Deeptone - Revision history

FloraC: Cleanup on infobox

2026-02-09T10:01:48Z

Cleanup on infobox

← Older revision		Revision as of 10:01, 9 February 2026
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	\| Title = Deeptone		\| Title = Deeptone
	\| Subgroups = 2.3.5, 2.3.5.13		\| 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		\| Edo join 1 = 7 \| Edo join 2 = 33
	\| Mapping = 1; 1 11 -4		\| Mapping = 1; 1 11 -4
	\| ~~Generator~~ = 3/2		\| Generators = 3/2
	\| ~~Generator~~ tuning = 689.6		\| Generators tuning = 689.6
	\| Optimization method = CWE		\| Optimization method = CWE
	\| MOS scales = [[5L 2s]], [[7L 5s]], [[7L 12s]]		\| MOS scales = [[5L 2s]], [[7L 5s]], [[7L 12s]]
	\| Pergen = (P8, P5)		\| 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]].		'''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]].

Xenllium at 06:55, 27 January 2026

2026-01-27T06:55:04Z

@@ Line 1: / Line 1: @@
 '''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]]

Lériendil: /* Extensions */

2025-09-08T03:04:52Z

Extensions

← Older revision		Revision as of 03:04, 8 September 2025
Line 9:		Line 9:

	== Extensions ==		== 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-[[subgroup]] [[extension]] tempering out both [[~~177147~~/~~163840~~]] and [[1053/1024]] (the tridecimal quartertone). This also gives a more simple interpretation of deeptone's major and minor thirds as tridecimal neutral thirds [[16/13]] and [[39/32]] respectively. Tuning this deeptone extension in [[40edo]] results in essentially perfect tuning of [[13/8]] and [[16/13]], which is inherited from [[10edo]].		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-[[subgroup]] [[extension]] tempering out both [[2187/2080]] and [[1053/1024]] (the tridecimal quartertone). This also gives a more simple interpretation of deeptone's major and minor thirds as tridecimal neutral thirds [[16/13]] and [[39/32]] respectively. Tuning this deeptone extension in [[40edo]] results in essentially perfect tuning of [[13/8]] and [[16/13]], which is inherited from [[10edo]].

	== Scales ==		== Scales ==

FloraC: - parent category

2025-04-28T14:00:50Z

- parent category

← Older revision		Revision as of 14:00, 28 April 2025
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	<references/>		<references/>

	[[Category:~~Temperaments~~]]		[[Category:Deeptone\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	~~[[Category:Deeptone\| ]] <!-- main article -->~~

CompactStar at 00:52, 21 April 2025

2025-04-21T00:52:37Z

← Older revision		Revision as of 00:52, 21 April 2025
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	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:Deeptone\| ]] <!-- main article -->		[[Category:Deeptone\| ]] <!-- main article -->

	~~{{todo\|inline=1\|expand}}~~

CompactStar at 00:51, 21 April 2025

2025-04-21T00:51:55Z

← Older revision		Revision as of 00:51, 21 April 2025
Line 1:		Line 1:
	'''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 ~~usually~~ rated as high-[[badness]] by most badness metrics due to the combination of high [[error]] and high [[complexity]], but it is still ~~within the realm~~ of ~~usability~~. Four edos support deeptone in their [[patent val]] ([[7edo]], [[33edo]], [[40edo]], and [[47edo]]), and additionally there is the near-patent val [[54edo\|54b-edo]].		'''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]].

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

CompactStar at 00:51, 21 April 2025

2025-04-21T00:51:22Z

← Older revision		Revision as of 00:51, 21 April 2025
Line 1:		Line 1:
	'''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. 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 is generally considered an [[efficiency\|inefficient]] temperament due to the combination of high [[error]] and high [[complexity]], but it is still within the realm of usability~~.		'''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 usually rated as high-[[badness]] by most badness metrics due to the combination of high [[error]] and high [[complexity]], but it is still within the realm of usability. Four 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.		See [[Syntonic–chromatic equivalence continuum #Deeptone a.k.a. tragicomical]] for technical data.

CompactStar at 00:49, 21 April 2025

2025-04-21T00:49:29Z

← Older revision		Revision as of 00:49, 21 April 2025
Line 1:		Line 1:
	'''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. Four edos support deeptone in their [[patent val]] ([[7edo]], [[33edo]], [[40edo]], and [[47edo]]), and additionally there is the near-patent val [[54edo\|54b-edo]].		'''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. 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 is generally considered an [[efficiency\|inefficient]] temperament due to the combination of high [[error]] and high [[complexity]], but it is still within the realm of usability.

