Submerged: Difference between revisions
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{{Infobox regtemp | |||
| Title = Submerged | |||
| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13 | |||
| Comma basis = [[525/512]], [[3125/3087]] (7-limit); <br>[[121/120]], [[441/440]], [[525/512]] (11-limit); <br>[[65/64]], [[105/104]], [[121/120]], [[441/440]]<br>(13-limit) | |||
| Edo join 1 = 16 | Edo join 2 = 29 | |||
| Mapping = 1; 11 -1 -9 5 1 | |||
| Generators = 8/5 | Generators tuning = 827.0 | Optimization method = CWE | |||
| MOS scales = [[3L 7s]], [[3L 10s]], [[13L 3s]] | |||
| Odd limit 1 = 9 | Mistuning 1 = 13.2 | Complexity 1 = 45 | |||
| Odd limit 2 = 13 | Mistuning 2 = 14.7 | Complexity 2 = 45 | |||
}} | |||
'''Submerged''' is a [[regular temperament|temperament]] [[periods and generators|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 and supraminor|submajor]] third. The comma's [[monzo]] is {{monzo| -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. | '''Submerged''' is a [[regular temperament|temperament]] [[periods and generators|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 and supraminor|submajor]] third. The comma's [[monzo]] is {{monzo| -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. | ||
| Line 28: | Line 39: | ||
| 2 | | 2 | ||
| 745.2 | | 745.2 | ||
| [[ | | [[25/16]], [[32/21]] | ||
|- | |- | ||
| 3 | | 3 | ||
| 1117.8 | | 1117.8 | ||
| [[40/21 | | [[40/21]] | ||
|- | |- | ||
| 4 | | 4 | ||
| 290.4 | | 290.4 | ||
| [[ | | [[25/21]] | ||
|- | |- | ||
| 5 | | 5 | ||
| 663.0 | | 663.0 | ||
| '''[[16/11]]''' | | '''[[16/11]]''' | ||
|- | |- | ||
| 6 | | 6 | ||
| 1035.6 | | 1035.6 | ||
| [[20/11 | | [[20/11]] | ||
|- | |- | ||
| 7 | | 7 | ||
| 208.2 | | 208.2 | ||
| [[25 | | [[28/25]] | ||
|- | |- | ||
| 8 | | 8 | ||
| 580.8 | | 580.8 | ||
| [[7/5 | | [[7/5]] | ||
|- | |- | ||
| 9 | | 9 | ||
| 953.4 | | 953.4 | ||
| | | '''[[7/4]]''' | ||
|- | |- | ||
| 10 | | 10 | ||
| 126.0 | | 126.0 | ||
| '''[[16/15]]''' | | '''[[16/15]]''' | ||
|- | |- | ||
| 11 | | 11 | ||
| 498.6 | | 498.6 | ||
| '''[[4/3]]''' | | '''[[4/3]]''' | ||
|- | |- | ||
| 12 | | 12 | ||
| 871.2 | | 871.2 | ||
| | | [[5/3]] | ||
|- | |- | ||
| 13 | | 13 | ||
| 43.8 | | 43.8 | ||
| | | [[25/24]] | ||
|} | |} | ||
<nowiki/>* In 5-limit CTE tuning | <nowiki/>* In 5-limit CTE tuning | ||
| Line 103: | Line 114: | ||
| 1/10-comma | | 1/10-comma | ||
|- | |- | ||
| [[29edo|8\29]] | | '''[[29edo|8\29]]''' | ||
| | | | ||
| '''372.414''' | |||
| '''Lower bound of 7-odd-limit diamond monotone''' | |||
|- | |- | ||
| | | | ||
| Line 116: | Line 127: | ||
| | | | ||
| 373.333 | | 373.333 | ||
| | | 45ef val | ||
|- | |- | ||
| | | | ||
| Line 128: | Line 139: | ||
| 1/13-comma | | 1/13-comma | ||
|- | |- | ||
| [[16edo|5\16]] | | '''[[16edo|5\16]]''' | ||
| | | | ||
| 375.000 | | '''375.000''' | ||
| | | '''Upper bound of 7-odd-limit diamond monotone''', major thirds slightly sharper than this fall under [[magic]] | ||
|} | |} | ||
Latest revision as of 13:39, 8 August 2026
| Submerged |
121/120, 441/440, 525/512 (11-limit);
65/64, 105/104, 121/120, 441/440
(13-limit)
13-odd-limit: 14.7 ¢
13-odd-limit: 45 notes
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