﻿La symétrie est retirée, reste 40 intervalles : 
DE l'Union de 4 échelles 17√13 19√13 27√13 et 31√13 (résultat par intervalles en cent)
261centsU233centsU164centsU143ceznts.acyclic.choir.merge.scale13div17&19&27&31
Intervalles inférieurs à 13 cents retirés et symétrie retirée :
au lieu de 91 intervalles, au lieu de 79 (pour toute l'étendue élargie de 10,08 à 13 des voix du choeur) nous en avons 40 :

  0:          1/1               0.000000 unison, perfect prime
  1:        143.243 cents     143.242830
  2:        164.464 cents     164.463990
  3:        233.712 cents     233.711980
  4:        261.208 cents     261.207510
  5:        286.486 cents     286.485660
  6:        328.928 cents     328.927970
  7:        429.728 cents     429.728480
  8:        467.424 cents     467.423960
  9:        493.392 cents     493.391960
 10:        522.415 cents     522.415020
 11:        572.971 cents     572.971310
 12:        657.856 cents     657.855950
 13:        701.136 cents     701.135950
 14:        716.214 cents     716.214140
 15:        783.623 cents     783.622530
 16:        822.320 cents     822.319940
 17:        859.457 cents     859.456970
 18:        934.848 cents     934.847930
 19:        986.784 cents     986.783920
 20:       1002.700 cents    1002.699790
 21:       1044.830 cents    1044.830040
 22:       1145.943 cents    1145.942620
 23:       1168.560 cents    1168.559910
 24:       1289.185 cents    1289.185450
 25:       1306.038 cents    1306.037550
 26:       1402.272 cents    1402.271890
 27:       1432.428 cents    1432.428280
 28:       1480.176 cents    1480.175890
 29:       1567.245 cents    1567.245060
 30:       1635.984 cents    1635.983880
 31:       1718.914 cents    1718.913930
 32:       1809.104 cents    1809.103860
 33:       1828.453 cents    1828.452570
 34:       1862.157 cents    1862.156760
 35:       1973.568 cents    1973.567850
 36:       2005.400 cents    2005.399590
 37:       2089.660 cents    2089.660080
 38:       2103.408 cents    2103.407840
 39:       2138.032 cents    2138.031840
 40:       2291.885 cents    2291.885240
|
  0:        153.8534 cents    153.8534
  1:        143.2428 cents    143.2428
  2:         21.2212 cents     21.2212
  3:         69.2480 cents     69.2480
  4:         27.4955 cents     27.4955
  5:         25.2781 cents     25.2781
  6:         42.4423 cents     42.4423
  7:        100.8005 cents    100.8005
  8:         37.6955 cents     37.6955
  9:         25.9680 cents     25.9680
 10:         29.0231 cents     29.0231
 11:         50.5563 cents     50.5563
 12:         84.8846 cents     84.8846
 13:         43.2800 cents     43.2800
 14:         15.0782 cents     15.0782
 15:         67.4084 cents     67.4084
 16:         38.6974 cents     38.6974
 17:         37.1370 cents     37.1370
 18:         75.3910 cents     75.3910
 19:         51.9360 cents     51.9360
 20:         15.9159 cents     15.9159
 21:         42.1303 cents     42.1303
 22:        101.1126 cents    101.1126
 23:         22.6173 cents     22.6173
 24:        120.6255 cents    120.6255
 25:         16.8521 cents     16.8521
 26:         96.2343 cents     96.2343
 27:         30.1564 cents     30.1564
 28:         47.7476 cents     47.7476
 29:         87.0692 cents     87.0692
 30:         68.7388 cents     68.7388
 31:         82.9300 cents     82.9300
 32:         90.1899 cents     90.1899
 33:         19.3487 cents     19.3487
 34:         33.7042 cents     33.7042
 35:        111.4111 cents    111.4111
 36:         31.8317 cents     31.8317
 37:         84.2605 cents     84.2605
 38:         13.7478 cents     13.7478
 39:         34.6240 cents     34.6240
 40:        153.8534 cents    153.8534

