Kite's thoughts on fifthspans: Difference between revisions
Created page with "The fifthspan is an attribute of every interval in certain edos and rank-2 temperaments. == 12-edo example == For every interval of..." |
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* Bill Wesley's [https://www.arraymbira.com/ array mbiras] | * Bill Wesley's [https://www.arraymbira.com/ array mbiras] | ||
* Starr Labs' [https://www.starrlabs.com/product/microzone-u648/ Microtone keyboard] | * Starr Labs' [https://www.starrlabs.com/product/microzone-u648/ Microtone keyboard] | ||
When playing these instruments, one might want to locate a specific ratio on the keyboard. The dot product of the ratio's monzo with the edo's fifthspan mapping, reduced modulo N, gives the ratio's fifthspan, and hence its location on the instrument. For example, the fifhspan of 7/5 in 31-edo is (0 0 -1 1) ⋅ (0 1 4 10) = -4 + 10 = 6. Whereas in 41-edo, it's (0 0 -1 1) ⋅ (0 1 -8 -14) = -6. | When playing these instruments, one might want to locate a specific ratio on the keyboard. The dot product of the ratio's monzo with the edo's fifthspan mapping, reduced modulo N, gives the ratio's fifthspan, and hence its location on the instrument. For example, the fifhspan of 7/5 in 31-edo is (0 0 -1 1) ⋅ (0 1 4 10) = -4 + 10 = 6. Whereas in 41-edo, it's (0 0 -1 1) ⋅ (0 1 -8 -14) = -6. Note that this location is based on the indirect (consistent) mapping, not the direct (possibly inconsistent) mapping. The consistent mapping is arguably of greater value on an isomorphic keyboard. | ||