11/10: Difference between revisions
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{{Wikipedia| Neutral interval #Second }} | {{Wikipedia| Neutral interval #Second }} | ||
'''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|S10]] is tempered out). | '''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|S10]] 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 ([[100/99]])/([[121/120]]) = [[4000/3993|S10/S11]] = ([[4/3|12/9]])/([[11/10]])<sup>3</sup>. | ||
== Approximation == | == Approximation == | ||
Revision as of 23:31, 10 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 S10 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 (100/99)/(121/120) = S10/S11 = (12/9)/(11/10)3.
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 is treated as a comma in edos 1, 2, 3, 5, and some very low accuracy temperaments such as antietam. If it is used as a generator instead, it produces porcupine, although it is slightly sharper than the optimal tuning for porcupine and does not fit the 80edo patent val mapping.
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.