11/10: Difference between revisions
Restore some old discussions. -s-expressions in the opening section since learning about the basics of a JI interval shouldn't rely on that knowledge |
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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. | '''11/10''', the '''large undecimal neutral second''' or '''undecimal submajor second''', is an interval favored by {{w|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 == | == Approximation == | ||
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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 [[echidna]], a [[hedgehog]] lookalike that detempers [[100/99]] and [[121/120]] and which efficiently and accurately finds [[11-limit]] and (no-13's) [[17-limit]] harmonies. | 11/10 is treated as a comma in edos 1, 2, 3, 5, and some very low accuracy temperaments such as [[Very low accuracy temperaments #Antietam|antietam]]. | ||
It 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 [[echidna]], a [[hedgehog]] lookalike that detempers [[100/99]] and [[121/120]] and which efficiently and accurately finds [[11-limit]] and (no-13's) [[17-limit]] harmonies. | |||
== Trivia == | == Trivia == | ||
Revision as of 09:03, 12 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 is treated as a comma in edos 1, 2, 3, 5, and some very low accuracy temperaments such as antietam.
It 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 echidna, a hedgehog lookalike that detempers 100/99 and 121/120 and which efficiently and accurately finds 11-limit and (no-13's) 17-limit harmonies.
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.