Just play your 53-TET keyboard


Tuning:

Instrument layout:
Jammer and Guitar have similar layouts (4ths up left, 5th up right)

Full 53-TET
microtonal
input via PC keyboard, shift for higher tones
String !63 (shift ...
String Q54 (shift ...
String A45 (F M7, L octave)
String Z36 (Z m6, V M6, > m7)
String 127 (5 P5)
String q18 (t P4, o Tri)
String a 9 (a M2, h m3, l M3)
String z 0 (z root, n m2)

Name 12-TETJust intonation 53-TET 9 steps (keyboard) cents Ptolemy
CentsJI Centsinterval ratio down from 9 equal 9 step
Unison (C) 0 0 ​1⁄1 = 1 (0) 0
Minor second (C♯/D♭) 100111.73​16⁄15 = 1.06… (4) 90.57(5) 113.21
Major second (D) 200203.91​9⁄8 = 1.125 (8) 181.13(9) 203.77
Minor third (D♯/E♭) 300315.64​6⁄5 = 1.2 (13) 294.34(14) 316.98
Major third (E) 400386.31​5⁄4 = 1.25 (17) 384.91(18) 407.55
Perfect fourth (F) 500498.04​4⁄3 = 1.33… (22) 498.11 (23) 520.75
Tritone (F♯/G♭) 600582.51​7⁄5 = 1.4 (​10⁄7)(26) 588.68(27) 611.3245/32, 590.2 cents
Perfect fifth (G) 700701.96​3⁄2 = 1.5 (30) 679.25(31) 701.89
Minor sixth (G♯/A♭) 800813.69​8⁄5 = 1.6 (35) 792.45(36) 815.09
Major sixth (A) 900884.36​5⁄3 = 1.66… (39) 883.02(40) 905.66
Minor seventh (A♯/B♭)1000996.09​16⁄9 = 1.77… (44) 996.23 (45) 1018.879/5, 1017.6 cents
Major seventh (B) 11001088.27​15⁄8 = 1.875 (48) 1086.79(49) 1109.43
Octave (C) 12001200 ​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♭ 277.18264
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