Revision as of 06:48, 6 April 2021

Sensipent

Subgroup: 2.3.5

Mapping: [⟨1 6 8], ⟨0 -7 -9]]

Sensi

Main article: Sensi

Sensi tempers out 686/675, 245/243 and 4375/4374 in addition to 126/125, and can be described as the 19&27 temperament. It has as a generator half the size of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 13-limit sensi tempers out 91/90. 22/17, in the middle, is even closer to the generator. 46edo is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available. The name "sensi" is a play on the words "semi-" and "sixth."

Subgroup: 2.3.5.7

Comma list: 126/125, 245/243

Mapping: [⟨1 6 8 11], ⟨0 -7 -9 -13]]

Mapping generators: ~2, ~14/9

Wedgie: ⟨⟨ 7 9 13 -2 1 5 ]]

POTE generator: ~9/7 = 443.383

Minimax tuning:

7-odd-limit

[[1 0 0 0⟩, [1/13 0 0 7/13⟩, [5/13 0 0 9/13⟩, [0 0 0 1⟩]

Eigenmonzos: 2, 7

9-odd-limit

[[1 0 0 0⟩, [2/5 14/5 -7/5 0⟩, [4/5 18/5 -9/5 0⟩, [3/5 26/5 -13/5 0⟩]

Eigenmonzos: 2, 9/5

Algebraic generator: The real root of x⁵ + x⁴ - 4x² + x - 1, at 443.3783 cents.

