Website on tuning systems and microtonality

dewdrop_world

http://tonalsoft.com/enc/encyclopedia-index.aspx

Over last weekend I wrote some SuperCollider classes to make it easier to define alternate tunings. Then I found this website. I may never use ET again. Twisted Evil

James

seraph · Posted: Sat Jan 27, 2007 10:10 am Post subject:

http://electro-music.com/forum/links.php?id=31

check those out Idea

dewdrop_world · Posted: Sat Jan 27, 2007 1:29 pm Post subject:

Oh, OK, I searched the forum to see if anyone had posted tonalsoft before and there were no results. I guess the links section doesn't count in the search.

James

seraph · Posted: Sat Jan 27, 2007 1:52 pm Post subject:

James
feel free to add more microtonal links Very Happy

GovernorSilver · Posted: Mon Feb 05, 2007 9:23 pm Post subject:

GovernorSilver · Posted: Tue Feb 06, 2007 2:56 pm Post subject:

Added a link to an excellent podcast on the problems of associating Arabic microtones with Western quarter-tones.

http://shumays.libsyn.com/forums.html?post_id=177745

seraph · Posted: Tue Feb 06, 2007 3:04 pm Post subject:

yesterday I had posted this message:

http://electro-music.com/forum/topic-16073.html

but not added the link.

GovernorSilver · Posted: Thu Feb 08, 2007 11:51 am Post subject:

Sami Abu Shamays recently found his way onto the Yahoo tuning group and is now engaged in spirited discussion over his podcast concerning microtones in Arabic music.

One of the participants in this discussion, Ozan Yarman, is a Turkish music researcher who has proposed a 79-tone tuning which is a MOS subset of 159-tone equal temperament, which is in opposition to Shamays' assertion that any equal temperament is unsuitable for maqam based music. Yarman's point of view is different because he plays a fixed pitch instrument (qanun). His tuning takes advantage of the property of equal temperaments becoming less and less distinguishable from just intonation as the intervals get smaller and smaller. An excerpt from his post:

1. METHOD

A) Equally partition the pure fourth into 33:

1/33 of [log10 (4:3)] x 1200 / [log10 2] = 498.045 / 33 = 15.0923 cents

B) Carry the resultant comma to the 79th step:

15.0923 x 1 = 15.0923 cents

15.0923 x 2 = 30.1845 cents

15.0923 x 3 = 45.2768 cents

etc...

15.0923 x 79 = 1192.29 cents

C) Complete the last step to the octave (1200 cents), which yields a larger comma:

(1200-1192.29) + 15.0923 = 7.71 + 15.0923 = 22.80273 cents

D) Move the larger comma between steps 45-46:

(15.0923 x 45) + 22.80273 = 679.1523 + 22.80273 = 701.955001 cents = [log10 (3:2)] x 1200 / [log10 2]

701.955001 + (15.0923 x 1) = 717.047 cents
701.955001 + (15.0923 x 2) = 732.140 cents
701.955001 + (15.0923 x 3) = 747.232 centsetc...
701.955001 + (15.0923 x 32) = 717.047 cents

