Rank-4 temperament

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A rank-4 temperament has a period and three additional independent generators. Typical examples include 7-limit JI, full 11-limit temperament with a one-dimensional comma basis, and full 13-limit temperament with a two-dimensional comma basis.

Ptolemismic (100/99)

Subgroup: 2.3.5.7.11

Comma list: 100/99

Mapping[1 0 0 0 2], 0 1 0 0 -2], 0 0 1 0 2], 0 0 0 1 0]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.9532, ~5/4 = 384.0675, ~7/4 = 970.8803

Optimal ET sequence7d, 8d, 10e, 12, 15, 19, 22, 27e, 34d, 41, 90e, 131e *

* optimal patent val: 104

Badness: 0.0225 × 10-6

Biyatismic (121/120)

Subgroup: 2.3.5.7.11

Comma list: 121/120

Mapping[1 0 1 0 2], 0 1 1 0 1], 0 0 -2 0 -1], 0 0 0 1 0]]

mapping generators: ~2, ~3, ~11/10, ~7

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.4578, ~11/10 = 157.7466, ~7/4 = 966.9589

Optimal ET sequence14c, 15, 22, 31, 46, 53, 60e, 68, 77, 91e, 99, 130e, 159ee, 190ee

Badness: 0.0345 × 10-6

Valinorsmic (176/175)

Subgroup: 2.3.5.7.11

Comma list: 176/175

Mapping[1 0 0 0 -4], 0 1 0 0 0], 0 0 1 0 2], 0 0 0 1 1]]

mapping generators: ~2, ~3, ~5, ~7

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 703.0449, ~5/4 = 389.7641, ~7/4 = 972.1113

Optimal ET sequence22, 31, 46, 53, 58, 80, 111

Badness: 0.0186 × 10-6

Rastmic (243/242)

Subgroup: 2.3.5.7.11

Comma list: 243/242

Mapping[1 1 0 0 2], 0 2 0 0 5], 0 0 1 0 0], 0 0 0 1 0]]

mapping generators: ~2, ~11/9, ~5, ~7

Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.5254, ~5/4 = 386.1653, ~7/4 = 968.6464

Optimal ET sequence7d, 10, 14c, 17c, 24, 27e, 31, 41, 58, 72, 130, 202

Badness: 0.0509 × 10-6

Akua (352/351, 847/845)

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 847/845

Mapping[1 0 0 10 0 5], 0 1 0 -6 0 -3], 0 0 1 1 0 0], 0 0 0 0 1 1]]

mapping generators: ~2, ~3, ~5, ~11

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.9075, ~5/4 = 387.0723, ~11/8 = 551.4538

Optimal ET sequence12f, 17c, 24d, 29, 41, 46, 53, 58, 87, 111, 140, 152f, 198, 350f, 437f, 490f

Badness: 2.550 × 10-6

Werckismic (441/440)

Subgroup: 2.3.5.7.11

Comma list: 441/440

Mapping[1 0 0 0 -3], 0 1 0 0 2], 0 0 1 0 -1], 0 0 0 1 2]]

mapping generators: ~2, ~3, ~5, ~7

Optimal ET sequence10, 12, 15, 19e, 26, 27e, 31, 41, 58, 72, 118, 130, 190, 248, 289, 320, 609d

Commas 364/363, 441/440

Subgroup: 2.3.5.7.11.13

Comma list: 364/363, 441/440

Mapping[1 0 0 0 -3 -8], 0 1 0 0 2 5], 0 0 1 0 -1 -2], 0 0 0 1 2 3]]

Mapping to lattice: [0 1 1 -1 -1 0], 0 0 1 0 -1 -2], 0 0 1 1 1 1]]

Lattice basis:

3/2 length = 1.2263, 14/11 length = 1.4629, 21/16 length = 1.4657

Minimax tuning:

