User:ArrowHead294/sandbox

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Harmonic series with harmonics stretched by 0.25% per octave:

Intervals of the 1.0025-Powharmonic series
Pitch Frequency multiplier Pitch
Definition Decimal Cents Change (cents) Octave-reduced (cents)
1 11.0025 1.0000 0.0000 0.0000 0.0000
2 21.0025 2.0035 1203.0000 1203.0000 3.0000
3 31.0025 3.0083 1906.7099 703.7099 706.7099
4 41.0025 4.0139 2406.0000 499.2901 6.0000
5 51.0025 5.0202 2793.2795 387.2795 393.2795
6 61.0025 6.0269 3109.7099 316.4304 709.7099
7 71.0025 7.0341 3377.2480 267.5381 977.2480
8 81.0025 8.0417 3609.0000 231.7520 9.0000
9 91.0025 9.0496 3813.4198 204.4198 213.4198
10 101.0025 10.0577 3996.2795 182.8597 396.2795
11 111.0025 11.0661 4161.6962 165.4167 561.6962
12 121.0025 12.0748 4312.7099 151.0137 712.7099
13 131.0025 13.0836 4451.6290 138.9191 851.6290
14 141.0025 14.0927 4580.2480 128.6190 980.2480
15 151.0025 15.1019 4699.9894 119.7414 1099.9894
16 161.0025 16.1113 4812.0000 112.0106 12.0000
17 171.0025 17.1208 4917.2178 105.2178 117.2178
18 181.0025 18.1305 5016.4198 99.2020 216.4198
19 191.0025 19.1404 5110.2568 93.8370 310.2568
20 201.0025 20.1503 5199.2795 89.0227 399.2795
21 211.0025 21.1604 5283.9579 84.6784 483.9579
22 221.0025 22.1707 5364.6962 80.7384 564.6962
23 231.0025 23.1810 5441.8450 77.1488 641.8450
24 241.0025 24.1914 5515.7099 73.8649 715.7099
25 251.0025 25.2020 5586.5590 70.8491 786.5590
26 261.0025 26.2126 5654.6290 68.0700 854.6290
27 271.0025 27.2234 5720.1297 65.5007 920.1297
28 281.0025 28.2342 5783.2480 63.1183 983.2480
29 291.0025 29.2452 5844.1511 60.9032 1044.1511
30 301.0025 30.2562 5902.9894 58.8382 1102.9894
31 311.0025 31.2673 5959.8982 56.9088 1159.8982
32 321.0025 32.2785 6015.0000 55.1018 15.0000
33 331.0025 33.2897 6068.4061 53.4061 68.4061
34 341.0025 34.3011 6120.2178 51.8117 120.2178
35 351.0025 35.3125 6170.5275 50.3097 170.5275
36 361.0025 36.3240 6219.4198 48.8923 219.4198
37 371.0025 37.3355 6266.9724 47.5526 266.9724
38 381.0025 38.3471 6313.2568 46.2844 313.2568
39 391.0025 39.3588 6358.3389 45.0821 358.3389
40 401.0025 40.3706 6402.2795 43.9406 402.2795
41 411.0025 41.3824 6445.1351 42.8556 445.1351
42 421.0025 42.3943 6486.9579 41.8228 486.9579
43 431.0025 43.4062 6527.7965 40.8386 527.7965
44 441.0025 44.4182 6567.6962 39.8997 567.6962
45 451.0025 45.4303 6606.6993 39.0030 606.6993
46 461.0025 46.4424 6644.8450 38.1458 644.8450
47 471.0025 47.4546 6682.1704 37.3254 682.1704
48 481.0025 48.4668 6718.7099 36.5395 718.7099
49 491.0025 49.4791 6754.4959 35.7861 754.4959
50 501.0025 50.4914 6789.5590 35.0631 789.5590
51 511.0025 51.5038 6823.9277 34.3687 823.9277
52 521.0025 52.5162 6857.6290 33.7013 857.6290
