editing disabled

47 tone Equal Temperament


47-EDO divides the octave into 47 equal parts of 25.5319 cents each. It has a fifth which is 12.5933 cents flat, unless you use the alternative fifth which is 12.9386 cents sharp, similar to 35edo. It has therefore not aroused much interest, but its best approximation to 9/8 is actually quite good, one-third of a cent sharp. It does a good job of approximating the 2.9.5.7.33.13.17.57.69 23-limit 2*47 subgroup of the 23-limit, on which it tempers out the same commas as 94edo. It provides a good tuning for baldy and silver temperaments and relatives.

47edo is the 15th prime edo, following 43edo and preceding 53edo.

47edo is a regular edo because its 5th falls between 4\7 = 686¢ and 3\5 = 720¢. (Its alternate 5th does as well.) 47edo is one of the most difficult regular edos to notate, because no other regular edo's 5th is as flat (see 42edo for the opposite extreme).

A notation using the best 5th has major and minor 2nds of 7 and 6 edosteps respectively, with the naturals creating a roughly 7edo-ish scale:
D * * * * * * E * * * * * F * * * * * * G * * * * * * A * * * * * * B * * * * * C * * * * * * D
D# is next to D. This notation requires triple, quadruple and in some keys, quintuple or more sharps and flats. For example, a 0-15-27-38 chord (an approximate 4:5:6:7) on the note three edosteps above D would be spelled either as D#3 - F#5 - A#3 - C# or as Eb4 - Gbb - Ab4 - Db6. This is an aug-three double-dim-seven chord, written D#3(A3)dd7 or Eb4(A3)dd7. It could also be called a sharp-three triple-flat-seven chord, written D#3(#3)b37 or Eb4(#3)b37.

Using the 2nd best 5th is even more awkward. The major 2nd is 9 edosteps and the minor is only one. The naturals create a roughly 5edo-ish scale, with two of the notes inflected by a comma-sized edostep:
D * * * * * * * * E F * * * * * * * * G * * * * * * * * A * * * * * * * * B C * * * * * * * * D
D# is next to E. This notation requires quadruple, quintuple, and even sextuple ups and downs, as well as single sharps and flats.

Intervals of 47edo


Degree
Size (Cents)
relative notation
absolute notation
0
0.0000
perfect unison
P1
D
1
25.5319
aug 1sn
A1
D#
2
51.0638
double-aug 1sn
AA1
Dx
3
76.5957
triple-aug 1sn, triple-dim 2nd
A31, d32
D#3, Eb4
4
102.1277
double-dim 2nd
dd2
Eb3
5
127.6596
dim 2nd
d2
Ebb
6
153.1915
minor 2nd
m2
Eb
7
178.7234
major 2nd
M2
E
8
204.2553
aug 2nd
A2
E#
9
229.7872
double-aug 2nd
AA2
Ex
10
255.3191
triple-aug 2nd, triple-dim 3rd
A32, d33
E#3, Fb3
11
280.8511
double-dim 3rd
dd3
Fbb
12
306.3830
dim 3rd
d3
Fb
13
331.9149
minor 3rd
m3
F
14
357.4468
major 3rd
M3
F#
15
382.9787
aug 3rd
A3
Fx
16
408.5106
double-aug 3rd
AA3
F#3
17
434.0426
triple-aug 3rd, triple-dim 4th
A33, d34
F#4, Gb3
18
459.5745
double-dim 4th
dd4
Gbb
19
485.1064
dim 4th
d4
Gb
20
510.6383
perfect 4th
P4
G
21
536.1702
aug 4th
A4
G#
22
561.7021
double-aug 4th
AA4
Gx
23
587.2340
triple-aug 4th
A34
G#3
24
612.7660
triple-dim 5th
d35
Ab3
25
638.2979
double-dim 5th
dd5
Abb
26
663.8298
dim 5th
d5
Ab
27
689.3617
perfect 5th
P5
A
28
714.8936
aug 5th
A5
A#
29
740.4255
double-aug 5th
AA5
Ax
30
765.9574
triple-aug 5th, triple-dim 6th
A35, d36
A#3, Bb4
31
791.4894
double-dim 6th
dd6
Bb3
32
817.0213
dim 6th
d6
Bbb
33
842.5532
minor 6th
m6
Bb
34
868.0851
major 6th
M6
B
35
893.6170
aug 6th
A6
B#
36
919.1489
double-aug 6th
AA6
Bx
37
944.6809
triple-aug 6th, triple-dim 7th
A36, d37
B#3, Cb3
38
970.2128
double-dim 7th
dd7
Cbb
39
995.7447
dim 7th
d7
Cb
40
1021.2766
minor 7th
m7
C
41
1046.8085
major 7th
M7
C#
42
1072.3404
aug 7th
A7
Cx
43
1097.8723
double-aug 7th
AA7
C#3
44
1123.4043
triple-aug 7th, triple-dim 8ve
A37, d38
C#4, Db3
45
1148.9362
double-dim 8ve
dd8
Dbb
46
1174.4681
dim 8ve
d8
Db
47
1200.0000
perfect 8ve
P8
D