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 2nd,
Sanogu comma
FJS name [math]\text{d2}^{19}_{5}[/math]
Special properties superparticular,
reduced
Tenney height (log2 nd) 20.4947
Weil height (log2 max(n, d)) 20.4959
Wilson height (sopfr (nd)) 51
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~1.21876 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 undevicesimal comma and the schisma.

Commatic relations

This comma is the difference between the following superparticular pairs:

* both of these commas are also within the 2.3.5.19 subgroup.

It factors into the following superparticular pairs:

Temperaments

By tempering out this comma 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