POUR LES SOPRANI : 

  0:  261.62 Hertz		MIDI: 60.00000	8.00000 oct	4 0.000 El
  1:  284.19 Hertz		MIDI: 61.43243	8.11937 oct	4 143.243 El
  2:  287.69 Hertz		MIDI: 61.64464	8.13705 oct	4 164.464 El
  3:  299.43 Hertz		MIDI: 62.33712	8.19476 oct	4 233.712 El
  4:  304.23 Hertz 		MIDI: 62.61208	8.21767 oct	4 261.208 El
  5:  308.70 Hertz		MIDI: 62.86486	8.23874 oct	4 286.486 El
  6:  316.369421875 Hertz 8.27411 oct    MIDI: 63.28928      4 328.928 El
  7:  335.336748084 Hertz 8.35811 oct    MIDI: 64.29728      4 429.728 El
  8:  342.718362111 Hertz 8.38952 oct    MIDI: 64.67424      4 467.424 El
  9:  347.897784229 Hertz 8.41116 oct    MIDI: 64.93392      4 493.392 El
 10:  353.779235473 Hertz 8.43535 oct    MIDI: 65.22415      4 522.415 El
 11:  364.262786544 Hertz 8.47748 oct    MIDI: 65.72971      4 572.971 El
 12:  382.568162100 Hertz 8.54821 oct    MIDI: 66.57856      4 657.856 El
 13:  392.252728366 Hertz 8.58428 oct    MIDI: 67.01136      4 701.136 El
 14:  395.683975642 Hertz 8.59685 oct    MIDI: 67.16214      4 716.214 El
 15:  411.394440797 Hertz 8.65302 oct    MIDI: 67.83623      4 783.623 El
 16:  420.693678682 Hertz 8.68527 oct    MIDI: 68.22320      4 822.320 El
 17:  429.815546258 Hertz 8.71621 oct    MIDI: 68.59457      4 859.457 El
 18:  448.946479185 Hertz 8.77904 oct    MIDI: 69.34848      4 934.848 El
 19:  462.618659350 Hertz 8.82232 oct    MIDI: 69.86784      4 986.784 El
 20:  466.891292321 Hertz 8.83558 oct    MIDI: 70.02700      4 1002.700 El
 21:  478.392649847 Hertz 8.87069 oct    MIDI: 70.44830      4 1044.830 El
 22:  507.165182837 Hertz 8.95495 oct    MIDI: 71.45943      4 1145.943 El
 23:  513.834389405 Hertz 8.97380 oct    MIDI: 71.68560      4 1168.560 El
 24:  550.913086007 Hertz 9.07432 oct    MIDI: 72.89185      5 89.185 El
 25:  556.301944635 Hertz 9.08836 oct    MIDI: 73.06038      5 106.038 El
 26:  588.100791468 Hertz 9.16856 oct    MIDI: 74.02272      5 202.272 El
 27:  598.434669027 Hertz 9.19369 oct    MIDI: 74.32428      5 232.428 El
 28:  615.169267862 Hertz 9.23348 oct    MIDI: 74.80176      5 280.176 El
 29:  646.899265078 Hertz 9.30604 oct    MIDI: 75.67245      5 367.245 El
 30:  673.101197691 Hertz 9.36332 oct    MIDI: 76.35984      5 435.984 El
 31:  706.129015052 Hertz 9.43243 oct    MIDI: 77.18914      5 518.914 El
 32:  743.890396967 Hertz 9.50759 oct    MIDI: 78.09104      5 609.104 El
 33:  752.250937093 Hertz 9.52371 oct    MIDI: 78.28453      5 628.453 El
 34:  767.039473461 Hertz 9.55180 oct    MIDI: 78.62157      5 662.157 El
 35:  818.024129134 Hertz 9.64464 oct    MIDI: 79.73568      5 773.568 El
 36:  833.204048135 Hertz 9.67117 oct    MIDI: 80.05400      5 805.400 El
 37:  874.759800955 Hertz 9.74138 oct    MIDI: 80.89660      5 889.660 El
 38:  881.733938127 Hertz 9.75284 oct    MIDI: 81.03408      5 903.408 El

