6L 2s: Difference between revisions

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6L 2s can be seen as a [[Warped diatonic|warped diatonic scale]], where one additional large step is added to diatonic (5L 2s).
6L 2s can be seen as a [[Warped diatonic|warped diatonic scale]], where one additional large step is added to diatonic (5L 2s).


In addition to the true MOS, LLLsLLLs, there is also a near-MOS, LLLLsLLs, in which the period is the only interval with more than two varieties. Although the true MOS (LLLsLLLs or its rotations) is always proper, the near-MOS is only proper if the generator is smaller than 2\14 (which includes hedgehog).  
In addition to the true MOS pattern, there is a near-mos pattern, LLLLsLLs, in which the period is the only interval with more than two varieties. This near-MOS pattern is only proper if the generator is smaller than 2\14. Hedgehog is among these tunings.


== Modes ==
== Modes ==
Line 11: Line 11:


== Scale tree ==
== Scale tree ==
 
{{Scale tree|Comments=6/5: Bison;
{| class="wikitable center-all"
3/2: [[Hedgehog]] is around here;
! colspan="6" | Generator
11/7: Echidna;
! Cents
13/8: Supers, pogo;
! L
13/5: Golden ekic;
! s
11/3: Unidec;
! L/s
9/2: Secant}}
! Comments
|-
| 1\8 || || || || || || 150.000 || 1 || 1 || 1.000 ||
|-
| || || || || || 6\46 || 156.522 || 6 || 5 || 1.200 || Bison
|-
| || || || || 5\38 || || 157.895 || 5 || 4 || 1.250 ||
|-
| || || || || || 9\68 || 158.824 || 9 || 7 || 1.286 ||
|-
| || || || 4\30 || || || 160.000 || 4 || 3 || 1.333 ||
|-
| || || || || || 11\82 || 160.976 || 11 || 8 || 1.375 ||
|-
| || || || || 7\52 || || 161.538 || 7 || 5 || 1.400 ||
|-
| || || || || || 10\74 || 162.162 || 10 || 7 || 1.428 ||
|-
| || || 3\22 || || || || 163.636 || 3 || 2 || 1.500 || L/s = 3/2, hedgehog is around here
|-
| || || || || || 11\80 || 165.000 || 11 || 7 || 1.571 || Echidna
|-
| || || || || 8\58 || || 165.517 || 8 || 5 || 1.600 ||
|-
| || || || || || 13\94 || 165.957 || 13 || 8 || 1.625 || Supers, pogo
|-
| || || || 5\36 || || || 166.667 || 5 || 3 || 1.667 ||
|-
| || || || || || 12\86 || 167.442 || 12 || 7 || 1.714 ||
|-
| || || || || 7\50 || || 168.000 || 7 || 4 || 1.750 ||
|-
| || || || || || 9\64 || 168.750 || 9 || 5 || 1.800 ||
|-
| || 2\14 || || || || || 171.429 || 2 || 1 || 2.000 || Basic ekic<br>(Generators smaller than this are proper)
|-
| || || || || || 9\62 || 174.194 || 9 || 4 || 2.250 ||
|-
| || || || || 7\48 || || 175.000 || 7 || 3 || 2.333 ||
|-
| || || || || || 12\82 || 175.610 || 12 || 5 || 2.400 ||
|-
| || || || 5\34 || || || 176.471 || 5 || 2 || 2.500 ||
|-
| || || || || || 13\88 || 177.273 || 13 || 5 || 2.600 || Golden ekic
|-
| || || || || 8\54 || || 177.778 || 8 || 3 || 2.667 ||
|-
| || || || || || 11\74 || 178.378 || 11 || 4 || 2.750 ||
|-
| || || 3\20 || || || || 180.000 || 3 || 1 || 3.000 || L/s = 3/1
|-
| || || || || || 10\66 || 181.818 || 10 || 3 || 3.333 ||
|-
| || || || || 7\46 || || 182.609 || 7 || 2 || 3.500 ||
|-
| || || || || || 11\72 || 183.333 || 11 || 3 || 3.667 || Unidec
|-
| || || || 4\26 || || || 184.615 || 4 || 1 || 4.000 ||
|-
| || || || || || 9\58 || 186.207 || 9 || 2 || 4.500 || Secant
|-
| || || || || 5\32 || || 187.500 || 5 || 1 || 5.000 ||
|-
| || || || || || 6\38 || 189.474 || 6 || 1 || 6.000 ||
|-
| 1\6 || || || || || || 200.000 || 1 || 0 || → inf ||
|}
 
[[Category:Ekic| ]]
[[Category:Ekic| ]]
[[Category:8-tone scales]]
[[Category:8-tone scales]]
  <!-- main article -->
  <!-- main article -->

Revision as of 08:47, 24 April 2024

↖ 5L 1s ↑ 6L 1s 7L 1s ↗
← 5L 2s 6L 2s 7L 2s →
↙ 5L 3s ↓ 6L 3s 7L 3s ↘ 
┌╥╥╥┬╥╥╥┬┐
│║║║│║║║││
││││││││││
└┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLsLLLs
sLLLsLLL
Equave 2/1 (1200.0 ¢)
Period 1\2 (600.0 ¢)
Generator size
Bright 1\8 to 1\6 (150.0 ¢ to 200.0 ¢)
Dark 2\6 to 3\8 (400.0 ¢ to 450.0 ¢)
TAMNAMS information
Name ekic
Prefix ek-
Abbrev. ek
Related MOS scales
Parent 2L 4s
Sister 2L 6s
Daughters 8L 6s, 6L 8s
Neutralized 4L 4s
2-Flought 14L 2s, 6L 10s
Equal tunings
Equalized (L:s = 1:1) 1\8 (150.0 ¢)
Supersoft (L:s = 4:3) 4\30 (160.0 ¢)
Soft (L:s = 3:2) 3\22 (163.6 ¢)
Semisoft (L:s = 5:3) 5\36 (166.7 ¢)
Basic (L:s = 2:1) 2\14 (171.4 ¢)
Semihard (L:s = 5:2) 5\34 (176.5 ¢)
Hard (L:s = 3:1) 3\20 (180.0 ¢)
Superhard (L:s = 4:1) 4\26 (184.6 ¢)
Collapsed (L:s = 1:0) 1\6 (200.0 ¢)

6L 2s, named ekic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 2 small steps, with a period of 3 large steps and 1 small step that repeats every 600.0 ¢, or twice every octave. Generators that produce this scale range from 150 ¢ to 200 ¢, or from 400 ¢ to 450 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period. There is only one significant (though small) harmonic entropy minimum with this MOS pattern: hedgehog, in which two generators are 6/5 and three are 4/3, same as porcupine.

6L 2s can be seen as a warped diatonic scale, where one additional large step is added to diatonic (5L 2s).

In addition to the true MOS pattern, there is a near-mos pattern, LLLLsLLs, in which the period is the only interval with more than two varieties. This near-MOS pattern is only proper if the generator is smaller than 2\14. Hedgehog is among these tunings.

Modes

Modes of 6L 2s
UDP Cyclic
order		 Step
pattern
6|0(2) 1 LLLsLLLs
4|2(2) 2 LLsLLLsL
2|4(2) 3 LsLLLsLL
0|6(2) 4 sLLLsLLL

Scale tree

Template:Scale tree

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