53 531.0025 53.5287 6890.6883 33.0593 890.6883
54 541.0025 54.5412 6923.1297 32.4414 923.1297
55 551.0025 55.5538 6954.9757 31.8461 954.9757
56 561.0025 56.5664 6986.2480 31.2722 986.2480
57 571.0025 57.5791 7016.9667 30.7187 1016.9667
58 581.0025 58.5918 7047.1511 30.1845 1047.1511
59 591.0025 59.6045 7076.8196 29.6685 1076.8196
60 601.0025 60.6173 7105.9894 29.1698 1105.9894
61 611.0025 61.6301 7134.6770 28.6876 1134.6770
62 621.0025 62.6430 7162.8982 28.2211 1162.8982
63 631.0025 63.6559 7190.6677 27.7696 1190.6677
64 641.0025 64.6689 7218.0000 27.3323 18.0000
65 651.0025 65.6819 7244.9085 26.9085 44.9085
66 661.0025 66.6949 7271.4061 26.4976 71.4061
67 671.0025 67.7080 7297.5053 26.0992 97.5053
68 681.0025 68.7211 7323.2178 25.7125 123.2178
69 691.0025 69.7343 7348.5549 25.3371 148.5549
70 701.0025 70.7474 7373.5275 24.9725 173.5275
71 711.0025 71.7607 7398.1458 24.6183 198.1458
72 721.0025 72.7739 7422.4198 24.2740 222.4198
73 731.0025 73.7872 7446.3589 23.9392 246.3589
74 741.0025 74.8006 7469.9724 23.6135 269.9724
75 751.0025 75.8139 7493.2689 23.2965 293.2689
76 761.0025 76.8273 7516.2568 22.9879 316.2568
77 771.0025 77.8407 7538.9442 22.6874 338.9442
78 781.0025 78.8542 7561.3389 22.3947 361.3389
79 791.0025 79.8677 7583.4482 22.1094 383.4482
80 801.0025 80.8812 7605.2795 21.8313 405.2795
81 811.0025 81.8948 7626.8396 21.5601 426.8396
82 821.0025 82.9084 7648.1351 21.2955 448.1351
83 831.0025 83.9220 7669.1724 21.0374 469.1724
84 841.0025 84.9356 7689.9579 20.7854 489.9579
85 851.0025 85.9493 7710.4973 20.5394 510.4973
86 861.0025 86.9630 7730.7965 20.2992 530.7965
87 871.0025 87.9768 7750.8610 20.0645 550.8610
88 881.0025 88.9905 7770.6962 19.8352 570.6962
89 891.0025 90.0043 7790.3073 19.6111 590.3073
90 901.0025 91.0182 7809.6993 19.3920 609.6993
91 911.0025 92.0320 7828.8770 19.1777 628.8770
92 921.0025 93.0459 7847.8450 18.9681 647.8450
93 931.0025 94.0598 7866.6080 18.7630 666.6080
94 941.0025 95.0738 7885.1704 18.5623 685.1704
95 951.0025 96.0877 7903.5363 18.3659 703.5363
96 961.0025 97.1017 7921.7099 18.1736 721.7099
97 971.0025 98.1157 7939.6951 17.9853 739.6951
98 981.0025 99.1298 7957.4959 17.8008 757.4959
99 991.0025 100.1438 7975.1160 17.6201 775.1160
100 1001.0025 101.1579 7992.5590 17.4430 792.5590
101 1011.0025 102.1721 8009.8284 17.2694 809.8284
102 1021.0025 103.1862 8026.9277 17.0993 826.9277
103 1031.0025 104.2004 8043.8601 16.9324 843.8601
104 1041.0025 105.2146 8060.6290 16.7688 860.6290
105 1051.0025 106.2288 8077.2374 16.6084 877.2374
106 1061.0025 107.2430 8093.6883 16.4509 893.6883
107 1071.0025 108.2573 8109.9848 16.2965 909.9848
108 1081.0025 109.2716 8126.1297 16.1449 926.1297