[[1 0 0 0 0 0, [5/3 0 1/3 -1/3 -1/3 1/3, [1/6 0 5/6 2/3 -5/6 1/3, [0 0 0 1 0 0, [1/6 0 -1/6 2/3 1/6 1/3, [0 0 0 0 0 1]
Eigenmonzos (unchanged-intervals): 2, 11/10, 8/7, 16/13
[[1 0 0 0 0 0, [5/4 1/4 1/4 -1/4 -1/4 1/4, [5/4 -3/4 5/4 -1/4 -1/4 1/4, [17/8 -11/8 5/8 -1/8 3/8 1/8, [5/2 -3/2 1/2 -1/2 1/2 1/2, [17/8 -11/8 5/8 -9/8 3/8 9/8]
Eigenmonzos (unchanged-intervals): 2, 14/13, 6/5, 11/9

Optimal ET sequence12f, 14cf, 15, 17c, 26, 29, 31f, 41, 46, 58, 72, 87, 130, 217, 289

Commas 351/350, 441/440

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 441/440

Mapping[1 0 0 0 -3 1], 0 1 0 0 2 -3], 0 0 1 0 -1 2], 0 0 0 1 2 1]]

Optimal ET sequence12f, 14cf, 19e, 26, 27e, 31, 45ef, 46, 58, 72, 103, 130, 233, 279, 409, 512bf, 642bf

Commas 196/195, 352/351

Subgroup: 2.3.5.7.11.13

Comma list: 196/195, 352/351

Mapping[1 0 0 0 -3 2], 0 1 0 0 2 -1], 0 0 1 0 -1 -1], 0 0 0 1 2 2]]

Optimal ET sequence10, 12f, 17c, 19e, 27e, 29, 31, 41, 46, 58, 87, 118, 145, 232

Tannic

Subgroup: 2.3.5.7.11.13

Comma list: 441/440, 1287/1280

Mapping[1 0 0 0 -3 11], 0 1 0 0 2 -4], 0 0 1 0 -1 2], 0 0 0 1 2 -2]]

Optimal ET sequence17c, 26, 29, 31, 43, 46, 60e, 72, 103, 149, 221ef, 324bdef, 473bdeeff, 545bddeefff

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 273/272, 441/440, 561/560

Mapping[1 0 0 0 -3 11 7], 0 1 0 0 2 -4 -3], 0 0 1 0 -1 2 2], 0 0 0 1 2 -2 -1]]

Optimal ET sequence17cg, 26, 29g, 31, 43, 46, 60e, 72, 103, 149, 221ef

Commas 441/440, 847/845

Subgroup: 2.3.5.7.11.13

Comma list: 441/440, 847/845

Mapping[1 0 0 0 -3 -3], 0 1 0 0 2 2], 0 0 1 1 1 1], 0 0 0 2 4 5]]

mapping generators: ~2, ~3, ~5, ~13/11

Optimal ET sequence12f, 16, 17c, 25e, 29, 41, 46, 58, 87, 103, 145, 149, 161, 190, 248, 438d

Keenanismic (385/384)

Subgroup: 2.3.5.7.11

Comma list: 385/384

Mapping[1 0 0 0 7], 0 1 0 0 1], 0 0 1 0 -1], 0 0 0 1 -1]]

mapping generators: ~2, ~3, ~5, ~7

Transpose: [2 3 5 7 385/35]

Minimax tuning:

[[1 0 0 0 0, [0 1 0 0 0, [7/3 1/3 2/3 -1/3 -1/3, [7/3 1/3 -1/3 2/3 -1/3, [7/3 1/3 -1/3 -1/3 2/3]
Eigenmonzo (unchanged-interval) basis: 2.3.7/5.11/5

Optimal ET sequence9, 10, 12e, 15, 19, 22, 31, 41, 53, 68, 72, 118, 159, 190, 212, 284, 330e, 402de

Badness: 15.2 × 10-9

Martwin

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 385/384

Mapping[1 0 0 0 7 2], 0 1 0 0 1 4], 0 0 1 0 -1 -2], 0 0 0 1 -1 0]]

Transpose: [2 3 5 7 385/35 324/25]

