11/10: Difference between revisions

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'''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>~~.

'''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 ==

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== 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 ==

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 }}
 {{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). 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>.
+'''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 ==
@@ Line 11: / Line 11: @@
 == Temperaments ==
-/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.
+/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 ==