109 1091.0025 110.2859 8142.1257 15.9961 942.1257
110 1101.0025 111.3003 8157.9757 15.8500 957.9757
111 1111.0025 112.3146 8173.6823 15.7066 973.6823
112 1121.0025 113.3290 8189.2480 15.5657 989.2480
113 1131.0025 114.3434 8204.6753 15.4273 1004.6753
114 1141.0025 115.3578 8219.9667 15.2914 1019.9667
115 1151.0025 116.3723 8235.1245 15.1578 1035.1245
116 1161.0025 117.3868 8250.1511 15.0266 1050.1511
117 1171.0025 118.4013 8265.0488 14.8976 1065.0488
118 1181.0025 119.4158 8279.8196 14.7708 1079.8196
119 1191.0025 120.4303 8294.4658 14.6462 1094.4658
120 1201.0025 121.4449 8308.9894 14.5236 1108.9894
121 1211.0025 122.4595 8323.3925 14.4031 1123.3925
122 1221.0025 123.4741 8337.6770 14.2845 1137.6770
123 1231.0025 124.4887 8351.8449 14.1679 1151.8449
124 1241.0025 125.5033 8365.8982 14.0532 1165.8982
125 1251.0025 126.5180 8379.8385 13.9403 1179.8385
126 1261.0025 127.5327 8393.6677 13.8293 1193.6677
127 1271.0025 128.5474 8407.3877 13.7199 7.3877
128 1281.0025 129.5621 8421.0000 13.6123 21.0000
Approximation of odd harmonics in 311edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) +0.30 -0.46 -0.34 +0.59 +0.45 +0.63 -0.17 -0.78 -0.41 -0.04 +0.66 -0.92 +0.89 +0.65 +0.95
Relative (%) +7.7 -12.0 -8.7 +15.3 +11.7 +16.3 -4.3 -20.1 -10.5 -1.1 +17.2 -23.9 +23.0 +16.8 +24.5
Steps
(reduced) 		493
(182) 		722
(100) 		873
(251) 		986
(53) 		1076
(143) 		1151
(218) 		1215
(282) 		1271
(27) 		1321
(77) 		1366
(122) 		1407
(163) 		1444
(200) 		1479
(235) 		1511
(267) 		1541
(297)
Approximation of odd harmonics in 3159811edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61
Error Absolute (¢) +0.00 +0.00 +0.00 +0.00 -0.00 -0.00 +0.00 -0.00 -0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 -0.00 +0.00 -0.00 -0.00 +0.00 -0.00 +0.00 +0.00 +0.00 +0.00 -0.00 -0.00 -0.00 -0.00 -0.00
Relative (%) +5.6 +6.5 +3.6 +11.1 -8.2 -12.6 +12.0 -4.8 -8.4 +9.2 +17.2 +12.9 +16.7 +21.4 +0.2 -2.7 +10.1 -4.9 -7.1 +24.3 -6.1 +17.6 +4.6 +7.3 +0.8 -5.9 -1.8 -2.9 -21.6 -7.7
Steps
(reduced) 		5008182
(1848371) 		7336854
(1017232) 		8870711
(2551089) 		10016364
(536931) 		10931150
(1451717) 		11692690
(2213257) 		12345036
(2865603) 		12915610
(276366) 		13422648
(783404) 		13878893
(1239649) 		14293601
(1654357) 		14673708
(2034464) 		15024546
(2385302) 		15350302
(2711058) 		15654324
(3015080) 		15939332
(140277) 		16207565
(408510) 		16460888
(661833) 		16700872
(901817) 		16928852
(1129797) 		17145971
(1346916) 		17353218
(1554163) 		17551451
(1752396) 		17741422
(1942367) 		17923792
(2124737) 		18099146
(2300091) 		18268004
(2468949) 		18430830
(2631775) 		18588040
(2788985) 		18740009
(2940954)
