11/10: Difference between revisions
m im not sure why i previously wrote that they are all find the (no-13's) 17-limit "efficiently"; this isnt true; echidna's 5 and 11 are much simpler than pogo's and supers' |
m it's harry which is high accuracy; also clarify the gen |
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Using 11/10 as a generator tempering out 4000/3993 (as previously mentioned) leads to scales that look like [[porcupine]] but whose harmonies can more accurately be explained. With a half-octave period, a generator of 11/10 leads to temperaments in the [[stearnsmic clan]] such as [[pogo]], [[supers]], or [[echidna]], all of which detemper [[100/99]] and [[121/120]] and accurately find [[11-limit]] and (no-13's) [[17-limit]] harmonies. Of these, echidna's mapping of the no-13's 17-limit is the simplest, though all three have the same mapping of the 2.3.7.11/10.17 subgroup so that they only differ on the mapping of 5 and 11. The complexity of 5 and 11 in pogo are used to increase accuracy, being a weak schismic extension. That leaves supers as the odd one out; if you are using an edo tuning for it, 58edo supports echidna while 94edo supports pogo, so it seems to exist as a portable alternate way of finding primes 5 and 11 across systems, unless you use the 152edo tuning, which requires using the second-best mapping of 13 (the 152f [[val]]). | Using 11/10 as a generator tempering out 4000/3993 (as previously mentioned) leads to scales that look like [[porcupine]] but whose harmonies can more accurately be explained. With a half-octave period, a generator of 11/10 leads to temperaments in the [[stearnsmic clan]] such as [[pogo]], [[supers]], or [[echidna]], all of which detemper [[100/99]] and [[121/120]] and accurately find [[11-limit]] and (no-13's) [[17-limit]] harmonies. Of these, echidna's mapping of the no-13's 17-limit is the simplest, though all three have the same mapping of the 2.3.7.11/10.17 subgroup so that they only differ on the mapping of 5 and 11. The complexity of 5 and 11 in pogo are used to increase accuracy, being a weak schismic extension. That leaves supers as the odd one out; if you are using an edo tuning for it, 58edo supports echidna while 94edo supports pogo, so it seems to exist as a portable alternate way of finding primes 5 and 11 across systems, unless you use the 152edo tuning, which requires using the second-best mapping of 13 (the 152f [[val]]). | ||
Using sqrt(11/10) as a generator leads to low-complexity [[Nautilus]] with one period to the octave and high-accuracy [[Harry]] | Using sqrt(11/10) (22/21[[~]]21/20) as a generator leads to the low-complexity [[Nautilus]] with one period to the octave, and if you use two periods to the octave with this generator you get the high-accuracy temperament [[Harry]]; using cbrt(11/10) as a generator leads to [[Escapade]] with one period to the octave. | ||
== See also == | == See also == | ||