Deeptone: Difference between revisions

Line 2:

| 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)

| 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

| Generators = 3/2

| ~~Generator~~ tuning = 689.6

| Generators tuning = 689.6

| Optimization method = CWE

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

| Pergen = (P8, P5)

| Odd limit 1 = 5

| Odd limit 1 = 5 | Mistuning 1 = 12.3 | Complexity 1 = 12

| 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 2: / Line 2: @@
 | 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)
+| 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
+| Generators = 3/2
-| Generator tuning = 689.6
+| Generators tuning = 689.6
 | Optimization method = CWE
 | MOS scales = [[5L&nbsp;2s]], [[7L&nbsp;5s]], [[7L&nbsp;12s]]
 | Pergen = (P8, P5)
-| Odd limit 1 = 5
+| Odd limit 1 = 5 | Mistuning 1 = 12.3 | Complexity 1 = 12
-| 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]].