Tarot equivalence continuum
The Tarot equivalence continuum is a continuum of 2.3.5 subgroup temperaments which all equate a number of 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 (2-1933154･5-22)n ~ (2-225･3224･5-56). 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.
| n | Temperament | Comma (monzo) |
|---|---|---|
| 0 | Major Arcana | [-193 154 -22⟩ |
| 1 | Minortone | [16 35 -17⟩ |
| 2 | Atomic | [161 -84 -12⟩ |
| 3 | 1848 & 53 | [-177 119 -5⟩ |
| 4 | 1848 & 3296 | [-547 392 -32⟩ |
| 5 | 1848 & 3243 | [-370 273 -27⟩ |
| … | … | … |
| ∞ | Barium |
Empress
Empress tempers out the [-177 119 -5⟩ comma, and since it's number 3 in the equivalence continuum, it is named after the 3rd Major Arcana card.
Subgroup: 2.3.5
Comma list: [-177 119 -5⟩
Mapping: [⟨1 3 36], ⟨0 -5 -119]]
Optimal tuning (CTE): ~343597383680/282429536481 = 339.611
Optimal ET sequence: 53, 1530, 1583, 1636, 1689, 1742, 1795, 1848, 1901, 1954, ...