1216/1215: Difference between revisions
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Expansion. This one induces essentially tempered chords so I must give it an adjective |
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'''1216/1215''', the '''password comma''' or '''Eratosthenes' comma''' is a [[19-limit]] (also 2.3.5.19 subgroup) unnoticeable comma. It is the | '''1216/1215''', the '''password comma''' 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 [[81/64|Pythagorean major third (81/64)]], or [[20/19]] falls short of the [[256/243|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 [[513/512|undevicesimal comma]] and the [[schisma]]. | ||
By tempering it out is defined the '''eratosthenes temperament''', which enables the '''eratosthenes chords'''. Edos supporting this temperament includes {{EDOs| 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 == | == See also == | ||
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[[Category:Superparticular]] | [[Category:Superparticular]] | ||
[[Category:Unnoticeable comma]] | [[Category:Unnoticeable comma]] | ||
[[Category: | [[Category:Eratosthenes]] | ||
Revision as of 12:36, 5 February 2021
| Interval information |
Eratosthenes' comma
reduced
1216/1215, the password comma 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.