Shallowtone: Difference between revisions
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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]]. | '''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]]. | ||
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 | 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 | See [[Syntonic–chromatic equivalence continuum#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" | 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]] | ||
|- | |- | ||
|7 | | 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 | |||
[[Category:Shallowtone| ]] <!-- main article --> | [[Category:Shallowtone| ]] <!-- main article --> | ||
[[Category:Rank-2 temperaments]] | |||
[[Category:Mint temperaments]] | [[Category:Mint temperaments]] | ||