53 notes and 23 cents

A study of 53 tone equal temperament. Try out a few different tunings and "instrument" layouts. In all cases, you'll need to use a PC keyboard to play notes. In some cases the SHIFT key will transpose the key (change mode, micro-re-tune the scale), with other instrument layouts, the SHIFT just provides higher pitches.

Versions: v0 (September 2020), v1 (October 2020)

Try a different Tuning such as Pythagorean (which stacks perfect fifths on tone 31 of 53). Can you hear a difference? The individual notes differ by less than 23 cents (somewhat as if there were four black keys between white keys on a piano).

The instrument layouts differ quite a bit (and differed far more in offline development and experiments). The Guitar, Mandolin, and Lutes present a chromatic scale on the PC keyboard ascending with keys to the right. The rows are analogous to strings tuned fourths, fifths, or sixths above. The lowest notes are on the keyboard keys z,x,c,v,b,n. The keyboard keys z c b n , play the beginning of a scale.

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