Shallowtone
| Shallowtone |
36/35, 295245/262144 (7-limit)
9-odd-limit: 45.3 ¢
9-odd-limit: 23 notes
Shallowtone is a temperament where the shallowtone comma is tempered out. It is generated by a flattened perfect fifth, typically sharper than in mavila but flatter than in 7edo, and 5/4 is reached by minus ten fifths 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, debatably making it an exotemperament or near-exotemperament. It is of very high badness due to a combination of this high error and a fairly high complexity (but it's still within the realm of usability, e.g. it could be conceivably used with a 7L 9s scale).
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".
A related somewhat more practical temperament is deeptone, which is generated by a fifth slightly sharp of 7edo's fifth instead of slightly flat, and shallowtone's mapping of 6/5 is the same as deeptone's mapping of 5/4. Basically, shallowtone is to deeptone as mavila is to meantone. Undecimation is a more accurate temperament with a similar generator.
See Mint temperaments #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, octave reduced