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The 30 equal division divides the octave into 30 equal steps of precisely 40 cents each. Its patent val is a doubled version of the patent val for 15edo through the 11-limit, so 30 can be viewed as a contorted version of 15. In the 13-limit it supplies the optimal patent val for quindecic temperament.

However, 5\30 is 200 cents, which is a good (and familiar) approximation for 9/8, and hence 30 can be viewed inconsistently, as having a 9' at 95\30 as well as a 9 at 96\30. Instead of the 18\30 fifth of 720 cents, 30 also makes available a 17\30 fifth of 680 cents. This is an ideal tuning for pelogic (5-limit mavila), which tempers out 135/128. When 30 is used for pelogic, 5\30 can again be used inconsistently as a 9/8.

Below is a plot of the Z function around 30:

plot30.png


Intervals

Step
Cents
ups and downs notation
0

P1
unison
D
1
40
^1, ^m2
up unison, upminor 2nd
D^, Eb^
2
80
^^1, v~2
double-up unison, downmid 2nd
D^^, Eb^^
3
120
~2
mid 2nd
Ev3
4
160
^~2
upmid 2nd
Evv
5
200
vM2
downmajor 2nd
Ev
6
240
M2, m3
major 2nd, minor 3rd
E, F
7
280
^m3
upminor 3rd
F^
8
320
v~3
downmid 3rd
F^^
9
360
~3
mid 3rd
F^3
10
400
^~3
upmid 3rd
F#vv
11
440
vM3, v4
downmajor 3rd, down 4th
F#v, Gv
12
480
P4
perfect 4th
G
13
520
^4, ^d5
up 4th, updim 5th
G^, Ab^
14
560
^^4, ^^d5
double-up 4th, double-up dim 5th
G^^, Ab^^
15
600
^34, v35
triple-up 4th, triple-down 5th
G^3, Av3
16
640
vvA4, vv5
double-down aug 4th, double-down 5th
G#vv, Avv
17
680
vA4, v5
downaug 4th, down 5th
G#v, Av
18
720
P5
perfect 5th
A
19
760
^5, ^m6
up 5th, upminor 6th
A^, Bb^
20
800
v~6
downmid 6th
Bb^^
21
840
~6
mid 6th
Bv3
22
880
^~6
upmid 6th
Bvv
23
920
vM6
downmajor 6th
Bv
24
960
M6. m7
major 6th, minor 7th
B, C
25
1000
^m7
upminor 7th
C^
26
1040
v~7
downmid 7th
C^^
27
1080
~7
mid 7th
C^3
28
1120
^~7, vv8
upmid 7th, double-down 8ve
C#vv, Dvv
29
1160
vM7, v8
downmajor 7th, down 8ve
C#v, Dv
30
1200
P8
8ve
D

Commas

30 EDO tempers out the following commas. (Note: This assumes the val < 30 48 70 84 104 111 | .)
Comma
Monzo
Value (Cents)
Name 1
Name 2
Name 3
256/243
| 8 -5 >
90.22
Limma
Pythagorean Minor 2nd

250/243
| 1 -5 3 >
49.17
Maximal Diesis
Porcupine Comma

128/125
| 7 0 -3 >
41.06
Diesis
Augmented Comma

15625/15552
| -6 -5 6 >
8.11
Kleisma
Semicomma Majeur

1029/1000
| -3 1 -3 3 >
49.49
Keega


49/48
| -4 -1 0 2 >
35.70
Slendro Diesis


64/63
| 6 -2 0 -1 >
27.26
Septimal Comma
Archytas' Comma
Leipziger Komma
64827/64000
| -9 3 -3 4 >
22.23
Squalentine


875/864
| -5 -3 3 1 >
21.90
Keema


126/125
| 1 2 -3 1 >
13.79
Septimal Semicomma
Starling Comma

4000/3969
| 5 -4 3 -2 >
13.47
Octagar


1029/1024
| -10 1 0 3 >
8.43
Gamelisma


6144/6125
| 11 1 -3 -2 >
5.36
Porwell


250047/250000
| -4 6 -6 3 >
0.33
Landscape Comma


100/99
| 2 -2 2 0 -1 >
17.40
Ptolemisma


121/120
| -3 -1 -1 0 2 >
14.37
Biyatisma


176/175
| 4 0 -2 -1 1 >
9.86
Valinorsma


65536/65219
| 16 0 0 -2 -3 >
8.39
Orgonisma


385/384
| -7 -1 1 1 1 >
4.50
Keenanisma


441/440
| -3 2 -1 2 -1 >
3.93
Werckisma


4000/3993
| 5 -1 3 0 -3 >
3.03
Wizardharry


3025/3024
| -4 -3 2 -1 2 >
0.57
Lehmerisma



Music


Fifteen Short Pieces by Todd Harrop