 39:  899.545791388 Hertz 9.78169 oct    MIDI: 81.38032      5 938.032 El
 40:  983.147508487 Hertz 9.90990 oct    MIDI: 82.91885      5 1091.885 El


Union de 4 échelles 17√13 19√13 27√13 et 31√13 (résultat par intervalles en cent)
261centsU233centsU164centsU143ceznts.acyclic.choir.merge.scale13div17&19&27&31
Intervalles inférieurs à 13 cents retirés :
au lieu de 91 intervalles, nous en avons 79 (pour toute l'étendue élargie de 10,08 à 13 des voix du choeur) :

  0:        0
  1:        143.24
  2:         21.22
  3:         69.24
  4:         27.49
  5:         25.27
  6:         42.44
  7:        100.80
  8:         37.69
  9:         25.96
 10:         29.02
 11:         50.55
 12:         84.88
 13:         43.28
 14:         15.07
 15:         67.40
 16:         38.69
 17:         37.13
 18:         75.39
 19:         51.93
 20:         15.91
 21:         42.13
 22:        101.11
 23:         22.61
 24:        120.62
 25:         16.85
 26:         96.23
 27:         30.15
 28:         47.74
 29:         87.06
 30:         68.73
 31:         82.93
 32:         90.18
 33:         19.34
 34:         33.70
 35:        111.41
 36:         31.83
 37:         84.26
 38:         13.74
 39:         34.62
 40:        153.85		intervalle du milieu, fontière de la symétrie
 41:         45.23
 42:         13.74
 43:         84.26
 44:         31.83
 45:        103.87
 46:         41.24
 47:         19.34
 48:         90.18
 49:         74.27
 50:         68.96
 51:         95.49
 52:         47.74
 53:         30.15
 54:         86.56
 55:         26.52
 56:        120.62
 57:         17.31
 58:        106.41
 59:         42.13
 60:         15.91
 61:         51.93
 62:         75.39
 63:         37.13
 64:         38.69
 65:         67.40
 66:         15.07
 67:         43.28
 68:         84.88
 69:         50.55
 70:         29.02
 71:         25.96
 72:         37.69
 73:        100.80
 74:         42.44
 75:         25.27
 76:         27.49
 77:         69.24
 78:         21.22
 79:        143.24



