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 {{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, however, 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 due to [[100/99]] being tempered out. Meanwhile, when tuned just or near-just, it not only has the very exotic melodic role of being almost exactly a third of [[4/3]], leading to [[4000/3993]] being tempered out, but is also very close in size to a stack consisting of an [[apotome]] and [[33/32]], leading to the [[schisma]] being tempered out. Assuming you go with either of the aforementioned options, keeping 11/10 distinct from 12/11 ensures that 11/10 has a way of bridging quartertone-based chords with more typical [[5-limit]] and Pythagorean chords as a sort of step between notes, however, if you temper out [[121/120]], expect this ability to vanish.

'''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, however, 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 due to [[100/99]] being tempered out. Meanwhile, when tuned just or near-just, it not only has the very exotic melodic role of being almost exactly a third of [[4/3]], leading to [[4000/3993]] being fudged or tempered out, but is also very close in size to a stack consisting of an [[apotome]] and [[33/32]], leading to the [[schisma]] being fudged or tempered out. Assuming you go with either of the aforementioned options, keeping 11/10 distinct from 12/11 ensures that 11/10 has a way of bridging quartertone-based chords with more typical [[5-limit]] and Pythagorean chords as a sort of step between notes, however, if you temper out [[121/120]], expect this ability to vanish.

== Approximation ==

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 {{Wikipedia| Neutral interval #Second }}
-'''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, however, 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 due to [[100/99]] being tempered out.  Meanwhile, when tuned just or near-just, it not only has the very exotic melodic role of being almost exactly a third of [[4/3]], leading to [[4000/3993]] being tempered out, but is also very close in size to a stack consisting of an [[apotome]] and [[33/32]], leading to the [[schisma]] being tempered out.  Assuming you go with either of the aforementioned options, keeping 11/10 distinct from 12/11 ensures that 11/10 has a way of bridging quartertone-based chords with more typical [[5-limit]] and Pythagorean chords as a sort of step between notes, however, if you temper out [[121/120]], expect this ability to vanish.
+'''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, however, 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 due to [[100/99]] being tempered out.  Meanwhile, when tuned just or near-just, it not only has the very exotic melodic role of being almost exactly a third of [[4/3]], leading to [[4000/3993]] being fudged or tempered out, but is also very close in size to a stack consisting of an [[apotome]] and [[33/32]], leading to the [[schisma]] being fudged or tempered out.  Assuming you go with either of the aforementioned options, keeping 11/10 distinct from 12/11 ensures that 11/10 has a way of bridging quartertone-based chords with more typical [[5-limit]] and Pythagorean chords as a sort of step between notes, however, if you temper out [[121/120]], expect this ability to vanish.
 == Approximation ==