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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 | 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" | # | ||
!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]] | | [[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 | |||
[[Category:Shallowtone| ]] <!-- main article --> | [[Category:Shallowtone| ]] <!-- main article --> | ||
[[Category:Rank-2 temperaments]] | |||
[[Category:Mint temperaments]] | [[Category:Mint temperaments]] | ||
Latest revision as of 14:40, 28 April 2025
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 semishallowtone with a half-octave period, tempering out 405/392.
The name was coined by 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.
Interval chain
In the following table, prime harmonics are labeled in bold.
| # | Cents* | 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 |
* In 5-limit CTE tuning