Xenllium at 23:59, 13 February 2026

2026-02-13T23:59:01Z

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-Examples of temperaments with fractional values of ''n'':
+We may invert the continuum by setting ''m'' such that {{nowrap|''m'' − 1/''n'' {{=}} 1}}. This may be called the ''marvel–gamelismic equivalence continuum'', which is essentially the same thing. The just value of ''m'' is approximately 1.09352, and temperaments having ''n'' near this value tend to be the most accurate ones.
-* [[Syntonic–31 equivalence continuum #Ampersand|Ampersand]] ({{nowrap|''n'' {{=}} {{frac|3|4}} {{=}} 0.75}})
 [[Category:Miracle]]
 [[Category:Equivalence continua]]

Xenllium: Created page with "{{Mathematical interest}} The '''marvel–breedsmic equivalence continuum''' is a continuum of 7-limit temperament families which equate a number of breedsmas (2401/2400) with a marvel comma (225/224). This continuum is theoretically interesting in that these are all 7-limit temperament families supported by septimal miracle temperament. All temperaments in the continuum satisfy {{nowrap|..."

2026-02-13T22:37:12Z

Created page with "{{Mathematical interest}} The '''marvel–breedsmic equivalence continuum''' is a continuum of 7-limit temperament families which equate a number of breedsmas (2401/2400) with a marvel comma (225/224). This continuum is theoretically interesting in that these are all 7-limit temperament families supported by septimal miracle temperament. All temperaments in the continuum satisfy {{nowrap|..."

New page

{{Mathematical interest}}

The '''marvel–breedsmic equivalence continuum''' is a [[equivalence continuum|continuum]] of 7-limit temperament families which equate a number of [[2401/2400|breedsmas (2401/2400)]] with a [[225/224|marvel comma (225/224)]]. This continuum is theoretically interesting in that these are all 7-limit temperament families supported by [[Gamelismic clan #Miracle|septimal miracle]] temperament.

All temperaments in the continuum satisfy {{nowrap|(2401/2400)<sup>''n''</sup> ~ 225/224}}. Varying ''n'' results in different temperament families listed in the table below. It converges to [[Breedsmic temperaments|breedsmic]] 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 sensi (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 10.69267, 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
|-
| −3
| {{nowrap|31 & 41 & 244}}
| [[1977326743/1966080000]]
| {{Monzo| −20 −1 −4 11 }}
|-
| −2
| [[Quince clan|Quince]]
| [[823543/819200]]
| {{Monzo| −15 0 −2 7 }}
|-
| −1
| [[Gamelismic clan|Gamelismic]]
| [[1029/1024]]
| {{Monzo| −10 1 0 3 }}
|-
| 0
| [[Marvel temperaments|Marvel]]
| [[225/224]]
| {{Monzo| −5 2 2 −1 }}
|-
| 1
| [[Mirkwai clan|Mirkwai]]
| [[16875/16807]]
| {{Monzo| 0 3 4 −5 }}
|-
| 2
| {{nowrap|31 & 41 & 179}}
| [[40500000/40353607]]
| {{Monzo| 5 4 6 −9 }}
|-
| 3
| {{nowrap|31 & 41 & 278cd}}
|
| {{Monzo| 10 5 8 −13 }}
|-
| 4
| {{nowrap|31 & 41 & 336cd}}
|
| {{Monzo| 15 6 10 −17 }}
|-
| …
| …
| …
| …
|-
| ∞
| [[Breedsmic temperaments|Breedsmic]]
| [[2401/2400]]
| {{Monzo| −5 −1 −2 4 }}
|}

Examples of temperaments with fractional values of ''n'':
* [[Syntonic–31 equivalence continuum #Ampersand|Ampersand]] ({{nowrap|''n'' {{=}} {{frac|3|4}} {{=}} 0.75}})

[[Category:Miracle]]
[[Category:Equivalence continua]]

Marvel–breedsmic equivalence continuum - Revision history

Xenllium at 23:59, 13 February 2026