Mercator family: Difference between revisions

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 ~~Boiler, 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 cartography, pentacontatritonic and boiler.

Comma list: 15625/15552, 32805/32768

Line 33:

Badness: 0.0870

~~== Boiler ==~~

Compared to Joliet, Boiler nails down both the 7-limit and the 11-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, as well as to a number of mechanical devices that are boil water for various purposes.

~~Comma list:~~

~~POTE generator:~~

~~Mapping:~~

~~Mapping generators:~~

~~Vals:~~

~~Badness:~~

== Cartography ==

Cartography nails down both the 7-limit and the 11-limit by adding the [[symbiotic comma]] to Schismerc's list of tempered commas. The name for this temperament comes from how good the mappings are, and also from the idea of "Mercator" being a dual reference to both Nicolas Mercator and Gerardus Mercator.

Comma list: 385/384, 6250/6237, 19712/19683

Line 108:

Line 93:

Badness: 0.0612

== Boiler ==

Compared to Joliet, Boiler nails down both the 7-limit and the 11-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, as well as to a number of mechanical devices that are boil water for various purposes.

Comma list: 9801/9800, 15625/15552, 32805/32768

POTE generator: ~4.9232 or ~6.3976

Mapping: [{{val| 106 168 246 0 69 }}, {{val| 0 0 0 1 1 }}]

Mapping generators: ~2835/2816, ~7

Badness:

= Joliet =

Line 124:

Badness: 0.0633

=== 13-limit ===

== 13-limit ==

Comma list: 169/168, 225/224, 325/324, 640/637

@@ 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 Boiler, 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 cartography, pentacontatritonic and boiler.
 Comma list: 15625/15552, 32805/32768
@@ Line 33: / Line 33: @@
 Badness: 0.0870
-== Boiler ==
-Compared to Joliet, Boiler nails down both the 7-limit and the 11-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, as well as to a number of mechanical devices that are boil water for various purposes.
-Comma list:
-POTE generator:
-Mapping:
-Mapping generators:
-Vals:
-Badness:
 == Cartography ==
-Cartography nails down both the 7-limit and the 11-limit by adding the [[symbiotic comma]] to Schismerc's list of tempered commas.  The name for this temperament comes from how good the mappings are, and also from the idea of "Mercator" being a dual reference to both Nicolas Mercator and Gerardus Mercator.
+Cartography nails down both the 7-limit and the 11-limit by adding the [[symbiotic comma]] to Schismerc's list of tempered commas. The name for this temperament comes from how good the mappings are, and also from the idea of "Mercator" being a dual reference to both Nicolas Mercator and Gerardus Mercator.
 Comma list: 385/384, 6250/6237, 19712/19683
@@ Line 108: / Line 93: @@
 Badness: 0.0612
+== Boiler ==
+Compared to Joliet, Boiler nails down both the 7-limit and the 11-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, as well as to a number of mechanical devices that are boil water for various purposes.
+Comma list: 9801/9800, 15625/15552, 32805/32768
+POTE generator: ~4.9232 or ~6.3976
+Mapping: [{{val| 106 168 246 0 69 }}, {{val| 0 0 0 1 1 }}]
+Mapping generators: ~2835/2816, ~7
+{{Val list|legend=1| 106, 212 }}
+Badness:
 = Joliet =
@@ Line 124: / Line 124: @@
 Badness: 0.0633
-=== 13-limit ===
+== 13-limit ==
 Comma list: 169/168, 225/224, 325/324, 640/637