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]].

{{Infobox regtemp

| Title = Shallowtone

| Subgroups = 2.3.5, 2.3.5.7

| Comma basis = [[295245/262144]] (5-limit);<br>[[36/35]], [[295245/262144]] (7-limit)

| Mapping = 1; 1 -10 12

| Edo join 1 = 7 | Edo join 2 = 30b

| Generators = 3/2

| Generators tuning = 681.2

| Optimization method = CWE

| 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, 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".

See [[~~Syntonic–chromatic equivalence continuum~~#Shallowtone]] for technical data.

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 ==

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{| class="wikitable"

|-

! rowspan="2" | &#~~35;~~

! rowspan="2" | #

! rowspan="2" | Cents*

! colspan="2" | Approximate ratios

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| [[117/80]], [[189/128]]

|}

<nowiki />* In 5-limit CTE tuning

<nowiki/>* In 5-limit CTE tuning, octave reduced

~~[[Category:Temperaments]]~~

[[Category:Shallowtone| ]]

[[Category:Rank-2 temperaments]]

[[Category:Mint temperaments]]

[[Category:Exotemperaments]]

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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]].
+{{Infobox regtemp
+| Title = Shallowtone
+| Subgroups = 2.3.5, 2.3.5.7
+| Comma basis = [[295245/262144]] (5-limit);<br>[[36/35]], [[295245/262144]] (7-limit)
+| Mapping = 1; 1 -10 12
+| Edo join 1 = 7 | Edo join 2 = 30b
+| Generators = 3/2
+| Generators tuning = 681.2
+| Optimization method = CWE
+| 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, 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".
-See [[Syntonic&ndash;chromatic equivalence continuum#Shallowtone]] for technical data.
+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 ==
@@ Line 10: / Line 27: @@
 {| class="wikitable"
 |-
-! rowspan="2" | &#35;
+! rowspan="2" | #
 ! rowspan="2" | Cents*
 ! colspan="2" | Approximate ratios
@@ Line 97: / Line 114: @@
 | [[117/80]], [[189/128]]
 |}
-<nowiki />* In 5-limit CTE tuning
+<nowiki/>* In 5-limit CTE tuning, octave reduced
-[[Category:Temperaments]]
 [[Category:Shallowtone| ]] <!-- main article -->
+[[Category:Rank-2 temperaments]]
 [[Category:Mint temperaments]]
+[[Category:Exotemperaments]]

Shallowtone: Difference between revisions

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