27edt

27edt means 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 70.4428 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

Steps	Cent	~17edo	Sigma Scale
1	70.443	70.588	Db
2	140.886	141.176	C#
3	211.328	211.765	D
4	281.771	282.353	Eb
5	352.214	352.941	D#
6	422.657	423.529	E
7	493.099	494.118	Fb
8	563.542	564.706	E#
9	633.985	635.294	F
10	704.428	705.882	G
11	774.871	776.471	Hb
12	845.313	847.059	G#
13	915.756	917.647	H
14	986.199	988.235	Jb
15	1056.642	1058.824	H#
16	1127.084	1129.412	J
17	1197.527	1200.000	Kb
18	1267.970	1270.588	J#
19	1338.413	1341.176	K
20	1408.856	1411.765	L
21	1479.298	1482.353	Ab
22	1549.741	1552.941	L#
23	1620.184	1623.529	A
24	1690.627	1694.118	Bb
25	1761.069	1764.706	A#
26	1831.512	1835.294	B
27	1901.955	1905.882	C