SandBox: Difference between revisions
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<math>φ^11 = δ_s^{6}</math> | <math>φ^11 = δ_s^{6}</math> | ||
<math>φ = | <math>φ = {\sqrt[11]{δ_s}}^{6}</math> OR <math>δ_s = {\sqrt[6]{φ}}^{11}</math> | ||
The solution on the left provides for an equal division of <math>δ_s</math> into 11 notes to approximate <math>φ</math> as step 6\11. Reversely, the alternative solution provides for an equal division of <math>φ</math> into 6 notes to approximate the period <math>δ_s</math> with 5 extra steps above <math>φ</math>. The former equal temperament puts more weight on the silver ratio while the latter preserves the golden ratio. | The solution on the left provides for an equal division of <math>δ_s</math> into 11 notes to approximate <math>φ</math> as step 6\11. Reversely, the alternative solution provides for an equal division of <math>φ</math> into 6 notes to approximate the period <math>δ_s</math> with 5 extra steps above <math>φ</math>. The former equal temperament puts more weight on the silver ratio while the latter preserves the golden ratio. | ||
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|- | |- | ||
|''11'' | |''11'' | ||
|<math>{\sqrt[6]{φ}}^11</math> | |<math>{\sqrt[6]{φ}}^{11}</math> | ||
|''1527.332'' | |''1527.332'' | ||
| - | | - | ||