Deeptone: Difference between revisions

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'''Deeptone''' or '''tragicomical''' is a [[5-limit]] [[temperament]] that tempers out the [[comma]] [[177147/163840]]. It is generated by a fifth (~[[3/2]]), which is typically sharper than in 7edo but flatter than in [[flattone]] or [[flattertone]] (approximately 686-691{{cent}}). The ~[[5/4]] is reached by eleven fifths octave-reduced, which is an augmented third (C–E♯). A characteristic feature of deeptone is that the [[81/80|syntonic comma]] is tuned negative, represented by a diminished unison (C–C♭). This means that ~[[81/64]] is a ''submajor third'', tuned flatter than ~[[5/4]], and ~[[32/27]] is a ''supraminor third'', tuned sharper than ~[[6/5]]. It has high [[error]] because of its flat tuning of 3/2, although the well-known [[~~Mavila~~]] temperament has a 3/2 that is much flatter still. ~~4 EDOs~~ support ~~Deeptone~~ in their [[patent val]] ([[7edo]], [[33edo]], [[40edo]], and [[47edo]]), and additionally there is the near-patent val [[54edo|54b-edo]].

'''Deeptone''' or '''tragicomical''' is a [[5-limit]] [[regular temperament|temperament]] that [[tempering out|tempers out]] the [[comma]] [[177147/163840]]. It is generated by a fifth (~[[3/2]]), which is typically sharper than in [[7edo]] but flatter than in [[flattone]] or [[flattertone]] (approximately 686-691{{cent}}). The ~[[5/4]] is reached by eleven fifths octave-reduced, which is an augmented third (C–E♯). A characteristic feature of deeptone is that the [[81/80|syntonic comma]] is tuned negative, represented by a diminished unison (C–C♭). This means that ~[[81/64]] is a ''submajor third'', tuned flatter than ~[[5/4]], and ~[[32/27]] is a ''supraminor third'', tuned sharper than ~[[6/5]]. It has high [[error]] because of its flat tuning of 3/2, although the well-known [[mavila]] temperament has a 3/2 that is much flatter still. Four edos support deeptone in their [[patent val]] ([[7edo]], [[33edo]], [[40edo]], and [[47edo]]), and additionally there is the near-patent val [[54edo|54b-edo]].

See [[Syntonic–chromatic equivalence continuum#Deeptone a.k.a. tragicomical]] for technical data.

See [[Syntonic–chromatic equivalence continuum #Deeptone a.k.a. tragicomical]] for technical data.

[[File:Deeptone7.mp3|none|thumb|Deeptone[7] major scale in 40edo.]]

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== Extensions ==

Deeptone has an accurate [[13/8]], represented by the interval notated as a minor sixth, so it is very plausible to have a 2.3.5.13 [[subgroup]] extension tempering out both [[177147/163840]] and [[1053/1024]] (the ''tridecimal ~~comma''~~). This also gives a more simple interpretation of ~~Deeptone~~'s major and minor thirds as tridecimal neutral thirds [[16/13]] and [[39/32]] respectively. Tuning this Deeptone extension in [[40edo]] results in essentially perfect tuning of [[13/8]] and [[16/13]], which is inherited from [[10edo]].

Deeptone has an accurate [[13/8]], represented by the interval notated as a minor sixth, so it is very plausible to have a 2.3.5.13-[[subgroup]] [[extension]] tempering out both [[177147/163840]] and [[1053/1024]] (the tridecimal quartertone). This also gives a more simple interpretation of deeptone's major and minor thirds as tridecimal neutral thirds [[16/13]] and [[39/32]] respectively. Tuning this Deeptone extension in [[40edo]] results in essentially perfect tuning of [[13/8]] and [[16/13]], which is inherited from [[10edo]].

== Scales ==

When properly tuned, Deeptone features [[~~MOS~~ scale]]s of the families [[2L 3s]], [[5L 2s]], [[7L 5s]], [[7L 12s]], and [[7L 19s]]. Another important scale, intermediate between the [[7L 5s]] and [[7L 12s]] scales, is the "Deeptone[14]" non-~~MOS~~ scale. This scale is notable for being the smallest ~~Deeptone~~ scale that is generally "complete" for 5-limit purposes (as noted by [[groundfault]]) since Deeptone[12] has a paucity of 5-limit triads. Deeptone[14] is essentially just two interlaced Deeptone[7] diatonic scales with one of them being offset by an augmented unison above the other.

When properly tuned, Deeptone features [[mos scale]]s of the families [[2L 3s]], [[5L 2s]], [[7L 5s]], [[7L 12s]], and [[7L 19s]]. Another important scale, intermediate between the [[7L 5s]] and [[7L 12s]] scales, is the "Deeptone[14]" non-mos scale. This scale is notable for being the smallest deeptone scale that is generally "complete" for 5-limit purposes (as noted by [[groundfault]]) since Deeptone[12] has a paucity of 5-limit triads. Deeptone[14] is essentially just two interlaced Deeptone[7] diatonic scales with one of them being offset by an augmented unison above the other.