  0:          1/1               0.000000 unison, perfect prime
  1:        143.243 cents     143.242830
  2:        164.464 cents     164.463990
  3:        233.712 cents     233.711980
  4:        261.208 cents     261.207510
  5:        286.486 cents     286.485660
  6:        328.928 cents     328.927970
  7:        429.728 cents     429.728480
  8:        467.424 cents     467.423960
  9:        493.392 cents     493.391960
 10:        522.415 cents     522.415020
 11:        572.971 cents     572.971310
 12:        657.856 cents     657.855950
 13:        701.136 cents     701.135950
 14:        716.214 cents     716.214140
 15:        783.623 cents     783.622530
 16:        822.320 cents     822.319940
 17:        859.457 cents     859.456970
 18:        934.848 cents     934.847930
 19:        986.784 cents     986.783920
 20:       1002.700 cents    1002.699790
 21:       1044.830 cents    1044.830040
 22:       1145.943 cents    1145.942620
 23:       1168.560 cents    1168.559910
 24:       1289.185 cents    1289.185450
 25:       1306.038 cents    1306.037550
 26:       1402.272 cents    1402.271890
 27:       1432.428 cents    1432.428280
 28:       1480.176 cents    1480.175890
 29:       1567.245 cents    1567.245060
 30:       1635.984 cents    1635.983880
 31:       1718.914 cents    1718.913930
 32:       1809.104 cents    1809.103860
 33:       1828.453 cents    1828.452570
 34:       1862.157 cents    1862.156760
 35:       1973.568 cents    1973.567850
 36:       2005.400 cents    2005.399590
 37:       2089.660 cents    2089.660080
 38:       2103.408 cents    2103.407840
 39:       2138.032 cents    2138.031840
 40:       2291.885 cents    2291.885240
 41:       2337.120 cents    2337.119820
 42:       2350.868 cents    2350.867590
 43:       2435.128 cents    2435.128070
 44:       2466.960 cents    2466.959810
 45:       2570.832 cents    2570.831800
 46:       2612.075 cents    2612.075100
 47:       2631.424 cents    2631.423800
 48:       2721.614 cents    2721.613730
 49:       2795.888 cents    2795.887790
 50:       2864.857 cents    2864.856560
 51:       2960.352 cents    2960.351770
 52:       3008.099 cents    3008.099380
 53:       3038.256 cents    3038.255770
 54:       3124.816 cents    3124.815760
 55:       3151.342 cents    3151.342210
 56:       3271.968 cents    3271.967750
 57:       3289.280 cents    3289.279750
 58:       3395.698 cents    3395.697620
 59:       3437.828 cents    3437.827870
 60:       3453.744 cents    3453.743740
 61:       3505.680 cents    3505.679730
 62:       3581.071 cents    3581.070700
 63:       3618.208 cents    3618.207720
 64:       3656.905 cents    3656.905130
 65:       3724.314 cents    3724.313520
 66:       3739.392 cents    3739.391720
 67:       3782.672 cents    3782.671710
 68:       3867.556 cents    3867.556350
 69:       3918.113 cents    3918.112640
 70:       3947.136 cents    3947.135700
 71:       3973.104 cents    3973.103700
 72:       4010.799 cents    4010.799180
 73:       4111.600 cents    4111.599690
 74:       4154.042 cents    4154.042010
 75:       4179.320 cents    4179.320150
 76:       4206.816 cents    4206.815680
 77:       4276.064 cents    4276.063670
 78:       4297.285 cents    4297.284830
 79:       4440.528 cents    4440.527660



|
  0:        143.2428 cents    143.2428
  1:        143.2428 cents    143.2428
  2:         21.2212 cents     21.2212
  3:         69.2480 cents     69.2480
  4:         27.4955 cents     27.4955
  5:         25.2781 cents     25.2781
  6:         42.4423 cents     42.4423
  7:        100.8005 cents    100.8005
  8:         37.6955 cents     37.6955
  9:         25.9680 cents     25.9680
 10:         29.0231 cents     29.0231
 11:         50.5563 cents     50.5563
 12:         84.8846 cents     84.8846
 13:         43.2800 cents     43.2800
 14:         15.0782 cents     15.0782
 15:         67.4084 cents     67.4084
 16:         38.6974 cents     38.6974
 17:         37.1370 cents     37.1370
 18:         75.3910 cents     75.3910
 19:         51.9360 cents     51.9360
 20:         15.9159 cents     15.9159
 21:         42.1303 cents     42.1303
 22:        101.1126 cents    101.1126
 23:         22.6173 cents     22.6173
 24:        120.6255 cents    120.6255
 25:         16.8521 cents     16.8521
 26:         96.2343 cents     96.2343
 27:         30.1564 cents     30.1564
 28:         47.7476 cents     47.7476
 29:         87.0692 cents     87.0692
 30:         68.7388 cents     68.7388
 31:         82.9300 cents     82.9300
 32:         90.1899 cents     90.1899
 33:         19.3487 cents     19.3487
 34:         33.7042 cents     33.7042
 35:        111.4111 cents    111.4111
 36:         31.8317 cents     31.8317
 37:         84.2605 cents     84.2605
 38:         13.7478 cents     13.7478
 39:         34.6240 cents     34.6240
 40:        153.8534 cents    153.8534		intervalle du milieu, fontière de la symétrie
 41:         45.2346 cents     45.2346
 42:         13.7478 cents     13.7478
 43:         84.2605 cents     84.2605
 44:         31.8317 cents     31.8317
 45:        103.8720 cents    103.8720
 46:         41.2433 cents     41.2433
 47:         19.3487 cents     19.3487
 48:         90.1899 cents     90.1899
 49:         74.2741 cents     74.2741
 50:         68.9688 cents     68.9688
 51:         95.4952 cents     95.4952
 52:         47.7476 cents     47.7476
 53:         30.1564 cents     30.1564
 54:         86.5600 cents     86.5600
 55:         26.5264 cents     26.5264
 56:        120.6255 cents    120.6255
 57:         17.3120 cents     17.3120
 58:        106.4179 cents    106.4179
 59:         42.1303 cents     42.1303
 60:         15.9159 cents     15.9159
 61:         51.9360 cents     51.9360
 62:         75.3910 cents     75.3910
 63:         37.1370 cents     37.1370
 64:         38.6974 cents     38.6974
 65:         67.4084 cents     67.4084
 66:         15.0782 cents     15.0782
 67:         43.2800 cents     43.2800
 68:         84.8846 cents     84.8846
 69:         50.5563 cents     50.5563
 70:         29.0231 cents     29.0231
 71:         25.9680 cents     25.9680
 72:         37.6955 cents     37.6955
 73:        100.8005 cents    100.8005
 74:         42.4423 cents     42.4423
 75:         25.2781 cents     25.2781
 76:         27.4955 cents     27.4955
 77:         69.2480 cents     69.2480
 78:         21.2212 cents     21.2212
 79:        143.2428 cents    143.2428


