Dicot

This page is about the regular temperament. For the ploidacot signature, see Ploidacot/Dicot.

Dicot is an exotemperament that tempers out 25/24. It is also the first fully prototypical dicot temperament. It tempers 6/5 and 5/4 into the same neutral third interval, which, when the fifth is tuned pure, is sqrt(3/2). It is useful to represent the structure of 5-limit harmonies without fully representing them in its greater accuracy, with mos scales 3L 4s and 7L 3s.

It can be extended by tempering out 15/14 and 36/35 in the 7-limit, though this could turn the 3L 4s mos into a 4L 3s mos. This makes 7/6 and 9/7 equated to the neutral third, viewing 6:7:9 as a tertian chord.

Another notable extension of dicot is decimal, which splits the octave in two for 7/5~10/7 by tempering out 50/49, and equates 7/6 and 8/7 to the tritone complement of 5/4~6/5, neutralizing the 6:7:8 chord as well. This represents the structure of 7-limit harmonies in a way that is not based on tertian harmony and a heptatonic system, but rather a decatonic one.

For technical data, see Dicot family #Dicot.

Interval chain

In the following table, odd harmonics 1–9 are labeled in bold.

#	Cents*	Approximate ratios
0	0.0	1/1
1	351.1	5/4, 6/5
2	702.2	3/2
3	1053.3	9/5, 15/8
4	204.3	9/8

* In 5-limit CWE tuning

Tunings

Norm-based tunings

Todo: complete section

Tuning Spectrum

Edo generator	Eigenmonzo (Unchanged-interval)*	Generator (¢)	Comments
1\4		300.000	Lower bound of 5-odd-limit diamond monotone
	6/5	315.641	Full comma
	9/5	339.199	2/3-comma
2\7		342.857	Lower bound of 5-limit 9-odd-limit diamond monotone
	27/20	343.910	3/5-comma
7\24		350.000	24c val
	3/2	350.978	1/2-comma
5\17		352.941
	27/20	358.405	2/5-comma
3\10		360.000
	15/8	362.756	1/3-comma
	5/4	386.314	Untempered tuning
1\3		400.000	Upper bound of 5-odd-limit, 5-limit 9-odd-limit diamond monotone

* Besides the octave