Tarot equivalence continuum: Difference between revisions
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The Tarot equivalence continuum is a continuum of 2.3.5 subgroup temperaments which all equate a number of [[22nd-octave temperaments#Major Arcana|Major Arcana]] commas with the [[barium]] comma, which due to it being period-56 can also be called Minor Arcana comma. Since there's 22 cards in the Major Arcana, and 56 in the Minor Arcana, the natural name that arises is Tarot equivalence continuum. | The Tarot equivalence continuum is a continuum of 2.3.5 subgroup temperaments which all equate a number of [[22nd-octave temperaments#Major Arcana|Major Arcana]] commas with the [[barium]] comma, which due to it being period-56 can also be called Minor Arcana comma. Since there's 22 cards in the Major Arcana, and 56 in the Minor Arcana, the natural name that arises is Tarot equivalence continuum. | ||
All temperaments in this continuum satisfy (2<sup>-193</sup>3<sup>154</sup>･5<sup>-22</sup>)<sup>''n''</sup> ~ (2<sup>-225</sup>･3<sup>224</sup>･5<sup>-56</sup>). If we allow non-integer and infinite ''n'', the continuum describes the set of all 5-limit temperaments supported by [[1848edo]] due to it being the unique equal temperament that tempers both commas and thus tempers all combinations of them. The just value of n is approximately 2.0070839..., and temperaments having ''n'' near this value tend to be the most accurate ones. | All temperaments in this continuum satisfy (2<sup>-193</sup>3<sup>154</sup>･5<sup>-22</sup>)<sup>''n''</sup> ~ (2<sup>-225</sup>･3<sup>224</sup>･5<sup>-56</sup>). If we allow non-integer and infinite ''n'', the continuum describes the set of all 5-limit temperaments supported by [[1848edo]], due to it being the unique equal temperament that tempers both commas and thus tempers all combinations of them. The just value of n is approximately 2.0070839..., and temperaments having ''n'' near this value tend to be the most accurate ones. | ||
The continuum contains two notable 5-limit temperaments supported by 1848edo, minortone and atomic. | |||
{| class="wikitable center-1 center-2 center-4 center-5" | {| class="wikitable center-1 center-2 center-4 center-5" | ||
|- | |- | ||
! | !''n'' | ||
! | !Temperament | ||
! | !Comma (monzo) | ||
|- | |- | ||
|0 | |0 | ||
| | |[[22nd-octave temperaments#Major Arcana|Major Arcana]] | ||
| | |[-193 154 -22⟩ | ||
| | |||
|- | |- | ||
|1 | |1 | ||
| | |[[Minortone]] | ||
| | |[-16 35 -17⟩ | ||
|- | |- | ||
|2 | |2 | ||
| | |[[Atomic]] | ||
| | |[[Kirnberger's atom|[161 -84 -12⟩]] | ||
| | |||
|- | |- | ||
|3 | |3 | ||
| | |1848 & 53 | ||
| | |[-177 119 -5⟩ | ||
| | |- | ||
| | |4 | ||
| | |1848 & 3296 | ||
| | |[-547,392,-32> | ||
| | |- | ||
|5 | |||
|1848 & 3243 | |||
| -370,273,-27> | |||
|- | |- | ||
|… | |… | ||
|… | |… | ||
| Line 62: | Line 39: | ||
|- | |- | ||
|∞ | |∞ | ||
| | |[[Barium]] | ||
| | | | ||
|} | |} | ||