Mercator family - Revision history

FloraC: Name for 4096/4095

2026-03-03T11:02:33Z

Name for 4096/4095

← Older revision		Revision as of 11:02, 3 March 2026
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	==== 13-limit ====		==== 13-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.		13-limit pentacontatritonic adds the minisma to the list of commas being tempered out – in this extension the harmonic 13 is connected to the generator.

	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

Xenllium at 23:38, 25 February 2026

2026-02-25T23:38:51Z

Show changes

FloraC: Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

2025-11-27T12:31:31Z

Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

← Older revision		Revision as of 12:31, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Mercator family]] <!-- main article -->		[[Category:Mercator family]] <!-- main article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: Text replacement - "Category:Temperament collections↵Category:Pages with mostly numerical content" to "Category:Temperament collections"

2025-11-27T12:21:39Z

Text replacement - "Category:Temperament collections↵Category:Pages with mostly numerical content" to "Category:Temperament collections"

← Older revision		Revision as of 12:21, 27 November 2025
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	[[Category:Fractional-octave temperaments]]		[[Category:Fractional-octave temperaments]]
	[[Category:Temperament collections]]		[[Category:Temperament collections]]
	~~[[Category:Pages with mostly numerical content]]~~

	The '''Mercator family''' tempers out [[Mercator's comma]], {{monzo\| -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.		The '''Mercator family''' tempers out [[Mercator's comma]], {{monzo\| -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.

Lériendil: Text replacement - "Category:Temperament collections" to "Category:Temperament collections Category:Pages with mostly numerical content"

2025-06-24T00:38:25Z

Text replacement - "Category:Temperament collections" to "Category:Temperament collections Category:Pages with mostly numerical content"

← Older revision		Revision as of 00:38, 24 June 2025
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	[[Category:Fractional-octave temperaments]]		[[Category:Fractional-octave temperaments]]
	[[Category:Temperament collections]]		[[Category:Temperament collections]]
			[[Category:Pages with mostly numerical content]]

	The '''Mercator family''' tempers out [[Mercator's comma]], {{monzo\| -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.		The '''Mercator family''' tempers out [[Mercator's comma]], {{monzo\| -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.

Lériendil: Text replacement - "Category:Temperament families" to "Category:Temperament families Category:Pages with mostly numerical content"

2025-06-24T00:34:30Z

Text replacement - "Category:Temperament families" to "Category:Temperament families Category:Pages with mostly numerical content"

← Older revision		Revision as of 00:34, 24 June 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Mercator family]] <!-- main article -->		[[Category:Mercator family]] <!-- main article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

VectorGraphics at 05:13, 12 June 2025

2025-06-12T05:13:25Z

← Older revision		Revision as of 05:13, 12 June 2025
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	Mapping generators: ~531441/524288, ~5/1		Mapping generators: ~531441/524288, ~5/1

	~~{{Multival\|legend=1\| 0 53 84 }}~~

	[[Optimal tuning]] ([[POTE]]): ~5/4 = 386.264		[[Optimal tuning]] ([[POTE]]): ~5/4 = 386.264
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	Mapping generators: ~81/80, ~7/1		Mapping generators: ~81/80, ~7/1

	~~{{Multival\|legend=1\| 0 0 53 0 84 123 }}~~

	[[Optimal tuning]] ([[POTE]]): ~225/224 = 5.3666		[[Optimal tuning]] ([[POTE]]): ~225/224 = 5.3666

FloraC: Text replacement - "{{Technical data page}}

" to "{{Technical data page}}"

2025-04-13T13:44:56Z

Text replacement - "{{Technical data page}}<br><br>" to "{{Technical data page}}"

← Older revision		Revision as of 13:44, 13 April 2025
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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	<div class="toccolours" style="float: right">		<div class="toccolours" style="float: right">
	<center>'''[[Fractional-octave temperaments]]'''</center>		<center>'''[[Fractional-octave temperaments]]'''</center>

BudjarnLambeth: {{Technical data page}}

2025-04-13T10:39:03Z

{{Technical data page}}<br><br>

← Older revision		Revision as of 10:39, 13 April 2025
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			{{Technical data page}}<br><br>
	<div class="toccolours" style="float: right">		<div class="toccolours" style="float: right">
	<center>'''[[Fractional-octave temperaments]]'''</center>		<center>'''[[Fractional-octave temperaments]]'''</center>

ArrowHead294 at 06:13, 9 December 2024

2024-12-09T06:13:13Z

← Older revision		Revision as of 06:13, 9 December 2024
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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 cartography, pentacontatritonic and boiler.		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.

	Subgroup: 2.3.5.7		Subgroup: 2.3.5.7