Marvel–sensamagic equivalence continuum - Revision history

FloraC: Move breeze to misc. 7-limit temps

2026-01-10T10:52:46Z

Move breeze to misc. 7-limit temps

@@ Line 92: / Line 92: @@
 [[Badness]] (Sintel): 16.808
 [[Category:Magic]]
 [[Category:Equivalence continua]]

Xenllium at 16:19, 9 January 2026

2026-01-09T16:19:56Z

← Older revision		Revision as of 16:19, 9 January 2026
Line 16:		Line 16:
	\|-		\|-
	\| −4		\| −4
	\| ~~18b~~ & 19 & 22		\| 19 & 41 & 141
	\| [[52734375/51380224]]		\| [[52734375/51380224]]
	\| {{Monzo\| -20 3 9 -2 }}		\| {{Monzo\| -20 3 9 -2 }}
	\|-		\|-
	\| −3		\| −3
	\| 19 & 22 & 28		\| 19 & 41 & 69
	\| [[234375/229376]]		\| [[234375/229376]]
	\| {{Monzo\| -15 1 7 -1 }}		\| {{Monzo\| -15 1 7 -1 }}
Line 75:		Line 75:
	* 19 & 41 & 42bc ({{nowrap\|''n'' {{=}} −{{frac\|3\|2}} {{=}} −1.5}})		* 19 & 41 & 42bc ({{nowrap\|''n'' {{=}} −{{frac\|3\|2}} {{=}} −1.5}})
	* 19 & 41 & 42 ({{nowrap\|''n'' {{=}} −{{frac\|1\|2}} {{=}} −0.5}})		* 19 & 41 & 42 ({{nowrap\|''n'' {{=}} −{{frac\|1\|2}} {{=}} −0.5}})
	* ~~19 & 41 & 145~~ ({{nowrap\|''n'' {{=}} {{frac\|1\|2}} {{=}} 0.5}})		* [[septimagic]] ({{nowrap\|''n'' {{=}} {{frac\|1\|2}} {{=}} 0.5}})
	* ~~19 & 41 & 229~~ ({{nowrap\|''n'' {{=}} {{frac\|3\|2}} {{=}} 1.5}})		* [[acromagic]] ({{nowrap\|''n'' {{=}} {{frac\|3\|2}} {{=}} 1.5}})
	* 19 & 41 & 359 ({{nowrap\|''n'' {{=}} {{frac\|5\|3}} {{=}} 1.666…}})		* 19 & 41 & 359 ({{nowrap\|''n'' {{=}} {{frac\|5\|3}} {{=}} 1.666…}})
	* 19 & 41 & 511 ({{nowrap\|''n'' {{=}} {{frac\|7\|4}} {{=}} 1.75}})		* 19 & 41 & 511 ({{nowrap\|''n'' {{=}} {{frac\|7\|4}} {{=}} 1.75}})

Xenllium at 14:58, 9 January 2026

2026-01-09T14:58:14Z

@@ Line 79: / Line 79: @@
 * 19 & 41 & 359 ({{nowrap|''n'' {{=}} {{frac|5|3}} {{=}} 1.666…}})
 * 19 & 41 & 511 ({{nowrap|''n'' {{=}} {{frac|7|4}} {{=}} 1.75}})
 [[Category:Magic]]
 [[Category:Equivalence continua]]

Xenllium: Created page with "{{Mathematical interest}} The '''marvel–sensamagic equivalence continuum''' is a continuum of 7-limit temperament families which equate a number of marvel commas (225/224) with a sensamagic comma (245/243). This continuum is theoretically interesting in that these are all 7-limit temperament families supported by septimal magic temperament. All temperaments in the continuum satisfy {{..."

2026-01-09T13:40:51Z

Created page with "{{Mathematical interest}} The '''marvel–sensamagic equivalence continuum''' is a continuum of 7-limit temperament families which equate a number of marvel commas (225/224) with a sensamagic comma (245/243). This continuum is theoretically interesting in that these are all 7-limit temperament families supported by septimal magic temperament. All temperaments in the continuum satisfy {{..."

New page

{{Mathematical interest}}

The '''marvel–sensamagic equivalence continuum''' is a [[equivalence continuum|continuum]] of 7-limit temperament families which equate a number of [[225/224|marvel commas (225/224)]] with a [[245/243|sensamagic comma (245/243)]]. This continuum is theoretically interesting in that these are all 7-limit temperament families supported by [[Magic family #Septimal magic|septimal magic]] temperament.

All temperaments in the continuum satisfy {{nowrap|(225/224)<sup>''n''</sup> ~ 245/243}}. Varying ''n'' results in different temperament families listed in the table below. It converges to [[Marvel temperaments|marvel]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[7-limit]] temperament families supported by septimal magic (due to it being the unique rank-2 temperament that tempers both commas and thus tempers all combinations of them). The just value of ''n'' is approximately 1.84017119, and temperaments having ''n'' near this value tend to be the most accurate ones.

{| class="wikitable center-1 center-2"
|+ style="font-size: 105%;" | Temperament families in the continuum
|-
! rowspan="2" | ''n''
! rowspan="2" | Temperament family
! colspan="2" | Comma
|-
! Ratio
! Monzo
|-
| −4
| 18b & 19 & 22
| [[52734375/51380224]]
| {{Monzo| -20 3 9 -2 }}
|-
| −3
| 19 & 22 & 28
| [[234375/229376]]
| {{Monzo| -15 1 7 -1 }}
|-
| −2
| [[Magic family|5-limit magic]]
| [[3125/3072]]
| {{Monzo| -10 -1 5 }}
|-
| −1
| [[Keemic temperaments|Keemic]]
| [[875/864]]
| {{Monzo| -5 -3 3 1 }}
|-
| 0
| [[Sensamagic clan|Sensamagic]]
| [[245/243]]
| {{Monzo| 0 -5 1 2 }}
|-
| 1
| [[Hemimage temperaments|Hemimage]]
| [[10976/10935]]
| {{Monzo| 5 -7 -1 3 }}
|-
| 2
| [[Breeze]]
| [[2460375/2458624]]
| {{Monzo| -10 9 3 -4 }}
|-
| 3
| 19 & 41 & 142
| [[553584375/550731776]]
| {{Monzo| -15 11 5 -5 }}
|-
| 4
| 19 & 41 & 214
|
| {{Monzo| -20 13 7 -6 }}
|-
| …
| …
| …
| …
|-
| ∞
| [[Marvel temperaments|Marvel]]
| [[225/224]]
| {{Monzo| -5 2 2 -1 }}
|}

Examples of temperaments with fractional values of ''n'':
* 19 & 41 & 126bc ({{nowrap|''n'' {{=}} −{{frac|5|2}} {{=}} −2.5}})
* 19 & 41 & 42bc ({{nowrap|''n'' {{=}} −{{frac|3|2}} {{=}} −1.5}})
* 19 & 41 & 42 ({{nowrap|''n'' {{=}} −{{frac|1|2}} {{=}} −0.5}})
* 19 & 41 & 145 ({{nowrap|''n'' {{=}} {{frac|1|2}} {{=}} 0.5}})
* 19 & 41 & 229 ({{nowrap|''n'' {{=}} {{frac|3|2}} {{=}} 1.5}})
* 19 & 41 & 359 ({{nowrap|''n'' {{=}} {{frac|5|3}} {{=}} 1.666…}})
* 19 & 41 & 511 ({{nowrap|''n'' {{=}} {{frac|7|4}} {{=}} 1.75}})

[[Category:Magic]]
[[Category:Equivalence continua]]