https://en.xen.wiki/index.php?action=history&feed=atom&title=User%3ARoyalmilktea%2FKeemic_equivalence_continuumUser:Royalmilktea/Keemic equivalence continuum - Revision history2026-10-13T21:52:24ZRevision history for this page on the wikiMediaWiki 1.43.6https://en.xen.wiki/index.php?title=User:Royalmilktea/Keemic_equivalence_continuum&diff=238744&oldid=prevFloraC: FloraC moved page Keemic equivalence continuum to User:Royalmilktea/Keemic equivalence continuum without leaving a redirect: XW:NG2026-10-06T07:59:56Z<p>FloraC moved page <a href="/index.php?title=Keemic_equivalence_continuum&action=edit&redlink=1" class="new" title="Keemic equivalence continuum (page does not exist)">Keemic equivalence continuum</a> to <a href="/w/User:Royalmilktea/Keemic_equivalence_continuum" title="User:Royalmilktea/Keemic equivalence continuum">User:Royalmilktea/Keemic equivalence continuum</a> without leaving a redirect: XW:NG</p>
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<p><b>New page</b></p><div>The '''keemic equivalence continuum''' is a [[Equivalence continuum|continuum]] of temperaments which equate a number of [[100/99|ptolemismas (100/99)]] with the [[875/864|keema (875/864)]].<br />
<br />
All temperaments in the continuum satisfy (100/99)<sup>''n''</sup> ~ 875/864. Varying ''n'' results in different temperaments listed in the table below. It converges to the [[11-limit]] temperament of [[Catalog of rank-4 temperaments#Ptolemismic (100/99)|ptolemismic]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all 11-limit temperaments supported by [[Keemic family#Undecimal keemic|undecimal keemic]] 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 1.2588, and temperaments near this tend to be the most accurate ones.<br />
{| class="wikitable"<br />
|+Temperament families in the continuum<br />
! rowspan="2" |n<br />
! rowspan="2" |Temperament<br />
! colspan="2" |Comma<br />
|-<br />
!Ratio<br />
!Monzo<br />
|-<br />
| -1<br />
|Nokotanmic(?)<br />
|[[Nokotan|21875/21384]]<br />
|{{Monzo|-3 -5 5 1 -1}}<br />
|-<br />
|0<br />
|[[Keemic]] extension<br />
|[[875/864]]<br />
|{{Monzo|-5 -3 3 1 0}}<br />
|-<br />
|1<br />
|[[Keenanismic]]<br />
|[[385/384]]<br />
|{{Monzo|-7 -1 1 1 1}}<br />
|-<br />
|2<br />
|Absinthmic(?)<br />
|[[2560/2541]]<br />
|{{Monzo|9 -1 1 -1 -2}}<br />
|-<br />
|...<br />
|...<br />
|...<br />
|...<br />
|-<br />
|∞<br />
|Ptolemismic<br />
|[[100/99]]<br />
|{{Monzo|2 -2 2 0 -1}}<br />
|}<br />
{| class="wikitable"<br />
|+Temperaments with fractional n<br />
!n<br />
!Temperament<br />
!Comma<br />
|-<br />
|5/4 = 1.25<br />
|{{Nowrap|270 & 836 & 2190 & 311}}<br />
|{{Monzo|-30 -2 2 4 5}}<br />
|-<br />
|9/7 = 1.{{Overline|285714}}<br />
|{{Nowrap|494 & 472 & 41 & 981}}<br />
|{{Monzo|-53 -3 3 7 9}}<br />
|-<br />
|4/3 = 1.{{Overline|3}}<br />
|{{Nowrap|224 & 41 & 239 & 22}}<br />
|{{Monzo|-23 -1 1 3 4}}<br />
|-<br />
|3/2 = 1.5<br />
|[[Orgonia#Orgonismic|Orgonismic]]<br />
|{{Monzo|16 0 0 -2 -3}}<br />
|}</div>Royalmilktea