Submerged: Difference between revisions
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'''Submerged''' (16 & 29) is a temperament [[generator|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 | '''Submerged''' (16 & 29) is a temperament [[generator|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_and_supraminor|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 [[User:Fitzgerald_Lee|Fitzgerald Lee]] as a play on the term "submajor third". | Submerged was named by [[User:Fitzgerald_Lee|Fitzgerald Lee]] as a play on the term "submajor third". | ||
==Interval Chain== | ==Interval Chain== | ||
In the following table, odd harmonics 1-15 and their inverses are in bold. | In the following table, odd harmonics 1-15 and their inverses are in bold. | ||
Revision as of 13:56, 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 | 14/9, 20/13 |
| 3 | 1117.8 | 21/11, 40/21 |
| 4 | 290.4 | 13/11, 32/27 |
| 5 | 663.0 | 16/11, 22/15 |
| 6 | 1035.6 | 20/11 |
| 7 | 208.2 | 9/8 |
| 8 | 580.8 | 7/5 |
| 9 | 953.4 | 26/15 |
| 10 | 126.0 | 15/14, 14/13 |
| 11 | 498.6 | 3/2 |
| 12 | 871.2 | 5/3 |
| 13 | 43.8 | 40/39 |
* 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 |