55/54: Difference between revisions

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'''55/54''', the '''telepathma''', otherwise known as the '''undecimal diasecundal comma''' or the '''eleventyfive comma''', is an [[11-limit]] [[superparticular]] interval that marks the difference between the classic minor third ([[6/5]]) and the undecimal neutral third ([[11/9]]), between the classic major third ([[5/4]]) and the rastmic neutral third ([[27/22]]), as well as the difference between the keenanismic supermajor sixth ([[55/32]]) and the 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}}.

'''55/54''', the '''telepathma''', otherwise known as the '''undecimal diasecundal comma''' or the '''eleventyfive comma''', is an [[11-limit]] [[superparticular]] interval that marks the difference between the classic minor third ([[6/5]]) and the undecimal neutral third ([[11/9]]), between the classic major third ([[5/4]]) and the rastmic neutral third ([[27/22]]), between the minor whole tone ([[10/9]]) and the lesser undecimal neutral second ([[12/11]]), as well as the difference between the keenanismic supermajor sixth ([[55/32]]) and the Pythagorean major sixth ([[27/16]]).

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|appoggiatura]], an [[Wikipedia:Acciaccatura|acciaccatura]], or a quick passing tone. Tempering out the lehmerisma ([[3025/3024]]) 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 432 Hz pitch standard.

== Temperaments ==

Tempering out this comma means that 6/5 and 11/9 are equated, as are 55/32 and 27/16. [[Edo]]s that temper out this interval by patent val include {{EDOs| 5, 7, 8, 10, 15, 17, 22, 27, 29, 30, 32, 37, 42, 44, 51, 54, 59 and 66}}. Since tempering out 55/54 equates 10/9 with 12/11, it is natural to equate both with [[11/10]] as well (tempering out [[100/99]] and [[121/120]]), leading to the [[2.3.5.11 subgroup|2.3.5.11-subgroup]] version of [[porcupine]] temperament. Additionally, tempering out 55/54 requires tuning the [[3/2|perfect fifth]] sharply to maintain accuracy, meaning it is natural to temper out 64/63 as well, finding [[7/4]] at two perfect fourths, extending porcupine to the full 11-limit. Other extensions of porcupine to prime 7 are detailed in the [[porcupine family]].

Non-porcupine temperaments that temper out 55/54 include [[telepathy]], [[intuition]], [[pajarous]], [[darjeeling]], [[suprapyth]], [[fleetwood]], and [[negroni]].

== Sagittal notation ==

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-'''55/54''', the '''telepathma''', otherwise known as the '''undecimal diasecundal comma''' or the '''eleventyfive comma''', is an [[11-limit]] [[superparticular]] interval that marks the difference between the classic minor third ([[6/5]]) and the undecimal neutral third ([[11/9]]), between the classic major third ([[5/4]]) and the rastmic neutral third ([[27/22]]), as well as the difference between the keenanismic supermajor sixth ([[55/32]]) and the 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}}.
+'''55/54''', the '''telepathma''', otherwise known as the '''undecimal diasecundal comma''' or the '''eleventyfive comma''', is an [[11-limit]] [[superparticular]] interval that marks the difference between the classic minor third ([[6/5]]) and the undecimal neutral third ([[11/9]]), between the classic major third ([[5/4]]) and the rastmic neutral third ([[27/22]]), between the minor whole tone ([[10/9]]) and the lesser undecimal neutral second ([[12/11]]), as well as the difference between the keenanismic supermajor sixth ([[55/32]]) and the Pythagorean major sixth ([[27/16]]).
 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|appoggiatura]], an [[Wikipedia:Acciaccatura|acciaccatura]], or a quick passing tone. Tempering out the lehmerisma ([[3025/3024]]) 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 432 Hz pitch standard.
+== Temperaments ==
+Tempering out this comma means that 6/5 and 11/9 are equated, as are 55/32 and 27/16. [[Edo]]s that temper out this interval by patent val include {{EDOs| 5, 7, 8, 10, 15, 17, 22, 27, 29, 30, 32, 37, 42, 44, 51, 54, 59 and 66}}. Since tempering out 55/54 equates 10/9 with 12/11, it is natural to equate both with [[11/10]] as well (tempering out [[100/99]] and [[121/120]]), leading to the [[2.3.5.11 subgroup|2.3.5.11-subgroup]] version of [[porcupine]] temperament. Additionally, tempering out 55/54 requires tuning the [[3/2|perfect fifth]] sharply to maintain accuracy, meaning it is natural to temper out 64/63 as well, finding [[7/4]] at two perfect fourths, extending porcupine to the full 11-limit. Other extensions of porcupine to prime 7 are detailed in the [[porcupine family]].
+Non-porcupine temperaments that temper out 55/54 include [[telepathy]], [[intuition]], [[pajarous]], [[darjeeling]], [[suprapyth]], [[fleetwood]], and [[negroni]].
 == Sagittal notation ==