Xenllium at 00:36, 31 January 2026

2026-01-31T00:36:44Z

← Older revision		Revision as of 00:36, 31 January 2026
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	\| {{monzo\| -1 5 0 -2 }}		\| {{monzo\| -1 5 0 -2 }}
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			Examples of temperaments with fractional values of ''n'':
			* [[Tetracot\|Tetracot expansion]] ({{nowrap\|''n'' {{=}} {{frac\|1\|2}} {{=}} 0.5}})
			* 7 & 34 & 164 ({{nowrap\|''n'' {{=}} {{frac\|3\|2}} {{=}} 1.5}})
			* 7 & 34 & 453 ({{nowrap\|''n'' {{=}} {{frac\|7\|3}} {{=}} 2.333…}})
			* 7 & 34 & 301 ({{nowrap\|''n'' {{=}} {{frac\|5\|2}} {{=}} 2.5}})

	[[Category:Tetracot]]		[[Category:Tetracot]]
	[[Category:Equivalence continua]]		[[Category:Equivalence continua]]

Xenllium: Created page with "The '''rastmic–ptolemismic equivalence continuum''' is a continuum of temperaments which equate a number of rastmas (243/242) with the ptolemisma (100/99). All temperaments in the continuum satisfy {{nowrap|(243/242)^''n'' ~ 100/99}}. Varying ''n'' results in different temperaments listed in the table below. It converges to the 2.3.5.11 subgroup temperament of {243/242} as ''n'' approaches infinity. If we allo..."

2026-01-31T00:06:49Z

Created page with "The '''rastmic–ptolemismic equivalence continuum''' is a continuum of temperaments which equate a number of rastmas (243/242) with the ptolemisma (100/99). All temperaments in the continuum satisfy {{nowrap|(243/242)<sup>''n''</sup> ~ 100/99}}. Varying ''n'' results in different temperaments listed in the table below. It converges to the 2.3.5.11 subgroup temperament of {243/242} as ''n'' approaches infinity. If we allo..."

New page

The '''rastmic–ptolemismic equivalence continuum''' is a [[equivalence continuum|continuum]] of temperaments which equate a number of [[243/242|rastmas (243/242)]] with the [[100/99|ptolemisma (100/99)]].

All temperaments in the continuum satisfy {{nowrap|(243/242)<sup>''n''</sup> ~ 100/99}}. Varying ''n'' results in different temperaments listed in the table below. It converges to the 2.3.5.11 subgroup temperament of {243/242} as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all 2.3.5.11 subgroup temperaments supported by [[tetracot]] due to it being the unique temperament that tempers out both commas and thus tempers out all combinations of them. The just value of ''n'' is approximately 2.4372, and temperaments near this tend to be the most accurate ones.

{| class="wikitable center-1"
|+ style="font-size: 105%;" | Temperaments in the continuum
|-
! rowspan="2" | ''n''
! rowspan="2" | Temperament
! colspan="2" | Comma
|-
! Ratio
! 2.3.5.11 monzo
|-
| −2
| {{nowrap|7 & 34 & 40}}
| [[164025/161051]]
| {{monzo| 0 8 2 -5 }}
|-
| −1
| [[Tetracot-diesic]] ({{nowrap|7 & 9 & 34}})
| [[1350/1331]]
| {{monzo| 1 3 2 -3 }}
|-
| 0
| [[Ptolemismic]] ({{nowrap|7 & 12 & 15}})
| [[100/99]]
| {{monzo| 2 -2 2 -1 }}
|-
| 1
| [[Tetracot-kleismic]] ({{nowrap|7 & 34 & 46}})
| [[2200/2187]]
| {{monzo| 3 -7 2 1 }}
|-
| 2
| [[Anthill]] ({{nowrap|7 & 34 & 118}})
| [[532400/531441]]
| {{monzo| 4 -12 2 3 }}
|-
| 3
| {{nowrap|7 & 34 & 183}}
| [[129140163/128840800]]
| {{monzo| -5 17 -2 -5 }}
|-
| …
| …
| …
| …
|-
| ∞
| Neutral expansion
| [[243/242]]
| {{monzo| -1 5 0 -2 }}
|}

[[Category:Tetracot]]
[[Category:Equivalence continua]]

Rastmic–ptolemismic equivalence continuum - Revision history

Xenllium at 00:36, 31 January 2026