79MOS159tET (33rd of pure fourth) with modified SA79 notation
0: 1/1 C
1: 15.092 cents C/| D\Y/
2: 30.185 cents C|\ DY/
3: 45.277 cents C/|\ D\Y
4: 60.369 cents C/|| D\!!!/
5: 75.461 cents C||\ D!!!/
6: 90.554 cents C/||\ D\!!!
7: 105.646 cents C/||| D\!!/
8: 120.738 cents C|||\ D!!/
9: 135.830 cents C/|||\ D\!!
10: 150.923 cents C/X D\!/
11: 166.015 cents CX\ D!/
12: 181.107 cents C/X\ D\!
13: 196.200 cents D
14: 211.292 cents D/| E\Y/
15: 226.384 cents D|\ EY/
16: 241.476 cents D/|\ E\Y
17: 256.569 cents D/|| E\!!!/
18: 271.661 cents D||\ E!!!/
19: 286.753 cents D/||\ E\!!!
20: 301.845 cents D/||| E\!!/
21: 316.938 cents D|||\ E!!/
22: 332.030 cents D/|||\ E\!!
23: 347.122 cents D/X E\!/
24: 362.215 cents DX\ E!/
25: 377.307 cents D/X\ E\!
26: 392.399 cents E
27: 407.491 cents E/| F\!!/
28: 422.584 cents E|\ F!!/
29: 437.676 cents E/|\ F\!!
30: 452.768 cents E/|| F\!/
31: 467.860 cents E||\ F!/
32: 482.953 cents E/||\ F\!
33: 505.755 cents F
34: 520.848 cents F/| G\Y/
35: 535.940 cents F|\ GY/
36: 551.032 cents F/|\ G\Y
37: 566.125 cents F/|| G\!!!/
38: 581.217 cents F||\ G!!!/
39: 596.309 cents F/||\ G\!!!
40: 611.401 cents F/||| G\!!/
41: 626.494 cents F|||\ G!!/
42: 641.586 cents F/|||\ G\!!
43: 656.678 cents F/X G\!/
44: 671.770 cents FX\ G!/
45: 686.863 cents F/X\ G\!
46: 701.955 cents G
47: 717.047 cents G/| A\Y/
48: 732.140 cents G|\ AY/
49: 747.232 cents G/|\ A\Y
50: 762.324 cents G/|| A\!!!/
51: 777.416 cents G||\ A!!!/
52: 792.509 cents G/||\ A\!!!
53: 807.601 cents G/||| A\!!/
54: 822.693 cents G|||\ A!!/
55: 837.785 cents G/|||\ A\!!
56: 852.878 cents G/X A\!/
57: 867.970 cents GX\ A!/
58: 883.062 cents G/X\ A\!
59: 898.155 cents A
60: 913.247 cents A/| B\Y/
61: 928.339 cents A|\ BY/
62: 943.431 cents A/|\ B\Y
63: 958.524 cents A/|| B\!!!/
64: 973.616 cents A||\ B!!!/
65: 988.708 cents A/||\ B\!!!
66: 1003.800 cents A/||| B\!!/
67: 1018.893 cents A|||\ B!!/
68: 1033.985 cents A/|||\ B\!!
69: 1049.077 cents A/X B\!/
70: 1064.170 cents AX\ B!/
71: 1079.262 cents A/X\ B\!
72: 1094.354 cents B
73: 1109.446 cents B/| C\!!/
74: 1124.539 cents B|\ C!!/
75: 1139.631 cents B/|\ C\!!
76: 1154.723 cents B/|| C\!/
77: 1169.815 cents B||\ C!/
78: 1184.908 cents B/||\ C\!
79: 1200.000 cents C

2. METHOD

Equally divide the octave into 159 parts and pick degrees 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 93 95 97 99 101 103 105 107 109 111 113 115 117 119 121 123 125 127 129 131 133 135 137 139 141 143 145 147 149 151 153 155 157 159:

(1200/159) x {0, 2, 4 …159} = cent values for 79 MOS 159-tET.