Union de 4 échelles 17√13 19√13 27√13 et 31√13 (résultat par intervalles en cent)
261centsU233centsU164centsU143ceznts.acyclic.choir.merge.scale13div17&19&27&31
résultat par intervalles (en cent) 91 intervalles :

00:	0 cent
01:	143.24
02:         21.22
03:         69.24
04:         27.49
05:         25.27
06:         42.44
07:        100.80		1/2 ton	
08:         37.69
09:         25.96
10:         29.02
11:         50.55
12:         84.88
13:         43.28
14:         15.07
15:         67.40
16:         38.69
17:         37.13
18:         75.39
19:         51.93
20:         15.91
21:         42.13
22:        101.11		1/2 ton
23:          5.30			trop petit
24:         17.312
25:        120.62
26:         16.85
27:          9.67			trop petit
28:         86.56
29:         30.15
30:         47.74
31:         87.06
32:          8.42			trop petit
33:         60.31
34:          8.65			trop petit
35:         74.27
36:         90.18
37:         19.34
38:         33.70
39:          7.53			trop petit
40:        103.87		1/2 ton
41:         31.83
42:         84.26
43:         13.74
44:         34.62
45:         10.61			trop petit
46:        143.24		intervalle du milieu, fontière de la symétrie
47:         10.61			trop petit
48:         34.62
49:         13.74
50:         84.26
51:         31.83
52:        103.87		1/2 ton
53:          7.53			trop petit
54:         33.70
55:         19.34
56:         90.18
57:         74.27
58:          8.65			trop petit
59:         60.31
60:          8.42			trop petit
61:         87.06
62:         47.74
63:         30.15
64:         86.56
65:          9.67			trop petit
66:         16.85
67:        120.62
68:         17.31
69:          5.30			trop petit
70:        101.11		1/2 ton
71:         42.13
72:         15.91
73:         51.93
74:         75.39
75:         37.13
76:         38.69
77:         67.40
78:         15.07
79:         43.28
80:         84.88
81:         50.55
82:         29.02
83:         25.96
84:         37.69
85:        100.80		1/2 ton
86:         42.44
87:         25.27
88:         27.49
89:         69.24
90:         21.22
91:        143.24



