6L 1s: Difference between revisions

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== Scale tree ==
== Scale tree ==
Generator ranges:
* Chroma-positive generator: 171.4286 cents (1\7) to 200 cents (1\6)
* Chroma-negative generator: 1000 cents (5\6) to 1028.5714 cents (6\7)
{| class="wikitable center-all"
{| class="wikitable center-all"
! colspan="6" | Generator
! colspan="6" | Generator
Line 44: Line 48:
| || || || || || 6\41 || 175.610 || 6 || 5 || 1.200 ||
| || || || || || 6\41 || 175.610 || 6 || 5 || 1.200 ||
|-
|-
| || || || || 5\34 || || 176.471 || 5 || 4 || 1.250 || Tetracot is in this region
| || || || || 5\34 || || 176.471 || 5 || 4 || 1.250 || [[Tetracot]] is in this region
|-
|-
| || || || || || 9\61 || 177.049 || 9 || 7 || 1.286 ||
| || || || || || 9\61 || 177.049 || 9 || 7 || 1.286 || Tetracot/[[modus]]/[[wollemia]]
|-
|-
| || || || 4\27 || || || 177.778 || 4 || 3 || 1.333 ||
| || || || 4\27 || || || 177.778 || 4 || 3 || 1.333 ||
Line 54: Line 58:
| || || || || 7\47 || || 178.723 || 7 || 5 || 1.400 ||
| || || || || 7\47 || || 178.723 || 7 || 5 || 1.400 ||
|-
|-
| || || || || || 10\67 || 179.104 || 10 || 7 || 1.428 ||
| || || || || || 10\67 || 179.104 || 10 || 7 || 1.429 ||
|-
|-
| || || 3\20 || || || || 180.000 || 3 || 2 || 1.500 || L/s = 3/2
| || || 3\20 || || || || 180.000 || 3 || 2 || 1.500 ||  
|-
|-
| || || || || || 11\73 || 180.822 || 11 || 7 || 1.571 ||
| || || || || || 11\73 || 180.822 || 11 || 7 || 1.571 ||
Line 62: Line 66:
| || || || || 8\53 || || 181.132 || 8 || 5 || 1.600 ||  
| || || || || 8\53 || || 181.132 || 8 || 5 || 1.600 ||  
|-
|-
| || || || || || 13\86 || 181.395 || 13 || 8 || 1.625 || Unnamed golden tuning
| || || || || || 13\86 || 181.395 || 13 || 8 || 1.625 || Wilson Golden 2 (181.3227¢)
|-
|-
| || || || 5\33 || || || 181.818 || 5 || 3 || 1.667 ||
| || || || 5\33 || || || 181.818 || 5 || 3 || 1.667 ||
|-
|-
| || || || || || 12\79 || 182.278 || 12 || 7 || 1.714 || Bluebirds
| || || || || || 12\79 || 182.278 || 12 || 7 || 1.714 || [[Bluebirds]]
|-
|-
| || || || || 7\46 || || 182.609 || 7 || 4 || 1.750 ||
| || || || || 7\46 || || 182.609 || 7 || 4 || 1.750 ||
Line 82: Line 86:
| || || || 5\32 || || || 187.500 || 5 || 2 || 2.500 ||  
| || || || 5\32 || || || 187.500 || 5 || 2 || 2.500 ||  
|-
|-
| || || || || || 13\83 || 187.952 || 13 || 5 || 2.600 || Unnamed golden tuning
| || || || || || 13\83 || 187.952 || 13 || 5 || 2.600 || Golden [[glacial]] (188.0298¢)
|-
|-
| || || || || 8\51 || || 188.235 || 8 || 3 || 2.667 ||
| || || || || 8\51 || || 188.235 || 8 || 3 || 2.667 ||
Line 88: Line 92:
| || || || || || 11\70 || 188.571 || 11 || 4 || 2.750 ||
| || || || || || 11\70 || 188.571 || 11 || 4 || 2.750 ||
|-
|-
| || || 3\19 || || || || 189.474 || 3 || 1 || 3.000 || L/s = 3/1
| || || 3\19 || || || || 189.474 || 3 || 1 || 3.000 || [[Spell]]
|-
|-
| || || || || || 10\63 || 190.476 || 10 || 3 || 3.333 ||
| || || || || || 10\63 || 190.476 || 10 || 3 || 3.333 ||
|-
|-
| || || || || 7\44 || || 190.909 || 7 || 2 || 3.500 ||
| || || || || 7\44 || || 190.909 || 7 || 2 || 3.500 || [[Isra]]/[[deutone]]
|-
|-
| || || || || || 11\69 || 191.304 || 11 || 3 || 3.667 ||
| || || || || || 11\69 || 191.304 || 11 || 3 || 3.667 ||
|-
|-
| || || || 4\25 || || || 192.000 || 4 || 1 || 4.000 ||
| || || || 4\25 || || || 192.000 || 4 || 1 || 4.000 || Isra/[[leantone]]
|-
|-
| || || || || || 9\56 || 192.857 || 9 || 2 || 4.500 ||
| || || || || || 9\56 || 192.857 || 9 || 2 || 4.500 ||
|-
|-
| || || || || 5\31 || || 193.548 || 5 || 1 || 5.000 || Didacus/hemithirds/hemiwürschmidt
| || || || || 5\31 || || 193.548 || 5 || 1 || 5.000 || [[Didacus]]/[[hemithirds]]/[[hemiwürschmidt]]
|-
|-
| || || || || || 6\37 || 194.595 || 6 || 1 || 6.000 || Didacus/roulette
| || || || || || 6\37 || 194.595 || 6 || 1 || 6.000 || Didacus/[[roulette]]
|-
|-
| 1\6 || || || || || || 200.000 || 1 || 0 || → inf ||
| 1\6 || || || || || || 200.000 || 1 || 0 || → inf ||