Lattice basis:

4/3 length = 1.0820, 6/5 length = 1.3935, 10/9 length = 1.6247

Minimax tuning: [to be confirmed]

[1 0 0 0 0 0], 0 1 0 0 0 0], 2/3 4/3 1/3 0 0 -1/3], 19/6 -1/6 -1/6 1/2 -1/2 1/6], 19/6 -1/6 -1/6 -1/2 1/2 1/6], 2/3 4/3 -2/3 0 0 2/3]]
Eigenmonzo (unchanged-interval) basis: 2.3.11/7.13/5

Optimal ET sequence12e, 15, 19, 22f, 26, 31f, 41, 46, 53, 72, 87, 125f, 140, 159, 212, 299, 371df, 465cef, 677cdeeff, 764cdeeff

Badness: 2.21 × 10-6

Ancient

Subgroup: 2.3.5.7.11.13

Comma list: 385/384, 625/624

Mapping[1 0 0 0 7 -4], 0 1 0 0 1 -1], 0 0 1 0 -1 4], 0 0 0 1 -1 0]]

Transpose: [2 3 5 7 385/35 625/48]

Optimal ET sequence15, 19, 22, 31, 50, 53, 72, 87, 103, 140, 159, 190, 243e, 315ef, 330e, 402def

Badness: 2.57 × 10-6

Commas 351/350, 385/384

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 385/384

Mapping[1 0 0 0 7 1], 0 1 0 0 1 -3], 0 0 1 0 -1 2], 0 0 0 1 -1 1]]

Optimal ET sequence19, 22, 26, 31, 46, 53, 72, 103, 149, 221ef, 324bdef, 473bdeeff, 495bdeefff, 545bddeefff, 598bcdeeefff

Badness: 2.98 × 10-6

Zaxa

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 385/384

Mapping[1 0 0 0 7 12], 0 1 0 0 1 -2], 0 0 1 0 -1 -1], 0 0 0 1 -1 -1]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.657, ~5/4 = 385.632, ~7/4 = 967.829

Optimal ET sequence22, 31, 41, 46, 53, 77, 87, 118, 140, 258e, 461e

Badness: 3.35 × 10-6

Commas 364/363, 385/384

Subgroup: 2.3.5.7.11.13

Comma list: 364/363, 385/384

Mapping[1 0 0 0 7 12], 0 1 0 0 1 3], 0 0 1 0 -1 -2], 0 0 0 1 -1 -3]]

Optimal ET sequence9, 15, 22, 26, 31f, 37, 41, 46, 63, 72, 87, 159

Badness: 3.32 × 10-6

Commas 385/384, 847/845

Subgroup: 2.3.5.7.11.13

Comma list: 385/384, 847/845

Mapping[1 0 0 0 7 7], 0 1 0 0 1 1], 0 0 1 1 -2 -2], 0 0 0 2 -2 -1]]

mapping generators: ~2, ~3, ~5, ~13/11

Optimal ET sequence34, 37, 41, 46, 53, 87, 103, 140, 190, 243e, 330e, 520de, 573dee

Badness: 4.15 × 10-6

Swetismic (540/539)

Subgroup: 2.3.5.7.11

Comma list: 540/539

Mapping[1 0 0 0 2], 0 1 0 0 3], 0 0 1 0 1], 0 0 0 1 -2]]

mapping generators: ~2, ~3, ~5, ~7

Optimal tunings:

  • CTE: ~2 = 1\1, ~3/2 = 701.6167, ~5/4 = 386.0717, ~7/4 = 969.5334
  • CWE: ~2 = 1\1, ~3/2 = 701.6950, ~5/4 = 386.1796, ~7/4 = 969.6366

Optimal ET sequence8d, 9, 10, 12e, 14c, 17c, 19, 22, 27e, 31, 41, 53, 58, 72, 130, 152, 224, 354, 506e, 578, 730de, 761d, 985d, 1115de, 1267dde

