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- | '''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. | The name was coined by [[User:CompactStar|CompactStar]] in 2024. | ||
Revision as of 00:52, 4 August 2024
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.
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 |
| 3 | 845.403 | 27/16 | 13/8, 117/70 |
| 4 | 327.204 | 81/64 | 39/32, 99/80 |
| 5 | 1009.0511 | ||
| 6 | 490.806 | ||
| 7 |
| ||
- in 5-limit CTE tuning
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