  0:        0 cents               0
  1:        143.2428 cents    143.2428
  2:         21.2212 cents     21.2212
  3:         69.2480 cents     69.2480
  4:         27.4955 cents     27.4955
  5:         25.2781 cents     25.2781
  6:         42.4423 cents     42.4423
  7:        100.8005 cents    100.8005		
  8:         37.6955 cents     37.6955
  9:         25.9680 cents     25.9680
 10:         29.0231 cents     29.0231
 11:         50.5563 cents     50.5563
 12:         84.8846 cents     84.8846
 13:         43.2800 cents     43.2800
 14:         15.0782 cents     15.0782
 15:         67.4084 cents     67.4084
 16:         38.6974 cents     38.6974
 17:         37.1370 cents     37.1370
 18:         75.3910 cents     75.3910
 19:         51.9360 cents     51.9360
 20:         15.9159 cents     15.9159
 21:         42.1303 cents     42.1303
 22:        101.1126 cents    101.1126
 23:          5.3053 cents      5.3053
 24:         17.3120 cents     17.3120
 25:        120.6255 cents    120.6255
 26:         16.8521 cents     16.8521
 27:          9.6743 cents      9.6743
 28:         86.5600 cents     86.5600
 29:         30.1564 cents     30.1564
 30:         47.7476 cents     47.7476
 31:         87.0692 cents     87.0692
 32:          8.4260 cents      8.4260
 33:         60.3128 cents     60.3128
 34:          8.6560 cents      8.6560
 35:         74.2741 cents     74.2741
 36:         90.1899 cents     90.1899
 37:         19.3487 cents     19.3487
 38:         33.7042 cents     33.7042
 39:          7.5391 cents      7.5391
 40:        103.8720 cents    103.8720
 41:         31.8317 cents     31.8317
 42:         84.2605 cents     84.2605
 43:         13.7478 cents     13.7478
 44:         34.6240 cents     34.6240
 45:         10.6106 cents     10.6106
 46:        143.2428 cents    143.2428		intervalle du milieu, fontière de la symétrie
 47:         10.6106 cents     10.6106
 48:         34.6240 cents     34.6240
 49:         13.7478 cents     13.7478
 50:         84.2605 cents     84.2605
 51:         31.8317 cents     31.8317
 52:        103.8720 cents    103.8720
 53:          7.5391 cents      7.5391
 54:         33.7042 cents     33.7042
 55:         19.3487 cents     19.3487
 56:         90.1899 cents     90.1899
 57:         74.2741 cents     74.2741
 58:          8.6560 cents      8.6560
 59:         60.3128 cents     60.3128
 60:          8.4260 cents      8.4260
 61:         87.0692 cents     87.0692
 62:         47.7476 cents     47.7476
 63:         30.1564 cents     30.1564
 64:         86.5600 cents     86.5600
 65:          9.6743 cents      9.6743
 66:         16.8521 cents     16.8521
 67:        120.6255 cents    120.6255
 68:         17.3120 cents     17.3120
 69:          5.3053 cents      5.3053
 70:        101.1126 cents    101.1126
 71:         42.1303 cents     42.1303
 72:         15.9159 cents     15.9159
 73:         51.9360 cents     51.9360
 74:         75.3910 cents     75.3910
 75:         37.1370 cents     37.1370
 76:         38.6974 cents     38.6974
 77:         67.4084 cents     67.4084
 78:         15.0782 cents     15.0782
 79:         43.2800 cents     43.2800
 80:         84.8846 cents     84.8846
 81:         50.5563 cents     50.5563
 82:         29.0231 cents     29.0231
 83:         25.9680 cents     25.9680
 84:         37.6955 cents     37.6955
 85:        100.8005 cents    100.8005
 86:         42.4423 cents     42.4423
 87:         25.2781 cents     25.2781
 88:         27.4955 cents     27.4955
 89:         69.2480 cents     69.2480
 90:         21.2212 cents     21.2212
 91:        143.2428 cents    143.2428