680edo: Difference between revisions
m changed EDO intro to ED intro |
m fixed headings |
||
| Line 2: | Line 2: | ||
{{ED intro}} | {{ED intro}} | ||
== Odd harmonics == | |||
680edo retains a reasonable 3rd and 5th [[harmonic]], though nowhere near the accuracy of the prior multiple [[612edo]]; as a multiple of [[34edo]], 680edo borrows that edo's accurate representation of the interval [[25/24]], implying that the error on [[prime]] 3 is approximately twice that on prime 5. However, 680edo is most notable for its approximation of the 7th harmonic, 680 being the denominator of a semiconvergent to log<sub>2</sub>([[7/4]]). | 680edo retains a reasonable 3rd and 5th [[harmonic]], though nowhere near the accuracy of the prior multiple [[612edo]]; as a multiple of [[34edo]], 680edo borrows that edo's accurate representation of the interval [[25/24]], implying that the error on [[prime]] 3 is approximately twice that on prime 5. However, 680edo is most notable for its approximation of the 7th harmonic, 680 being the denominator of a semiconvergent to log<sub>2</sub>([[7/4]]). | ||
| Line 9: | Line 9: | ||
{{Harmonics in equal|680|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 680edo (continued)}} | {{Harmonics in equal|680|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 680edo (continued)}} | ||
== Subsets and supersets == | |||
Since 680 factors into {{factorization|680}}, 680edo has subset edos {{EDOs| 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, and 340 }}. | Since 680 factors into {{factorization|680}}, 680edo has subset edos {{EDOs| 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, and 340 }}. | ||
{{todo|expand}} | {{todo|expand}} | ||