Just play your 53-TET keyboard
Name | 12-TET | Just intonation | 53-TET 9 steps (keyboard) cents |
Ptolemy |
| Cents | JI Cents | interval ratio | down from 9 | equal 9 step |
Unison (C) | 0 | 0 | 1⁄1 = 1 | | (0) 0 |
Minor second (C♯/D♭) | 100 | 111.73 | 16⁄15 = 1.06… | (4) 90.57 | (5) 113.21 |
Major second (D) | 200 | 203.91 | 9⁄8 = 1.125 | (8) 181.13 | (9) 203.77 |
Minor third (D♯/E♭) | 300 | 315.64 | 6⁄5 = 1.2 | (13) 294.34 | (14) 316.98 |
Major third (E) | 400 | 386.31 | 5⁄4 = 1.25 | (17) 384.91 | (18) 407.55 |
Perfect fourth (F) | 500 | 498.04 | 4⁄3 = 1.33… | (22) 498.11 | (23) 520.75 |
Tritone (F♯/G♭) | 600 | 582.51 | 7⁄5 = 1.4 (10⁄7) | (26) 588.68 | (27) 611.32 | 45/32, 590.2 cents |
Perfect fifth (G) | 700 | 701.96 | 3⁄2 = 1.5 | (30) 679.25 | (31) 701.89 |
Minor sixth (G♯/A♭) | 800 | 813.69 | 8⁄5 = 1.6 | (35) 792.45 | (36) 815.09 |
Major sixth (A) | 900 | 884.36 | 5⁄3 = 1.66… | (39) 883.02 | (40) 905.66 |
Minor seventh (A♯/B♭) | 1000 | 996.09 | 16⁄9 = 1.77… | (44) 996.23 | (45) 1018.87 | 9/5, 1017.6 cents |
Major seventh (B) | 1100 | 1088.27 | 15⁄8 = 1.875 | (48) 1086.79 | (49) 1109.43 |
Octave (C) | 1200 | 1200 | 2⁄1 = 2 | (53) 1200 | |
Shrutis
|
12-TET
| 53-TET
|
Name | Ratio | Cents | Hz |
Sargam | Solfège | Pitch | Hz |
Chandovatī | 1 | 0 | 261.6256 |
Sa | Do | C | 261.6256 | 0 |
Dayāvatī | 256/243 | 90 | 275.6220 |
ri, | re, | D♭ | 277.1826 | 4 |
Ranjanī | 16/15 | 112 | 279.0673 | 5 |
Ratikā | 10/9 | 182 | 290.6951 |
Ri | Re | D | 293.6648 | 8 |
Raudrī | 9/8 | 203 | 294.3288 | 9 |
Krodhā | 32/27 | 294 | 310.0747 |
ga, | mi, | E♭ | 311.1270 | 13 |
Vajrikā | 6/5 | 316 | 313.9507 | 14 |
Prasāriṇī | 5/4 | 386 | 327.0319 | Ga | Mi | E | 329.6275 | 17 |
Prīti | 81/64 | 407 | 331.1198 | 18 |
Mārjanī | 4/3 | 498 | 348.8341 | Ma | Fa | F | 349.2282 | 22 |
Kṣhiti | 27/20 | 519 | 353.1945 | 23 |
Raktā | 45/32 | 590 | 367.9109 | ma' | sol, | F# | 369.9944 | 26 |
Sandīpanī | 729/512 | 612 | 372.5098 | 27 |
Ālāpinī | 3/2 | 702 | 392.4383 | Pa | Sol | G | 391.9954 | 31 |
Madantī | 128/81 | 792 | 413.4330 | dha, | la, | A♭ | 415.3047 | 35 |
Rohiṇī | 8/5 | 814 | 418.6009 | 36 |
Ramyā | 5/3 | 884 | 436.0426 | Dha | La | A | 440.0000 | 39 |
Ugrā | 27/16 | 906 | 441.4931 | 40 |
Kṣobhinī | 16/9 | 996 | 465.1121 | ni, | ti, | B♭ | 466.1638 | 44 |
Tīvrā | 9/5 | 1017 | 470.9260 | 45 |
Kumudvatī | 15/8 | 1088 | 490.5479 | Ni | Ti | B | 493.8833 | 48 |
Mandā | 243/128 | 1110 | 496.6798 | 49 |
Chandovatī | 2 | 1200 | 523.2511 | SA | DO | C | 523.2511 | 53 |
Shruti Svara Frequencies Just intervals Cents Solfège 53tet
====== ===== =============== ================= ================== ======= =====
0 Sa 100 1/1 0 Do 0
1- 2 ri 105.35 - 106.66 256/243 - 16/15 90.225 - 111.731 (re) 4-5
3- 4 Ri 111.11 - 112.50 10/9 - 9/8 182.404 - 203.910 Re 8-9
5- 6 ga 118.51 - 120 32/27 - 6/5 294.135 - 315.641 (mi) 13-14
7- 8 Ga 125 - 126.26 5/4 - 81/64 386.314 - 407.820 Mi 17-18
9-10 Mi 133.33 - 140.62 4/3 - 27/20 498.045 - 519.551 Fa 22-23
11-12 mi 140.62 - 142.38 45/32 - 729/512 590.224 - 611.730 (fa) 26-27
13 Pa 150 3/2 701.955 Sol 31
14-15 dha 158.02 - 160 128/81 - 8/5 792.180 - 813.686 (la) 35-36
16-17 Dha 166.66 - 169.75 5/3 - 27/16 884.359 - 905.865 La 39-40
18-19 ni 177.77 - 180 16/9 - 9/5 996.090 -1017.596 (ti) 44-45
20-21 Ni 187.50 - 189.84 15/8 - 243/128 1088.269 -1109.775 Ti 48-49
22 SA 200 2/1 1200 DO 53
====== ===== =============== ================= ================== ======= =====
Shruti Svara Frequencies Just intervals Cents Solfège 53tet
==
Parallel pure scales shifted on 1,2,3,4,5,6,7 (all major modes) in 53-TET
.0 .5 .9 .14.17 .22 .26 .31 .36.39 .44 .48 .53
1----m---2----m--3----4---T----5----m--6----m---7----1----
2----m--3----4---T----5----m--6----m---7----1----m---2----
3----4---T----5----m--6----m---7----1----m---2----m--3----
4---T----5----m--6----m---7----1----m---2----m--3----4---
5----m--6----m---7----1----m---2----m--3----4---T----5----
6----m---7----1----m---2----m--3----4---T----5----m--6----
7----1----m---2----m--3----4---T----5----m--6----m---7----
.0 .5 .9 .14.17 .22 .26 .31 .36.39 .44 .48 .53
==
Parallel chromatic scales shifted by a fifth (and fourth). Steps 30 and 45 emerge as good candidates for a scale (matching intervals 5-4 and 5-3).
