Deeptone: Difference between revisions
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'''Deeptone''' | '''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 example of a [[cluster temperament]] with | 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). | ||
See [[Syntonic–chromatic equivalence continuum #Deeptone a.k.a. tragicomical]] for technical data. | 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 (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]] and [[No-sevens subgroup temperaments#Deeptone a.k.a. tragicomical]] for technical data. | |||
[[File:Deeptone7.mp3|none|thumb|Deeptone[7] major scale in 40edo.]] | [[File:Deeptone7.mp3|none|thumb|Deeptone[7] major scale in 40edo.]] | ||
== Extensions == | == Extensions == | ||
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It is possible to map [[8/7]] to the double-augmented 2nd, but this necessitates the usage of a 19-note or larger MOS, and [[33edo]] does not support it in the patent val, only [[40edo]] and [[47edo]] do. | It is possible to map [[8/7]] to the double-augmented 2nd, but this necessitates the usage of a 19-note or larger MOS, and [[33edo]] does not support it in the patent val, only [[40edo]] and [[47edo]] do. | ||
== | == Intervals == | ||
In the following table, prime harmonics and subharmonics are labeled in '''bold'''. | In the following table, prime harmonics and subharmonics are labeled in '''bold'''. | ||
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! colspan="3" | Notation | ! colspan="3" | Notation | ||
! Cents* | ! Cents* | ||
! Approximate ratios (5-limit) | ! Approximate ratios<br>([[5-limit]]) | ||
! Additional ratios in 2.3.5.13 extension | ! Additional ratios<br>in 2.3.5.13 extension | ||
|- | |- | ||
| 0 || perfect unison || P1 || C || 0.0 || [[1/1]] || | | 0 || perfect unison || P1 || C || 0.0 || [[1/1]] || | ||
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<nowiki/>* In 5-limit CTE tuning | <nowiki/>* In 5-limit CTE tuning | ||
== 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 being offset by an augmented unison above the other. | |||
== Tunings == | |||
=== Tuning spectrum === | === Tuning spectrum === | ||
{| class="wikitable center-all left-4" | {| class="wikitable center-all left-4" | ||
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| [[6/5]] | | [[6/5]] | ||
| 688.436 | | 688.436 | ||
| | | 1/10-comma tuning | ||
|- | |- | ||
| [[61edo|35\61]] | | [[61edo|35\61]] | ||
| | | | ||
| 688.524 | | 688.524 | ||
| | | 61bc val | ||
|- | |- | ||
| [[54edo|31\54]] | | [[54edo|31\54]] | ||
| | | | ||
| 688.889 | | 688.889 | ||
| | | 54b val | ||
|- | |- | ||
| [[47edo|27\47]] | | [[47edo|27\47]] | ||
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| [[5/4]] | | [[5/4]] | ||
| 689.665 | | 689.665 | ||
| 1/11-comma | | 1/11-comma tuning | ||
|- | |- | ||
| | | | ||
| [[13 | | [[20/13]] | ||
| 689.719 | | 689.719 | ||
| | | | ||
| Line 140: | Line 142: | ||
| 690.484 | | 690.484 | ||
| | | | ||
|- | |||
| | |||
| [[15/8]] | |||
| 690.689 | |||
| 1/12-comma tuning | |||
|- | |- | ||
| [[33edo|19\33]] | | [[33edo|19\33]] | ||
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|} | |} | ||
== | == References == | ||
<references/> | <references/> | ||
[[Category:Deeptone| ]] <!-- main article --> | [[Category:Deeptone| ]] <!-- main article --> | ||
[[Category:Rank-2 temperaments]] | [[Category:Rank-2 temperaments]] | ||