Shallowtone: Difference between revisions

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| Generators tuning = 681.2

| Optimization method = CWE

| MOS scales = [[2L 3s]], [[2L 5s]], [[7L 2s]]

| MOS scales = [[2L 3s]], [[2L 5s]], [[7L 2s]], [[7L 9s]]

| Odd limit 1 = 5 | Mistuning 1 = 18.7 | Complexity 1 = 16

| Odd limit 2 = 9 | Mistuning 2 = 45.3 | Complexity 2 = 23

}}

'''Shallowtone''' is a [[regular temperament|temperament]] where the [[shallowtone comma]] is [[tempering out|tempered out]]. It is generated by a flattened [[3/2|perfect fifth]], typically sharper than in [[mavila]] but flatter than in [[7edo]], and [[5/4]] is reached by minus ten fifths [[octave reduction|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. It is very high [[badness]] ~~as it is both~~ of fairly high complexity ~~and an~~ [[~~exotemperament~~]] ~~or near-exotemperament~~.

'''Shallowtone''' is a [[regular temperament|temperament]] where the [[shallowtone comma]] is [[tempering out|tempered out]]. It is generated by a flattened [[3/2|perfect fifth]], typically sharper than in [[mavila]] but flatter than in [[7edo]], and [[5/4]] is reached by minus ten fifths [[octave reduction|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 [[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".

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.

@@ Line 8: / Line 8: @@
 | Generators tuning = 681.2
 | Optimization method = CWE
-| MOS scales = [[2L&nbsp;3s]], [[2L&nbsp;5s]], [[7L&nbsp;2s]]
+| MOS scales = [[2L&nbsp;3s]], [[2L&nbsp;5s]], [[7L&nbsp;2s]], [[7L&nbsp;9s]]
 | Odd limit 1 = 5 | Mistuning 1 = 18.7 | Complexity 1 = 16
 | Odd limit 2 = 9 | Mistuning 2 = 45.3 | Complexity 2 = 23
 }}
-'''Shallowtone''' is a [[regular temperament|temperament]] where the [[shallowtone comma]] is [[tempering out|tempered out]]. It is generated by a flattened [[3/2|perfect fifth]], typically sharper than in [[mavila]] but flatter than in [[7edo]], and [[5/4]] is reached by minus ten fifths [[octave reduction|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. It is very high [[badness]] as it is both of fairly high complexity and an [[exotemperament]] or near-exotemperament.
+'''Shallowtone''' is a [[regular temperament|temperament]] where the [[shallowtone comma]] is [[tempering out|tempered out]]. It is generated by a flattened [[3/2|perfect fifth]], typically sharper than in [[mavila]] but flatter than in [[7edo]], and [[5/4]] is reached by minus ten fifths [[octave reduction|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 [[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".
+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.

Shallowtone: Difference between revisions

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