5 4 5 3 5 4 5 5 3 5 4 5 5 4 5 3 5 4 5 5 3 5 4 5 5
00 05 09 14 17 22 26 31 36 39 44 48 00 05 09 14 17 22 26 31 36 39 44 48 00 05
4 3 4 4 5 4 6 6 3 4 3 4 4 4 5 4
04 08 13 27(30) (45) 04 08 13 18 27
5 6 5 6 5
5 3 5 4 5 5 4 5 3 5 4 5 5 3 5 4 5 5 4 5 3 5 4 5 5
31 36 39 44 48 00 05 09 14 17 22 26 31 36 39 44 48 00 05 09 14 17 22 26 31 36
4 4 4 (3) 4 3 6 4 4 4 (3) 4 4 5
35 40(45) 04 08 35 40(45)49 04
5 6 5 5 (6) 5
==
Interval Cents 53-tet step
======= ============ ===========
1:1 0 0/53
22.64150943 1/53
45.28301886 2/53
67.92452830 3/53
90.56603773 4/53
17:16 104.95540950
16:15 111.73128527
113.20754716 5/53
15:14 119.44280826
14:13 128.29824470
135.84905660 6/53
13:12 138.57266090
12:11 150.63705850
158.49056603 7/53
11:10 165.00422850
181.13207547 8/53
10:9 182.40371213
203.77358490 9/53
9:8 203.91000173
17:15 216.68669477
226.41509433 10/53
8:7 231.17409353
15:13 247.74105296
249.05660377 11/53
7:6 266.87090560
271.69811320 12/53
13:11 289.20971940
294.33962264 13/53
19:16 297.51301613
6:5 315.64128700
316.98113207 14/53
17:14 336.12950303
339.62264150 15/53
11:9 347.40794063
16:13 359.47233823
362.26415094 16/53
384.90566037 17/53
5:4 386.31371386
407.54716981 18/53
19:15 409.24430140
14:11 417.50796410
430.18867924 19/53
9:7 435.08409526
452.83018867 20/53
13:10 454.21394790
17:13 464.42774773
21:16 470.78090733
475.47169811 21/53
4:3 498.04499913
498.11320754 22/53
520.75471698 23/53
19:14 528.68710966
15:11 536.95077237
543.39622641 24/53
11:8 551.31794236
18:13 563.38233996
566.03773584 25/53
7:5 582.51219260
588.67924528 26/53
17:12 603.00040864
611.32075471 27/53
10:7 617.48780740
23:16 628.27434727
633.96226415 28/53
13:9 636.61766004
16:11 648.68205764
656.60377358 29/53
19:13 656.98535436
22:15 663.04922763
679.24528301 30/53
701.88679245 31/53
3:2 701.95500087
724.52830188 32/53
23:15 740.00563254
20:13 745.78605210
747.16981132 33/53
17:11 753.63746714
14:9 764.91590474
769.81132075 34/53
25:16 772.62742773
11:7 782.49203590
792.45283018 35/53
19:12 795.55801527
8:5 813.68628614
815.09433962 36/53
21:13 830.25324557
837.73584905 37/53
13:8 840.52766177
18:11 852.59205937
23:14 859.44844080
860.37735849 38/53
883.01886792 39/53
5:3 884.35871300
905.66037735 40/53
928.30188679 41/53
950.94339622 42/53
973.58490566 43/53
996.22641509 44/53
25:14 1003.80152126
9:5 1017.59628787
1018.86792452 45/53
29:16 1029.57719415
20:11 1034.99577150
1041.50943396 46/53
11:6 1049.36294150
24:13 1061.42733910
1064.15094339 47/53
13:7 1071.70175530
28:15 1080.55719174
1086.79245283 48/53
15:8 1088.26871473
17:9 1101.04540777
1109.43396226 49/53
19:10 1111.19930227
21:11 1119.46296497
23:12 1126.31934640
1132.07547169 50/53
25:13 1132.09976596
27:14 1137.03909613
29:15 1141.30847942
31:16 1145.03557246
1154.71698113 51/53
1177.35849056 52/53
1200.00000000 53/53
======= ============ ===========
Interval Cents 53-tet step