27edt

From Xenharmonic Wiki
Jump to: navigation, search

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 Hekt Sigma Scale
27edt 17edo 27edt 17edo
1 70.443 70.588 48.148 48.248 Db
2 140.886 141.1765 96.296 96.495 C#
3 211.328 211.765 144.444 144.743 D
4 281.771 282.353 192.593 192.99 Eb
5 352.214 352.941 240.741 241.238 D#
6 422.657 423.529 288.889 289.485 E
7 493.099 494.118 337.037 337.733 Fb
8 563.542 564.706 385.185 385.981 E#
9 633.985 635.294 433.333 434.228 F
10 704.428 705.882 481.4815 482.476 G
11 774.871 776.471 529.63 530.723 Hb
12 845.313 847.059 577.778 578.971 G#
13 915.756 917.647 625.926 627.218 H
14 986.199 988.235 674.074 675.466 Jb
15 1056.642 1058.8235 722.222 723.7135 H#
16 1127.084 1129.412 770.37 771.961 J
17 1197.527 1200 818.5185 820.209 Kb
18 1267.97 1270.588 866.667 868.456 J#
19 1338.413 1341.1765 914.815 916.704 K
20 1408.856 1411.765 962.963 964.951 L
21 1479.298 1482.353 1011.111 1013.199 Ab
22 1549.741 1552.941 1059.259 1061.4465 L#
23 1620.184 1623.529 1107.407 1109.694 A
24 1690.627 1694.118 1155.556 1157.941 Bb
25 1761.069 1764.706 1203.704 1206.189 A#
26 1831.512 1835.294 1251.852 1254.437 B
27 1901.955 1905.882 1300 1302.684 C