Submerged

Submerged (16 & 29) is a temperament generated by a ~373¢ 5/4, tempering out the submerged comma in the 5-limit. Its major third is slightly flat of magic's major third, which itself is slightly flat of a just 5/4, making submerged's generator arguably a submajor third. The comma's monzo is [-27 1 11⟩, which implies that 11 5/4s stack to make a 4/3, thus making its ploidacot omega-hendecacot.

For limits higher than 5, 9 5/4s stack to reach 7/4, and it tempers out 525/512 and 3125/3087 in the 7-limit, and in the 11-limit, 441/440 and 121/120. In the 13-limit, in addition to tempering out 105/104, if we look at a submerged third, it sits in between 16/13 and 5/4, and a very logical thing to do is to temper out the difference between these two intervals, thus also tempering out 65/64.

Submerged was named by Fitzgerald Lee as a play on the term "submajor third".

Interval Chain

In the following table, odd harmonics 1-15 and their inverses are in bold.

#	Cents*	Approximate ratios
0	0.0	1/1
1	372.6	5/4, 16/13
2	745.2	32/21, 20/13
3	1117.8	40/21, 25/13
4	290.4	64/55, 13/11
5	663.0	16/11, 22/15
6	1035.6	20/11, 11/6
7	208.2	25/22, 55/48
8	580.8	7/5, 55/39
9	953.4	26/15, 7/4
10	126.0	16/15, 14/13
11	498.6	4/3, 35/26
12	871.2	64/39, 5/3
13	43.8	40/39, 25/24

* In 5-limit CTE tuning

Scales

Submerged generates the MOSes 3L 4s, 3L 7s, 3L 10s and 13L 3s.

Tunings

Tuning Spectrum

Edo generator	Unchanged interval (eigenmonzo)	Generator (¢)	Comments
4\13		369.231	Major thirds slightly flatter than this fall under 13&23
	75/64	369.491	1/9-comma
	15/8	371.173	1/10-comma
8\29		372.414
	3/2	372.550	1/11-comma
14\45		373.333
	5/3	373.697	1/12-comma
	25/24	374.667	1/13-comma
5\16		375.000	Major thirds slightly sharper than this fall under magic

See also

• 26/21, the 13-limit submajor third
• 16edo
• 29edo