Mercator family

The Mercator family tempers out Mercator's comma, [-84 53⟩, and hence the fifths form a closed 53-note circle of fifths, identical to 53edo. While the tuning of the fifth will be that of 53edo, 0.069 cents flat, the tuning of the larger primes is not so constrained, and the point of these temperaments is to improve on it.

POTE generator: ~5/4 = 386.264

Mapping: [⟨53 84 123], ⟨0 0 1]]

Wedgie: ⟨⟨0 53 84]]

Badness: 0.2843

Cartography temperament

In terms of the normal comma list, Cartography 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 is exactly the same as the 5-limit of 53edo. Cartography can also be characterized as the 53&159 temperament, with 212edo being a possible tuning.

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Pentacontatritonic

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13-limit

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