Deeptone: Difference between revisions

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'''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]].

'''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. It is rated as high-[[badness]] by most badness metrics due to the combination of high [[error]] and high [[complexity]], but it is still of a low enough badness to be usable. 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.

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| 10 || aug 6th || A6 || A# || 898.79 || [[5/3]] ||

|-

| 11 || aug 3rd || A3 || E# || 388.67 || '''[[5/4]]''' ||

| 11 || aug 3rd || A3 || E# || 388.669 || '''[[5/4]]''' ||

|-

| 12 || aug 7th || A7 || B# || 1078.55 || [[15/8]] ||

| 12 || aug 7th || A7 || B# || 1078.548 || [[15/8]] ||

|-

| 13 || doubly-aug 4th || AA4 || Fx || 568.427 || [[45/32]] ||

|}

<nowiki/>* In 5-limit CTE tuning

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[[Category:~~Temperaments~~]]

[[Category:Deeptone| ]]

[[Category:Rank-2 temperaments]]

~~[[Category:Deeptone| ]] ~~

~~{{todo|inline=1|expand}}~~

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-'''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]].
+'''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. It is rated as high-[[badness]] by most badness metrics due to the combination of high [[error]] and high [[complexity]], but it is still of a low enough badness to be usable. 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.
@@ Line 47: / Line 47: @@
 | 10 || aug 6th || A6 || A# || 898.79 || [[5/3]] ||
 |-
-| 11 || aug 3rd || A3 || E# || 388.67 || '''[[5/4]]''' ||
+| 11 || aug 3rd || A3 || E# || 388.669 || '''[[5/4]]''' ||
 |-
-| 12 || aug 7th || A7 || B# || 1078.55 || [[15/8]] ||
+| 12 || aug 7th || A7 || B# || 1078.548 || [[15/8]] ||
+|-
+| 13 || doubly-aug 4th || AA4 || Fx || 568.427 || [[45/32]] ||
 |}
 <nowiki/>* In 5-limit CTE tuning
@@ Line 57: / Line 58: @@
 <references/>
-[[Category:Temperaments]]
+[[Category:Deeptone| ]] <!-- main article -->
 [[Category:Rank-2 temperaments]]
-[[Category:Deeptone| ]] <!-- main article -->
-{{todo|inline=1|expand}}