5L 7s: Difference between revisions

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{{interwiki

| de =

| en = 5L 7s

| es =

| ja = 5L 7s

}}

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]].

~~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~~.

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 for this scale correspond to schismic and superpyth.

==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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* [[Pepperoni12]] – 271edo tuning

* [[Supra12]] – 56edo tuning

* [[Archy12]] – ~~472edo~~ tuning

* [[Archy12]] – 49edo tuning

* [[12-22a]] – 22edo tuning

== 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¢~~);

| 9/5 = [[Leapmonth]]

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

| 7/3 = [[Supra]]

3/1: [[Suprapyth]];

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

7/2: [[Superpyth]];

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

6/1: ↓ [[Oceanfront]] / [[ultrapyth]]

| 3/1 = [[Suprapyth]]

| 7/2 = [[Superpyth]]

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

}}

[[Category:12-tone scales]]

[[Category:P-chromatic| ]]

[[Category:Chromatic scales]]

@@ Line 1: / Line 1: @@
+{{interwiki
+| de =
+| en = 5L 7s
+| es =
+| ja = 5L 7s
+}}
 {{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]].
-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.
+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 for this scale correspond to schismic and superpyth.
-==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 21: / Line 48: @@
 * [[Pepperoni12]] – 271edo tuning
 * [[Supra12]] – 56edo tuning
-* [[Archy12]] – 472edo tuning
+* [[Archy12]] – 49edo tuning
 * [[12-22a]] – 22edo tuning
 == 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¢);
+| 9/5 = [[Leapmonth]]
-/3: [[Quasisuper]] / [[quasisupra]];
+| 7/3 = [[Supra]]
-/1: [[Suprapyth]];
+| 13/5 = Golden supra (708.054{{c}})
-/2: [[Superpyth]];
+| 8/3 = [[Quasisuper]] / [[quasisupra]]
-/1: ↓ [[Oceanfront]] / [[ultrapyth]]
+| 3/1 = [[Suprapyth]]
+| 7/2 = [[Superpyth]]
+| 6/1 = ↓&nbsp;[[Oceanfront]] / [[ultrapyth]]
 }}
 [[Category:12-tone scales]]
 [[Category:P-chromatic| ]]<!-- main article -->
 [[Category:Chromatic scales]]

5L 7s: Difference between revisions

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