Submerged

Submerged is a temperament generated by a sharply tuned minor sixth (or its octave complement, a flatly tuned major third, adopted by this article for a comparison with magic), tempering out the submerged comma in the 5-limit. The 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 eleven 8/5's minus seven octaves stack to make a 3/2, thus making its ploidacot zeta-hendecacot.

For limits higher than 5, nine 5/4's 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.

Possible tunings include 16edo, 29edo, and 45edo.

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

See Avicennmic temperaments #Submerged for technical data.

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	25/16, 32/21
3	1117.8	40/21
4	290.4	25/21
5	663.0	16/11
6	1035.6	20/11
7	208.2	28/25
8	580.8	7/5
9	953.4	7/4
10	126.0	16/15
11	498.6	4/3
12	871.2	5/3
13	43.8	25/24

* In 5-limit CTE tuning

Scales

Submerged generates the mos scales 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	Lower bound of 7-odd-limit diamond monotone
	3/2	372.550	1/11-comma
14\45		373.333	45ef val
	5/3	373.697	1/12-comma
	25/24	374.667	1/13-comma
5\16		375.000	Upper bound of 7-odd-limit diamond monotone, major thirds slightly sharper than this fall under magic

See also

• 26/21, the 13-limit submajor third