55/54

From Xenharmonic Wiki
Jump to navigation Jump to search
Interval information
Ratio 55/54
Monzo [-1 -3 1 0 1
Size in cents 31.76665
Name(s) undecimal diasecundal comma,
eleventyfive comma,
telepathma
Color name 1oy1, loyo 1sn
FJS name P155
open this interval in xen-calc

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 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. EDOs that temper out this interval include 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 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 appoggiatura, an 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 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.

See also