SandBox: Difference between revisions
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== Tempering out the comma == | == Tempering out the comma == | ||
As shown above, the largest comma between the hyper-scale and the hypo-scale, produced by the two generators <math>φ</math> and <math>δ_s</math>, is a mere <math>{δ_s^{-6}} {φ^11}</math> ≈ 8.809¢, much smaller and more imperceptible than both the [[Pythagorean comma]] (23.460¢) and the [[Syntonic comma]] (81/80, 21.506¢). Hence, it is practically safe to temper it out: | As shown above, the largest comma between the hyper-scale and the hypo-scale, produced by the two generators <math>φ</math> and <math>δ_s</math>, is a mere <math>{δ_s^{-6}} {φ^{11}}</math> ≈ 8.809¢, much smaller and more imperceptible than both the [[Pythagorean comma]] (23.460¢) and the [[Syntonic comma]] (81/80, 21.506¢). Hence, it is practically safe to temper it out: | ||
<math>{δ_s^{-6}} {φ^11} = 1</math> | <math>{δ_s^{-6}} {φ^{11}} = 1</math> | ||
<math>φ^11 = δ_s^{6}</math> | <math>φ^11 = δ_s^{6}</math> | ||