@@ Line 6: / Line 6: @@
 }}
 = Sensipent =
+Subgroup: 2.3.5
 [[Comma list]]: 78732/78125
@@ Line 19: / Line 22: @@
 Sensi tempers out [[686/675]], [[245/243]] and [[4375/4374]] in addition to [[126/125]], and can be described as the 19&amp;27 temperament. It has as a generator half the size of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as [[13-limit]] sensi tempers out 91/90. 22/17, in the middle, is even closer to the generator. [[46edo]] is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available. The name "sensi" is a play on the words "semi-" and "sixth."
+Subgroup: 2.3.5.7
 [[Comma list]]: 126/125, 245/243
@@ Line 45: / Line 50: @@
 == Sensor ==
+Subgroup: 2.3.5.7.11
 Comma list: 126/125, 245/243, 385/384
@@ Line 56: / Line 64: @@
 === 13-limit ===
+Subgroup: 2.3.5.7.11.13
 Comma list: 91/90, 126/125, 169/168, 385/384
@@ Line 67: / Line 78: @@
 == Sensis ==
+Subgroup: 2.3.5.7.11
 Comma list: 56/55, 100/99, 245/243
@@ Line 78: / Line 92: @@
 === 13-limit ===
+Subgroup: 2.3.5.7.11.13
 Comma list: 56/55, 78/77, 91/90, 100/99
@@ Line 89: / Line 106: @@
 == Sensus ==
+Subgroup: 2.3.5.7.11
 Comma list: 126/125, 176/175, 245/243
@@ Line 100: / Line 120: @@
 === 13-limit ===
+Subgroup: 2.3.5.7.11.13
 Comma list: 91/90, 126/125, 169/168, 352/351
@@ Line 111: / Line 134: @@
 == Sensa ==
+Subgroup: 2.3.5.7.11
 Comma list: 55/54, 77/75, 99/98
@@ Line 122: / Line 148: @@
 === 13-limit ===
+Subgroup: 2.3.5.7.11.13
 Comma list: 55/54, 66/65, 77/75, 143/140
@@ Line 133: / Line 162: @@
 == Hemisensi ==
+Subgroup: 2.3.5.7.11
 Comma list: 126/125, 243/242, 245/242
@@ Line 144: / Line 176: @@
 = Sensei =
-Comma list: 225/224, 78732/78125
-Mapping: [&lt;1 6 8 23|, &lt;0 -7 -9 -32|]
+Subgroup: 2.3.5.7
-Wedgie: &lt;&lt;7 9 32 -2 31 49||
+[[Comma list]]: 225/224, 78732/78125
-POTE generator: ~125/81 = 757.245
+[[Mapping]]: [{{val| 1 6 8 23 }}, {{val| 0 -7 -9 -32 }}]
+{{Multival|legend=1| 7 9 32 -2 31 49 }}
+[[POTE generator]]: ~125/81 = 757.245
 {{Val list|legend=1| 19, 84, 103, 187, 290b }}
-Badness: 0.0592
+[[Badness]]: 0.0592
 = Bison =
-Comma list: 6144/6125, 78732/78125
-Mapping: [&lt;2 5 7 3|, &lt;0 -7 -9 10|]
+Subgroup: 2.3.5.7
+[[Comma list]]: 6144/6125, 78732/78125
+[[Mapping]]: [{{val| 2 5 7 3 }}, {{val| 0 -7 -9 10 }}]
-Wedgie: &lt;&lt;14 18 -20 -4 -71 -97||
+{{Multival|legend=1| 14 18 -20 -4 -71 -97 }}
-POTE generator: ~35/32 = 156.925
+[[POTE generator]]: ~35/32 = 156.925
 {{Val list|legend=1| 8, 38, 46, 84, 130 }}
-Badness: 0.0704
+[[Badness]]: 0.0704
 == 11-limit ==
+Subgroup: 2.3.5.7.11
 Comma list: 441/440, 6144/6125, 8019/8000
-Mapping: [&lt;2 5 7 3 3|, &lt;0 -7 -9 10 15|]
+Mapping: [{{val| 2 5 7 3 3 }}, {{val| 0 -7 -9 10 15 }}]
 POTE generator: ~35/32 = 156.883
@@ Line 180: / Line 221: @@
 Badness: 0.0371
-==13-limit==
+== 13-limit ==
+Subgroup: 2.3.5.7.11.13
 Comma list: 351/350, 364/363, 441/440, 10985/10976
-Mapping: [&lt;2 5 7 3 3 4|, &lt;0 -7 -9 10 15 13|]
+Mapping: [{{val| 2 5 7 3 3 4 }}, {{val| 0 -7 -9 10 15 13 }}]
 POTE generator: ~35/32 = 156.904
@@ Line 192: / Line 236: @@
 = Heinz =
-[[Comma list]]: 78732/78125, 1029/1024
-[[Mapping]]: [&lt;1 13 17 -1|, &lt;0 -21 -27 7|]
+Subgroup: 2.3.5.7
+[[Comma list]]: 1029/1024, 78732/78125
+[[Mapping]]: [{{val| 1 13 17 -1 }}, {{val| 0 -21 -27 7 }}]
 [[POTE generator]]: ~48/35 = 546.815
@@ Line 203: / Line 250: @@
 == 11-limit ==
-Comma list: 385/384, 441/440, 88208/87500
-Mapping: [&lt;1 13 17 -1 4|, &lt;0 -21 -27 7 -1|]
+Subgroup: 2.3.5.7.11
+Comma list: 385/384, 441/440, 78732/78125
+Mapping: [{{val| 1 13 17 -1 4 }}, {{val| 0 -21 -27 7 -1 }}]
 POTE generator: ~11/8 = 547.631
@@ Line 214: / Line 264: @@
 == 13-limit ==
+Subgroup: 2.3.5.7.11.13
 Comma list: 351/350, 385/384, 441/440, 847/845
-Mapping: [&lt;1 13 17 -1 4 -5|, &lt;0 -21 -27 7 -1 16|]
+Mapping: [{{val| 1 13 17 -1 4 -5 }}, {{val| 0 -21 -27 7 -1 16 }}]
 POTE generator: ~11/8 = 547.629
@@ Line 225: / Line 278: @@
 == 17-limit ==
+Subgroup: 2.3.5.7.11.13.17
 Comma list: 273/272, 351/350, 385/384, 441/440, 847/845
-Mapping: [&lt;1 13 17 -1 4 -5 3|, &lt;0 -21 -27 7 -1 16 2|]
+Mapping: [{{val| 1 13 17 -1 4 -5 3 }}, {{val| 0 -21 -27 7 -1 16 2 }}]
 POTE generator: ~11/8 = 547.635
@@ Line 236: / Line 292: @@
 == 19-limit ==
+Subgroup: 2.3.5.7.11.13.17.19
 Comma list: 171/170, 209/208, 351/350, 385/384, 441/440, 969/968
-Mapping: [&lt;1 13 17 -1 4 -5 3 -5|, &lt;0 -21 -27 7 -1 16 2 17|]
+Mapping: [{{val| 1 13 17 -1 4 -5 3 -5 }}, {{val| 0 -21 -27 7 -1 16 2 17 }}]
 POTE generator: ~11/8 = 547.614

Sensipent family: Difference between revisions

Revision as of 06:48, 6 April 2021

Sensipent

Sensi

Sensor

13-limit

Sensis

13-limit

Sensus

13-limit

Sensa

13-limit

Hemisensi

Sensei

Bison

11-limit

13-limit

Heinz

11-limit

13-limit

17-limit

19-limit

Navigation menu

Search