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This category feels fitting enough (no 9-odd-limit monotone and high error)
 
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'''Shallowtone''' is a [[5-limit]] and higher [[temperament]] which tempers out the [[shallowtone comma]]. It is generated by a flat fifth, which is typically sharper than in [[mavila]] but flatter than in [[7edo]]. This gives it a high [[error]], although not as much as mavila. The ~[[5/4]] is reached by minus ten fifths octave-reduced, which is an augmented third (C-Ex) in melodic antidiatonic notation and a diminished third (C-Ebb) in harmonic antidiatonic notation. The only reasonable extension to the 7-limit tempers out [[36/35]]. Additionally, there is a weak extension [[Greenwoodmic temperaments#Semishallowtone|semishallowtone]] with a half-octave period, tempering out [[405/392]].   
{{Infobox regtemp
| Title = Shallowtone
| Subgroups = 2.3.5, 2.3.5.7
| Comma basis = [[295245/262144]] (5-limit)<br>[[36/35]], [[295245/262144]] (7-limit)
| Mapping = 1; 1 -10 12
| Edo join 1 = 7 | Edo join 2 = 30b
| Generators = 3/2
| Generators tuning = 681.2
| Optimization method = CWE
| MOS scales = [[2L&nbsp;3s]], [[2L&nbsp;5s]], [[7L&nbsp;2s]]
| Odd limit 1 = 5 | Mistuning 1 = 18.7 | Complexity 1 = 16
| Odd limit 2 = 9 | Mistuning 2 = 45.3 | Complexity 2 = 23
}}
'''Shallowtone''' is a [[regular temperament|temperament]] where the [[shallowtone comma]] is [[tempering out|tempered out]]. It is generated by a flattened [[3/2|perfect fifth]], typically sharper than in [[mavila]] but flatter than in [[7edo]], and [[5/4]] is reached by minus ten fifths [[octave reduction|octave-reduced]], which is an augmented third (C–E𝄪) in melodic antidiatonic notation and a diminished third (C–E𝄫) in harmonic antidiatonic notation. This gives it a high [[error]], although not as much as mavila.
 
The only reasonable [[extension]] to the [[7-limit]] tempers out [[36/35]]. Additionally, there is a weak extension [[Greenwoodmic temperaments #Semishallowtone|semishallowtone]] with a half-octave period, tempering out [[405/392]].   


The name was coined by [[User:CompactStar|CompactStar]] in 2024. It refers to how it is an opposite to [[deeptone]] (which is on the other side of 7edo), as well as because it is just below the diatonic "surface".
The name was coined by [[User:CompactStar|CompactStar]] in 2024. It refers to how it is an opposite to [[deeptone]] (which is on the other side of 7edo), as well as because it is just below the diatonic "surface".


See [[Syntonic-chromatic equivalence continuum#Shallowtone]] for technical data.  
See [[Mint temperaments #Shallowtone]] for technical data.  


== Interval chain ==
== Interval chain ==
In the following table, prime harmonics are labeled in '''bold'''.  
In the following table, prime harmonics are labeled in '''bold'''.
{|class="wikitable"
 
{| class="wikitable"
|-
|-
!rowspan="2"|#
! rowspan="2" | #
!rowspan="2"|Cents*
! rowspan="2" | Cents*
!colspan="2"|Approximate ratios
! colspan="2" | Approximate ratios
|-
|-
!5-limit
! 5-limit
!13-limit extension
! 13-limit extension
|-
|-
|0
| 0
|0.000
| 0.000
|[[1/1]]
| [[1/1]]
|
|  
|-
|-
|1
| 1
|681.801
| 681.801
|'''[[3/2]]'''
| '''[[3/2]]'''
|[[13/9]]
| [[13/9]]
|-
|-
|2
| 2
|163.602
| 163.602
|[[9/8]]
| [[9/8]]
|[[11/10]], [[13/12]], [[35/32]], [[81/70]], [[8192/8019]]
| [[11/10]], [[13/12]], [[35/32]], [[81/70]], [[8192/8019]]
|-
|-
|3
| 3
|845.403
| 845.403
|[[27/16]]
| [[27/16]]
|'''[[13/8]]''', [[117/70]], [[4096/2673]]
| '''[[13/8]]''', [[117/70]], [[4096/2673]]
|-
|-
|4
| 4
|327.204
| 327.204
|[[81/64]]
| [[81/64]]
|[[39/32]], [[99/80]], [[1024/891]]
| [[39/32]], [[99/80]], [[1024/891]]
|-
|-
|5
| 5
|1009.0511
| 1009.0511
|[[243/128]]
| [[243/128]]
|[[117/64]], [[512/297]]
| [[117/64]], [[512/297]]
|-
|-
|6
| 6
|490.806
| 490.806
|[[512/405]], [[729/512]]
| [[512/405]], [[729/512]]
|[[128/99]]
| [[128/99]]
|-
|-
|7
| 7
|1172.607
| 1172.607
|[[256/135]]
| [[256/135]]
|[[64/33]]
| [[64/33]]
|-
|-
|8
| 8
|654.408
| 654.408
|[[64/45]]
| [[64/45]]
|'''[[16/11]]''', [[112/81]]
| '''[[16/11]]''', [[112/81]]
|-
|-
|9
| 9
|136.209
| 136.209
|[[16/15]]
| [[16/15]]
|[[12/11]], [[28/27]]
| [[12/11]], [[28/27]]
|-
|-
|10
| 10
|818.010
| 818.010
|'''[[8/5]]'''
| '''[[8/5]]'''
|[[14/9]], [[18/11]], [[64/39]]
| [[14/9]], [[18/11]], [[64/39]]
|-
|-
|11
| 11
|299.811
| 299.811
|[[6/5]]
| [[6/5]]
|[[7/6]], [[27/22]], [[63/52]]
| [[7/6]], [[27/22]], [[63/52]]
|-
|-
|12
| 12
|981.612
| 981.612
|[[9/5]]
| [[9/5]]
|'''[[7/4]]''', [[26/15]], [[81/44]]
| '''[[7/4]]''', [[26/15]], [[81/44]]
|-
|-
|13
| 13
|463.413
| 463.413
|[[27/20]]
| [[27/20]]
|[[13/10]], [[21/16]], [[243/176]]
| [[13/10]], [[21/16]], [[243/176]]
|-
|-
|14
| 14
|1145.214
| 1145.214
|[[81/40]]
| [[81/40]]
|[[39/20]], [[63/32]], [[729/352]]
| [[39/20]], [[63/32]], [[729/352]]
|-
|-
|15
| 15
|627.015
| 627.015
|[[243/160]]
| [[243/160]]
|[[117/80]], [[189/128]]
| [[117/80]], [[189/128]]
|}
|}
<nowiki/>* In 5-limit CTE tuning, octave reduced


<nowiki>*</nowiki> in 5-limit CTE tuning
[[Category:Temperaments]]
[[Category:Shallowtone| ]] <!-- main article -->
[[Category:Shallowtone| ]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Mint temperaments]]
[[Category:Mint temperaments]]
[[Category:Exotemperaments]]
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