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.