1216/1215

Interval information

Ratio	1216/1215
Subgroup monzo	2.3.5.19 [6 -5 -1 1⟩
Size in cents	1.424298¢
Names	password, Eratosthenes' comma
FJS name	[math]\displaystyle{ \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
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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 the difference between 19/18, the undevicesimal semitone and 135/128, the major chroma, and in addition, 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

• Unnoticeable comma
• List of superparticular intervals