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4L 5s: Difference between revisions

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In the case of 9edo, L and s are the same size; in the case of 4edo, s is so small it disappears. The spectrum, then, goes something like:
In the case of 9edo, L and s are the same size; in the case of 4edo, s is so small it disappears. The spectrum, then, goes something like:


{| class="wikitable"
{| class="wikitable center-all"
! colspan="6" | Generator
! Cents
! L
! s
! L/s
! Comments
|-
|-
! colspan="5" | Generator
| 2\9 || || || || || || 266.667 || 1 || 1 || 1.000 ||
! | Scale
! | Generator in cents
! | Comments
|-
|-
| | 2\9
| || || || || || 11\49 || 269.388 || 6 || 5 || 1.200 ||
| |  
| |  
| |  
| |  
| style="text-align:center;" | 1 1 1 1 1 1 1 1 1
| | 266.667
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 9\40 || || 270.000 || 5 || 4 || 1.250 ||
| |  
| |  
| |
| | 9\40
| style="text-align:center;" | 4 5 4 5 4 5 4 5 4
| | 270
| |  
|-
|-
| |  
| || || || || || 16\71 || 270.423 || 9 || 7 || 1.286 ||
| |  
| |  
| | 7\31
| |  
| style="text-align:center;" | 3 4 3 4 3 4 3 4 3
| | 270.968
| style="text-align:center;" |  
|-
|-
| |  
| || || || 7\31 || || || 270.968 || 4 || 3 || 1.333 ||
| |  
| |  
| |  
| | 12\53
| style="text-align:center;" | 5 7 5 7 5 7 5 7 5
| | 271.698
| style="text-align:center;" | <!--Orwell is around here-->
|-
|-
| |  
| || || || || || 19\84 || 271.429 || 11 || 8 || 1.375 || Orwell is in this region
| |  
| | 5\22
| |  
| |  
| style="text-align:center;" | 2 3 2 3 2 3 2 3 2
| | 272.727
| style="text-align:center;" | <!--Optimum rank range (L/s=3/2) orwell-->
|-
|-
| |  
| || || || || 12\53 || || 271.698 || 7 || 5 || 1.400 ||
| |  
| |  
| |  
| | 13\57
| style="text-align:center;" | 5 8 5 8 5 8 5 8 5
| | 273.684
| style="text-align:center;" | <!--Golden orwell (bad tuning)-->
|-
|-
| |  
| || || || || || 17\75 || 272.000 || 10 || 7 || 1.428 ||
| |  
| |  
| | 8\35
| |  
| style="text-align:center;" | 3 5 3 5 3 5 3 5 3
| | 274.286
| style="text-align:center;" |  
|-
|-
| |  
| || || 5\22 || || || || 272.727 || 3 || 2 || 1.500 || L/s = 3/2
| |  
| |  
| |  
| | 11\48
| style="text-align:center;" | 4 7 4 7 4 7 4 7 4
| | 275
| |  
|-
|-
| |  
| || || || || || 18\79 || 273.418 || 11 || 7 || 1.571 ||
| | 3\13
|-
| |  
| || || || || 13\57 || || 273.684 || 8 || 5 || 1.600 ||
| |  
|-
| |  
| || || || || || 21\92 || 273.913 || 13 || 8 || 1.625 || Unnamed golden tuning
| style="text-align:center;" | 1 2 1 2 1 2 1 2 1
|-
| | 276.923
| || || || 8\35 || || || 274.286 || 5 || 3 || 1.667 ||
| style="text-align:center;" | Boundary of propriety:
|-
 
