55/54: Difference between revisions

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'''55/54''', the '''undecimal diasecundal comma''', otherwise known as the '''eleventyfive comma''' or the '''telepathma''', is an [[11-limit]] [[superparticular]] interval that marks the difference between the [[6/5|classic minor third (6/5)]] and the [[11/9|undecimal neutral third (11/9)]], between the [[5/4|classic major third (5/4)]] and the [[27/22|rastmic neutral third (27/22)]], as well as the difference between the [[55/32|keenanismic supermajor sixth (55/32)]] and the [[27/16|Pythagorean major sixth (27/16)]]. This means that 6/5 and 11/9 are equated – as are 55/32 and 27/16 – when this comma is tempered out. [[EDO]]s that temper out this interval include {{EDOs| 5, 7, 8, 10, 15, 17, 22, 27, 29, 30, 32, 37, 42, 44, 51, 54, 59 and 66}}.

When treated as an interval in its own right, it acts as a sort of parachroma in much the same fashion as [[33/32]], from which it differs by a [[81/80|syntonic comma]]. However, given that it's noticeably smaller in size than 33/32, one can also easily use it as either an [[Wikipedia:Appoggiatura|appoggitura]], an [[Wikipedia:Acciaccatura|acciaccatura]], or a quick passing tone. Tempering out the [[3025/3024|lehmerisma]] equates this interval with [[56/55]], splitting the [[28/27]] septimal chroma into two equal halves. Furthermore, when the [[385/384|keenanisma]] is tempered out, 55/54 is equated with [[64/63]], and it is partially on this basis that one can reasonably make the argument that 64/63 can act as the septimal equivalent for 55/54.

When treated as an interval in its own right, it acts as a sort of parachroma in much the same fashion as [[33/32]], from which it differs by a [[81/80|syntonic comma]]. However, given that it's noticeably smaller in size than 33/32, one can also easily use it in melodies as either an [[Wikipedia:Appoggiatura|appoggitura]], an [[Wikipedia:Acciaccatura|acciaccatura]], or a quick passing tone. Tempering out the [[3025/3024|lehmerisma]] equates this interval with [[56/55]], splitting the [[28/27]] septimal chroma into two equal halves. Furthermore, when the [[385/384|keenanisma]] is tempered out, 55/54 is equated with [[64/63]], and it is partially on this basis that one can reasonably make the argument that 64/63 can act as the septimal equivalent for 55/54.

It is also the difference between the universally accepted 440 Hz pitch standard and the esoteric and non-scientific, but rather popular proposed 432 Hz pitch standard.

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 '''55/54''', the '''undecimal diasecundal comma''', otherwise known as the '''eleventyfive comma''' or the '''telepathma''', is an [[11-limit]] [[superparticular]] interval that marks the difference between the [[6/5|classic minor third (6/5)]] and the [[11/9|undecimal neutral third (11/9)]], between the [[5/4|classic major third (5/4)]] and the [[27/22|rastmic neutral third (27/22)]], as well as the difference between the [[55/32|keenanismic supermajor sixth (55/32)]] and the [[27/16|Pythagorean major sixth (27/16)]]. This means that 6/5 and 11/9 are equated – as are 55/32 and 27/16 – when this comma is tempered out. [[EDO]]s that temper out this interval include {{EDOs| 5, 7, 8, 10, 15, 17, 22, 27, 29, 30, 32, 37, 42, 44, 51, 54, 59 and 66}}.
-When treated as an interval in its own right, it acts as a sort of parachroma in much the same fashion as [[33/32]], from which it differs by a [[81/80|syntonic comma]].  However, given that it's noticeably smaller in size than 33/32, one can also easily use it as either an [[Wikipedia:Appoggiatura|appoggitura]], an [[Wikipedia:Acciaccatura|acciaccatura]], or a quick passing tone. Tempering out the [[3025/3024|lehmerisma]] equates this interval with [[56/55]], splitting the [[28/27]] septimal chroma into two equal halves.  Furthermore, when the [[385/384|keenanisma]] is tempered out, 55/54 is equated with [[64/63]], and it is partially on this basis that one can reasonably make the argument that 64/63 can act as the septimal equivalent for 55/54.
+When treated as an interval in its own right, it acts as a sort of parachroma in much the same fashion as [[33/32]], from which it differs by a [[81/80|syntonic comma]].  However, given that it's noticeably smaller in size than 33/32, one can also easily use it in melodies as either an [[Wikipedia:Appoggiatura|appoggitura]], an [[Wikipedia:Acciaccatura|acciaccatura]], or a quick passing tone. Tempering out the [[3025/3024|lehmerisma]] equates this interval with [[56/55]], splitting the [[28/27]] septimal chroma into two equal halves.  Furthermore, when the [[385/384|keenanisma]] is tempered out, 55/54 is equated with [[64/63]], and it is partially on this basis that one can reasonably make the argument that 64/63 can act as the septimal equivalent for 55/54.
 It is also the difference between the universally accepted 440 Hz pitch standard and the esoteric and non-scientific, but rather popular proposed 432 Hz pitch standard.