55/54

Interval information

Ratio	55/54
Factorization	2-1 × 3-3 × 5 × 11
Monzo	[-1 -3 1 0 1⟩
Size in cents	31.76665¢
Names	telepathma, undecimal diasecundal comma, eleventyfive comma
Color name	1oy1, loyo 1sn, Loyo comma
FJS name	[math]\displaystyle{ \text{P1}^{5,11} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	11.5362
Weil norm (log2 max(n, d))	11.5627
Wilson norm (sopfr(nd))	27
Comma size	medium
S-expression	S10⋅S11
Open this interval in xen-calc

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 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 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. Edos that temper out this interval by patent val include 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 version of porcupine temperament. Additionally, tempering out 55/54 requires tuning the 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

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 .

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. It was named after the telepathy temperament, which tempers it out.

See also

• List of superparticular intervals
• Gallery of just intervals