| Prime factorization
|
13 × 19
|
| Step size
|
4.8583¢
|
| Fifth
|
144\247 (699.595¢)
|
| Semitones (A1:m2)
|
20:21 (97.17¢ : 102¢)
|
| Dual sharp fifth
|
145\247 (704.453¢)
|
| Dual flat fifth
|
144\247 (699.595¢)
|
| Dual major 2nd
|
42\247 (204.049¢)
|
| Consistency limit
|
3
|
| Distinct consistency limit
|
3
|
The 247 equal divisions of the octave (247EDO), or the 247(-tone) equal temperament (247TET, 247ET) when viewed from a regular temperament perspective, is the equal division of the octave into 247 parts of 4.8583 cents each.
Theory
In 247EDO, 144 degree represents 3/2 (2.36¢ flat), 80 degree represents 5/4 (2.35¢ sharp), 199 degree represents 7/4 (2.02¢ flat), and 113 degree represents 11/8 (2.33¢ flat). 247EDO lacks consistency to the 5 and higher odd-limit. It is the largest number EDO that interval representing 3/2 is flatter than that of 12EDO (700¢, compton fifth). It tempers out 126/125, 243/242 and 1029/1024 in the 11-limit patent mapping, so it supports the hemivalentino temperament (31&61e).
Approximation of odd harmonics in 247 EDO
| Odd harmonic
|
3
|
5
|
7
|
9
|
11
|
13
|
15
|
17
|
19
|
21
|
23
|
25
|
27
|
29
|
31
|
| Error
|
absolute (¢)
|
-2.36
|
+2.35
|
-2.02
|
+0.14
|
-2.33
|
-0.04
|
-0.01
|
+1.93
|
-1.16
|
+0.47
|
-1.55
|
-0.16
|
-2.22
|
+0.38
|
+1.52
|
| relative (%)
|
-49
|
+48
|
-42
|
+3
|
-48
|
-1
|
-0
|
+40
|
-24
|
+10
|
-32
|
-3
|
-46
|
+8
|
+31
|
| Steps (reduced)
|
391 (144)
|
574 (80)
|
693 (199)
|
783 (42)
|
854 (113)
|
914 (173)
|
965 (224)
|
1010 (22)
|
1049 (61)
|
1085 (97)
|
1117 (129)
|
1147 (159)
|
1174 (186)
|
1200 (212)
|
1224 (236)
|