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

CompactStar: /* Interval chain */

2025-04-21T00:44:01Z

Interval chain

← Older revision		Revision as of 00:44, 21 April 2025
Line 47:		Line 47:
	\| 10 \|\| aug 6th \|\| A6 \|\| A# \|\| 898.79 \|\| [[5/3]] \|\|		\| 10 \|\| aug 6th \|\| A6 \|\| A# \|\| 898.79 \|\| [[5/3]] \|\|
	\|-		\|-
	\| 11 \|\| aug 3rd \|\| A3 \|\| E# \|\| 388.67 \|\| '''[[5/4]]''' \|\|		\| 11 \|\| aug 3rd \|\| A3 \|\| E# \|\| 388.669 \|\| '''[[5/4]]''' \|\|
	\|-		\|-
	\| 12 \|\| aug 7th \|\| A7 \|\| B# \|\| 1078.55 \|\| [[15/8]] \|\|		\| 12 \|\| aug 7th \|\| A7 \|\| B# \|\| 1078.548 \|\| [[15/8]] \|\|
			\|-
			\| 13 \|\| doubly-aug 4th \|\| AA4 \|\| Fx \|\| 568.427 \|\| [[45/32]] \|\|
	\|}		\|}
	<nowiki/>* In 5-limit CTE tuning		<nowiki/>* In 5-limit CTE tuning

CompactStar at 00:41, 21 April 2025

2025-04-21T00:41:36Z

← Older revision		Revision as of 00:41, 21 April 2025
Line 9:		Line 9:

	== Extensions ==		== 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-[[subgroup]] [[extension]] tempering out both [[177147/163840]] and [[1053/1024]] (the tridecimal quartertone). This also gives a more simple interpretation of deeptone's major and minor thirds as tridecimal neutral thirds [[16/13]] and [[39/32]] respectively. Tuning this ~~Deeptone~~ extension in [[40edo]] results in essentially perfect tuning of [[13/8]] and [[16/13]], which is inherited from [[10edo]].		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-[[subgroup]] [[extension]] tempering out both [[177147/163840]] and [[1053/1024]] (the tridecimal quartertone). This also gives a more simple interpretation of deeptone's major and minor thirds as tridecimal neutral thirds [[16/13]] and [[39/32]] respectively. Tuning this deeptone extension in [[40edo]] results in essentially perfect tuning of [[13/8]] and [[16/13]], which is inherited from [[10edo]].

	== Scales ==		== Scales ==
Line 15:		Line 15:

	== Interval chain ==		== Interval chain ==
	In the following table, prime harmonics are labeled in '''bold'''.		In the following table, prime harmonics and subharmonics are labeled in '''bold'''.

	{\| class="wikitable center-1 right-2"		{\| class="wikitable center-1 right-2"
Line 27:		Line 27:
	\| 0 \|\| perfect unison \|\| P1 \|\| C \|\| 0.0 \|\| [[1/1]] \|\|		\| 0 \|\| perfect unison \|\| P1 \|\| C \|\| 0.0 \|\| [[1/1]] \|\|
	\|-		\|-
	\| 1 \|\| perfect 5th \|\| P5 \|\| G \|\| 689.879 \|\| [[3/2]] \|\|		\| 1 \|\| perfect 5th \|\| P5 \|\| G \|\| 689.879 \|\| '''[[3/2]]''' \|\|
	\|-		\|-
	\| 2 \|\| major 2nd \|\| M2 \|\| D \|\| 179.758 \|\| [[9/8]] \|\| [[128/117]]		\| 2 \|\| major 2nd \|\| M2 \|\| D \|\| 179.758 \|\| [[9/8]] \|\| [[128/117]]
Line 33:		Line 33:
	\| 3 \|\| major 6th \|\| M6 \|\| A \|\| 869.637 \|\| [[27/16]] \|\| [[64/39]]		\| 3 \|\| major 6th \|\| M6 \|\| A \|\| 869.637 \|\| [[27/16]] \|\| [[64/39]]
	\|-		\|-
	\| 4 \|\| major 3rd \|\| M3 \|\| E \|\| 359.516 \|\| [[81/64]] \|\| [[16/13]]		\| 4 \|\| major 3rd \|\| M3 \|\| E \|\| 359.516 \|\| [[81/64]] \|\| '''[[16/13]]'''
	\|-		\|-
	\| 5 \|\| major 7th \|\| M7 \|\| B \|\| 1049.395 \|\| [[243/128]], \|\| [[24/13]]		\| 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 \|\| G# \|\| 539.274 \|\| [[729/512]], [[320/243]] \|\| [[18/13]]
	\|-		\|-
	\| 7 \|\| aug unison \|\| A1 \|\| C# \|\| 29.153 \|\| [[2187/2048]], [[81/80\|80/81]] \|\| [[27/26]]		\| 7 \|\| aug unison \|\| A1 \|\| C# \|\| 29.153 \|\| [[2187/2048]], [[81/80\|80/81]] \|\| [[27/26]]
			\|-
			\| 8 \|\| aug 5th \|\| A5 \|\| G# \|\| 719.032 \|\| [[40/27]] \|\|
			\|-
			\| 9 \|\| aug 2nd \|\| A2 \|\| D# \|\| 208.911 \|\| [[10/9]] \|\|
			\|-
			\| 10 \|\| aug 6th \|\| A6 \|\| A# \|\| 898.79 \|\| [[5/3]] \|\|
			\|-
			\| 11 \|\| aug 3rd \|\| A3 \|\| E# \|\| 388.67 \|\| '''[[5/4]]''' \|\|
			\|-
			\| 12 \|\| aug 7th \|\| A7 \|\| B# \|\| 1078.55 \|\| [[15/8]] \|\|

	\|}		\|}
	<nowiki/>* In 5-limit CTE tuning		<nowiki/>* In 5-limit CTE tuning