User:Royalmilktea/Jubilismic equivalence continuum: Difference between revisions
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The '''jubilismic equivalence continuum''' is a [[Equivalence continuum|continuum]] of temperaments which equate a number of [[99/98|mothwellismas (99/98)]] with the [[50/49|jubilisma (50/49)]]. | The '''jubilismic equivalence continuum''' is a [[Equivalence continuum|continuum]] of temperaments which equate a number of [[99/98|mothwellismas (99/98)]] with the [[50/49|jubilisma (50/49)]]. | ||
All temperaments in the continuum satisfy (99/89)<sup>''n''</sup> ~ 50/49. Varying ''n'' results in different temperaments listed in the table below. It converges to the 11-limit temperament of [[Catalog of rank-4 temperaments#Mothwellsmic (99/98)|mothwellismic]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all 11-limit temperaments supported by [[Jubilismic family#Undecimal jubilismic|undecimal jubilismic]] 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 1.9899, and temperaments near this tend to be the most accurate ones. | All temperaments in the continuum satisfy (99/89)<sup>''n''</sup> ~ 50/49. Varying ''n'' results in different temperaments listed in the table below. It converges to the [[11-limit]] temperament of [[Catalog of rank-4 temperaments#Mothwellsmic (99/98)|mothwellismic]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all 11-limit temperaments supported by [[Jubilismic family#Undecimal jubilismic|undecimal jubilismic]] 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 1.9899, and temperaments near this tend to be the most accurate ones. | ||
{| class="wikitable" | {| class="wikitable" | ||
|+Temperaments in the continuum | |+Temperaments in the continuum | ||
Revision as of 02:18, 6 October 2026
The jubilismic equivalence continuum is a continuum of temperaments which equate a number of mothwellismas (99/98) with the jubilisma (50/49).
All temperaments in the continuum satisfy (99/89)n ~ 50/49. Varying n results in different temperaments listed in the table below. It converges to the 11-limit temperament of mothwellismic as n approaches infinity. If we allow non-integer and infinite n, the continuum describes the set of all 11-limit temperaments supported by undecimal jubilismic 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 1.9899, and temperaments near this tend to be the most accurate ones.
| n | Temperament | Comma | |
|---|---|---|---|
| Ratio | Monzo | ||
| -1 | 12 & 8d & 14c & 21e | 2475/2401 | [0 2 2 -4 1⟩ |
| 0 | Jubilismic extension | 50/49 | [1 0 2 -2 0⟩ |
| 1 | Ptolemismic | 100/99 | [2 -2 2 0 -1⟩ |
| 2 | Kalismic | 9801/9800 | [-3 4 -2 -2 2⟩ |
| 3 | 31 & 12 & 19 & 364 | 970299/960400 | [-4 6 -2 -4 3⟩ |
| ... | ... | ... | ... |
| ∞ | Mothwellismic | 99/98 | [-1 2 0 -2 1⟩ |