1216/1215

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Interval information
Ratio 1216/1215
Subgroup monzo 2.3.5.19 [6 -5 -1 1
Size in cents 1.4242979¢
Names password,
Eratosthenes' comma
Color name s19og2, Sanogu comma
FJS name [math]\text{d2}^{19}_{5}[/math]
Special properties superparticular,
reduced
Tenney height (log2 n⋅d) 20.4947
Weil height (max(n, d)) 1216
Benedetti height (n⋅d) 1477440
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.40674 bits
Comma size unnoticeable
S-expression S16 / S18
open this interval in xen-calc

1216/1215, the password or Eratosthenes' comma, is a 19-limit (also 2.3.5.19 subgroup) unnoticeable comma. It is the amount by which 19/15 exceeds the Pythagorean major third (81/64), or 20/19 falls short of the Pythagorean minor second (256/243). It is also the difference between 19/18, the undevicesimal semitone and 135/128, the major chroma, and in addition, between the septendecimal kleisma and the nusu comma, between the go comma and the undevicesimal comma, and between the undevicesimal comma and the schisma.

By tempering it out is defined the eratosthenes temperament, which enables the eratosthenes chords. EDOs supporting this temperament includes 12, 29, 41, 53, 65, 77, 87, 94, 99, 106, 111, 118, 130, 140, 152, 159, 183, 193, 205, 217, 270, 282, 311, 323, 364, 400, 422, 581, and 692.

See also