Revision as of 06:45, 21 February 2022

← 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 ¢)

6L 1s is the MOS scale built from a generator between 1\7 (171¢) and 1\6 (200¢). Scales of this form are always proper, because there is only one small step.

Names

The TAMNAMS system uses the name archeotonic.

Notation

JKLMNOPJ = LLLsLLL (Horthathian mode), &/@ = chroma up/down

Modes

MOS modes

Archeotonic.png

MODMOSes

Temperaments

There are two notable harmonic entropy minima with this MOS pattern. The first is tetracot, in which four generators make a 3/2, and the second is known as roulette7, the seven note albitonic scale for the 2.5.7.11.13 subgroup temperament 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

Scale tree

Generator ranges:

  • Chroma-positive generator: 171.4286 cents (1\7) to 200 cents (1\6)
  • Chroma-negative generator: 1000 cents (5\6) to 1028.5714 cents (6\7)
Generator Cents L s L/s Comments
1\7 171.429 1 1 1.000
6\41 175.610 6 5 1.200
5\34 176.471 5 4 1.250 Tetracot is in this region
9\61 177.049 9 7 1.286 Tetracot/modus/wollemia
4\27 177.778 4 3 1.333
11\74 178.378 11 8 1.375
7\47 178.723 7 5 1.400
10\67 179.104 10 7 1.429
3\20 180.000 3 2 1.500
11\73 180.822 11 7 1.571
8\53 181.132 8 5 1.600
13\86 181.395 13 8 1.625 Wilson Golden 2 (181.3227¢)
5\33 181.818 5 3 1.667
12\79 182.278 12 7 1.714 Bluebirds
7\46 182.609 7 4 1.750
9\59 183.051 9 5 1.800
2\13 184.615 2 1 2.000 Basic archeotonic
9\58 186.207 9 4 2.250
7\45 186.667 7 3 2.333
12\77 187.013 12 5 2.400
5\32 187.500 5 2 2.500
13\83 187.952 13 5 2.600 Golden glacial (188.0298¢)
8\51 188.235 8 3 2.667
11\70 188.571 11 4 2.750
3\19 189.474 3 1 3.000 Spell
10\63 190.476 10 3 3.333
7\44 190.909 7 2 3.500 Isra/deutone
11\69 191.304 11 3 3.667
4\25 192.000 4 1 4.000 Isra/leantone
9\56 192.857 9 2 4.500
5\31 193.548 5 1 5.000 Didacus/hemithirds/hemiwürschmidt
6\37 194.595 6 1 6.000 Didacus/roulette
1\6 200.000 1 0 → inf
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