79MOS159tET (actual) with modified SA79 notation

0: 1/1 C
1: 15.092 cents C/| D\Y/
2: 30.185 cents C|\ DY/
3: 45.277 cents C/|\ D\Y
4: 60.369 cents C/|| D\!!!/
5: 75.461 cents C||\ D!!!/
6: 90.554 cents C/||\ D\!!!
7: 105.646 cents C/||| D\!!/
8: 120.738 cents C|||\ D!!/
9: 135.830 cents C/|||\ D\!!
10: 150.923 cents C/X D\!/
11: 166.015 cents CX\ D!/
12: 181.107 cents C/X\ D\!
13: 196.200 cents D
14: 211.292 cents D/| E\Y/
15: 226.384 cents D|\ EY/
16: 241.476 cents D/|\ E\Y
17: 256.569 cents D/|| E\!!!/
18: 271.661 cents D||\ E!!!/
19: 286.753 cents D/||\ E\!!!
20: 301.845 cents D/||| E\!!/
21: 316.938 cents D|||\ E!!/
22: 332.030 cents D/|||\ E\!!
23: 347.122 cents D/X E\!/
24: 362.215 cents DX\ E!/
25: 377.307 cents D/X\ E\!
26: 392.399 cents E
27: 407.491 cents E/| F\!!/
28: 422.584 cents E|\ F!!/
29: 437.676 cents E/|\ F\!!
30: 452.768 cents E/|| F\!/
31: 467.860 cents E||\ F!/
32: 482.953 cents E/||\ F\!
33: 505.755 cents F
34: 520.848 cents F/| G\Y/
35: 535.940 cents F|\ GY/
36: 551.032 cents F/|\ G\Y
37: 566.125 cents F/|| G\!!!/
38: 581.217 cents F||\ G!!!/
39: 596.309 cents F/||\ G\!!!
40: 611.401 cents F/||| G\!!/
41: 626.494 cents F|||\ G!!/
42: 641.586 cents F/|||\ G\!!
43: 656.678 cents F/X G\!/
44: 671.770 cents FX\ G!/
45: 686.863 cents F/X\ G\!
46: 701.955 cents G
47: 717.047 cents G/| A\Y/
48: 732.140 cents G|\ AY/
49: 747.232 cents G/|\ A\Y
50: 762.324 cents G/|| A\!!!/
51: 777.416 cents G||\ A!!!/
52: 792.509 cents G/||\ A\!!!
53: 807.601 cents G/||| A\!!/
54: 822.693 cents G|||\ A!!/
55: 837.785 cents G/|||\ A\!!
56: 852.878 cents G/X A\!/
57: 867.970 cents GX\ A!/
58: 883.062 cents G/X\ A\!
59: 898.155 cents A
60: 913.247 cents A/| B\Y/
61: 928.339 cents A|\ BY/
62: 943.431 cents A/|\ B\Y
63: 958.524 cents A/|| B\!!!/
64: 973.616 cents A||\ B!!!/
65: 988.708 cents A/||\ B\!!!
66: 1003.800 cents A/||| B\!!/
67: 1018.893 cents A|||\ B!!/
68: 1033.985 cents A/|||\ B\!!
69: 1049.077 cents A/X B\!/
70: 1064.170 cents AX\ B!/
71: 1079.262 cents A/X\ B\!
72: 1094.354 cents B
73: 1109.446 cents B/| C\!!/
74: 1124.539 cents B|\ C!!/
75: 1139.631 cents B/|\ C\!!
76: 1154.723 cents B/|| C\!/
77: 1169.815 cents B||\ C!/
78: 1184.908 cents B/||\ C\!
79: 1200.000 cents C

3. METHOD

Temper the fifth as much as 19/53 of a syntonic comma, and form a closed cycle composed of 46 pure and 33 thusly tempered fifths following this pattern:

AB

AB AB AAB

AB AB AAB
AB AAB

AB AB AAB
AB AAB

AB AB AAB
AB AAB

AB AB AAB
AB AAB

AB AB AAB
AB AAB

AB AB AAB
AB A

{[log10 (3:2)] x 1200 / [log10 (2)]} – {(19:53) x [log10 (81/80)] x 1200 / log10 (2)} =

701.955001 – (0.3584906 x 21.5062896) =

701.955001 cents (A) – 7.709802 =

694.2451989 cents (B)

A*46 + B*33 =

32289.93004 + 22910.09156 =

1200.00047 cents x 46 =

55200.0216 cents (cycle is closed 46 octaves above the fundamental tone)

