100ed10

From Xenharmonic Wiki
Jump to navigation Jump to search

The 100 equal divisions of the 10th harmonic is a nonoctave tuning of about 39.8631 steps each. It corresponds to 30.102999 EDO, the first digits of the decimal logarithm of 2. It can be thought of as 30edo, but with 10/1 instead of 2/1 being just.

100ed10 can be labeled as a "Homo sapiens tunning", by analogy of how 27ed3 is labeled "Klingon tuning".

Theory

Approximation of harmonics in 100ed10
Harmonic 2 3 4 5 6 7 8 9 10 11
Error absolute (¢) -4.1 +11.5 -8.2 +4.1 +7.4 +19.5 -12.3 -16.9 +0.0 -5.6
relative (%) -10 +29 -21 +10 +18 +49 -31 -42 +0 -14
Steps
(reduced)
30
(30)
48
(48)
60
(60)
70
(70)
78
(78)
85
(85)
90
(90)
95
(95)
100
(0)
104
(4)

The step error of any given harmonic in 100ed10 can be simply extracted through 3rd and 4th base digits of the decimal logarithm.

100ed10 contains a unique coincidence - it is contorted order-10 in the 2.5 subgroup, which makes up the number 10. In the 2.3.5, it is contorted order-2. While in the 7-limit it no longer has contorsion, the individual harmonics still do derive from smaller ED10s - 2.7 subgroup is contorted order-5. 100ed10 is suitable for use with the 2.5.11.17 subgroup, a significant departure from it simply being "30edo with stretched octaves", and it is suitable with the following commas:

  • [7, -3, 0, 0⟩ (128/125)
  • [0, -5, 1, 2⟩ (3179/3125)
  • [7, 2, -1, -2⟩ (3200/3179)
  • [-1, -2, 4, -2⟩ (14641/14450)
  • [14, -1, -1, -2⟩ (16384/15895)
  • [8, -1, -4, 2⟩ (73984/73205)