1L 5s: Difference between revisions

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{{Infobox MOS
| Periods = 1
| nLargeSteps = 1
| nSmallSteps = 5
| Equalized = 5
| Paucitonic = 1
| Pattern = Lsssss
}}
'''1L 5s''' is the MOS pattern Lsssss with small steps ranging from 0\1 (0¢) to 1\6 (one step of [[6edo]] = 200¢).
There are two notable low-harmonic-entropy scales with this [[MOS scale|MOS]] pattern. The first is [[tetracot]], in which four generators make a 3/2. The second is a scale in which two generators make a 5/4, which could be referred to by various names. The temperaments "luna", "hemithird", and "hemiwürschmidt" all have 6-note MOSes that are very similar. But perhaps it is best known as [[roulette6]], the six note haplitonic scale for the roulette [[Chromatic pair]].
There are two notable low-harmonic-entropy scales with this [[MOS scale|MOS]] pattern. The first is [[tetracot]], in which four generators make a 3/2. The second is a scale in which two generators make a 5/4, which could be referred to by various names. The temperaments "luna", "hemithird", and "hemiwürschmidt" all have 6-note MOSes that are very similar. But perhaps it is best known as [[roulette6]], the six note haplitonic scale for the roulette [[Chromatic pair]].


Other scales include very improper (incomplete) versions of porcupine, negri, etc.
Other scales include very improper (incomplete) versions of porcupine, negri, etc.
== Modes ==
* 5|0 Lsssss
* 4|1 sLssss
* 3|2 ssLsss
* 2|3 sssLss
* 1|4 ssssLs
* 0|5 sssssL


== Scales ==
== Scales ==
Line 11: Line 30:


== Scale tree ==
== Scale tree ==
Generator ranges:
* Chroma-positive generator: 1000 cents (5\6) to 1200 cents (1\1)
* Chroma-negative generator: 0 cents (0\1) to 200 cents (1\6)
{| class="wikitable center-all"
{| class="wikitable center-all"
! colspan="6" rowspan="2" | Generator
! colspan="6" rowspan="2" | Generator
Line 24: Line 47:
| 5\6 || || || || || || 1000.000 || 200.000 || 1 || 1 || 1.000 ||  
| 5\6 || || || || || || 1000.000 || 200.000 || 1 || 1 || 1.000 ||  
|-
|-
| || || || || || 26\31 || 1006.452 || 193.548 || 6 || 5 || 1.200 || Luna/hemithirds/hemiwürschmidt, didacus/roulette, tutone/deutone/leantone
| || || || || || 26\31 || 1006.452 || 193.548 || 6 || 5 || 1.200 || [[Luna]]/[[hemithirds]]/[[hemiwürschmidt]], [[didacus]]/[[roulette]], [[isra]]/[[tutone]]/[[leantone]]
|-
|-
| || || || || 21\25 || || 1008.000 || 192.000 || 5 || 4 || 1.250 ||
| || || || || 21\25 || || 1008.000 || 192.000 || 5 || 4 || 1.250 || Isra/[[leantone]]
|-
|-
| || || || || || 37\44 || 1009.091 || 190.909 || 9 || 7 || 1.286 ||  
| || || || || || 37\44 || 1009.091 || 190.909 || 9 || 7 || 1.286 || Isra/[[deutone]]
|-
|-
| || || || 16\19 || || || 1010.526 || 189.474 || 4 || 3 || 1.333 ||  
| || || || 16\19 || || || 1010.526 || 189.474 || 4 || 3 || 1.333 ||  
Line 36: Line 59:
| || || || || 27\32 || || 1012.500 || 187.500 || 7 || 5 || 1.400 ||
| || || || || 27\32 || || 1012.500 || 187.500 || 7 || 5 || 1.400 ||
|-
|-
| || || || || || 38\45 || 1013.333 || 186.667 || 10 || 7 || 1.428 ||  
| || || || || || 38\45 || 1013.333 || 186.667 || 10 || 7 || 1.429 ||  
|-
|-
| || || 11\13 || || || || 1015.385 || 184.615 || 3 || 2 || 1.500 || L/s = 3/2, glacial
| || || 11\13 || || || || 1015.385 || 184.615 || 3 || 2 || 1.500 || [[Glacial]]
|-
|-
| || || || || || 39\46 || 1017.391 || 182.609 || 11 || 7 || 1.571 ||
| || || || || || 39\46 || 1017.391 || 182.609 || 11 || 7 || 1.571 ||
Line 44: Line 67:
| || || || || 28\33 || || 1018.182 || 181.818 || 8 || 5 || 1.600 ||  
| || || || || 28\33 || || 1018.182 || 181.818 || 8 || 5 || 1.600 ||  
|-
|-
| || || || || || 45\53 || 1018.868 || 181.132 || 13 || 8 || 1.625 || [http://launch.groups.yahoo.com/group/tuning/message/100254 Unnamed golden tuning]{{dead link}}
| || || || || || 45\53 || 1018.868 || 181.132 || 13 || 8 || 1.625 || Wilson Golden 2 (1018.6773¢)
|-
|-
| || || || 17\20 || || || 1020.000 || 180.000 || 5 || 3 || 1.667 ||  
| || || || 17\20 || || || 1020.000 || 180.000 || 5 || 3 || 1.667 ||  
Line 52: Line 75:
| || || || || 23\27 || || 1022.222 || 177.778 || 7 || 4 || 1.750 ||
| || || || || 23\27 || || 1022.222 || 177.778 || 7 || 4 || 1.750 ||
|-
|-
| || || || || || 29\34 || 1023.529 || 176.471 || 9 || 5 || 1.800 || Tetracot
| || || || || || 29\34 || 1023.529 || 176.471 || 9 || 5 || 1.800 || [[Tetracot]]
|-
|-
| || 6\7 || || || || || 1028.571 || 171.429 || 2 || 1 || 2.000 || Basic 1L 5s<br>(Generators smaller than this are proper)
| || 6\7 || || || || || 1028.571 || 171.429 || 2 || 1 || 2.000 || Basic 1L 5s <br>(Generators smaller than this are proper)
|-
|-
| || || || || || 25\29 || 1034.483 || 165.517 || 9 || 4 || 2.250 ||
| || || || || || 25\29 || 1034.483 || 165.517 || 9 || 4 || 2.250 ||
|-
|-
| || || || || 19\22 || || 1036.364 || 163.636 || 7 || 3 || 2.333 || Porcupine (incomplete)
| || || || || 19\22 || || 1036.364 || 163.636 || 7 || 3 || 2.333 || [[Porcupine]] (incomplete)
|-
|-
| || || || || || 32\37 || 1037.838 || 162.162 || 12 || 5 || 2.400 ||
| || || || || || 32\37 || 1037.838 || 162.162 || 12 || 5 || 2.400 ||
Line 64: Line 87:
| || || || 13\15 || || || 1040.000 || 160.000 || 5 || 2 || 2.500 ||
| || || || 13\15 || || || 1040.000 || 160.000 || 5 || 2 || 2.500 ||
|-
|-
| || || || || || 33\38 || 1042.105 || 157.895 || 13 || 5 || 2.600 || Golden hemikleismic (?)
| || || || || || 33\38 || 1042.105 || 157.895 || 13 || 5 || 2.600 || Golden [[hemikleismic]] (1042.4790¢)
|-
|-
| || || || || 20\23 || || 1043.478 || 156.522 || 8 || 3 || 2.667 ||  
| || || || || 20\23 || || 1043.478 || 156.522 || 8 || 3 || 2.667 ||  
Line 70: Line 93:
| || || || || || 27\31 || 1045.161 || 154.839 || 11 || 4 || 2.750 ||
| || || || || || 27\31 || 1045.161 || 154.839 || 11 || 4 || 2.750 ||
|-
|-
| || || 7\8 || || || || 1050.000 || 150.000 || 3 || 1 || 3.000 || L/s = 3/1
| || || 7\8 || || || || 1050.000 || 150.000 || 3 || 1 || 3.000 ||  
|-
|-
| || || || || || 22\25 || 1056.000 || 144.000 || 10 || 3 || 3.333 ||
| || || || || || 22\25 || 1056.000 || 144.000 || 10 || 3 || 3.333 ||
|-
|-
| || || || || 15\17 || || 1058.824 || 141.176 || 7 || 2 || 3.500 || Progression (incomplete)
| || || || || 15\17 || || 1058.824 || 141.176 || 7 || 2 || 3.500 || [[Progression]] (incomplete)
|-
|-
| || || || || || 23\26 || 1061.538 || 138.462 || 11 || 3 || 3.667 ||  
| || || || || || 23\26 || 1061.538 || 138.462 || 11 || 3 || 3.667 ||  
Line 80: Line 103:
| || || || 8\9 || || || 1066.667 || 133.333 || 4 || 1 || 4.000 ||
| || || || 8\9 || || || 1066.667 || 133.333 || 4 || 1 || 4.000 ||
|-
|-
| || || || || || 17\19 || 1073.684 || 126.316 || 9 || 2 || 4.500 || Negri (incomplete)
| || || || || || 17\19 || 1073.684 || 126.316 || 9 || 2 || 4.500 || [[Negri]] (incomplete)
|-
|-
| || || || || 9\10 || || 1080.000 || 120.000 || 5 || 1 || 5.000 || Miracle (incomplete)
| || || || || 9\10 || || 1080.000 || 120.000 || 5 || 1 || 5.000 || [[Miracle]] (incomplete)
|-
|-
| || || || || || 10\11 || 1090.909 || 109.091 || 6 || 1 || 6.000 || Passion↓ (incomplete), ripple↓ (incomplete)
| || || || || || 10\11 || 1090.909 || 109.091 || 6 || 1 || 6.000 || [[Passion]]↓ (incomplete), [[ripple]]↓ (incomplete)
|-
|-
| 1\1 || || || || || || 1200.000 || 0.000 || 1 || 0 || → inf ||
| 1\1 || || || || || || 1200.000 || 0.000 || 1 || 0 || → inf ||

