4225/4224

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Interval information
Ratio 4225/4224
Factorization 2-7 × 3-1 × 52 × 11-1 × 132
Monzo [-7 -1 2 0 -1 2
Size in cents 0.40980804¢
Name leprechaun comma
FJS name [math]\text{P1}^{5,5,13,13}_{11}[/math]
Special properties square superparticular,
reduced
Tenney height (log2 n⋅d) 24.0891
Weil height (max(n, d)) 4225
Benedetti height (n⋅d) 17846400
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.39821 bits
Comma size unnoticeable
S-expression S65
open this interval in xen-calc

4225/4224, the leprechaun comma, is an unnoticeable 13-limit superparticular interval. It is the difference between the following pairs:

Temperaments

Tempering out this comma in the full 13-limit leads to the rank-5 leprechaun temperament. It is also tempered out in lower-rank temperaments including abigail, newt, decoid, donar, etc. Tempering it out also splits the 33/32 Alpharabian quarter-tone in two, each part corresponding to 65/64 and 66/65. You may find a list of good equal temperaments that support this temperament below.

Subgroup: 2.3.5.7.11.13

Mapping:
[1 0 0 0 1 4]
0 1 0 0 1 1]
0 0 1 0 0 -1]
0 0 0 1 0 0]
0 0 0 0 2 1]]

Mapping generators: ~2, ~3, ~5, ~7, ~65/48

Optimal GPV sequence41, 46, 53, 80, 87, 103, 121, 130, 183, 190, 217, 224, 270, 494, 684, 764, 935, 954, 1178, 1308, 1448, 1578, 1889, 2756, 2843, 3337, 4421f, 4915f, 7758cff, 10514cdff

See also