100ed10: Difference between revisions
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100ed10 can be labeled as a "Homo sapiens tunning", by analogy of how [[27edt|27ed3]] is labeled "Klingon tuning". | 100ed10 can be labeled as a "Homo sapiens tunning", by analogy of how [[27edt|27ed3]] is labeled "Klingon tuning". | ||
== Theory == | == Theory == | ||
{{Harmonics in equal|100|10}} | {{Harmonics in equal|100|10|columns=10}} | ||
The step error of any given harmonic in 100ed10 can be simply extracted through 3rd and 4th base digits of the decimal logarithm. | 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" | 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) | |||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
[[Category:Ed10]] | [[Category:Ed10]] | ||