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 [[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~~]]. When properly tuned, it features [[MOS scale]]s of the families [[2L 3s]], [[5L 2s]], [[7L 5s]], [[7L 12s]], and [[7L 19s~~]]. 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.

'''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}}). It is , . 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]].

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

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== 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>

== 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 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.

== 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 offset by an augmented unison.

== Notes ==

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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 [[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]]. When properly tuned, it features [[MOS scale]]s of the families [[2L 3s]], [[5L 2s]], [[7L 5s]], [[7L 12s]], and [[7L 19s]]. 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.
+'''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}}). It is , . 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]].
 See [[Syntonic&ndash;chromatic equivalence continuum#Deeptone a.k.a. tragicomical]] for technical data.
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 == 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>
+== 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 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.
+== 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 offset by an augmented unison.
 == Notes ==