Badness: 0.0105 × 10-6

Commas 540/539, 729/728

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 729/728

Mapping[1 0 0 0 2 -3], 0 1 0 0 3 6], 0 0 1 0 1 0], 0 0 0 1 -2 -1]]

mapping generators: ~2, ~3, ~5, ~7

Optimal tunings:

  • CTE: ~2 = 1\1, ~3/2 = 701.6687, ~5/4 = 386.0441, ~7/4 = 969.5668
  • CWE: ~2 = 1\1, ~3/2 = 701.7230, ~5/4 = 386.1818, ~7/4 = 969.6607

Optimal ET sequence12e, 14cf, 17c, 19, 22f, 31f, 39df, 41, 53, 58, 72, 111, 130, 183, 224, 354, 578, 985d, 1267ddef

Badness: 1.73 × 10-6

Commas 540/539, 847/845

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 847/845

Mapping[1 0 0 0 2 2], 0 1 0 0 3 3], 0 0 1 1 -1 -1], 0 0 0 2 -4 -3]]

mapping generators: ~2, ~3, ~5, ~13/11

Optimal ET sequence8d, 9, 12e, 17c, 32f, 33cd, 36ce, 41, 53, 58, 94, 103, 111, 152f, 255, 407f

Badness: 3.97 × 10-6

Commas 540/539, 625/624

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 625/624

Mapping[1 0 0 0 2 -4], 0 1 0 0 3 -1], 0 0 1 0 1 4], 0 0 0 1 -2 0]]

Optimal ET sequence19, 22, 31, 49f, 50, 53, 72, 103, 121, 152f, 193, 224

Badness: 3.59 × 10-6

Commas 540/539, 676/675

Subgroup: 2.3.5.7.11

Comma list: 540/539, 676/675

Mapping[1 0 0 0 2 -1], 0 2 0 0 6 3], 0 0 1 0 1 1], 0 0 0 1 -2 0]]

mapping generators: ~2, ~26/15, ~5, ~7

Optimal ET sequence9, 10, 14cf, 19, 33cdff, 39df, 48c, 49, 53, 58, 72, 111, 121, 130, 183, 251e, 304d, 376, 434de

Badness: 3.06 × 10-6

Pentacircle (896/891)

Subgroup: 2.3.5.7.11

Comma list: 896/891

Mapping[1 0 0 0 7], 0 1 0 0 -4], 0 0 1 0 0], 0 0 0 1 1]]

mapping generators: ~2, ~3, ~5, ~7

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 703.8345, ~5/4 = 387.7585, ~7/4 = 969.8722

Optimal ET sequence12, 17c, 19e, 22, 34d, 39d, 41, 58, 80, 87, 99e, 121, 145, 167, 208, 266e, 699bbcdeee

Badness: 0.0658 × 10-6

Tridecimal pentacircle a.k.a. gentle

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 364/363

Mapping[1 0 0 0 7 12], 0 1 0 0 -4 -7], 0 0 1 0 0 0], 0 0 0 1 1 1]]

Optimal ET sequence12f, 17c, 22, 29, 34d, 41, 46, 58, 80, 87, 121, 167, 179ef, 208, 266ef, 433bceef, 641bbceeeff, 699bbcdeeeff

Badness: 3.375 × 10-6

Topsy (847/845, 1001/1000)

Subgroup: 2.3.5.7.11.13

Comma list: 847/845, 1001/1000

Mapping[1 0 0 2 0 1], 0 1 0 0 0 0], 0 0 1 1 1 1], 0 0 0 4 -3 1]]

mapping generators: ~2, ~3, ~5, ~13/10

Optimal ET sequence16, 21, 24d, 29, 37, 45ef, 50, 53, 58, 87, 103, 111, 140, 190, 198, 301, 388, 689e

Lehmerismic (3025/3024)

