Deeptone: Difference between revisions

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{{Infobox regtemp

| Title = Deeptone

| Subgroups = 2.3.5, 2.3.5.13

| Comma basis = [[177147/163840]] (5-limit);<br>[[1053/1024]], [[2187/2080]] (2.3.5.13)

| Edo join 1 = 7 | Edo join 2 = 33

| Mapping = 1; 1 11 -4

| Generator = 3/2

| Generator tuning = 689.6

| Optimization method = CWE

| MOS scales = [[5L 2s]], [[7L 5s]], [[7L 12s]]

| Pergen = (P8, P5)

| Odd limit 1 = 5

| Mistuning 1 = 12.3

| Complexity 1 = 12

}}

'''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]].

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| 5 || major 7th || M7 || B || 1049.395 || [[243/128]] || [[24/13]]

|-

| 6 || aug 4th || A4 || G# || 539.274 || [[729/512]], [[320/243]] || [[18/13]]

| 6 || aug 4th || A4 || F# || 539.274 || [[729/512]], [[320/243]] || [[18/13]]

|-

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

@@ Line 1: / Line 1: @@
+{{Infobox regtemp
+| Title = Deeptone
+| Subgroups = 2.3.5, 2.3.5.13
+| Comma basis = [[177147/163840]] (5-limit);<br>[[1053/1024]], [[2187/2080]] (2.3.5.13)
+| Edo join 1 = 7 | Edo join 2 = 33
+| Mapping = 1; 1 11 -4
+| Generator = 3/2
+| Generator tuning = 689.6
+| Optimization method = CWE
+| MOS scales = [[5L&nbsp;2s]], [[7L&nbsp;5s]], [[7L&nbsp;12s]]
+| Pergen = (P8, P5)
+| Odd limit 1 = 5
+| Mistuning 1 = 12.3
+| Complexity 1 = 12
+}}
 '''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]].
@@ Line 37: / Line 52: @@
 | 5 || major 7th || M7 || B || 1049.395 || [[243/128]] || [[24/13]]
 |-
-| 6 || aug 4th || A4 || G# || 539.274 || [[729/512]], [[320/243]] || [[18/13]]
+| 6 || aug 4th || A4 || F# || 539.274 || [[729/512]], [[320/243]] || [[18/13]]
 |-
 | 7 || aug unison || A1 || C# || 29.153 || [[2187/2048]], [[81/80|80/81]] || [[27/26]]