOS tuning spectrum
-/4: [[Helmholtz]], [[Pythagorean tuning]] (701.955¢);
+| 6/5 = [[Photia]], ↑&nbsp;[[grackle]]
-/7: [[Garibaldi]] / [[cassandra]];
+| 5/4 = [[Helmholtz (temperament)|Helmholtz]], [[Pythagorean tuning]] (701.955{{c}})
-/3: Garibaldi / [[andromeda]];
+| 9/7 = [[Garibaldi]] / [[cassandra]]
-/8: [[Kwai]];
+| 4/3 = Garibaldi / [[andromeda]]
-/7: [[Undecental]], argent tuning (702.944¢);
+| 11/8 = [[Kwai]]
-/2: [[Edson]];
+| 10/7 = [[Undecental]], argent tuning (702.944{{c}})
-/8: [[Polypyth]], golden neogothic (704.096¢);
+| 3/2 = [[Edson]]
-/3: [[Leapday]];
+| 13/8 = [[Polypyth]], golden neogothic (704.096{{c}})
-/7: [[Leapweek]];
+| 5/3 = [[Leapday]]
-/3: [[Supra]];
+| 12/7 = [[Leapweek]]
-/5: Golden supra (708.054¢);
+| 7/3 = [[Supra]]
-/3: [[Quasisuper]] / [[quasisupra]];
+| 13/5 = Golden supra (708.054{{c}})
-/1: [[Suprapyth]];
+| 8/3 = [[Quasisuper]] / [[quasisupra]]
-/2: [[Superpyth]];
+| 3/1 = [[Suprapyth]]
-/1: ↓ [[Oceanfront]] / [[ultrapyth]]
+| 7/2 = [[Superpyth]]
+| 6/1 = ↓&nbsp;[[Oceanfront]] / [[ultrapyth]]
 }}
 [[Category:12-tone scales]]
 [[Category:P-chromatic| ]]<!-- main article -->
 [[Category:Chromatic scales]]