6L 1s: Difference between revisions

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| Pattern = LLLLLLs
| Pattern = LLLLLLs
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There are two notable harmonic entropy minima with this [[MOSScales|MOS]] pattern. The first is [[Tetracot_family|tetracot]], in which four generators make a 3/2, and the second is known as [[roulette7|roulette7]], the seven note albitonic scale for the 2.5.7.11.13 subgroup temperament [[Chromatic_pairs#Roulette|roulette]]. (Other temperaments like [[didacus]], [[luna]], [[hemithirds]], and [[hemiwürschmidt]] have very similar 7-note MOSes.)
The 6L+1s pattern also houses a temperament of the 11th and 13th harmonics, for example L=7 s=4 (46 edo) is such a scale.


Scales of this form are always [[Rothenberg_propriety|proper]], because there is only one small step.
Scales of this form are always [[Rothenberg_propriety|proper]], because there is only one small step.
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| style="text-align:center;" | Tetracot is around here
| style="text-align:center;" | <!--Tetracot is around here-->
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| style="text-align:center;" | Optimum rank range glacial (L/s=2/1)
| style="text-align:center;" | Optimum rank range <!--glacial--> (L/s=2/1)
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| style="text-align:center;" | Didacus/hemithirds/roulette is around here
| style="text-align:center;" | <!--Didacus/hemithirds/roulette is around here-->
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Revision as of 18:38, 5 April 2021

User:IlL/Template:RTT restriction

← 5L 1s 6L 1s 7L 1s →
↙ 5L 2s ↓ 6L 2s 7L 2s ↘
Scale structure
Step pattern LLLLLLs
sLLLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 1\7 to 1\6 (171.4 ¢ to 200.0 ¢)
Dark 5\6 to 6\7 (1000.0 ¢ to 1028.6 ¢)
TAMNAMS information
Name archaeotonic
Prefix arch-
Abbrev. arc
Related MOS scales
Parent 1L 5s
Sister 1L 6s
Daughters 7L 6s, 6L 7s
Neutralized 5L 2s
2-Flought 13L 1s, 6L 8s
Equal tunings
Equalized (L:s = 1:1) 1\7 (171.4 ¢)
Supersoft (L:s = 4:3) 4\27 (177.8 ¢)
Soft (L:s = 3:2) 3\20 (180.0 ¢)
Semisoft (L:s = 5:3) 5\33 (181.8 ¢)
Basic (L:s = 2:1) 2\13 (184.6 ¢)
Semihard (L:s = 5:2) 5\32 (187.5 ¢)
Hard (L:s = 3:1) 3\19 (189.5 ¢)
Superhard (L:s = 4:1) 4\25 (192.0 ¢)
Collapsed (L:s = 1:0) 1\6 (200.0 ¢)
ViewTalkEdit

Scales of this form are always proper, because there is only one small step.

Generator Cents Comments
1\7 171.43
6\41 175.61
5\34 176.47
4\27 177.78
3\20 180
180.815
8\53 181.13
1200/(5+phi) Golden archeotonic
5\33 181.82
182.44
7\46 182.61
2\13 184.62 Optimum rank range (L/s=2/1)
5\32 187.5
188.03
8\51 188.235
188.45 L/s = e
3\19 189.47 L/s = 3
189.92 L/s = pi
4\25 192 L/s = 4
5\31 193.55
6\37 194.595
1\6 200