== Interval chain ==

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{| class="wikitable center-1 right-2"

|-

! &#~~35;~~

! #

! colspan="3" | Notation

! Cents*

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| 7 || aug unison || A1 || C# || 29.153 || [[2187/2048]], [[81/80|80/81]] || [[27/26]]

|}

<nowiki />* In 5-limit CTE tuning

<nowiki/>* In 5-limit CTE tuning

== Notes ==

[[Category:Temperaments]]

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-'''Deeptone''' or '''tragicomical''' is a [[5-limit]] [[temperament]] that tempers out the [[comma]] [[177147/163840]]. It is generated by a fifth (~[[3/2]]), which is typically sharper than in 7edo but flatter than in [[flattone]] or [[flattertone]] (approximately 686-691{{cent}}). The ~[[5/4]] is reached by eleven fifths octave-reduced, which is an augmented third (C–E♯). A characteristic feature of deeptone is that the [[81/80|syntonic comma]] is tuned negative, represented by a diminished unison (C–C♭). This means that ~[[81/64]] is a ''submajor third'', tuned flatter than ~[[5/4]], and ~[[32/27]] is a ''supraminor third'', tuned sharper than ~[[6/5]]. It has high [[error]] because of its flat tuning of 3/2, although the well-known [[Mavila]] temperament has a 3/2 that is much flatter still. 4 EDOs support Deeptone in their [[patent val]] ([[7edo]], [[33edo]], [[40edo]], and [[47edo]]), and additionally there is the near-patent val [[54edo|54b-edo]].
+'''Deeptone''' or '''tragicomical''' is a [[5-limit]] [[regular temperament|temperament]] that [[tempering out|tempers out]] the [[comma]] [[177147/163840]]. It is generated by a fifth (~[[3/2]]), which is typically sharper than in [[7edo]] but flatter than in [[flattone]] or [[flattertone]] (approximately 686-691{{cent}}). The ~[[5/4]] is reached by eleven fifths octave-reduced, which is an augmented third (C–E♯). A characteristic feature of deeptone is that the [[81/80|syntonic comma]] is tuned negative, represented by a diminished unison (C–C♭). This means that ~[[81/64]] is a ''submajor third'', tuned flatter than ~[[5/4]], and ~[[32/27]] is a ''supraminor third'', tuned sharper than ~[[6/5]]. It has high [[error]] because of its flat tuning of 3/2, although the well-known [[mavila]] temperament has a 3/2 that is much flatter still. Four edos support deeptone in their [[patent val]] ([[7edo]], [[33edo]], [[40edo]], and [[47edo]]), and additionally there is the near-patent val [[54edo|54b-edo]].
-See [[Syntonic–chromatic equivalence continuum#Deeptone a.k.a. tragicomical]] for technical data.
+See [[Syntonic–chromatic equivalence continuum #Deeptone a.k.a. tragicomical]] for technical data.
 [[File:Deeptone7.mp3|none|thumb|Deeptone[7] major scale in 40edo.]]
@@ Line 10: / Line 10: @@
 == Extensions ==
-Deeptone has an accurate [[13/8]], represented by the interval notated as a minor sixth, so it is very plausible to have a 2.3.5.13 [[subgroup]] extension tempering out both [[177147/163840]] and [[1053/1024]] (the ''tridecimal comma''). This also gives a more simple interpretation of Deeptone's major and minor thirds as tridecimal neutral thirds [[16/13]] and [[39/32]] respectively. Tuning this Deeptone extension in [[40edo]] results in essentially perfect tuning of [[13/8]] and [[16/13]], which is inherited from [[10edo]].
+Deeptone has an accurate [[13/8]], represented by the interval notated as a minor sixth, so it is very plausible to have a 2.3.5.13-[[subgroup]] [[extension]] tempering out both [[177147/163840]] and [[1053/1024]] (the tridecimal quartertone). This also gives a more simple interpretation of deeptone's major and minor thirds as tridecimal neutral thirds [[16/13]] and [[39/32]] respectively. Tuning this Deeptone extension in [[40edo]] results in essentially perfect tuning of [[13/8]] and [[16/13]], which is inherited from [[10edo]].
 == Scales ==
-When properly tuned, Deeptone features [[MOS scale]]s of the families [[2L&nbsp;3s]], [[5L&nbsp;2s]], [[7L&nbsp;5s]], [[7L&nbsp;12s]], and [[7L&nbsp;19s]]. Another important scale, intermediate between the [[7L&nbsp;5s]] and [[7L&nbsp;12s]] scales, is the "Deeptone[14]" non-MOS scale. This scale is notable for being the smallest Deeptone scale that is generally "complete" for 5-limit purposes (as noted by [[groundfault]]) since Deeptone[12] has a paucity of 5-limit triads. Deeptone[14] is essentially just two interlaced Deeptone[7] diatonic scales with one of them being offset by an augmented unison above the other.
+When properly tuned, Deeptone features [[mos scale]]s of the families [[2L&nbsp;3s]], [[5L&nbsp;2s]], [[7L&nbsp;5s]], [[7L&nbsp;12s]], and [[7L&nbsp;19s]]. Another important scale, intermediate between the [[7L&nbsp;5s]] and [[7L&nbsp;12s]] scales, is the "Deeptone[14]" non-mos scale. This scale is notable for being the smallest deeptone scale that is generally "complete" for 5-limit purposes (as noted by [[groundfault]]) since Deeptone[12] has a paucity of 5-limit triads. Deeptone[14] is essentially just two interlaced Deeptone[7] diatonic scales with one of them being offset by an augmented unison above the other.
 == Interval chain ==
@@ Line 20: / Line 20: @@
 {| class="wikitable center-1 right-2"
 |-
-! &#35;
+! #
 ! colspan="3" | Notation
 ! Cents*
@@ Line 42: / Line 42: @@
 | 7 || aug unison || A1 || C# || 29.153 || [[2187/2048]], [[81/80|80/81]] || [[27/26]]
 |}
-<nowiki />* In 5-limit CTE tuning
+<nowiki/>* In 5-limit CTE tuning
 == Notes ==
-<references />
+<references/>
 [[Category:Temperaments]]