6L 1s: Difference between revisions

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== Scale tree ==
== Scale tree ==
Generator ranges:
{{Scale tree|Comments=
* Chroma-positive generator: 171.4286 cents (1\7) to 200 cents (1\6)
5/4: [[Tetracot]] is in this region;
* Chroma-negative generator: 1000 cents (5\6) to 1028.5714 cents (6\7)
9/7: Tetracot/[[modus]]/[[wollemia]];
 
13/8: Wilson Golden 2 (181.3227¢);
{| class="wikitable center-all"
12/7: [[Bluebirds]];
! colspan="6" | Generator
13/5: Golden [[glacial]] (188.0298¢);
! Cents
3/1: [[Spell]];
!Remainder
7/2: [[Isra]]/[[deutone]];
! L
4/1: Isra/[[leantone]];
! s
5/1: Didacus/[[hemithirds]]/[[hemiwürschmidt]];
! L/s
6/1: Didacus/[[roulette]]
! Comments
}}
|-
| 1\7 || || || || || || 171.429
|171.429|| 1 || 1 || 1.000 ||
|-
| || || || || || 6\41 || 175.610
|146.341|| 6 || 5 || 1.200 ||
|-
| || || || || 5\34 || || 176.471
|141.765|| 5 || 4 || 1.250 || [[Tetracot]] is in this region
|-
| || || || || || 9\61 || 177.049
|137.704|| 9 || 7 || 1.286 || Tetracot/[[modus]]/[[wollemia]]
|-
| || || || 4\27 || || || 177.778
|133.333|| 4 || 3 || 1.333 ||
|-
| || || || || || 11\74 || 178.378
|129.730|| 11 || 8 || 1.375 ||
|-
| || || || || 7\47 || || 178.723
|127.660|| 7 || 5 || 1.400 ||
|-
| || || || || || 10\67 || 179.104
|125.373|| 10 || 7 || 1.429 ||
|-
| || || 3\20 || || || || 180.000
|120.000|| 3 || 2 || 1.500 ||
|-
| || || || || || 11\73 || 180.822
|115.068|| 11 || 7 || 1.571 ||
|-
| || || || || 8\53 || || 181.132
|113.208|| 8 || 5 || 1.600 ||
|-
| || || || || || 13\86 || 181.395
|111.628|| 13 || 8 || 1.625 || Wilson Golden 2 (181.3227¢)
|-
| || || || 5\33 || || || 181.818
|109.091|| 5 || 3 || 1.667 ||
|-
| || || || || || 12\79 || 182.278
|106.329|| 12 || 7 || 1.714 || [[Chromatic_pairs#Bluebirds|Bluebirds]]
|-
| || || || || 7\46 || || 182.609
|104.348|| 7 || 4 || 1.750 ||
|-
| || || || || || 9\59 || 183.051
|101.695|| 9 || 5 || 1.800 ||
|-
| || 2\13 || || || || || 184.615
|92.308|| 2 || 1 || 2.000 || Basic archeotonic
|-
| || || || || || 9\58 || 186.207
|82.759|| 9 || 4 || 2.250 ||
|-
| || || || || 7\45 || || 186.667
|80.000|| 7 || 3 || 2.333 ||
|-
| || || || || || 12\77 || 187.013
|77.922|| 12 || 5 || 2.400 ||
|-
| || || || 5\32 || || || 187.500
|75.000|| 5 || 2 || 2.500 ||
|-
| || || || || || 13\83 || 187.952
|72.289|| 13 || 5 || 2.600 || Golden [[glacial]] (188.0298¢)
|-
| || || || || 8\51 || || 188.235
|70.588|| 8 || 3 || 2.667 ||
|-
| || || || || || 11\70 || 188.571
|68.571|| 11 || 4 || 2.750 ||
|-
| || || 3\19 || || || || 189.474
|63.159|| 3 || 1 || 3.000 || [[Spell]]
|-
| || || || || || 10\63 || 190.476
|57.143|| 10 || 3 || 3.333 ||
|-
| || || || || 7\44 || || 190.909
|54.545|| 7 || 2 || 3.500 || [[Isra]]/[[deutone]]
|-
| || || || || || 11\69 || 191.304
|52.174|| 11 || 3 || 3.667 ||
|-
| || || || 4\25 || || || 192.000
|48.000|| 4 || 1 || 4.000 || Isra/[[leantone]]
|-
| || || || || || 9\56 || 192.857
|42.857|| 9 || 2 || 4.500 ||
|-
| || || || || 5\31 || || 193.548
|38.709|| 5 || 1 || 5.000 || [[Didacus]]/[[hemithirds]]/[[hemiwürschmidt]]
|-
| || || || || || 6\37 || 194.595
|32.432|| 6 || 1 || 6.000 || Didacus/[[roulette]]
|-
| 1\6 || || || || || || 200.000
|0.000|| 1 || 0 || → inf ||
|}


[[Category:Archaeotonic| ]]
[[Category:Archaeotonic| ]]
[[Category:7-tone scales]]
[[Category:7-tone scales]]
  <!-- main article -->
  <!-- main article -->

Revision as of 09:47, 17 April 2024

← 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 ¢)
View • Talk • Edit

6L 1s, named archaeotonic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 1 small step, repeating every octave. Generators that produce this scale range from 171.4 ¢ to 200 ¢, or from 1000 ¢ to 1028.6 ¢. 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

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details:
Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: 
{{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}


The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.


Scale tree and tuning spectrum of 6L 1s
Generator(edo) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\7 171.429 1028.571 1:1 1.000 Equalized 6L 1s
6\41 175.610 1024.390 6:5 1.200
5\34 176.471 1023.529 5:4 1.250
9\61 177.049 1022.951 9:7 1.286
4\27 177.778 1022.222 4:3 1.333 Supersoft 6L 1s
11\74 178.378 1021.622 11:8 1.375
7\47 178.723 1021.277 7:5 1.400
10\67 179.104 1020.896 10:7 1.429
3\20 180.000 1020.000 3:2 1.500 Soft 6L 1s
11\73 180.822 1019.178 11:7 1.571
8\53 181.132 1018.868 8:5 1.600
13\86 181.395 1018.605 13:8 1.625
5\33 181.818 1018.182 5:3 1.667 Semisoft 6L 1s
12\79 182.278 1017.722 12:7 1.714
7\46 182.609 1017.391 7:4 1.750
9\59 183.051 1016.949 9:5 1.800
2\13 184.615 1015.385 2:1 2.000 Basic 6L 1s
9\58 186.207 1013.793 9:4 2.250
7\45 186.667 1013.333 7:3 2.333
12\77 187.013 1012.987 12:5 2.400
5\32 187.500 1012.500 5:2 2.500 Semihard 6L 1s
13\83 187.952 1012.048 13:5 2.600
8\51 188.235 1011.765 8:3 2.667
11\70 188.571 1011.429 11:4 2.750
3\19 189.474 1010.526 3:1 3.000 Hard 6L 1s
10\63 190.476 1009.524 10:3 3.333
7\44 190.909 1009.091 7:2 3.500
11\69 191.304 1008.696 11:3 3.667
4\25 192.000 1008.000 4:1 4.000 Superhard 6L 1s
9\56 192.857 1007.143 9:2 4.500
5\31 193.548 1006.452 5:1 5.000
6\37 194.595 1005.405 6:1 6.000
1\6 200.000 1000.000 1:0 → ∞ Collapsed 6L 1s
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