Subgroup: 2.3.5.7.11

Comma list: 3025/3024

Mapping[1 0 0 0 2], 0 1 0 1 2], 0 0 1 0 -1], 0 0 0 2 1]]

mapping generators: ~2, ~3, ~5, ~55/36

Optimal ET sequence7d, 8d, 10, 15, 23de, 24d, 26, 31, 41, 65d, 72, 118, 152, 224, 270, 342, 612, 836, 1106, 1448, 2554, 4002e, 5720e, 7168cee

Trimitone (8019/8000)

Subgroup: 2.3.5.7.11

Comma list: 8019/8000

Mapping[1 0 0 0 6], 0 1 0 0 -6], 0 0 1 0 3], 0 0 0 1 0]]

mapping generators: ~2, ~3, ~5, ~7

Optimal tunings:

  • CTE: ~2 = 1\1, ~3/2 = 701.5449, ~5/4 = 386.7538, ~7/4 = 968.8259
  • CWE: ~2 = 1\1, ~3/2 = 701.4729, ~5/4 = 386.5374, ~7/4 = 968.6210

Optimal ET sequence12, 19, 26, 39d, 46, 53, 58, 72, 118, 130, 183, 190, 248, 255, 301, 373, 804, 876, 1177be

Badness: 0.0820 × 10-6

Commas 729/728, 1001/1000

Subgroup: 2.3.5.7.11.13

Comma list: 729/728, 1001/1000

Mapping[1 0 0 0 6 -3], 0 1 0 0 -6 6], 0 0 1 0 3 0], 0 0 0 1 0 -1]]

mapping generators: ~2, ~3, ~5, ~7

Optimal tunings:

  • CTE: ~2 = 1\1, ~3/2 = 701.5537, ~5/4 = 386.7680, ~7/4 = 968.8144
  • CWE: ~2 = 1\1, ~3/2 = 701.4770, ~5/4 = 386.5437, ~7/4 = 968.6150

Optimal ET sequence53, 58, 72, 111, 130, 183, 190, 243e, 248, 301, 373, 804, 1177be

Badness: 3.33 × 10-6

Kalismic (9801/9800)

Subgroup: 2.3.5.7.11

Comma list: 9801/9800

Mapping[2 0 0 0 3], 0 1 0 0 -2], 0 0 1 0 1], 0 0 0 1 1]]

mapping generators: ~99/70, ~3, ~5, ~7

Optimal ET sequence8d, 10, 12, 22, 34d, 46, 58, 72, 118, 130, 152, 224, 270, 342, 612, 836, 1084, 1106, 1236, 1506, 1578, 1848, 2684, 4038, 4190, 4532, 11254, 15786e, 21896e

Commas 1716/1715, 2080/2079

Subgroup: 2.3.5.7.11.13

Comma list: 1716/1715, 2080/2079

Mapping[2 0 0 0 3 -7], 0 1 0 0 -2 1], 0 0 1 0 1 0], 0 0 0 1 1 2]]

Lattice basis:

3/2 length = 1.1956, 7/4 length = 1.4506, 14/13 length = 1.8299

Minimax tuning:

[[1 0 0 0 0 0, [7/10 4/5 0 -2/5 0 1/5, [7/10 -1/5 1 -2/5 0 1/5, [7/5 -2/5 0 1/5 0 2/5, [11/5 -11/5 1 3/5 0 1/5, [0 0 0 0 0 1]
Eigenmonzo (unchanged-intervals) basis: 2, 6/5, 16/13, 9/7

Optimal ET sequence10e, 12f, 14cf, 22f, 26, 36ce, 46, 58, 72, 130, 198, 224, 270, 494, 764, 1258, 1810d, 2304d, 2574d

Semicanousmic (14641/14580)

Subgroup: 2.3.5.7.11

Comma list: 14641/14580

Mapping[1 0 2 0 1], 0 1 2 0 2], 0 0 -4 0 -1], 0 0 0 1 0]]

mapping generators: ~2, ~3, ~18/11, ~7

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.2503, ~18/11 = 854.5421, ~7/4 = 968.6866

Optimal ET sequence14c, 17c, 24, 31, 63, 80, 87, 111, 118, 198, 212, 292, 323, 410, 851e

