1L 5s: Difference between revisions

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


{| class="wikitable"
== Scale tree ==
{| class="wikitable center-all"
! colspan="6" rowspan="2" | Generator
! colspan="2" | Cents
! rowspan="2" | L
! rowspan="2" | s
! rowspan="2" | L/s
! rowspan="2" | Comments
|-
|-
! colspan="7" | Generator
! Chroma-positive
! | Cents
! Chroma-negative
! | Comments
|-
|-
| | 0\1
| 5\6 || || || || || || 1000.000 || 200.000 || 1 || 1 || 1.000 ||  
| |  
| |  
| |  
| |  
| |  
| |  
| | 0
| style="text-align:center;" |  
|-
|-
|
| || || || || || 26\31 || 1006.452 || 193.548 || 6 || 5 || 1.200 || Luna/hemithirds/hemiwürschmidt, didacus/roulette, tutone/deutone/leantone
|
|
|
|
|
|1\12
|100
|
|-
|-
|
| || || || || 21\25 || || 1008.000 || 192.000 || 5 || 4 || 1.250 ||
|
|
|
|
|1\11
|
|109.09
|
|-
|-
|
| || || || || || 37\44 || 1009.091 || 190.909 || 9 || 7 || 1.286 ||  
|
|
|
|1\10
|
|
|120
|
|-
|-
| |  
| || || || 16\19 || || || 1010.526 || 189.474 || 4 || 3 || 1.333 ||
| |  
| |  
| | 1\9
| |  
| |  
| |  
| | 133.33
| style="text-align:center;" | L/s = 4
|-
|-
| |  
| || || || || || 43\51 || 1011.765 || 188.235 || 11 || 8 || 1.375 ||  
| |  
| |  
| |  
| |  
| |  
| |  
| | 1200/(5+pi)
| | <span style="display: block; text-align: center;"></span>
|-
|-
| |  
| || || || || 27\32 || || 1012.500 || 187.500 || 7 || 5 || 1.400 ||
| |  
| | 1\8
| |  
| |  
| |  
| |  
| | 150
| style="text-align:center;" | L/s = 3
|-
|-
| |  
| || || || || || 38\45 || 1013.333 || 186.667 || 10 || 7 || 1.428 ||  
| |  
| |  
| |  
| |  
| |  
| |  
| | 1200/(5+e)
| |  
|-
|-
| |  
| || || 11\13 || || || || 1015.385 || 184.615 || 3 || 2 || 1.500 || L/s = 3/2, glacial
| |  
| |  
| | 2\15
| |  
| |  
| |  
| | 160
| style="text-align:center;" |
|-
|-
| |  
| || || || || || 39\46 || 1017.391 || 182.609 || 11 || 7 || 1.571 ||
| |  
| |  
| |  
| |  
| |  
| |  
| | 1200/(6+phi)
| |  
|-
|-
| |  
| || || || || 28\33 || || 1018.182 || 181.818 || 8 || 5 || 1.600 ||  
| |  
| |  
| |  
| | 3\22
| |  
| |  
| | 163.64
| style="text-align:center;" | Porcupine is around here
|-
|-
| |  
| || || || || || 45\53 || 1018.868 || 181.132 || 13 || 8 || 1.625 || [http://launch.groups.yahoo.com/group/tuning/message/100254 Unnamed golden tuning]{{dead link}}
| | 1\7
|-
| |  
| || || || 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 ||
| | 171.43
|-
| style="text-align:center;" | Boundary of propriety
| || || || || || 29\34 || 1023.529 || 176.471 || 9 || 5 || 1.800 || Tetracot
 
|-
(generators larger 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 ||
|-
| || || || || 19\22 || || 1036.364 || 163.636 || 7 || 3 || 2.333 || Porcupine (incomplete)
|-
|-
| |  
| || || || || || 32\37 || 1037.838 || 162.162 || 12 || 5 || 2.400 ||
| |  
| |  
| |  
| |  
| | 5\34
| |  
| | 176.47
| style="text-align:center;" | Tetracot is around here
|-
|-
| |  
| || || || 13\15 || || || 1040.000 || 160.000 || 5 || 2 || 2.500 ||
| |  
| |  
| |  
| | 4\27
| |  
| |  
| | 177.78
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 33\38 || 1042.105 || 157.895 || 13 || 5 || 2.600 || Golden hemikleismic (?)
| |  
| |  
| | 3\20
| |  
| |  
| |  
| | 180
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 20\23 || || 1043.478 || 156.522 || 8 || 3 || 2.667 ||  
| |  
| |  
| |  
| |  
| |  
| |  
| | 1200/(5+sqrt(3))
| |  
|-
|-
| |  
| || || || || || 27\31 || 1045.161 || 154.839 || 11 || 4 || 2.750 ||
| |  
| |  
| |  
| |  
| | 8\53
| |  
| | 181.13
| style="text-align:center;" |  
|-
|-
| |  
| || || 7\8 || || || || 1050.000 || 150.000 || 3 || 1 || 3.000 || L/s = 3/1
| |  
| |  
| |  
| |  
| |  
| |  
| | 1200/(5+phi)
| style="text-align:center;" | Unnamed golden temperament (discussed in [http://launch.groups.yahoo.com/group/tuning/message/100254 this thread])
|-
|-
| |  
| || || || || || 22\25 || 1056.000 || 144.000 || 10 || 3 || 3.333 ||
| |  
| |  
| |  
| | 5\33
| |  
| |  
| | 181.82
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 15\17 || || 1058.824 || 141.176 || 7 || 2 || 3.500 || Progression (incomplete)
| |  
| |  
| |  
| |  
| |  
| |  
| | 1200/(10+pi)
| |
|-
|-
| |  
| || || || || || 23\26 || 1061.538 || 138.462 || 11 || 3 || 3.667 ||  
| |  
| | 2\13
| |  
| |  
| |  
| |  
| | 184.62
| style="text-align:center;" | Optimum rank range glacial (L/s=3/2)
|-
|-
| |  
| || || || 8\9 || || || 1066.667 || 133.333 || 4 || 1 || 4.000 ||
| |  
| |  
| | 3\19
| |  
| |  
| |  
| | 189.47
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 17\19 || 1073.684 || 126.316 || 9 || 2 || 4.500 || Negri (incomplete)
| |  
| |  
| |  
| | 4\25
| |  
| |  
| | 192
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 9\10 || || 1080.000 || 120.000 || 5 || 1 || 5.000 || Miracle (incomplete)
| |  
| |  
| |  
| |  
| | 5\31
| |  
| | 193.55
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 10\11 || 1090.909 || 109.091 || 6 || 1 || 6.000 || Passion↓ (incomplete), ripple↓ (incomplete)
| |  
| |  
| |  
| |  
| |  
| | 6\37
| | 194.59
| style="text-align:center;" | Luna/Hemithird/Roulette is around here: [[roulette6|roulette6]]
|-
|-
| | 1\6
| 1\1 || || || || || || 1200.000 || 0.000 || 1 || 0 || → inf ||
| |  
| |  
| |  
| |  
| |  
| |  
| | 200
| style="text-align:center;" |  
|}
|}
[[Category:Scales]]
[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]
[[Category:6-tone scales]]

Revision as of 09:34, 19 May 2021

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.

Scale tree

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, tutone/deutone/leantone
21\25 1008.000 192.000 5 4 1.250
37\44 1009.091 190.909 9 7 1.286
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 1.428
11\13 1015.385 184.615 3 2 1.500 L/s = 3/2, 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 Unnamed golden tuning[dead link]
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 (?)
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 L/s = 3/1
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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