Deeptone: Difference between revisions

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'''Deeptone''', a.k.a. '''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]].

It can be regarded as an unusual example of a [[cluster temperament]] with 7 clusters of notes in an octave. The chroma or "super-comma" in this case represents 80/81~[[2187/2048]] (in the 2.3.5.13 extension, 80/81~2187/2048~27/26).

The name ''deeptone'' was given by {{u|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>

A related.temperament is [[shallowtone]], which is generated by a fifth slightly flat of 7edo's fifth instead of slightly sharp (~~such as~~ [[37edo]]'s flat fifth), and its mapping of 6/5 is the same as deeptone's mapping of 5/4. Basically, shallowtone is to deeptone as [[mavila]] is to [[meantone]]. It is of even higher badness than deeptone.

A related temperament is [[shallowtone]], which is generated by a fifth slightly flat of 7edo's fifth instead of slightly sharp (one example of a shallowtone generator would be [[37edo]]'s flat fifth), and its mapping of 6/5 is the same as deeptone's mapping of 5/4. Basically, shallowtone is to deeptone as [[mavila]] is to [[meantone]]. It is of even higher badness than deeptone.

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

See [[Syntonic–chromatic equivalence continuum #Deeptone a.k.a. tragicomical]] and [[No-sevens subgroup temperaments#Deeptone a.k.a. tragicomical]] for technical data.

[[File:Deeptone7.mp3|none|thumb|Deeptone[7] major scale in 40edo.]]

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 '''Deeptone''', a.k.a. '''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]].
-It can be regarded as an unusual example of a [[cluster temperament]] with  7 clusters of notes in an octave. The chroma or "super-comma" in this case represents 80/81~[[2187/2048]] (in the 2.3.5.13 extension, 80/81~2187/2048~27/26).
+It can be regarded as an unusual example of a [[cluster temperament]] with 7 clusters of notes in an octave. The chroma or "super-comma" in this case represents 80/81~[[2187/2048]] (in the 2.3.5.13 extension, 80/81~2187/2048~27/26).
 The name ''deeptone'' was given by {{u|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>
-A related.temperament is [[shallowtone]], which is generated by a fifth slightly flat of 7edo's fifth instead of slightly sharp (such as [[37edo]]'s flat fifth), and its mapping of 6/5 is the same as deeptone's mapping of 5/4. Basically, shallowtone is to deeptone as [[mavila]] is to [[meantone]]. It is of even higher badness than deeptone.
+A related temperament is [[shallowtone]], which is generated by a fifth slightly flat of 7edo's fifth instead of slightly sharp (one example of a shallowtone generator would be [[37edo]]'s flat fifth), and its mapping of 6/5 is the same as deeptone's mapping of 5/4. Basically, shallowtone is to deeptone as [[mavila]] is to [[meantone]]. It is of even higher badness than deeptone.
-See [[Syntonic–chromatic equivalence continuum #Deeptone a.k.a. tragicomical]] for technical data.
+See [[Syntonic–chromatic equivalence continuum #Deeptone a.k.a. tragicomical]] and [[No-sevens subgroup temperaments#Deeptone a.k.a. tragicomical]] for technical data.
 [[File:Deeptone7.mp3|none|thumb|Deeptone[7] major scale in 40edo.]]

Deeptone: Difference between revisions

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