27/22

From Xenharmonic Wiki
Revision as of 16:45, 11 March 2026 by Hotcrystal0 (talk | contribs) (mention its closeness to 13\44)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
Interval information
Ratio 27/22
Factorization 2-1 × 33 × 11-1
Monzo [-1 3 0 0 -1
Size in cents 354.5471¢
Names rastmic neutral third,
Alpharabian tendoneutral third
Color name 1u3, lu 3rd
FJS name [math]\displaystyle{ \text{M3}_{11} }[/math]
Special properties reduced
Tenney norm (log2 nd) 9.21432
Weil norm (log2 max(n, d)) 9.50978
Wilson norm (sopfr(nd)) 22

[sound info]
Open this interval in xen-calc

27/22, conventionally called the rastmic neutral third, is 243/242 (7.1 ¢) sharp of 11/9, and together with 11/9 makes 3/2, so that we obtain the two neutral triads, 1-11/9-3/2 and 1-27/22-3/2, with intervals of 11/9 and 27/22. It is the interval between 10/9 and 15/11, and 11/9 and 3/2 and their inversions. As this is the larger of two 11-limit neutral thirds obtained by modifying Pythagorean intervals by 33/32, it is dubbed the Alpharabian tendoneutral third in Alpharabian tuning. It is extremely close to 44edo's 13\44 neutral third, however the first multiple of 44edo to map it consistently is 176edo.

Approximation

Edo approximations for 27/22 (354.55 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
7 2\7 342.86 -11.69 -6.82
10 3\10 360.00 +5.45 +4.54
17 5\17 352.94 -1.61 -2.28
20 6\20 360.00 +5.45 +9.09
24 7\24 350.00 -4.55 -9.09
27 8\27 355.56 +1.01 +2.27
34 10\34 352.94 -1.61 -4.55
37 11\37 356.76 +2.21 +6.81
44 13\44 354.55 -0.00 -0.01
51 15\51 352.94 -1.61 -6.83
54 16\54 355.56 +1.01 +4.54
61 18\61 354.10 -0.45 -2.28
64 19\64 356.25 +1.70 +9.08
68 20\68 352.94 -1.61 -9.10
71 21\71 354.93 +0.38 +2.26
78 23\78 353.85 -0.70 -4.56

See also