View source for Shallowtone

'''Shallowtone''' is a [[5-limit]] and higher [[regular temperament|temperament]] which [[tempering out|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]].  

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 [[Mint temperaments #Shallowtone]] for technical data. 

== Interval chain ==
In the following table, prime harmonics are labeled in '''bold'''.

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

[[Category:Shallowtone| ]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Mint temperaments]]