View source for Archytas–chromatic equivalence continuum

{{Mathematical interest}}
The '''Archytas–chromatic equivalence continuum''', or '''septimal–chromatic equivalence continuum''', is a [[equivalence continuum|continuum]] of [[7-limit]] temperaments which equate a number of [[64/63|Archytas commas (64/63)]] with the [[2187/2048|Pythagorean apotome (2187/2048)]].

All temperaments in the continuum satisfy {{nowrap|(64/63)<sup>''n''</sup> ~ 2187/2048}}. Varying ''n'' results in different temperaments listed in the table below. It converges to [[archy]] as ''n'' approaches infinity. The just value of ''n'' is 4.169771, and temperaments near this tend to be the most accurate ones.

{| class="wikitable center-1 center-2"
|+ style="font-size: 105%;" | Temperaments in the continuum
|-
! rowspan="2" | ''n''
! rowspan="2" | Temperament
! colspan="2" | Comma
|-
! Ratio
! Monzo
|-
| −2
| [[Dicot]]
| [[54/49]]
| {{monzo| 1 3 0 -2 }}
|-
| −1
| [[Armodue]]
| [[243/224]]
| {{monzo| -5 5 0 -1 }}
|-
| 0
| [[Whitewood]]
| [[2187/2048]]
| {{monzo| -11 7 }}
|-
| 1
| [[Flattone]]
| [[137781/131072]]
| {{monzo| -17 9 0 1 }}
|-
| 2
| [[Mohajira]]
| [[8680203/8388608]]
| {{monzo| -23 11 0 2 }}
|-
| 3
| (29 &amp; 36)
| [[546852789/536870912]]
| {{monzo| -29 13 0 3 }}
|-
| 4
| [[Sesquiquartififths]]
| [[34451725707/34359738368]]
| {{monzo| -35 15 0 4 }}
|-
| 4{{frac|1|6}}
| ({{nowrap|1848 &amp; 3431}})
| <abbr title="105343182492594861947326056299830127783078740498060829800981944087/105312291668557186697918027683670432318895095400549111254310977536">[very long]</abbr>
| {{monzo| -216 92 0 25 }}
|-
| …
| …
| …
|
|-
| ∞
| [[Archytas clan#Archy|Archy]]
| [[64/63]]
| {{monzo| 6 -2 0 -1 }}
|}

[[Category:Equivalence continua]]