Mercator family: Difference between revisions
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Joliet should not be listed as an extension of schismerc |
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= Schismerc = | = Schismerc = | ||
As per the name, Schismerc is characterized by the addition of the schisma, [[32805/32768]], to Mercator's comma, which completely reduces all commas in the [[Schismic-Mercator equivalence continuum]] to the [[unison]], and thus, the 5-limit part is exactly the same as the 5-limit of 53edo, with the addition of harmonic 7 represented by an independent generator. Among the known 11-limit extensions are | As per the name, Schismerc is characterized by the addition of the schisma, [[32805/32768]], to Mercator's comma, which completely reduces all commas in the [[Schismic-Mercator equivalence continuum]] to the [[unison]], and thus, the 5-limit part is exactly the same as the 5-limit of 53edo, with the addition of harmonic 7 represented by an independent generator. Among the known 11-limit extensions are Boiler, Cartography, and Pentacontatritonic. | ||
Comma list: 15625/15552, 32805/32768 | Comma list: 15625/15552, 32805/32768 | ||
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Badness: 0.0870 | Badness: 0.0870 | ||
== Boiler == | == Boiler == | ||
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Badness: 0.0612 | Badness: 0.0612 | ||
= Joliet = | |||
Joliet can be characterized as the 53 & 106 temperament, having 7-limit representation akin to 53edo with the addition of harmonic 11 represented by an independent generator. The name for this temperament is a reference to 106 being the maximum number of characters in the Joliet extension to the ISO 9660 file system. | |||
Comma list: 225/224, 1728/1715, 3125/3087 | |||
POTE generator: ~176/175 = 8.8283 | |||
Mapping: [{{val| 53 84 123 149 0 }}, {{val| 0 0 0 0 1 }}] | |||
Mapping generators: ~81/80, ~11/1 | |||
{{Val list|legend=1| 53, 106, 159d }} | |||
Badness: 0.0633 | |||
=== 13-limit === | |||
Comma list: 169/168, 225/224, 325/324, 640/637 | |||
POTE generator: ~176/175 = 8.1254 | |||
Mapping: [{{val| 53 84 123 149 0 196 }}, {{val| 0 0 0 0 1 0 }}] | |||
Mapping generators: ~81/80, ~11/1 | |||
{{Val list|legend=1| 53, 106, 159d }} | |||
Badness: 0.0370 | |||
[[Category:Theory]] | [[Category:Theory]] | ||