79MOS159tET (19/53 synt.) with modified SA79 notation

0: 1/1 C
1: 15.092 cents C/| D\Y/
2: 30.185 cents C|\ DY/
3: 45.277 cents C/|\ D\Y
4: 60.369 cents C/|| D\!!!/
5: 75.461 cents C||\ D!!!/
6: 90.554 cents C/||\ D\!!!
7: 105.646 cents C/||| D\!!/
8: 120.738 cents C|||\ D!!/
9: 135.831 cents C/|||\ D\!!
10: 150.923 cents C/X D\!/
11: 166.015 cents CX\ D!/
12: 181.107 cents C/X\ D\!
13: 196.200 cents D
14: 211.292 cents D/| E\Y/
15: 226.384 cents D|\ EY/
16: 241.477 cents D/|\ E\Y
17: 256.569 cents D/|| E\!!!/
18: 271.661 cents D||\ E!!!/
19: 286.753 cents D/||\ E\!!!
20: 301.846 cents D/||| E\!!/
21: 316.938 cents D|||\ E!!/
22: 332.030 cents D/|||\ E\!!
23: 347.123 cents D/X E\!/
24: 362.215 cents DX\ E!/
25: 377.307 cents D/X\ E\!
26: 392.399 cents E
27: 407.492 cents E/| F\!!/
28: 422.584 cents E|\ F!!/
29: 437.676 cents E/|\ F\!!
30: 452.769 cents E/|| F\!/
31: 467.861 cents E||\ F!/
32: 482.953 cents E/||\ F\!
33: 498.045 cents F
34: 513.138 cents F/| G\Y/
35: 528.230 cents F|\ GY/
36: 543.322 cents F/|\ G\Y
37: 558.415 cents F/|| G\!!!/
38: 573.507 cents F||\ G!!!/
39: 588.599 cents F/||\ G\!!!
40: 603.691 cents F/||| G\!!/
41: 618.784 cents F|||\ G!!/
42: 633.876 cents F/|||\ G\!!
43: 648.968 cents F/X G\!/
44: 664.061 cents FX\ G!/
45: 679.153 cents F/X\ G\!
46: 701.955 cents G
47: 717.047 cents G/| A\Y/
48: 732.140 cents G|\ AY/
49: 747.232 cents G/|\ A\Y
50: 762.324 cents G/|| A\!!!/
51: 777.416 cents G||\ A!!!/
52: 792.509 cents G/||\ A\!!!
53: 807.601 cents G/||| A\!!/
54: 822.693 cents G|||\ A!!/
55: 837.786 cents G/|||\ A\!!
56: 852.878 cents G/X A\!/
57: 867.970 cents GX\ A!/
58: 883.062 cents G/X\ A\!
59: 898.155 cents A
60: 913.247 cents A/| B\Y/
61: 928.339 cents A|\ BY/
62: 943.432 cents A/|\ B\Y
63: 958.524 cents A/|| B\!!!/
64: 973.616 cents A||\ B!!!/
65: 988.708 cents A/||\ B\!!!
66: 1003.801 cents A/||| B\!!/
67: 1018.893 cents A|||\ B!!/
68: 1033.985 cents A/|||\ B\!!
69: 1049.078 cents A/X B\!/
70: 1064.170 cents AX\ B!/
71: 1079.262 cents A/X\ B\!
72: 1094.354 cents B
73: 1109.447 cents B/| C\!!/
74: 1124.539 cents B|\ C!!/
75: 1139.631 cents B/|\ C\!!
76: 1154.724 cents B/|| C\!/
77: 1169.816 cents B||\ C!/
78: 1184.908 cents B/||\ C\!
79: 1200.000 cents C

4. METHOD

Choose the following subset of 1048-Arithmetic Divisions of the Octave, where notation is modified SA79:

