11/10: Difference between revisions
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== Temperaments == | == Temperaments == | ||
11/10 may be treated implicitly as a comma in JI scales that for example do not find [[11/8]] and [[5/4]] above the same degree, but usually it makes much more sense to use it as a generator, such as the aforementioned very accurate strategy of making it a third of [[4/3]], leading to scales that look like [[porcupine]] but whose harmonies can more accurately be explained in a number of ways depending partially on the exact tempering used. If you use a half-octave period you get temperaments in the [[stearnsmic clan]] such as [[pogo]], [[supers]], or [[echidna]], all of which detemper [[100/99]] and [[121/120]] and efficiently and accurately find [[11-limit]] and (no-13's) [[17-limit]] harmonies. | |||
=== | === Exotemperaments === | ||
11/10 is tempered out in the [[patent val]]s of [[edo]]s 1, 2, 3 and 5. An example rank-2 [[exotemperament]] that treats it as a comma to be tempered out is [[very low accuracy temperaments #Antietam|antietam]]. | |||
== Trivia == | == Trivia == | ||
Revision as of 10:39, 13 December 2024
| Interval information |
undecimal submajor second
reduced
[sound info]
11/10, the large undecimal neutral second or undecimal submajor second, is an interval favored by Ptolemy. Depending on who you ask, this interval, on its own, is either considerably more or considerably less exotic than 12/11 or a number of other simple 11-limit intervals. If tempered sharp one could make the argument that it functions a bit more like a narrowed 10/9 in light of its usage in such a capacity in systems like 41edo and 63edo where 11/10 and 10/9 are tempered together (so that 100/99 is tempered out). Meanwhile, when tuned just or near-just, it functions as almost exactly a third of 4/3, a very xenmelodic role corresponding to tempering out 4000/3993.
Approximation
11/10 is approximated extremely precisely by 80edo and its multiples, with a chain of 80 11/10's failing to close at the octave by a mere third of a cent, close enough that you could theoretically tune an instrument to 80edo by ear using it if you had the patience.
Temperaments
11/10 may be treated implicitly as a comma in JI scales that for example do not find 11/8 and 5/4 above the same degree, but usually it makes much more sense to use it as a generator, such as the aforementioned very accurate strategy of making it a third of 4/3, leading to scales that look like porcupine but whose harmonies can more accurately be explained in a number of ways depending partially on the exact tempering used. If you use a half-octave period you get temperaments in the stearnsmic clan such as pogo, supers, or echidna, all of which detemper 100/99 and 121/120 and efficiently and accurately find 11-limit and (no-13's) 17-limit harmonies.
Exotemperaments
11/10 is tempered out in the patent vals of edos 1, 2, 3 and 5. An example rank-2 exotemperament that treats it as a comma to be tempered out is antietam.
Trivia
Coincidentally, the interval between the most common tuning frequency (A440) and the second most common AC electrical frequency (50 Hz) is exactly 44/5, or three octaves above an 11/10.