Approximation of odd harmonics in 42586208631edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99 101 103 105 107 109 111 113 115 117 119 123 125 127
Error Absolute (¢) -0.00 -0.00 -0.00 -0.00 +0.00 -0.00 -0.00 +0.00 +0.00 -0.00 +0.00 -0.00 -0.00 +0.00 -0.00 +0.00 -0.00 -0.00 -0.00 -0.00 +0.00 -0.00 +0.00 -0.00 +0.00 +0.00 -0.00 +0.00 +0.00 -0.00 -0.00 -0.00 -0.00 +0.00 -0.00 +0.00 -0.00 +0.00 +0.00 -0.00 -0.00 -0.00 +0.00 +0.00 -0.00 -0.00 +0.00 +0.00 -0.00 +0.00 +0.00 -0.00 +0.00 -0.00 -0.00 -0.00 +0.00 -0.00 +0.00 -0.00 -0.00 -0.00
Relative (%) -2.3 -5.4 -1.0 -4.5 +3.4 -19.5 -7.6 +5.3 +12.6 -3.3 +10.2 -10.7 -6.8 +6.4 -6.6 +1.1 -6.3 -14.0 -21.8 -9.8 +21.4 -9.9 +2.9 -2.0 +3.0 +19.9 -2.0 +10.4 +17.5 -11.5 -5.5 -24.9 -8.9 +7.9 -11.8 +24.8 -13.0 +2.4 +4.9 -9.1 -19.2 -0.1 +4.2 +12.4 -20.5 -8.9 +7.3 +20.3 -1.1 +21.2 +8.4 -8.6 +12.2 -1.4 -16.2 -17.0 +4.8 -24.1 +4.3 -12.1 -16.1 -15.4
Steps
(reduced) 		67497543728
(24911335097) 		98882114275
(13709697013) 		119554602412
(34382185150) 		134995087456
(7236461563) 		147324076656
(19565450763) 		157587697863
(29829071970) 		166379658003
(38621032110) 		174069545329
(3724710805) 		180903127337
(10558292813) 		187052146140
(16707311616) 		192641353216
(22296518692) 		197764228550
(27419394026) 		202492631184
(32147796660) 		206882992184
(36538157660) 		210980437673
(40635603149) 		214821620384
(1890577229) 		218436716687
(5505673532) 		221850867882
(8919824727) 		225085241591
(12154198436) 		228157827420
(15226784265) 		231084042931
(18152999776) 		233877201731
(20946158576) 		236548879697
(23617836542) 		239109204824
(26178161669) 		241567089057
(28636045902) 		243930415500
(30999372345) 		246206190931
(33275147776) 		248400671065
(35469627910) 		250519464202
(37588421047) 		252567617593
(39636574438) 		254549689868
(41618646713) 		256469812138
(952560352) 		258331739839
(2814488053) 		260138896944
(4621645158) 		261894413859
(6377162073) 		263601160054
(8083908268) 		265261772278
(9744520492) 		266878679068
(11361427282) 		268454122106
(12936870320) 		269990174912
(14472923126) 		271488759254
(15971507468) 		272951659604
(17434407818) 		274380535912
(18863284126) 		275776934930
(20259683144) 		277142300275
(21625048489) 		278477981401
(22960729615) 		279785241612
(24267989826) 		281065265244
(25548013458) 		282319164112
(26801912326) 		283547983314
(28030731528) 		284752706462
(29235454676) 		285934260415
(30417008629) 		287093519562
(31576267776) 		288231309708
(32714057922) 		289348411610
(33831159824) 		290445564194
(34928312408) 		291523467491
(36006215705) 		292582785319
(37065533533) 		293624147741
(38106895955) 		295655371148
(40138119362) 		296646342825
(41129091039) 		297621584127
(42104332341)
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