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 is exactly the same as the 5-limit of 53edo~~. It should be noted that~~ the 7~~-limit is somewhat~~ independent ~~for this temperament and is only really fully nailed down in one way or another by extending to the 11-limit~~. Among the known 11-limit extensions are 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, and Pentacontatritonic.

Comma list: 15625/15552, 32805/32768

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POTE generator: ~225/224 = 6.1430

Mapping: [{{val| 53 84 123 0 332 ~~196~~ }}, {{val| 0 0 0 1 -1 0 }}]

Mapping: [{{val| 53 84 123 0 332 }}, {{val| 0 0 0 1 -1 }}]

Mapping generators: ~81/80, ~7

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=== 13-limit ===

13-limit Cartography adds the island comma to the list of tempered commas~~, and while~~ this extension is ~~connected to~~ the ~~5-limit, it is~~ independent of the 11~~-limit and 7-limit, so it can just as easily be added by itself to make a no-sevens no-elevens version of Cartography~~.

13-limit Cartography adds the island comma to the list of tempered commas. The harmonic 13 in this extension is part of the period and independent of the generator for harmonics 7 and 11.

Commas: 325/324, 385/384, 625/624, 19712/19683

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=== 13-limit ===

13-limit Pentacontatritonic adds the schismina to the list of commas being tempered out- this extension is connected to the ~~7-limit~~.

13-limit Pentacontatritonic adds the schismina to the list of commas being tempered out – in this extension the harmonic 13 is connected to the generator.

Comma list: 540/539, 729/728, 4096/4095, 13750/13689

@@ 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 is exactly the same as the 5-limit of 53edo. It should be noted that the 7-limit is somewhat independent for this temperament and is only really fully nailed down in one way or another by extending to the 11-limit. Among the known 11-limit extensions are 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, and Pentacontatritonic.
 Comma list: 15625/15552, 32805/32768
@@ Line 41: / Line 41: @@
 POTE generator: ~225/224 = 6.1430
-Mapping: [{{val| 53 84 123 0 332 196 }}, {{val| 0 0 0 1 -1 0 }}]
+Mapping: [{{val| 53 84 123 0 332 }}, {{val| 0 0 0 1 -1 }}]
 Mapping generators: ~81/80, ~7
@@ Line 50: / Line 50: @@
 === 13-limit ===
--limit Cartography adds the island comma to the list of tempered commas, and while this extension is connected to the 5-limit, it is independent of the 11-limit and 7-limit, so it can just as easily be added by itself to make a no-sevens no-elevens version of Cartography.
+-limit Cartography adds the island comma to the list of tempered commas. The harmonic 13 in this extension is part of the period and independent of the generator for harmonics 7 and 11.
 Commas: 325/324, 385/384, 625/624, 19712/19683
@@ Line 80: / Line 80: @@
 === 13-limit ===
--limit Pentacontatritonic adds the schismina to the list of commas being tempered out- this extension is connected to the 7-limit.
+-limit Pentacontatritonic adds the schismina to the list of commas being tempered out – in this extension the harmonic 13 is connected to the generator.
 Comma list: 540/539, 729/728, 4096/4095, 13750/13689