55/54
Ratio | 55/54 |
Factorization | 2^{-1} × 3^{-3} × 5 × 11 |
Monzo | [-1 -3 1 0 1⟩ |
Size in cents | 31.766654¢ |
Names | undecimal diasecundal comma, eleventyfive comma, telepathma |
Color name | 1oy1, loyo 1sn, Loyo comma |
FJS name | [math]\text{P1}^{5,11}[/math] |
Special properties | superparticular, reduced |
Tenney height (log_{2} nd) | 11.5362 |
Weil height (log_{2} max(n, d)) | 11.5627 |
Wilson height (sopfr (nd)) | 27 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.48296 bits |
Comma size | medium |
S-expression | S10 × S11 |
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.
Sagittal notation
In the Sagittal system, this comma (possibly tempered) is represented by the 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 . The downward version is called 1/55C or 55C down and is represented by .