Revision as of 09:05, 20 February 2022

↑ 1L 4s 2L 4s ↗
1L 5s 2L 5s →
↓ 1L 6s 2L 6s ↘
Scale structure
Step pattern Lsssss
sssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 5\6 to 1\1 (1000.0 ¢ to 1200.0 ¢)
Dark 0\1 to 1\6 (0.0 ¢ to 200.0 ¢)
TAMNAMS information
Name antimachinoid
Prefix amech-
Abbrev. amk
Related MOS scales
Parent 1L 4s
Sister 5L 1s
Daughters 6L 1s, 1L 6s
Neutralized 2L 4s
2-Flought 7L 5s, 1L 11s
Equal tunings
Equalized (L:s = 1:1) 5\6 (1000.0 ¢)
Supersoft (L:s = 4:3) 16\19 (1010.5 ¢)
Soft (L:s = 3:2) 11\13 (1015.4 ¢)
Semisoft (L:s = 5:3) 17\20 (1020.0 ¢)
Basic (L:s = 2:1) 6\7 (1028.6 ¢)
Semihard (L:s = 5:2) 13\15 (1040.0 ¢)
Hard (L:s = 3:1) 7\8 (1050.0 ¢)
Superhard (L:s = 4:1) 8\9 (1066.7 ¢)
Collapsed (L:s = 1:0) 1\1 (1200.0 ¢)
View • Talk • Edit

1L 5s is the MOS pattern Lsssss with small steps ranging from 0\1 (0¢) to 1\6 (one step of 6edo = 200¢).

There are two notable low-harmonic-entropy scales with this MOS pattern. The first is tetracot, in which four generators make a 3/2. The second is a scale in which two generators make a 5/4, which could be referred to by various names. The temperaments "luna", "hemithird", and "hemiwürschmidt" all have 6-note MOSes that are very similar. But perhaps it is best known as roulette6, the six note haplitonic scale for the roulette Chromatic pair.

Other scales include very improper (incomplete) versions of porcupine, negri, etc.

Modes

  • 5|0 Lsssss
  • 4|1 sLssss
  • 3|2 ssLsss
  • 2|3 sssLss
  • 1|4 ssssLs
  • 0|5 sssssL

Scales

Scale tree

Generator ranges:

  • Chroma-positive generator: 1000 cents (5\6) to 1200 cents (1\1)
  • Chroma-negative generator: 0 cents (0\1) to 200 cents (1\6)
Generator Cents L s L/s Comments
Chroma-positive Chroma-negative
5\6 1000.000 200.000 1 1 1.000
26\31 1006.452 193.548 6 5 1.200 Luna/hemithirds/hemiwürschmidt, didacus/roulette, isra/tutone/leantone
21\25 1008.000 192.000 5 4 1.250 Isra/leantone
37\44 1009.091 190.909 9 7 1.286 Isra/deutone
16\19 1010.526 189.474 4 3 1.333
43\51 1011.765 188.235 11 8 1.375
27\32 1012.500 187.500 7 5 1.400
38\45 1013.333 186.667 10 7 1.429
11\13 1015.385 184.615 3 2 1.500 Glacial
39\46 1017.391 182.609 11 7 1.571
28\33 1018.182 181.818 8 5 1.600
45\53 1018.868 181.132 13 8 1.625 Wilson Golden 2 (1018.6773¢)
17\20 1020.000 180.000 5 3 1.667
40\47 1021.277 178.723 12 7 1.714
23\27 1022.222 177.778 7 4 1.750
29\34 1023.529 176.471 9 5 1.800 Tetracot
6\7 1028.571 171.429 2 1 2.000 Basic 1L 5s
(Generators smaller than this are proper)
25\29 1034.483 165.517 9 4 2.250
19\22 1036.364 163.636 7 3 2.333 Porcupine (incomplete)
32\37 1037.838 162.162 12 5 2.400
13\15 1040.000 160.000 5 2 2.500
33\38 1042.105 157.895 13 5 2.600 Golden hemikleismic (1042.4790¢)
20\23 1043.478 156.522 8 3 2.667
27\31 1045.161 154.839 11 4 2.750
7\8 1050.000 150.000 3 1 3.000
22\25 1056.000 144.000 10 3 3.333
15\17 1058.824 141.176 7 2 3.500 Progression (incomplete)
23\26 1061.538 138.462 11 3 3.667
8\9 1066.667 133.333 4 1 4.000
17\19 1073.684 126.316 9 2 4.500 Negri (incomplete)
9\10 1080.000 120.000 5 1 5.000 Miracle (incomplete)
10\11 1090.909 109.091 6 1 6.000 Passion↓ (incomplete), ripple↓ (incomplete)
1\1 1200.000 0.000 1 0 → inf
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