Mercator family: Difference between revisions

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= 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 Joliet, Cartography, and Pentacontatritonic.

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 Joliet, Boiler, Cartography, and Pentacontatritonic.

Comma list: 15625/15552, 32805/32768

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Badness: 0.0370

== Boiler ==

Compared to Joliet, Boiler nails down the 7-limit by adding the [[kalisma]] to Schismerc's list of tempered commas, though unlike with the other extensions of Schismerc, this temperament lacks a good 13-limit extension. The name for this temperament is a reference to how 212 degrees Fahrenheit is the boiling point of water.

Comma list:

POTE generator:

Mapping:

Mapping generators:

Vals:

Badness:

== Cartography ==

@@ Line 18: / Line 18: @@
 = 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 Joliet, Cartography, and Pentacontatritonic.
+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 Joliet, Boiler, Cartography, and Pentacontatritonic.
 Comma list: 15625/15552, 32805/32768
@@ Line 62: / Line 62: @@
 Badness: 0.0370
+== Boiler ==
+Compared to Joliet, Boiler nails down the 7-limit by adding the [[kalisma]] to Schismerc's list of tempered commas, though unlike with the other extensions of Schismerc, this temperament lacks a good 13-limit extension.  The name for this temperament is a reference to how 212 degrees Fahrenheit is the boiling point of water.
+Comma list:
+POTE generator:
+Mapping:
+Mapping generators:
+Vals:
+Badness:
 == Cartography ==