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Division of the tritave (3/1) into 27 equal parts


Dividing the interval of 3/1 into 27 equal parts gives a scale with a basic step of 70.44 cents, corresponding to 17.035 edo, which is nearly identical to one step of 17edo (70.59 cents). Hence it has similar melodic and harmonic properties as 17edo, with the difference that 27 is not a prime number.

27 being the third power of 3, and the base interval being 3/1, 27edt is a tuning where the number 3 prevails. This property seems to predestine 27edt as base tuning for Klingon music (since the tradtional Klingon number system is also based on 3). The rather harsh harmonic character of 27edt would suit very well, too.

See, e.g., http://launch.dir.groups.yahoo.com/group/tuning/message/86909 and http://www.klingon.org/smboard/index.php?topic=1810.0.

Intervals

degrees of 27edt
cents value
approximation in 17edo
0
0.00
0.00
1
70.44
70.59
2
140.89
141.18
3
211.33
211.76
4
281.77
282.35
5
352.21
352.94
6
422.66
423.53
7
493.10
494.12
8
563.54
564.71
9
633.99
635.29
10
704.43
705.88
11
774.87
776.47
12
845.31
847.06
13
915.76
917.65
14
986.20
988.24
15
1056.64
1058.82
16
1127.08
1129.41
17
1197.53
1200.00
18
1267.97
1270.59
19
1338.41
1341.18
20
1408.86
1411.76
21
1479.30
1482.35
22
1549.74
1551.94
23
1620.18
1623.53
24
1690.63
1694.12
25
1761.07
1764.71
26
1831.51
1835.29
27
1901.96
1905.88