| || || || || || 19\83 || 274.699 || 12 || 7 || 1.714 ||
generators smaller than this are proper
|-
| || || || || 11\48 || || 275.000 || 7 || 4 || 1.750 ||
|-
| || || || || || 14\61 || 275.410 || 9 || 5 || 1.800 ||
|-
| || 3\13 || || || || || 276.923 || 2 || 1 || 2.000 || Basic orwelloid<br>(Generators smaller than this are proper)
|-
| || || || || || 13\56 || 278.571 || 9 || 4 || 2.250 ||
|-
| || || || || 10\43 || || 279.070 || 7 || 3 || 2.333 ||
|-
| || || || || || 17\73 || 279.452 || 12 || 5 || 2.400 ||
|-
| || || || 7\30 || || || 280.000 || 5 || 2 || 2.500 ||
|-
| || || || || || 18\77 || 280.519 || 13 || 5 || 2.600 || Unnamed golden tuning
|-
| || || || || 11\47 || || 280.851 || 8 || 3 || 2.667 ||
|-
| || || || || || 15\64 || 281.250 || 11 || 4 || 2.750 ||
|-
| || || 4\17 || || || || 282.353 || 3 || 1 || 3.000 || L/s = 3/1
|-
|-
| |  
| || || || || || 13\55 || 283.636 || 10 || 3 || 3.333 ||
| |  
| |  
| |  
| | 10\43
| style="text-align:center;" | 3 7 3 7 3 7 3 7 3
| | 279.07
| |  
|-
|-
| |  
| || || || || 9\38 || || 284.211 || 7 || 2 || 3.500 ||
| |  
| |  
| | 7\30
| |  
| style="text-align:center;" | 2 5 2 5 2 5 2 5 2
| | 280.000
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 14\59 || 284.746 || 11 || 3 || 3.667 ||
| |  
| |  
| |  
| | 11\47
| style="text-align:center;" | 3 8 3 8 3 8 3 8 3
| | 280.851
| |  
|-
|-
| |  
| || || || 5\21 || || || 285.714 || 4 || 1 || 4.000 ||
| |  
| | 4\17
| |  
| |  
| style="text-align:center;" | 1 3 1 3 1 3 1 3 1
| | 282.353
| style="text-align:center;" | L/s = 3
|-
|-
| |  
| || || || || || 11\46 || 286.957 || 9 || 2 || 4.500 ||
| |  
| |  
| |  
| | 9\38
| style="text-align:center;" | 2 7 2 <span style="font-size: 12.8000001907349px; line-height: 1.5;">7 </span><span style="font-size: 13px; line-height: 1.5;">2 7 2 7 2 </span>
| | 284.2105
| |  
|-
|-
| |  
| || || || || 6\25 || || 288.000 || 5 || 1 || 5.000 ||
| |  
| |  
| | 5\21
| |  
| style="text-align:center;" | 1 4 1 4 1 4 1 4 1
| | 285.714
| style="text-align:center;" | L/s = 4
|-
|-
| |  
| || || || || || 7\29 || 289.655 || 6 || 1 || 6.000 ||
| |  
| |  
| |  
| | 6\25
| style="text-align:center;" | 1 5 1 5 1 5 1 5 1
| | 288
| |  
|-
|-
| | 1\4
| 1\4 || || || || || || 300.000 || 1 || 0 || → inf ||
| |  
|}
| |  
<!--
| |  
Note that between 7\31 and 5\22, g approximates frequency ratio 7:6, 2g approximates 11:8, and 3g approximates 8:5. This defines the range of Orwell Temperament, which is the only notable harmonic entropy minimum with this MOS pattern. 4L 5s scales outside of that range are not suitable for Orwell.-->
| |  
| style="text-align:center;" | 0 1 0 1 0 1 0 1 0
| | 300.000
| style="text-align:center;" |  
|}<!--


Note that between 7\31 and 5\22, g approximates frequency ratio 7:6, 2g approximates 11:8, and 3g approximates 8:5. This defines the range of Orwell Temperament, which is the only notable harmonic entropy minimum with this MOS pattern. 4L 5s scales outside of that range are not suitable for Orwell.-->
[[Category:Scales]]
[[Category:MOS Scales]]
[[Category:9-tone scales]]
[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]
[[Category:scales]]
[[Category:Orwelloid]] <!-- main article -->
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