Neutral temperaments
Dicot[a] (7 & 10) is an exotemperament that can be defined to temper out 25/24, the dicot comma. The provided edo join also tempers out 45/44 and 64/63 in the 11-limit, representing the extension dichotic and also tempering out 55/54. Alternative extensions include 4 & 7 (which conflates 9/7~7/6~6/5~5/4).
Dicot makes 4:5:6 equidistant, suggesting the simplified structure of tertian harmony, the same way semaphore does for chthonic harmony. As a result, the temperament archetype dicot is named after it.
Interval chart
This interval chart uses Partch's 11-limit tonality diamond and maps it onto 7edo and 10edo. This also gives an idea of what intervals are possible in dicot temperament. Intervals in bold are in the 7-note MOS (symmetric mode) and intervals in italics are in the 10-note MOS (both near-symmetric modes). Note that the interval that can be mapped to 11/8 and 10/7 and the interval mapped to 7/5 and 16/11 cannot coexist in the same 10-note MOS.
| 0\7 | 1\7 | 2\7 | 3\7 | 4\7 | 5\7 | 6\7 | 7\7 | |
|---|---|---|---|---|---|---|---|---|
| 0\10 | 1/1 | |||||||
| 1\10 | 12/11, 10/9 | |||||||
| 2\10 | 11/10, 9/8, 8/7 | 7/6 | ||||||
| 3\10 | 6/5, 11/9, 5/4 | 14/11 | ||||||
| 4\10 | 9/7 | 4/3 | ||||||
| 5\10 | 11/8, 10/7 | 7/5, 16/11 | ||||||
| 6\10 | 3/2 | 14/9 | ||||||
| 7\10 | 11/7 | 8/5, 18/11, 5/3 | ||||||
| 8\10 | 12/7 | 7/4, 16/9, 20/11 | ||||||
| 9\10 | 9/5, 11/6 | |||||||
| 10\10 | 2/1 |
This chart additionally shows how the interval categories of the 7-form and 10-form are related.
Etymology
Dicot originates from the term "dicot" in botany, referring to plants with two embryonic leaves, perhaps by analogy with 3/2 being split into two generators. The name dicot would also inspire tetracot, alphatricot, and by extension the ploidacot temperament archetype naming system as a whole.
Tuning considerations
A perfect ~351c tuning of the generator, while useful for understanding tertian harmony and suggested by some temperament tuning optimization systems, does not reasonably approximate either 5/4 or 6/5. The optimal tunings of dicot are roughly bimodal, with ~360c (around 10edo) and ~343c (around 7edo) both being better tunings.
Theory
Dicot is generated by a neutral 3rd, or one half of a perfect fifth, representing 5/4 and 6/5. It may be notated with the 7-form as any neutral third temperament.
[a] The name interpental has been proposed, however it currently is used by 43 & 53, a weak extension of buzzard.
