69ed7: Difference between revisions
Contribution (talk | contribs) Created page with "69 equal divisions of the 7th harmonic (abbreviated 69ed7), is the tuning system that divides the 7th harmonic into 69 equal parts of about 48.82356 ¢ each. Each step represents a frequency ratio of <math>7^{\frac{1}{69}}</math>, or the 69th root of 7. == Theory == 69ed7 is a nice and strong 3.5.7.11.13 system. All ratios in the 3.5.7.11.13 subgroup and 21-integer-limit are approximated in 69ed7 with less than 7.7 ¢ error. 69ed7 is close to the different methods fo..." |
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* The Tenney–Euclidean regular temperement in the 3.5.7.11.13 subgroup mapped with [⟨39 57 69 85 91]] gives 48.82201 ¢. | * The Tenney–Euclidean regular temperement in the 3.5.7.11.13 subgroup mapped with [⟨39 57 69 85 91]] gives 48.82201 ¢. | ||
With a size of 48.82356 ¢, 69ed7 gives a better approximation than 39edt to Triple Bohlen-Pierce just intonation, yet still remaining a simple division. | With a size of 48.82356 ¢, 69ed7 gives a better approximation than [[39edt]] to Triple Bohlen-Pierce just intonation, yet still remaining a simple division. | ||
== Intervals and approximation to JI == | == Intervals and approximation to JI == | ||