70edo: Difference between revisions
→Theory: improve linking, cut out unnecessary formatting, fix math errors. |
m →Theory: increase readability of errors; this shows both how it works nicely as a subgroup temperament but also why one may want to extend it to 140 ET |
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== Theory == | == Theory == | ||
{{Harmonics in equal|70}} | {{Harmonics in equal|70|columns=10|intervals=prime}} | ||
{{Harmonics in equal|70|columns=8|intervals=prime|start=11}} | |||
This tuning was singled out by William Stoney in his article "Theoretical Possibilities for Equally Tempered Systems" (in the book [https://monoskop.org/images/c/c3/Lincoln_Harry_B_ed_The_Computer_and_Music_1970.pdf The Computer and Music]) as one of the six best systems of size 72 or smaller, along with [[72edo|72]], [[65edo|65]], [[58edo|58]], [[53edo|53]], and [[41edo|41]]. These other systems have had notice paid to them, but the same does not seem to be true of 70, which seems to have been ignored ever since, despite it's excellent 5th, which is the 4th number in the convergent sequence to the [[Logarithmic_approximants#Argent_temperament|silver ratio]], following [[29edo]], [[12edo]] & [[5edo]] and preceding [[169edo]]. | This tuning was singled out by William Stoney in his article "Theoretical Possibilities for Equally Tempered Systems" (in the book [https://monoskop.org/images/c/c3/Lincoln_Harry_B_ed_The_Computer_and_Music_1970.pdf The Computer and Music]) as one of the six best systems of size 72 or smaller, along with [[72edo|72]], [[65edo|65]], [[58edo|58]], [[53edo|53]], and [[41edo|41]]. These other systems have had notice paid to them, but the same does not seem to be true of 70, which seems to have been ignored ever since, despite it's excellent 5th, which is the 4th number in the convergent sequence to the [[Logarithmic_approximants#Argent_temperament|silver ratio]], following [[29edo]], [[12edo]] & [[5edo]] and preceding [[169edo]]. | ||