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-Cb~~). 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]] [[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]].

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.]]

== Etymology ==

''Deeptone'' was given by [[user:CompactStar|CompactStar]] in 2023, referring to the temperament featuring fifths even flatter than [[flattone]]. ''Tragicomical'' was allegedly given by [[groundfault]] no later than 2023.<ref>[https://en.xen.wiki/index.php?title=Talk:177147/163840&oldid=107105 Xenharmonic Wiki | Talk: 177147/163840]</ref>

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== 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 ==~~

== Interval chain ==

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

|-

!#

! #

!colspan=3|Notation

! colspan="3" | Notation

!Cents*

! Cents*

!Approximate ratios (5-limit)

! Approximate ratios (5-limit)

!~~Aditional~~ ratios in 2.3.5.13 extension

! Additional ratios in 2.3.5.13 extension

|-

| 0 || perfect unison || P1 || C || 0.0 || [[1/1]] ||

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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

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[[Category:Temperaments]]

[[Category:Deeptone| ]]

@@ Line 1: / Line 1: @@
-'''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-Cb). 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]] [[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]].
-See [[Syntonic&ndash;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.]]
 == Etymology ==
 ''Deeptone'' was given by [[user:CompactStar|CompactStar]] in 2023, referring to the temperament featuring fifths even flatter than [[flattone]]. ''Tragicomical'' was allegedly given by [[groundfault]] no later than 2023.<ref>[https://en.xen.wiki/index.php?title=Talk:177147/163840&oldid=107105 Xenharmonic Wiki | Talk: 177147/163840]</ref>
@@ Line 12: / Line 13: @@
 == 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&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 ==
 == Interval chain ==
@@ Line 21: / Line 20: @@
 {| class="wikitable center-1 right-2"
 |-
-!&#35;
+! &#35;
-!colspan=3|Notation
+! colspan="3" | Notation
-!Cents*
+! Cents*
-!Approximate ratios (5-limit)
+! Approximate ratios (5-limit)
-!Aditional ratios in 2.3.5.13 extension
+! Additional ratios in 2.3.5.13 extension
 |-
 | 0 || perfect unison || P1 || C || 0.0 || [[1/1]] ||
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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
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 [[Category:Temperaments]]
 [[Category:Deeptone| ]] <!-- main article -->
 {{todo|inline=1|expand}}