Badness: 0.351 × 10-6

Tridecimal semicanousmic

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 14641/14580

Mapping: [1 0 2 0 1 -6], 0 1 2 0 2 3], 0 0 -4 0 -1 3], 0 0 0 1 0 1]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.4931, ~18/11 = 854.6400, ~7/4 = 969.0099

Optimal ET sequence87, 111, 181, 198, 323, 410

Badness: 17.1 × 10-6

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 715/714, 1089/1088, 14641/14580

Mapping: [1 0 2 0 1 -6 -4], 0 1 2 0 2 3 6], 0 0 -4 0 -1 3 -2], 0 0 0 1 0 1 0]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.4099, ~18/11 = 854.6338, ~7/4 = 969.0228

Optimal ET sequence87, 94, 111, 181, 198g, 212g, 292, 323, 410

Badness: 34.0 × 10-6

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 715/714, 1089/1088, 1216/1215, 1445/1444

Mapping: [1 0 2 0 1 -6 -4 -4], 0 1 2 0 2 3 6 7], 0 0 -4 0 -1 3 -2 -4], 0 0 0 1 0 1 0 0]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.3413, ~18/11 = 854.6472, ~7/4 = 968.9734

Optimal ET sequence87, 94, 111, 181, 205, 212gh, 292h, 299, 323, 410, 622ef

Badness: 41.9 × 10-6

Semiporwellismic (16384/16335)

Subgroup: 2.3.5.7.11

Comma list: 16384/16335

Mapping[1 0 0 0 7], 0 1 1 0 -2], 0 0 2 0 -1], 0 0 0 1 0]]

mapping generators: ~2, ~3, ~128/99, ~7

Optimal ET sequence19, 22, 41, 65d, 68, 84, 87, 111, 130, 152, 239, 282, 328, 369, 521e, 1370bcdeee, 1411bcdeee, 1609bccdeee

Badness: 0.219 × 10-6

Symbiotic (19712/19683)

Subgroup: 2.3.5.7.11

Comma list: 19712/19683

Mapping[1 0 0 0 -8], 0 1 0 0 9], 0 0 1 0 0], 0 0 0 1 -1]]

mapping generators: ~2, ~3, ~5, ~7

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.2681, ~5/4 = 386.4785, ~7/4 = 968.9552

Optimal ET sequence17c, 19e, 24, 34d, 41, 53, 58, 94, 99e, 118, 152, 270, 581, 733, 851, 1003, 1273, 1854, 2124b

Badness: 0.120 × 10-6

Tridecimal symbiotic

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 19712/19683

Mapping[1 0 0 0 -8 -13], 0 1 0 0 9 12], 0 0 1 0 0 -1], 0 0 0 1 -1 0]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.2721, ~5/4 = 386.4790, ~7/4 = 968.9705

Optimal ET sequence17c, 34dff, 36ce, 41, 53, 58, 94, 111, 152f, 212, 217, 270, 581, 851, 1003, 1273, 1854, 2124b, 3127bf

Badness: 3.31 × 10-6

Olympic (131072/130977)

Subgroup: 2.3.5.7.11

Comma list: 131072/130977

Mapping[1 0 0 0 17], 0 1 0 0 -5], 0 0 1 0 0], 0 0 0 1 -2]]

mapping generators: ~2, ~3, ~5, ~7

Optimal ET sequence41, 53, 84, 87, 130, 183, 224, 270, 494, 764, 1164, 1205, 1475, 1969, 2239, 3133de, 4608cde, 5102bcde, 10474bbccdddeee

Tridecimal olympic

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 4096/4095

Mapping[1 0 0 0 17 12], 0 1 0 0 -5 -2], 0 0 1 0 0 -1], 0 0 0 1 -2 -1]]

Optimal ET sequence41, 46, 53, 84, 87, 130, 183, 217, 224, 270, 494, 764, 935, 1075, 1205, 1699, 2280, 2774e *

* optimal patent val: 3044