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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 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''' 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 was named by [[User:Fitzgerald_Lee|Fitzgerald Lee]] as a play on the term "submajor third".
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'''.  


==Interval Chain==
In the following table, odd harmonics 1-15 and their inverses are in bold.
{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
|-
|-
Line 11: Line 18:
! Approximate ratios
! Approximate ratios
|-
|-
|0
| 0
|0.0
| 0.0
|'''1/1'''
| '''[[1/1]]'''
|-
|-
|1
| 1
|372.6
| 372.6
|'''5/4''', '''16/13'''
| '''[[5/4]]''', '''[[16/13]]'''
|-
|-
|2
| 2
|745.2
| 745.2
|14/9, 20/13
| [[25/16]], [[32/21]]
|-
|-
|3
| 3
|1117.8
| 1117.8
|21/11, 40/21
| [[40/21]]
|-
|-
|4
| 4
|290.4
| 290.4
|13/11, 32/27
| [[25/21]]
|-
|-
|5
| 5
|663.0
| 663.0
|'''16/11''', 22/15
| '''[[16/11]]'''
|-
|-
|6
| 6
|1035.6
| 1035.6
|20/11
| [[20/11]]
|-
|-
|7
| 7
|208.2
| 208.2
|'''9/8'''
| [[28/25]]
|-
|-
|8
| 8
|580.8
| 580.8
|7/5
| [[7/5]]
|-
|-
|9
| 9
|953.4
| 953.4
|26/15
| '''[[7/4]]'''
|-
|-
|10
| 10
|126.0
| 126.0
|'''16/15''', 15/14, 14/13
| '''[[16/15]]'''
|-
|-
|11
| 11
|498.6
| 498.6
|'''4/3'''
| '''[[4/3]]'''
|-
|-
|12
| 12
|871.2
| 871.2
|5/3
| [[5/3]]
|-
|-
|13
| 13
|43.8
| 43.8
|40/39
| [[25/24]]
|}
|}
<nowiki/>* In 5-limit CTE tuning
<nowiki/>* In 5-limit CTE tuning


==Scales==
== Scales ==
Submerged generates the [[MOS scale|MOSes]] [[3L 4s]], [[3L 7s]], [[3L 10s]] and [[13L 3s]].
Submerged generates the [[mos scale]]s [[3L 4s]], [[3L 7s]], [[3L 10s]] and [[13L 3s]].
==Tunings==
 
===Tuning Spectrum===
== Tunings ==
=== Tuning spectrum ===
{| class="wikitable center-all left-4"
{| class="wikitable center-all left-4"
|-
|-
! Edo<br>generator
! Edo<br>generator
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]*
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]
! Generator (¢)
! Generator (¢)
! Comments
! Comments
|-
|-
|[[13edo|4\13]]
| [[13edo|4\13]]
|
|  
|369.231
| 369.231
|Major thirds slightly flatter than this fall under 13&23
| Major thirds slightly flatter than this fall under 13&23
|-
|-
|
|  
|[[75/64]]
| [[75/64]]
|369.491
| 369.491
|1/9-comma
| 1/9-comma
|-
|-
|
|  
|[[15/8]]
| [[15/8]]
|371.173
| 371.173
|1/10-comma
| 1/10-comma
|-
|-
|[[29edo|8\29]]
| '''[[29edo|8\29]]'''
|
|  
|372.414
| '''372.414'''
|
| '''Lower bound of 7-odd-limit diamond monotone'''
|-
|-
|
|  
|[[3/2]]
| [[3/2]]
|372.550
| 372.550
|1/11-comma
| 1/11-comma
|-
|-
|[[45edo|14\45]]
| [[45edo|14\45]]
|
|  
|373.333
| 373.333
|
| 45ef val
|-
|-
|
|  
|[[5/3]]
| [[5/3]]
|373.697
| 373.697
|1/12-comma
| 1/12-comma
|-
|-
|
|  
|[[25/24]]
| [[25/24]]
|374.667
| 374.667
|1/13-comma
| 1/13-comma
|-
|-
|[[16edo|5\16]]
| '''[[16edo|5\16]]'''
|
|  
|375.000
| '''375.000'''
|Major thirds slightly sharper than this fall under [[magic]]
| '''Upper bound of 7-odd-limit diamond monotone''', major thirds slightly sharper than this fall under [[magic]]
|}
|}
==See also==
 
== See also ==
* [[26/21]], the 13-limit submajor third
* [[26/21]], the 13-limit submajor third
* [[16edo]]
 
* [[29edo]]
[[Category:Submerged| ]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Avicennmic temperaments]]
[[Category:Gariboh clan]]

Latest revision as of 06:08, 17 February 2026

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
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