1216/1215
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 (log_{2} 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.