53 notes, 23 cents

Just play your 53-TET keyboard

Piano-esque layout:	Pure 53	Eagle 53	12 Tempered Piano
Scale in 53-Tet:
Cardinality:
Mode:
Mode:
Instrument layout:
Instrument layout:

Full 53-TET on PC keyboard typing lower, capital, numbers and %!$% things
		String !	63 (shift ...	70 (! M3 above)
		String Q	54 (shift ...	60 (E M2 above)
		String A	45 (F M7, L octave)	50 (F octave above)
		String Z	36 (Z m6, V M6, > m7)	40 (B m7, > M7)
		String 1	27 (5 P5)	30 (2 P5, 7 m6, 0 M6)
		String q	18 (t P4, o Tri)	20 (e P4, u Tri)
		String a	9 (a M2, h m3, l M3)	10 (g m3, k M3)
		String z	0 (z root, n m2)	0 (... / M2)

Everything below is probably wrong and broken

Mode shift:
	String !	Ionian
	String Q	Locrian
	String A	Aeolian (minor)
	String Z	Mixolydian
	String 1	Lydian
	String q	Phrygian
	String a	Dorian (ex. C -> D, yet base in C)
	String z	Ionian (Major)
Major transposition:
Chromatic transposition:
Base notes on the bottom zxcvbnm,./ keyboard row, higher rows for micro-sharps and -flats

Almost symmetrical horizontal (piano like) layouts: roughly 9 steps between whole tones layed horizontaly on the keyboard, with 1, 4, 5 up flats or down sharps to pure or nice semitones in the scale

Christian Petzold's "Bach Minuet in G"	in A Major	in A minor	in G (Hypophrygian)
Eagle 53 on A
Tempered 53 on A
12-TET (West std)

Name	12-TET	Just intonation		53-TET 9 steps (keyboard) cents
	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
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
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

	Equal Tempered Tuning	Eagle 53 Pure Tuning
Abs. Major Steps (in A)	(0 9 18 22 31 40 49 53)	(0 9 17 22 31 39 48 53)
Rel. Major intervals	9-9-4-9-9-9-4	9-8-5-9-8-9-5
A Major	zaqt5BGL	zalt5VFL
^A Major	xswy6NHQ	xsqy6BGQ
^^A Major	cdeu7MJW	cdwu7NHW
	Equal Tempered Tuning	Eagle 53 Pure Tuning
Abs. minor Steps (in A)	(0 9 13 22 31 35 44 53)	(0 9 14 22 31 36 45 53
Rel. minor intervals	9-4-9-9-4-9-9	9-5-8-9-5-9-8
A minor	zagt59>L	zaht50?L
	Equal Tempered Tuning	Eagle 53 Pure Tuning

53-TET has a lot more tones than 12-TET. And 53 is not just an arbitrarily larger division of the octave. But the prime 53 is so chosen because many of its tones match perfect fifths, thirds, and other divinely pleasing notes. The fourth and fifth are less than 0.006% (0.07 cents) from perfectly just pure (fx log2(3/2) > 31/53). The third, sixth, and seventh are much more pure and less sharp than standard 12-TET.

53 step	Freq	Cents	12-TET equiv	Eagle 53	Pythagorean Just intonation
0	440.00	0	A4	A (E)
4	463.63	90.57	A#4/Bb4 (466.16 Hz)
5	469.73	113.21		A# (F)	16/15 (469.33 Hz)
9	494.96	203.77	B4 (493.88)	B (F#)	9/8 (495 Hz)
12	514.77	217.70			7/6 (513.33 Hz)
13	521.54	294.34	C5 (523.25)
14	528.41	316.98		C (G)	6/5 (528.00 Hz)
17	549.55	384.91		C# (G#)	5/4 (550 Hz)
18	556.79	407.55	C#5/Db5 (554.37)
22	586.69	498.11	D5 (587.33)	D (A)	4/3 (586.67 Hz)
26	618.20	588.68	D#5/Eb5 (622.25)	D# (A#)	7/5 (616 Hz)
27	626.34	611.32	D#5/Eb5 (622.25)
31	659.97	701.89	E5 (659.25)	E (B)	3/2 (660 Hz)
35	695.42	792.45	F5 (698.46)
36	704.57	815.09		F (C)	8/5 (704 Hz)
39	732.77	883.02		F# (C#)	5/3 (733.33 Hz)
40	742.41	905.66	F#5/Gb5 (739.99)
43	772.12	973.58			7/4 (770 Hz)
44	782.28	996.23	G5 (783.99)
45	792.58	1018.87		G (D)
48	824.30	1086.79		G# (D#)	15/8 (825 Hz)
49	835.15	1109.43	G#5/Ab5 (830.61)
53	880.00	1200	A5 (880.00)	A (E)
	932.xx		A#5/Bb5 (932.33)
	987.xx		B5 (987.77)
	1046.xx		C6 (1046.50)
	1108.xx		C#6/Db6 (1108.73)
	1174.xx		D6 (1174.66)
	1244.xx		D#6/Eb6 (1244.51)
	1318.xx		E6 (1318.51)
	1396.xx		F6 (1396.91)
	1479.xx		F#6/Gb6 (1479.98)
	1567.xx		G6 (1567.98)
	1661.xx		G#6/Ab6 (1661.22)
	1760.xx		A6 (1760.00)

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