36edo: Difference between revisions
→Related equal tunings: correct data. Make the errors signed |
→Theory: Reduced number of subheadings |
||
| Line 21: | Line 21: | ||
Another 5-limit alternative val is {{val| 36 57 83 }} (36c-edo), which is similar to the patent val but has 5/4 mapped to the 367{{c}} submajor third rather than the major third. This mapping supports very sharp [[porcupine]] temperament using 5\36 as a generator. | Another 5-limit alternative val is {{val| 36 57 83 }} (36c-edo), which is similar to the patent val but has 5/4 mapped to the 367{{c}} submajor third rather than the major third. This mapping supports very sharp [[porcupine]] temperament using 5\36 as a generator. | ||
=== | === Additional properties === | ||
36edo has almost 50% relative error on harmonics 5/1 and 11/1. This means that whether one [[octave stretch|stretches]] or [[octave shrinking|compresses]] the octave, either way it will improve 36edo's approximations of [[JI]], but in opposite directions, as long as it is done by the right amount. | 36edo has almost 50% relative error on harmonics 5/1 and 11/1. This means that whether one [[octave stretch|stretches]] or [[octave shrinking|compresses]] the octave, either way it will improve 36edo's approximations of [[JI]], but in opposite directions, as long as it is done by the right amount. | ||
36edo also offers a good approximation to the [[acoustic phi|acoustic golden ratio]], as 25\36. [[Heinz Bohlen]] proposed 36edo as a suitable temperament for approximating his 833-cents scale. The 13th harmonic (octave reduced) is so closely mapped on [[acoustic phi]] that 36edo could be treated as a 2.3.7.ϕ.17 temperament. | 36edo also offers a good approximation to the [[acoustic phi|acoustic golden ratio]], as 25\36. [[Heinz Bohlen]] proposed 36edo as a suitable temperament for approximating his 833-cents scale. The 13th harmonic (octave reduced) is so closely mapped on [[acoustic phi]] that 36edo could be treated as a 2.3.7.ϕ.17 temperament. | ||