55/54: Difference between revisions
Dave Keenan (talk | contribs) →Sagittal notation: Changed "simplest ratio" to "simplest interval". Changed colons to slashes and dash. Gave the truly-simplest (2,3-free) interval in addition to the octave-reduced interval. Replaced hair-space with nbhsp template call. |
"Telepathma" takes priority. Who knows where the other two names come from. |
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{{Infobox Interval | {{Infobox Interval | ||
| Name = undecimal diasecundal comma, eleventyfive comma | | Name = telepathma, undecimal diasecundal comma, eleventyfive comma | ||
| Color name = 1oy1, loyo 1sn, Loyo comma | | Color name = 1oy1, loyo 1sn, Loyo comma | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
'''55/54''', the ''' | '''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}}. | ||
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. | 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. | ||
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== Sagittal notation == | == Sagittal notation == | ||
In the [[Sagittal]] system, this comma (possibly tempered) is represented by the sagittal {{sagittal | |\ }} and is called the '''55 comma''', or '''55C''' for short, because the simplest interval it notates is 55/1 = 5×11 (equiv. 55/32), as for example in C-A{{nbhsp}}{{sagittal | |\ }}. The downward version is called '''1/55C''' or '''55C down''' and is represented by {{sagittal| !/ }}. | In the [[Sagittal]] system, this comma (possibly tempered) is represented by the sagittal {{sagittal | |\ }} and is called the '''55 comma''', or '''55C''' for short, because the simplest interval it notates is 55/1 = 5×11 (equiv. 55/32), as for example in C-A{{nbhsp}}{{sagittal | |\ }}. The downward version is called '''1/55C''' or '''55C down''' and is represented by {{sagittal| !/ }}. | ||
== Etymology == | |||
The telepathma was presumably named by [[Gene Ward Smith]] in 2014 since it seems this wiki was the place where it made its first appearance<ref>See [https://en.xen.wiki/index.php?title=Small_comma&oldid=13398 Small comma (Revision as of 21:55, 6 August 2014 by Wikispaces>genewardsmith)]. </ref>. It was named after the [[telepathy]] temperament, which tempers it out. | |||
== See also == | == See also == | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
== Notes == | |||