1L 3s: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Nick Vuci (talk | contribs)
autopatrolled
348 edits
→Modes: added MOS mode degrees template
CompactStar (talk | contribs)
5,020 edits
No edit summary
Line 8: Line 8:
}}
}}


{{MOS intro}}
{{MOS intro|Other Names=tetric}}
 
In South Africa, the San use a tetratonic scale which is approximately basic 1L 3s.
 
== Modes ==
== Modes ==
{{MOS mode degrees}}
{{MOS mode degrees}}
Line 17: Line 20:
* Chroma-negative generator: 0 cents (0\1) to 300 cents (1\4)
* Chroma-negative generator: 0 cents (0\1) to 300 cents (1\4)


{| class="wikitable center-all"
{{Scale tree|Comments=10/7:[[Orson]]/[[Orwell]];9/5:[[Godzilla]];9/4:[[Laconic]]/[[gorgo]];13/5:Unnamed golden tuning (213.5979¢;10/3:[[Isra]]/[[deutone]];9/2:[[Porcupine}}
! colspan="6" | Small step <br><span style="font-size:0.85em">(Chroma-negative generator)</span>
! Cents
! L
! s
! L/s
! Comments
|-
| 1\4 || || || || || || 300.000 || 1 || 1 || 1.000 ||
|-
| || || || || || 5\21 || 285.714 || 6 || 5 || 1.200 ||
|-
| || || || || 4\17 || || 282.353 || 5 || 4 || 1.250 ||
|-
| || || || || || 7\30 || 280.000 || 9 || 7 || 1.286 ||
|-
| || || || 3\13 || || || 276.923 || 4 || 3 || 1.333 ||
|-
| || || || || || 8\35 || 274.286 || 11 || 8 || 1.375 ||
|-
| || || || || 5\22 || || 272.727 || 7 || 5 || 1.400 ||
|-
| || || || || || 7\31 || 270.968 || 10 || 7 || 1.429 || [[Orson]]/[[Orwell]]
|-
| || || 2\9 || || || || 266.667 || 3 || 2 || 1.500 ||
|-
| || || || || || 7\32 || 262.500 || 11 || 7 || 1.571 ||
|-
| || || || || 5\23 || || 260.870 || 8 || 5 || 1.600 ||
|-
| || || || || || 8\37 || 259.459 || 13 || 8 || 1.625 || Unnamed golden tuning (259.8508¢)
|-
| || || || 3\14 || || || 257.143 || 5 || 3 || 1.667 ||
|-
| || || || || || 7\33 || 254.545 || 12 || 7 || 1.714 ||
|-
| || || || || 4\19 || || 252.632 || 7 || 4 || 1.750 ||
|-
| || || || || || 5\24 || 250.000 || 9 || 5 || 1.800 || [[Godzilla]]
|-
| || 1\5 || || || || || 240.000 || 2 || 1 || 2.000 || Basic 1L 3s <br>(Small steps larger than this are proper)
|-
| || || || || || 4\21 || 228.571 || 9 || 4 || 2.250 || [[Laconic]]/[[gorgo]]
|-
| || || || || 3\16 || || 225.000 || 7 || 3 || 2.333 ||
|-
| || || || || || 5\27 || 222.222 || 12 || 5 || 2.400 ||
|-
| || || || 2\11 || || || 218.182 || 5 || 2 || 2.500 ||
|-
| || || || || || 5\28 || 214.286 || 13 || 5 || 2.600 || Unnamed golden tuning (213.5979¢)
|-
| || || || || 3\17 || || 211.765 || 8 || 3 || 2.667 ||
|-
| || || || || || 4\23 || 208.696 || 11 || 4 || 2.750 ||
|-
| || || 1\6 || || || || 200.000 || 3 || 1 || 3.000 ||
|-
| || || || || || 3\19 || 189.474 || 10 || 3 || 3.333 || [[Isra]]/[[deutone]]
|-
| || || || || 2\13 || || 184.615 || 7 || 2 || 3.500 ||
|-
| || || || || || 3\20 || 180.000 || 11 || 3 || 3.667 ||
|-
| || || || 1\7 || || || 171.429 || 4 || 1 || 4.000 ||
|-
| || || || || || 2\15 || 160.000 || 9 || 2 || 4.500 || [[Porcupine]]
|-
| || || || || 1\8 || || 150.000 || 5 || 1 || 5.000 ||
|-
| || || || || || 1\9 || 133.333 || 6 || 1 || 6.000 ||
|-
| 0\1 || || || || || || 0.000 || 1 || 0 || → inf ||
|}


[[Category:Tetrad]]
[[Category:Tetrad]]
[[Category:4-tone scales]]
[[Category:4-tone scales]]

Revision as of 08:23, 13 August 2024

↑ 1L 2s 2L 2s ↗
1L 3s 2L 3s →
↓ 1L 4s 2L 4s ↘ 
┌╥┬┬┬┐
│║││││
││││││
└┴┴┴┴┘
Scale structure
Step pattern Lsss
sssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 3\4 to 1\1 (900.0 ¢ to 1200.0 ¢)
Dark 0\1 to 1\4 (0.0 ¢ to 300.0 ¢)
Related MOS scales
Parent 1L 2s
Sister 3L 1s
Daughters 4L 1s, 1L 4s
Neutralized 2L 2s
2-Flought 5L 3s, 1L 7s
Equal tunings
Equalized (L:s = 1:1) 3\4 (900.0 ¢)
Supersoft (L:s = 4:3) 10\13 (923.1 ¢)
Soft (L:s = 3:2) 7\9 (933.3 ¢)
Semisoft (L:s = 5:3) 11\14 (942.9 ¢)
Basic (L:s = 2:1) 4\5 (960.0 ¢)
Semihard (L:s = 5:2) 9\11 (981.8 ¢)
Hard (L:s = 3:1) 5\6 (1000.0 ¢)
Superhard (L:s = 4:1) 6\7 (1028.6 ¢)
Collapsed (L:s = 1:0) 1\1 (1200.0 ¢)

1L 3s, also called tetric, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 3 small steps, repeating every octave. Generators that produce this scale range from 900 ¢ to 1200 ¢, or from 0 ¢ to 300 ¢.

In South Africa, the San use a tetratonic scale which is approximately basic 1L 3s.

Modes

Scale degrees of the modes of 1L 3s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4
3|0 1 Lsss Perf. Aug. Maj. Perf. Perf.
2|1 4 sLss Perf. Perf. Maj. Perf. Perf.
1|2 3 ssLs Perf. Perf. Min. Perf. Perf.
0|3 2 sssL Perf. Perf. Min. Dim. Perf.

Scale tree

Generator ranges:

  • Chroma-positive generator: 900 cents (3\4) to 1200 cents (1\1)
  • Chroma-negative generator: 0 cents (0\1) to 300 cents (1\4)

{{Scale tree|Comments=10/7:Orson/Orwell;9/5:Godzilla;9/4:Laconic/gorgo;13/5:Unnamed golden tuning (213.5979¢;10/3:Isra/deutone;9/2:[[Porcupine}}

Retrieved from "https://en.xen.wiki/index.php?title=1L_3s&oldid=150544"