Copper comma: Difference between revisions
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→Temperaments: this is indeed the correct fifth and it works out |
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|Monzo = -481 261 29 | |Monzo = -481 261 29 | ||
|Name = copper comma | |Name = copper comma | ||
|Color name = L<sup>41</sup>y<sup>29</sup>-33, fowela-theneyo negative 33rd | |||
|FJS name = - | |FJS name = - | ||
|Comma = yes | |Comma = yes | ||
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'''Copper comma''', or alternately '''29-atom''' is a 5-limit comma which is to [[29edo]] as is the Kirnberger's atom is to [[12edo]]. | '''Copper comma''', or alternately '''29-atom''' is a 5-limit comma which is to [[29edo]] as is the Kirnberger's atom is to [[12edo]]. | ||
==Temperaments== | ==Temperaments== | ||
Tempering it out results in the rank-2 '''copper''' temperament, which splits the octave into 29 parts, and the reduced generator is the difference between a more precise fifth and the 29-tone-tempered one, just as [[atomic]] does to 12edo. | Tempering it out results in the rank-2 '''copper''' temperament, which splits the octave into 29 parts, and the reduced generator is the difference between a more precise fifth and the 29-tone-tempered one, just as [[atomic]] does to 12edo. See: [[29th-octave temperaments#Copper]]. | ||
A circle of 29 of the sharpened fifths equal to {{monzo|-16 9 1}}, differs from 17 octaves by the copper comma. The difference is that since 29edo is an above-pythagorean temperament, the copper fifth is sharp of 3/2. | A circle of 29 of the sharpened fifths equal to 98415/65536 (monzo: {{monzo|-16 9 1}}), differs from 17 octaves by the copper comma. The difference is that since 29edo is an above-pythagorean temperament, the copper fifth is sharp of 3/2. Notably, in the case of copper, the comma which sharpens the fifth to be close to 29edo's is still the [[schisma]], 32805/32768. | ||
[[Category:Commas named after elements]] | |||
Latest revision as of 12:18, 3 November 2024
| Interval information |
reduced harmonic
Copper comma, or alternately 29-atom is a 5-limit comma which is to 29edo as is the Kirnberger's atom is to 12edo.
Temperaments
Tempering it out results in the rank-2 copper temperament, which splits the octave into 29 parts, and the reduced generator is the difference between a more precise fifth and the 29-tone-tempered one, just as atomic does to 12edo. See: 29th-octave temperaments#Copper.
A circle of 29 of the sharpened fifths equal to 98415/65536 (monzo: [-16 9 1⟩), differs from 17 octaves by the copper comma. The difference is that since 29edo is an above-pythagorean temperament, the copper fifth is sharp of 3/2. Notably, in the case of copper, the comma which sharpens the fifth to be close to 29edo's is still the schisma, 32805/32768.