79MOS159tET (1048-ADO) with modified SA79 notation
0: 1/1 C 0.000
1: 529/524 C/ Dbb 16.441
2: 1067/1048 Cy Dbb/ 31.106
3: 269/262 C^ Dbby 45.647
4: 1085/1048 C#k Dbv 60.068
5: 1095/1048 C#\ Dbk 75.951
6: 1105/1048 C# Db\ 91.689
7: 557/524 C#/ Db 105.733
8: 281/262 C#y Db/ 121.204
9: 567/524 C#^ Dby 136.538
10: 143/131 Cxk Dv 151.738
11: 577/524 Cx\ Dk 166.805
12: 291/262 Cx D\ 181.743
13: 587/524 D 196.552
14: 148/131 D/ Ebb 211.236
15: 1195/1048 Dy Ebb/ 227.246
16: 1205/1048 D^ Ebby 241.673
17: 152/131 D#k Ebv 257.405
18: 613/524 D#\ Ebk 271.584
19: 1237/1048 D# Eb\ 287.048
20: 156/131 D#/ Eb 302.375
21: 1259/1048 D#y Eb/ 317.567
22: 635/524 D#^ Eby 332.628
23: 1281/1048 Dxk Ev 347.558
24: 323/262 Dx\ Ek 362.361
25: 163/131 Dx E\ 378.366
26: 1315/1048 E 392.909
27: 1327/1048 E/ Fb 408.636
28: 669/524 Ey Fb/ 422.927
29: 675/524 E^ Fby 438.385
30: 681/524 E#k Fv 453.706
31: 687/524 E#\ Fk 468.892
32: 693/524 E# F\ 483.946
33: 4/3 F 498.045
34: 1411/1048 F/ Gbb 514.895
35: 1423/1048 Fy Gbb/ 529.556
36: 1435/1048 F^ Gbby 544.094
37: 1447/1048 F#k Gbv 558.511
38: 365/262 F#\ Gbk 573.996
39: 1473/1048 F# Gb\ 589.342
40: 1485/1048 F#/ Gb 603.389
41: 1499/1048 F#y Gb/ 619.634
42: 189/131 F#^ Gby 634.583
43: 1525/1048 Fxk Gv 649.405
44: 1539/1048 Fx\ Gk 665.225
45: 194/131 Fx G\ 679.788
46: 3/2 G 701.955
47: 793/524 G/ Abb 717.305
48: 200/131 Gy Abb/ 732.520
49: 807/524 G^ Abby 747.602
50: 407/262 G#k Abv 762.554
51: 821/524 G#\ Abk 777.378
52: 207/131 G# Ab\ 792.077
53: 1671/1048 G#/ Ab 807.688
54: 1685/1048 G#y Ab/ 822.132
55: 425/262 G#^ Aby 837.475
56: 1715/1048 Gxk Av 852.684
57: 865/524 Gx\ Ak 867.760
58: 1745/1048 Gx A\ 882.706
59: 220/131 A 897.524
60: 222/131 A/ Bbb 913.191
61: 1791/1048 Ay Bbb/ 927.752
62: 226/131 A^ Bbby 944.107
63: 228/131 A#k Bbv 959.360
64: 1839/1048 A#\ Bbk 973.539
65: 1855/1048 A# Bb\ 988.537
66: 2105/1179 (1871/1048) A#/ Bb 1003.508
67: 236/131 A#y Bb/ 1019.064
68: 238/131 A#^ Bby 1033.674
69: 1921/1048 Axk Bv 1049.063
70: 969/524 Ax\ Bk 1064.316
71: 1955/1048 Ax B\ 1079.436
72: 1971/1048 B 1093.547
73: 1989/1048 B/ Cb 1109.285
74: 1003/524 By Cb/ 1124.019
75: 253/131 B^ Cby 1139.485
76: 2041/1048 B#k Cv 1153.965
77: 2059/1048 B#\ Ck 1169.166
78: 2077/1048 B# C\ 1184.235
79: 2/1 C 1200.000

5. METHOD

Tune to simple frequencies at concert pitch with traditional perdes conforming to Supurde Ahenk:

