dyadic 53 JI from Philolaos tone-9-divsion 8:9=72:73:74:75:76:77:78:79:80:81

http://en.wikipedia.org/wiki/Anicius_Manlius_Severinus_Boethius
reports that
http://en.wikipedia.org/wiki/Philolaus
did so.

tune for that purpose the D2-string on a
http://en.wikipedia.org/wiki/Double_bass
down to exactly 72 Hz instead originally
http://en.wikipedia.org/wiki/Piano_key_frequencies
"#18 D D2 73.4162" a tone below
http://en.wikipedia.org/wiki/Deep_C

then play in commatic order the superparticular
sequence:

D\\ 72 Hz
D\_ 73
D__ 74
D/_ 75
D// 76
Eb\ 77
Eb_ 78
D#_ 79
E\\ 80
E\_ 81

memorize that 9 absolute pitches in yours mind
then fit inbtween P's 9-fold subdivision tempered 5ths,
that deviate from just pure 3:2 less than 1001:1000
= 0.1 %, but match the above frequencies exactly.

53JI-cycle of 5ths:

C\\ 1 unison @ 256 Hz middle-C\\
G\\ 3
D\\ 9
A\\ 27
E\\ 81
B\\ 243
Gb\ 729
Db\ (2187 <) 2188 1094 547
Ab\ (1641 <) 1642 821
Eb\ (2436 <) 2464 1232 616 308 154 _77_ = 11*7
Bb\ 237
F\ 693
C\ (2079 >) 2078 1039
G\ (3117 >) 3116 1558 779
D\ (2337 >) 2336 ..................... _73_
A\ 219
E\ 657
B\ 1971
Gb (5913 >) 5914 2957
Db (8871 >) 8872 4436 2218 1109
Ab (3327 >) 3326 ...................... 13
Eb ................................_78_ 39
Bb 117
F 351
C 1053
G (3159 >) 3158 1579
D (4737 >) 4736 ....................... _74_ 37
A 111
E 333
B 999
F# 2997
C# (8991 >) 8990 4495
G# (13485 >) 13484 6742 3371
D# (10113 >) 10112 ..........:128...... _79_
A# 237
F/ 711
C/ 2133
D/ (6933 >) 6400 ............... 25
A/ ......................... _75_
E/ 225
E/ 675
B/ (2025 >) 2024 1012 506 253
F#/ 759
C#/ (2277 >) 2276 1138 569
G#/ 1707
D# (5121 >) 5120.............. _80_ 40 20 10 5
A#/ 15
F// 45
C// 135
G// 405
D// (1215 >) 1216 608 304 152 _76_ 38 19
A// (57 114 228 456 912 1824 >) 1823 (> 1822 911)
E// = F\\ (2733 >) 2732 1366 683
B// = C\\ (2049 >) 2048 .... 256 ... 1

due to unison = 1:1 all pitches become
http://en.wikipedia.org/wiki/Dyadic_fraction

dyadic53tone9div.scl
!
from Philolaos tone-9-divsion 8:9=72:73:74:75:76:77:78:79:80:81
!
53
!
1039/1024 ! C\_ 519.5
1053/1024 ! C__ 526.5
2133/2048 ! C/_ 533.25
135/128 ! _ C// 540
547/512 ! _ Db\
1109/1024 ! Db_ 554.5
4495/4096 ! C#_ 561.675
569/512 ! _ C#/ 568.5
9/8 ! _ D\\ 72
73/64 ! D\_ 73
37/32 ! D__ 74
75/64 ! D/_ 75
19/16 ! D// 76
77/64 ! Eb\ 77
39/32 ! Eb_ 78
79/64 ! D#_ 79
5/4 ! _ D#/ 80
81/80 ! E\\ 81
657/512 ! E\
333/256 ! E
675/512 ! E/
683/512 ! E// = F\\
693/512 ! F\
351/256 ! F
711/512 ! F/
45/32 ! _ F//
729/512 ! Gb\ 3^6
2957/2048!Gb
2997/2048!F#
759/512 ! F#/
3/2 ! _ _ G\\
779/512 ! G\
1579/1024!G
25/16 ! _ G/
405/256 ! G//
821/512 ! Ab\
13/8
3371/2048
1707/1024
27/16
219/128
111/64
225/128
1823/1024
231/128
117/64
237/128
15/8
243/128
495/256
999/512
253/128
2/1

A.S.