Submerged: Difference between revisions
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→Interval Chain: Arranged intervals Tags: Mobile edit Mobile web edit Advanced mobile edit |
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| Line 21: | Line 21: | ||
|2 | |2 | ||
|745.2 | |745.2 | ||
|14/9 | |20/13, 14/9 | ||
|- | |- | ||
|3 | |3 | ||
|1117.8 | |1117.8 | ||
|21/11 | |40/21, 21/11 | ||
|- | |- | ||
|4 | |4 | ||
| Line 37: | Line 37: | ||
|6 | |6 | ||
|1035.6 | |1035.6 | ||
|20/11 | |9/5, 20/11, 11/6 | ||
|- | |- | ||
|7 | |7 | ||
| Line 45: | Line 45: | ||
|8 | |8 | ||
|580.8 | |580.8 | ||
|7/5 | |18/13, 7/5 | ||
|- | |- | ||
|9 | |9 | ||
|953.4 | |953.4 | ||
|26/15 | |12/7, 26/15, '''7/4''' | ||
|- | |- | ||
|10 | |10 | ||
|126.0 | |126.0 | ||
|'''16/15''', 15/14, 14/13 | |'''16/15''', 15/14, 14/13, 13/12 | ||
|- | |- | ||
|11 | |11 | ||
| Line 61: | Line 61: | ||
|12 | |12 | ||
|871.2 | |871.2 | ||
|5/3 | |18/11, 5/3 | ||
|- | |- | ||
|13 | |13 | ||
|43.8 | |43.8 | ||
|40/39 | |33/32, 40/39, 45/44 | ||
|} | |} | ||
<nowiki/>* In 5-limit CTE tuning | <nowiki/>* In 5-limit CTE tuning | ||
Revision as of 14:33, 7 November 2025
Submerged (16 & 29) is a temperament generated by a ~373¢ 5/4, tempering out 146484375/134217728 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 means that 11 5/4s stack to make a 4/3, thus making its ploidacot omega-hendecacot. 9 5/4s stack to reach 7/4, and it tempers out 525/512 and 3125/3087 in the 7-limit. A submerged third 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, tempering out 65/64 in the 13-limit.
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 | 20/13, 14/9 |
| 3 | 1117.8 | 40/21, 21/11 |
| 4 | 290.4 | 13/11, 32/27 |
| 5 | 663.0 | 16/11, 22/15 |
| 6 | 1035.6 | 9/5, 20/11, 11/6 |
| 7 | 208.2 | 9/8 |
| 8 | 580.8 | 18/13, 7/5 |
| 9 | 953.4 | 12/7, 26/15, 7/4 |
| 10 | 126.0 | 16/15, 15/14, 14/13, 13/12 |
| 11 | 498.6 | 4/3 |
| 12 | 871.2 | 18/11, 5/3 |
| 13 | 43.8 | 33/32, 40/39, 45/44 |
* 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 |