0. 262.00000000000 Hz C RAST

1. 264.50000000000 Hz Dbb
2. 266.75000000000 Hz
3. 269.00000000000 Hz
4. 271.25000000000 Hz
5. 273.75000000000 Hz Shuri
6. 276.25000000000 Hz C# Nim Zengule
7. 278.50000000000 Hz Db
8. 281.00000000000 Hz
9. 283.50000000000 Hz (Zengule zone)
10. 286.00000000000 Hz
11. 288.50000000000 Hz
12. 291.00000000000 Hz Cx Zengule
13. 293.50000000000 Hz D DUGAH
14. 296.00000000000 Hz Ebb Dik Dugah
15. 298.75000000000 Hz
16. 301.25000000000 Hz
17. 304.00000000000 Hz
18. 306.50000000000 Hz Nerm Kurdi
19. 309.25000000000 Hz D# Kurdi
20. 312.00000000000 Hz Eb Nihavend
21. 314.75000000000 Hz Dik Nihavend
22. 317.50000000000 Hz Segah of Hijaz
23. 320.25000000000 Hz Segah of Ushshaq
24. 323.00000000000 Hz Segah of Saba
25. 326.00000000000 Hz Dx Nerm Segah (Segahche)
26. 328.75000000000 Hz E SEGAH / Nishabur
27. 331.75000000000 Hz Fb Buselik
28. 334.50000000000 Hz Dik Buselik
29. 337.50000000000 Hz
30. 340.50000000000 Hz
31. 343.50000000000 Hz
32. 346.50000000000 Hz E#
33. 349.33333333333 Hz F CHARGAH
34. 352.75000000000 Hz Gbb Dik Chargah
35. 355.75000000000 Hz
36. 358.75000000000 Hz
37. 361.75000000000 Hz
38. 365.00000000000 Hz Nerm Hijaz
39. 368.25000000000 Hz F# Hijaz
40. 371.25000000000 Hz Gb Uzzal/Saba
41. 374.75000000000 Hz
42. 378.00000000000 Hz
43. 381.25000000000 Hz (Saba zone)
44. 384.75000000000 Hz
45. 388.00000000000 Hz Fx
46. 393.00000000000 Hz G NEVA
47. 396.50000000000 Hz Abb
48. 400.00000000000 Hz
49. 403.50000000000 Hz
50. 407.00000000000 Hz
51. 410.50000000000 Hz
52. 414.00000000000 Hz G# Bayati
53. 417.75000000000 Hz Ab Nim Hisar
54. 421.25000000000 Hz
55. 425.00000000000 Hz
56. 428.75000000000 Hz (Hisar/Huzzam zone)
57. 432.50000000000 Hz
58. 436.25000000000 Hz Gx Hisar
59. 440.00000000000 Hz A HUSEYNI / Hisarek
60. 444.00000000000 Hz Bbb Dik Huseyni
61. 447.75000000000 Hz
62. 452.00000000000 Hz
63. 456.00000000000 Hz
64. 459.75000000000 Hz Nerm Ajem
65. 463.75000000000 Hz A# Ajem
66. 467.77777777777 Hz Bb (Ajnab)
67. 472.00000000000 Hz (Dik Ajnab)
68. 476.00000000000 Hz
69. 480.25000000000 Hz
70. 484.50000000000 Hz
71. 488.75000000000 Hz Ax Nerm Evdj
72. 492.75000000000 Hz B EVDJ
73. 497.25000000000 Hz cb Mahur
74. 501.50000000000 Hz Mahurek
75. 506.00000000000 Hz
76. 510.25000000000 Hz
77. 514.75000000000 Hz
78. 519.25000000000 Hz B#
79. 524.00000000000 Hz c GERDANIYE

seraph · Posted: Thu Feb 08, 2007 1:50 pm Post subject:

I listened to that podcast. the most interesting thing he says, for me, is that you can only recognize single pitches "in context" not as absolute values. this is a really different concept if compared to our idea of perfect pitch, for example.

seraph · Posted: Thu Feb 08, 2007 1:54 pm Post subject:

GovernorSilver · Posted: Fri Feb 09, 2007 6:16 pm Post subject:

Sorry, sir, I forgot you joined the tuning group!

I just listened to your microtuned pieces at http://www.seraph.it/Detwelvulation.html

My favorites are Metashakti, Maqam Bayati, Piano 11, Nemovar, and Instant Gamelan.

I had no idea you've been composing microtonal music this seriously. Your skills are far above mine - respect to you, sir!

seraph · Posted: Sat Feb 10, 2007 3:14 am Post subject: