Marvel - Revision history

FloraC: Style

2026-11-10T08:52:00Z

Style

← Older revision		Revision as of 08:52, 10 November 2026
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	== Notation ==		== Notation ==
	Marvel can be notated the same as [[5-limit]] [[just intonation]] since they share the same lattice structure. One way to do this is to take the conventional [[circle-of-fifths notation]] with an additional module of accidentals for the [[81/80]] comma. In this system, 5/4 is a major third, 7/4 an augmented sixth, and 11/8 a double diminished ~~5th~~.		Marvel can be notated the same as [[5-limit]] [[just intonation]] since they share the same lattice structure. One way to do this is to take the conventional [[circle-of-fifths notation]] with an additional module of accidentals for the [[81/80]] comma. In this system, 5/4 is a major third, 7/4 an augmented sixth, and 11/8 a double-diminished fifth.

	{\| class="wikitable center-1 center-3"		{\| class="wikitable center-1 center-3"
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	\| 3/2		\| 3/2
	\| Perfect fifth		\| Perfect fifth
	\| ~~C-G~~		\| C–G
	\|-		\|-
	\| 5/4		\| 5/4
	\| Down major third		\| Down major third
	\| ~~C-vE~~		\| C–vE
	\|-		\|-
	\| 7/4		\| 7/4
	\| Dudaugmented sixth		\| Dudaugmented sixth
	\| ~~C-vvA#~~		\| C–vvA♯
	\|-		\|-
	\| 11/8		\| 11/8
	\| Trup double-diminished fifth		\| Trup double-diminished fifth
	\| C-^<sup>3</sup>~~Gbb~~		\| C–^<sup>3</sup>G𝄫
	\|-		\|-
	\| 13/8		\| 13/8
	\| Dup minor sixth		\| Dup minor sixth
	\| C-^^Ab		\| C–^^A♭
	\|-		\|-
	\| 19/16		\| 19/16
	\| Minor third		\| Minor third
	\| ~~C-Eb~~		\| C–E♭
	\|}		\|}

	Alternatively, it can be notated the same as full prime-limit just intonation, with a distinct accidental pair for each prime. That makes some intervals more intuitive, at the cost of hiding the structure of marvel tempering. For example, it is customary of the 5/4 to be a major third, and 7/4 to be a minor seventh. As a result, the fact that the 14/9 is a stack of two 5/4's is not revealed, and the related chords can be less convenient.		Alternatively, it can be notated the same as full prime-limit just intonation, with a distinct accidental pair for each prime. That makes some intervals more intuitive, at the cost of hiding the structure of marvel tempering. For example, it is customary of the 5/4 to be a major third and 7/4 to be a minor seventh. As a result, the fact that the 14/9 is a stack of two 5/4's is not revealed, and the related chords can be less convenient.

	== Chords and harmony ==		== Chords and harmony ==

FloraC: Expand with info from marvel temperaments page

2026-11-10T08:38:10Z

Expand with info from marvel temperaments page

← Older revision		Revision as of 08:38, 10 November 2026
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	'''Marvel''' is a [[rank-3 temperament]] with the same [[lattice]] structure as [[5-limit]] [[JI]], while identifying the [[7/4\|harmonic seventh (7/4)]] as a stack of two [[15/8\|classical major sevenths (15/8)]] [[octave reduction\|octave-reduced]], [[tempering out]] [[225/224]]. It is the head of the [[marvel family]].		'''Marvel''' is a [[rank-3 temperament]] with the same [[lattice]] structure as [[5-limit]] [[JI]], while identifying the [[7/4\|harmonic seventh (7/4)]] as a stack of two [[15/8\|classical major sevenths (15/8)]] [[octave reduction\|octave-reduced]], [[tempering out]] [[225/224]]. It is the head of the [[marvel family]].

	Marvel tends to tune [[5/4]] flat, such that a stack of two such thirds give a sharp [[14/9]], and a ~~stack~~ of three ~~such~~ thirds ~~give~~ a ~~sub-octave of~~ [[35/18]] just short of the octave by a quartertone of [[36/35]]. The canonical [[11-limit]] [[extension]], sometimes aliased ''unimarv'', identifies the quartertone as [[33/32]], so that [[11/8]] is that plus a [[4/3\|perfect fourth]]. This adds [[385/384]] and [[540/539]] to the comma list and makes it a member of both [[keenanismic temperaments\|keenansimic]] and [[swetismic temperaments]].		Marvel tends to tune [[5/4]] flat, such that a stack of two such thirds give a sharp [[14/9]]. In other words, it has a 5/4, 5/4, 9/7 version of the [[augmented triad]]. Since this is a chord of [[meantone]] in wide use in Western {{w\|common practice}} harmony long before [[12edo]] established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.

			Another ~5/4 on top of ~14/9 gives a [[35/18]] sub-octave just short of the octave by a quartertone of [[36/35]]. The canonical [[11-limit]] [[extension]], sometimes aliased ''unimarv'', identifies the quartertone as [[33/32]], so that [[11/8]] is that plus a [[4/3\|perfect fourth]]. This adds [[385/384]] and [[540/539]] to the comma list and makes it a member of both [[keenanismic temperaments\|keenansimic]] and [[swetismic temperaments]].

	The temperament was named by [[Gene Ward Smith]] in 2002–2003, when the 11-limit version was found first<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5145.html#5184 Yahoo! Tuning Group \| ''Relative complexity and scale construction''] – first mention of ''marvel''.</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5687.html Yahoo! Tuning Group \| ''Top 135 11-limit planar temperaments''] – establishment as an 11-limit temperament.</ref>. Gene carried it to the 7-limit restriction in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_50829.html Yahoo! Tuning Group \| ''Marvel'']</ref>.		The temperament was named by [[Gene Ward Smith]] in 2002–2003, when the 11-limit version was found first<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5145.html#5184 Yahoo! Tuning Group \| ''Relative complexity and scale construction''] – first mention of ''marvel''.</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5687.html Yahoo! Tuning Group \| ''Top 135 11-limit planar temperaments''] – establishment as an 11-limit temperament.</ref>. Gene carried it to the 7-limit restriction in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_50829.html Yahoo! Tuning Group \| ''Marvel'']</ref>.
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	== Chords and harmony ==		== Chords and harmony ==
	Marvel enables [[essentially tempered chord]]s of [[marvel chords\|marvel]], [[keenanismic chords\|keenanismic]], [[swetismic chords\|swetismic]], and [[undecimal marvel chords\|undecimal marvel]].		Marvel enables [[essentially tempered chord]]s of [[marvel chords\|marvel]], [[keenanismic chords\|keenanismic]], [[swetismic chords\|swetismic]], and [[undecimal marvel chords\|undecimal marvel]]. It also allows for a tritone substitution whereby the [[dominant seventh chord]] formed by adding 16/9 above the root shares its tritone with the [[harmonic seventh chord]]. (The tritone of the dominant seventh is {{nowrap\|(16/9)/(5/4) {{=}} 64/45}}. Setting this equal to 10/7 gives {{nowrap\|(10/7)/(64/45) {{=}} 225/224}}.)

	Extending the temperament to the 13-limit through 325/324, resulting in hecate, enables chords of [[marveltwin chords\|marveltwin]] and [[squbemic chords\|squbemic]]. [[Hecate hexad]] is a chord peculiar to this temperament. Alternatively, helios enables chords of [[ratwolfsmic chords\|ratwolfsmic]].		Extending the temperament to the 13-limit through 325/324, resulting in hecate, enables chords of [[marveltwin chords\|marveltwin]] and [[squbemic chords\|squbemic]]. [[Hecate hexad]] is a chord peculiar to this temperament. Alternatively, helios enables chords of [[ratwolfsmic chords\|ratwolfsmic]].

FloraC: Text replacement - "rank-3 temperament" to "rank-3 temperament"

2026-06-08T08:36:19Z

Text replacement - "rank-3 temperament" to "rank-3 temperament"

← Older revision		Revision as of 08:36, 8 June 2026
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	\| Odd limit 2 = 11-limit 21 \| Mistuning 2 = 3.86 \| Complexity 2 = ?		\| Odd limit 2 = 11-limit 21 \| Mistuning 2 = 3.86 \| Complexity 2 = ?
	}}		}}
	'''Marvel''' is a [[rank-3 ~~temperament\|rank-3]] [[regular temperament\|~~temperament]] with the same [[lattice]] structure as [[5-limit]] [[JI]], while identifying the [[7/4\|harmonic seventh (7/4)]] as a stack of two [[15/8\|classical major sevenths (15/8)]] [[octave reduction\|octave-reduced]], [[tempering out]] [[225/224]]. It is the head of the [[marvel family]].		'''Marvel''' is a [[rank-3 temperament]] with the same [[lattice]] structure as [[5-limit]] [[JI]], while identifying the [[7/4\|harmonic seventh (7/4)]] as a stack of two [[15/8\|classical major sevenths (15/8)]] [[octave reduction\|octave-reduced]], [[tempering out]] [[225/224]]. It is the head of the [[marvel family]].

	Marvel tends to tune [[5/4]] flat, such that a stack of two such thirds give a sharp [[14/9]], and a stack of three such thirds give a sub-octave of [[35/18]] just short of the octave by a quartertone of [[36/35]]. The canonical [[11-limit]] [[extension]], sometimes aliased ''unimarv'', identifies the quartertone as [[33/32]], so that [[11/8]] is that plus a [[4/3\|perfect fourth]]. This adds [[385/384]] and [[540/539]] to the comma list and makes it a member of both [[keenanismic temperaments\|keenansimic]] and [[swetismic temperaments]].		Marvel tends to tune [[5/4]] flat, such that a stack of two such thirds give a sharp [[14/9]], and a stack of three such thirds give a sub-octave of [[35/18]] just short of the octave by a quartertone of [[36/35]]. The canonical [[11-limit]] [[extension]], sometimes aliased ''unimarv'', identifies the quartertone as [[33/32]], so that [[11/8]] is that plus a [[4/3\|perfect fourth]]. This adds [[385/384]] and [[540/539]] to the comma list and makes it a member of both [[keenanismic temperaments\|keenansimic]] and [[swetismic temperaments]].

FloraC: Update & various cleanup

2026-05-19T07:52:50Z

Update & various cleanup

← Older revision		Revision as of 07:52, 19 May 2026
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	The temperament was named by [[Gene Ward Smith]] in 2002–2003, when the 11-limit version was found first<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5145.html#5184 Yahoo! Tuning Group \| ''Relative complexity and scale construction''] – first mention of ''marvel''.</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5687.html Yahoo! Tuning Group \| ''Top 135 11-limit planar temperaments''] – establishment as an 11-limit temperament.</ref>. Gene carried it to the 7-limit restriction in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_50829.html Yahoo! Tuning Group \| ''Marvel'']</ref>.		The temperament was named by [[Gene Ward Smith]] in 2002–2003, when the 11-limit version was found first<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5145.html#5184 Yahoo! Tuning Group \| ''Relative complexity and scale construction''] – first mention of ''marvel''.</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5687.html Yahoo! Tuning Group \| ''Top 135 11-limit planar temperaments''] – establishment as an 11-limit temperament.</ref>. Gene carried it to the 7-limit restriction in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_50829.html Yahoo! Tuning Group \| ''Marvel'']</ref>.

	Extending marvel to the 13-limit is not as obvious. ~~While~~ Gene has chosen [[351/350]] as the canonical extension, '''hecate''', tempering out [[325/324]] and [[729/728]], arguably makes more sense as it is closer in tuning<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101722.html Yahoo! Tuning Group \| ''13-limit marvel'']</ref>. Hecate has a natural extension to the no-17 19-limit, by tempering out [[400/399]] and [[513/512]].		Extending marvel to the 13-limit is not as obvious. Gene has chosen '''helios''', tempering out [[351/350]], as the canonical extension, but '''hecate''', tempering out [[325/324]] and [[729/728]], arguably makes more sense as it is closer in tuning<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101722.html Yahoo! Tuning Group \| ''13-limit marvel'']</ref>. Hecate has a natural extension to the no-17 19-limit, by tempering out [[400/399]] and [[513/512]].

	See [[Marvel family #Marvel]] for technical data.		See [[Marvel family #Marvel]] for technical data.
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	== Chords and harmony ==		== Chords and harmony ==
	Marvel enables [[essentially tempered chord]]s of [[~~Marvel~~ chords\|marvel]], [[~~Keenanismic~~ chords\|keenanismic]], [[~~Swetismic~~ chords\|swetismic]], and [[~~Undecimal~~ marvel chords\|undecimal marvel]]. Extending the temperament to the 13-limit through 325/324, resulting in hecate, enables chords of [[~~Marveltwin~~ chords\|marveltwin]] and [[~~Squbemic~~ chords\|squbemic]]. [[Hecate hexad]] is a chord peculiar to this temperament.		Marvel enables [[essentially tempered chord]]s of [[marvel chords\|marvel]], [[keenanismic chords\|keenanismic]], [[swetismic chords\|swetismic]], and [[undecimal marvel chords\|undecimal marvel]].

			Extending the temperament to the 13-limit through 325/324, resulting in hecate, enables chords of [[marveltwin chords\|marveltwin]] and [[squbemic chords\|squbemic]]. [[Hecate hexad]] is a chord peculiar to this temperament. Alternatively, helios enables chords of [[ratwolfsmic chords\|ratwolfsmic]].

	Alternative 11-limit extensions give different sets of chords. One notable example, tempering out [[441/440]], enables [[prodigy chords]].		Alternative 11-limit extensions give different sets of chords. One notable example, tempering out [[441/440]], enables [[prodigy chords]].
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	In the 7-limit, the optimal way such as that taken by [[TE]] and derivatives to close out the comma 225/224 is to tune primes 3 and 5 flat, and 2 and 7 sharp. If we tune the octave pure, the other inclinations remain. This indicates that the diminished third [[~]][[256/225]] should be sharp (towards [[~]][[8/7]]), the augmented second [[~]][[75/64]] be flat (towards [[~]][[7/6]]), the diminished fourth [[~]][[32/25]] be sharp (towards [[~]][[9/7]]) and the tritone [[~]][[45/32]] be flat (towards [[~]][[7/5]]), such that every [[7-limit]] [[9-odd-limit]] interval is tuned between itself and the [[5-limit]] interpretation it is separated from by [[225/224]]. If we take these as hard constraints, then [[53edo]] and [[84edo]] are the smallest edo tunings to satisfy them, but if overtempering is allowed, many smaller edos are possible, such as [[31edo\|31-]] and [[41edo]]. Interestingly, [[72edo]], though very performant as a 7- and 11-limit tuning, is overtempered for some of these constraints, whereas 53edo, though satisfying these constraints, tempers the intervals closer to the more complex [[5-limit]] interpretations, though the 7-limit concordances of the 9-odd-limit still clearly work. [[84edo]], another superset of 12edo, is an interesting edo to look at for its high performance in large odd-limits. Going up to larger edos, [[125edo\|125-]], [[166edo\|166-]], [[178edo\|178-]], [[197edo\|197-]], and [[240edo]] are all great choices with different intonational characteristics.		In the 7-limit, the optimal way such as that taken by [[TE]] and derivatives to close out the comma 225/224 is to tune primes 3 and 5 flat, and 2 and 7 sharp. If we tune the octave pure, the other inclinations remain. This indicates that the diminished third [[~]][[256/225]] should be sharp (towards [[~]][[8/7]]), the augmented second [[~]][[75/64]] be flat (towards [[~]][[7/6]]), the diminished fourth [[~]][[32/25]] be sharp (towards [[~]][[9/7]]) and the tritone [[~]][[45/32]] be flat (towards [[~]][[7/5]]), such that every [[7-limit]] [[9-odd-limit]] interval is tuned between itself and the [[5-limit]] interpretation it is separated from by [[225/224]]. If we take these as hard constraints, then [[53edo]] and [[84edo]] are the smallest edo tunings to satisfy them, but if overtempering is allowed, many smaller edos are possible, such as [[31edo\|31-]] and [[41edo]]. Interestingly, [[72edo]], though very performant as a 7- and 11-limit tuning, is overtempered for some of these constraints, whereas 53edo, though satisfying these constraints, tempers the intervals closer to the more complex [[5-limit]] interpretations, though the 7-limit concordances of the 9-odd-limit still clearly work. [[84edo]], another superset of 12edo, is an interesting edo to look at for its high performance in large odd-limits. Going up to larger edos, [[125edo\|125-]], [[166edo\|166-]], [[178edo\|178-]], [[197edo\|197-]], and [[240edo]] are all great choices with different intonational characteristics.

	The marvel extension [[hecate]] has the no-17's [[19-limit]] as its subgroup, and ~~tridecimal marvel, the extension chosen by [[Gene Ward Smith]],~~ is in the 13-limit. They merge in the rank-2 temperament [[catakleismic]], which can be conceptualized as accepting both rank-3 marvel structures simultaneously. One such tuning is excellently given by [[125edo]]. If we are looking for a small edo tuning instead, 53edo and 72edo are also reasonable edo tunings for the full no-17's 19-limit catakleismic, though in 53edo the 11 and 19 are a little off and in 72edo the 13 and 19 are a little off instead; 72edo is positioned better as a full [[17-limit]] marvel system while 53edo is positioned better as a (potentially no-11's) [[13-limit]] marvel system. If we focus on the 11-limit of undecimal marvel (discarding the mapping of 13), 31edo and 41edo are the smallest to clearly succeed, though many accept 41edo's mapping of [[~]][[13/8]] to the neutral sixth and some accept that mapping for 31edo as contextually usable too.		The marvel extension hecate has the no-17's [[19-limit]] as its subgroup, and helios is in the 13-limit. They merge in the rank-2 temperament [[catakleismic]], which can be conceptualized as accepting both rank-3 marvel structures simultaneously. One such tuning is excellently given by [[125edo]]. If we are looking for a small edo tuning instead, 53edo and 72edo are also reasonable edo tunings for the full no-17's 19-limit catakleismic, though in 53edo the 11 and 19 are a little off and in 72edo the 13 and 19 are a little off instead; 72edo is positioned better as a full [[17-limit]] marvel system while 53edo is positioned better as a (potentially no-11's) [[13-limit]] marvel system. If we focus on the 11-limit of undecimal marvel (discarding the mapping of 13), 31edo and 41edo are the smallest to clearly succeed, though many accept 41edo's mapping of [[~]][[13/8]] to the neutral sixth and some accept that mapping for 31edo as contextually usable too.

	=== Norm-based tunings ===		=== Norm-based tunings ===
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	This spectrum assumes pure 2 and 7.		This spectrum assumes pure 2 and 7.

	{\| class="wikitable center-all"		{\| class="wikitable center-all left-4"
	\|-		\|-
	! [[Eigenmonzo\|Eigenmonzo<br>(Unchanged-interval)]]		! [[Eigenmonzo\|Eigenmonzo<br>(Unchanged-interval)]]
	! ~~Fifth~~<br>(¢)		! Perfect<br>fifth (¢)
	! ~~Major~~<br>~~Third~~ (¢)		! Classical<br>major third (¢)
	! Comments		! Comments
	\|-		\|-

FloraC: Oops

2026-05-19T07:39:15Z

Oops

← Older revision		Revision as of 07:39, 19 May 2026
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	{{Interwiki		{{Interwiki
	\| en = Marvel ~~family~~		\| en = Marvel
	\| de = Marvel		\| de = Marvel
	\| es =		\| es =

FloraC: + interwiki

2026-05-19T07:38:49Z

+ interwiki

← Older revision		Revision as of 07:38, 19 May 2026
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			{{Interwiki
			\| en = Marvel family
			\| de = Marvel
			\| es =
			\| ja =
			}}
	{{Infobox regtemp		{{Infobox regtemp
	\| Title = Marvel		\| Title = Marvel

FloraC: Cleanup on infobox

2026-02-09T10:30:13Z

Cleanup on infobox

← Older revision		Revision as of 10:30, 9 February 2026
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	{{Infobox ~~Regtemp~~		{{Infobox regtemp
	\| Title = Marvel		\| Title = Marvel
	\| Subgroups = 2.3.5.7, 2.3.5.7.11		\| Subgroups = 2.3.5.7, 2.3.5.7.11
	\| Comma basis = [[225/224]] (7-limit);<br>[[225/224]], [[385/384]] (11-limit)		\| Comma basis = [[225/224]] (7-limit); <br>[[225/224]], [[385/384]] (11-limit)
	\| Edo join 1 = 19 \| Edo join 2 = 22 \| Edo join 3 = 31		\| Edo join 1 = 19 \| Edo join 2 = 22 \| Edo join 3 = 31
	\| Mapping = 1; 1 0 2 -1; 0 1 2 -3		\| Mapping = 1; 1 0 2 -1; 0 1 2 -3
	\| ~~Generator~~ = 3/2, 5/4		\| Generators = 3/2, 5/4
	\| ~~Generator~~ tuning = 700.6, 383.5		\| Generators tuning = 700.6, 383.5
	\| Optimization method = CWE		\| Optimization method = CWE
	\| Pergen = (P8, P5, ^1)		\| Pergen = (P8, P5, ^1)

Overthink: + infobox

2026-02-09T00:10:17Z

+ infobox

← Older revision		Revision as of 00:10, 9 February 2026
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			{{Infobox Regtemp
			\| Title = Marvel
			\| Subgroups = 2.3.5.7, 2.3.5.7.11
			\| Comma basis = [[225/224]] (7-limit);<br>[[225/224]], [[385/384]] (11-limit)
			\| Edo join 1 = 19 \| Edo join 2 = 22 \| Edo join 3 = 31
			\| Mapping = 1; 1 0 2 -1; 0 1 2 -3
			\| Generator = 3/2, 5/4
			\| Generator tuning = 700.6, 383.5
			\| Optimization method = CWE
			\| Pergen = (P8, P5, ^1)
			\| Color name = Ruyoyoti
			\| Odd limit 1 = 9 \| Mistuning 1 = 2.57 \| Complexity 1 = ?
			\| Odd limit 2 = 11-limit 21 \| Mistuning 2 = 3.86 \| Complexity 2 = ?
			}}
	'''Marvel''' is a [[rank-3 temperament\|rank-3]] [[regular temperament\|temperament]] with the same [[lattice]] structure as [[5-limit]] [[JI]], while identifying the [[7/4\|harmonic seventh (7/4)]] as a stack of two [[15/8\|classical major sevenths (15/8)]] [[octave reduction\|octave-reduced]], [[tempering out]] [[225/224]]. It is the head of the [[marvel family]].		'''Marvel''' is a [[rank-3 temperament\|rank-3]] [[regular temperament\|temperament]] with the same [[lattice]] structure as [[5-limit]] [[JI]], while identifying the [[7/4\|harmonic seventh (7/4)]] as a stack of two [[15/8\|classical major sevenths (15/8)]] [[octave reduction\|octave-reduced]], [[tempering out]] [[225/224]]. It is the head of the [[marvel family]].

FloraC: Derivation of prime 11

2026-02-07T10:31:17Z

Derivation of prime 11

← Older revision		Revision as of 10:31, 7 February 2026
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	'''Marvel''' is a [[rank-3 temperament\|rank-3]] [[regular temperament\|temperament]] with the same [[lattice]] structure as [[5-limit]] [[JI]], while identifying the [[7/4\|harmonic seventh (7/4)]] as a stack of two [[15/8\|classical major sevenths (15/8)]] [[octave reduction\|octave-reduced]], [[tempering out]] [[225/224]]. It is the head of the [[marvel family]].		'''Marvel''' is a [[rank-3 temperament\|rank-3]] [[regular temperament\|temperament]] with the same [[lattice]] structure as [[5-limit]] [[JI]], while identifying the [[7/4\|harmonic seventh (7/4)]] as a stack of two [[15/8\|classical major sevenths (15/8)]] [[octave reduction\|octave-reduced]], [[tempering out]] [[225/224]]. It is the head of the [[marvel family]].

	The canonical [[11-limit]] [[extension]], sometimes aliased ''unimarv'', ~~which~~ adds [[385/384]] and [[540/539]] to the comma list makes it a member of both [[keenanismic temperaments\|keenansimic]] and [[swetismic temperaments]].		Marvel tends to tune [[5/4]] flat, such that a stack of two such thirds give a sharp [[14/9]], and a stack of three such thirds give a sub-octave of [[35/18]] just short of the octave by a quartertone of [[36/35]]. The canonical [[11-limit]] [[extension]], sometimes aliased ''unimarv'', identifies the quartertone as [[33/32]], so that [[11/8]] is that plus a [[4/3\|perfect fourth]]. This adds [[385/384]] and [[540/539]] to the comma list and makes it a member of both [[keenanismic temperaments\|keenansimic]] and [[swetismic temperaments]].

	The temperament was named by [[Gene Ward Smith]] in 2002–2003, when the 11-limit version was found first<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5145.html#5184 Yahoo! Tuning Group \| ''Relative complexity and scale construction''] – first mention of ''marvel''.</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5687.html Yahoo! Tuning Group \| ''Top 135 11-limit planar temperaments''] – establishment as an 11-limit temperament.</ref>. Gene carried it to the 7-limit restriction in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_50829.html Yahoo! Tuning Group \| ''Marvel'']</ref>.		The temperament was named by [[Gene Ward Smith]] in 2002–2003, when the 11-limit version was found first<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5145.html#5184 Yahoo! Tuning Group \| ''Relative complexity and scale construction''] – first mention of ''marvel''.</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5687.html Yahoo! Tuning Group \| ''Top 135 11-limit planar temperaments''] – establishment as an 11-limit temperament.</ref>. Gene carried it to the 7-limit restriction in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_50829.html Yahoo! Tuning Group \| ''Marvel'']</ref>.

FloraC: Mention unimarv here as a historical note

2025-12-13T12:19:37Z

Mention unimarv here as a historical note

← Older revision		Revision as of 12:19, 13 December 2025
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	'''Marvel''' is a [[rank-3 temperament\|rank-3]] [[regular temperament\|temperament]] with the same [[lattice]] structure as [[5-limit]] [[JI]], while identifying the [[7/4\|harmonic seventh (7/4)]] as a stack of two [[15/8\|classical major sevenths (15/8)]] [[octave reduction\|octave-reduced]], [[tempering out]] [[225/224]]. It is the head of the [[marvel family]]~~, and the~~ canonical [[11-limit]] [[extension]] ~~adding~~ [[385/384]] and [[540/539]] to the comma list makes it a member of both [[keenanismic temperaments\|keenansimic]] and [[swetismic temperaments]].		'''Marvel''' is a [[rank-3 temperament\|rank-3]] [[regular temperament\|temperament]] with the same [[lattice]] structure as [[5-limit]] [[JI]], while identifying the [[7/4\|harmonic seventh (7/4)]] as a stack of two [[15/8\|classical major sevenths (15/8)]] [[octave reduction\|octave-reduced]], [[tempering out]] [[225/224]]. It is the head of the [[marvel family]].

			The canonical [[11-limit]] [[extension]], sometimes aliased ''unimarv'', which adds [[385/384]] and [[540/539]] to the comma list makes it a member of both [[keenanismic temperaments\|keenansimic]] and [[swetismic temperaments]].

	The temperament was named by [[Gene Ward Smith]] in 2002–2003, when the 11-limit version was found first<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5145.html#5184 Yahoo! Tuning Group \| ''Relative complexity and scale construction''] – first mention of ''marvel''.</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5687.html Yahoo! Tuning Group \| ''Top 135 11-limit planar temperaments''] – establishment as an 11-limit temperament.</ref>. Gene carried it to the 7-limit restriction in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_50829.html Yahoo! Tuning Group \| ''Marvel'']</ref>.		The temperament was named by [[Gene Ward Smith]] in 2002–2003, when the 11-limit version was found first<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5145.html#5184 Yahoo! Tuning Group \| ''Relative complexity and scale construction''] – first mention of ''marvel''.</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5687.html Yahoo! Tuning Group \| ''Top 135 11-limit planar temperaments''] – establishment as an 11-limit temperament.</ref>. Gene carried it to the 7-limit restriction in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_50829.html Yahoo! Tuning Group \| ''Marvel'']</ref>.

← Older revision		Revision as of 08:38, 10 November 2026
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	'''Marvel''' is a [[rank-3 temperament]] with the same [[lattice]] structure as [[5-limit]] [[JI]], while identifying the [[7/4\|harmonic seventh (7/4)]] as a stack of two [[15/8\|classical major sevenths (15/8)]] [[octave reduction\|octave-reduced]], [[tempering out]] [[225/224]]. It is the head of the [[marvel family]].		'''Marvel''' is a [[rank-3 temperament]] with the same [[lattice]] structure as [[5-limit]] [[JI]], while identifying the [[7/4\|harmonic seventh (7/4)]] as a stack of two [[15/8\|classical major sevenths (15/8)]] [[octave reduction\|octave-reduced]], [[tempering out]] [[225/224]]. It is the head of the [[marvel family]].

	Marvel tends to tune [[5/4]] flat, such that a stack of two such thirds give a sharp [[14/9]], and a ~~stack~~ of three ~~such~~ thirds ~~give~~ a ~~sub-octave of~~ [[35/18]] just short of the octave by a quartertone of [[36/35]]. The canonical [[11-limit]] [[extension]], sometimes aliased ''unimarv'', identifies the quartertone as [[33/32]], so that [[11/8]] is that plus a [[4/3\|perfect fourth]]. This adds [[385/384]] and [[540/539]] to the comma list and makes it a member of both [[keenanismic temperaments\|keenansimic]] and [[swetismic temperaments]].		Marvel tends to tune [[5/4]] flat, such that a stack of two such thirds give a sharp [[14/9]]. In other words, it has a 5/4, 5/4, 9/7 version of the [[augmented triad]]. Since this is a chord of [[meantone]] in wide use in Western {{w\|common practice}} harmony long before [[12edo]] established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.

			Another ~5/4 on top of ~14/9 gives a [[35/18]] sub-octave just short of the octave by a quartertone of [[36/35]]. The canonical [[11-limit]] [[extension]], sometimes aliased ''unimarv'', identifies the quartertone as [[33/32]], so that [[11/8]] is that plus a [[4/3\|perfect fourth]]. This adds [[385/384]] and [[540/539]] to the comma list and makes it a member of both [[keenanismic temperaments\|keenansimic]] and [[swetismic temperaments]].

	The temperament was named by [[Gene Ward Smith]] in 2002–2003, when the 11-limit version was found first<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5145.html#5184 Yahoo! Tuning Group \| ''Relative complexity and scale construction''] – first mention of ''marvel''.</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5687.html Yahoo! Tuning Group \| ''Top 135 11-limit planar temperaments''] – establishment as an 11-limit temperament.</ref>. Gene carried it to the 7-limit restriction in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_50829.html Yahoo! Tuning Group \| ''Marvel'']</ref>.		The temperament was named by [[Gene Ward Smith]] in 2002–2003, when the 11-limit version was found first<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5145.html#5184 Yahoo! Tuning Group \| ''Relative complexity and scale construction''] – first mention of ''marvel''.</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5687.html Yahoo! Tuning Group \| ''Top 135 11-limit planar temperaments''] – establishment as an 11-limit temperament.</ref>. Gene carried it to the 7-limit restriction in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_50829.html Yahoo! Tuning Group \| ''Marvel'']</ref>.
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	== Chords and harmony ==		== Chords and harmony ==
	Marvel enables [[essentially tempered chord]]s of [[marvel chords\|marvel]], [[keenanismic chords\|keenanismic]], [[swetismic chords\|swetismic]], and [[undecimal marvel chords\|undecimal marvel]].		Marvel enables [[essentially tempered chord]]s of [[marvel chords\|marvel]], [[keenanismic chords\|keenanismic]], [[swetismic chords\|swetismic]], and [[undecimal marvel chords\|undecimal marvel]]. It also allows for a tritone substitution whereby the [[dominant seventh chord]] formed by adding 16/9 above the root shares its tritone with the [[harmonic seventh chord]]. (The tritone of the dominant seventh is {{nowrap\|(16/9)/(5/4) {{=}} 64/45}}. Setting this equal to 10/7 gives {{nowrap\|(10/7)/(64/45) {{=}} 225/224}}.)

	Extending the temperament to the 13-limit through 325/324, resulting in hecate, enables chords of [[marveltwin chords\|marveltwin]] and [[squbemic chords\|squbemic]]. [[Hecate hexad]] is a chord peculiar to this temperament. Alternatively, helios enables chords of [[ratwolfsmic chords\|ratwolfsmic]].		Extending the temperament to the 13-limit through 325/324, resulting in hecate, enables chords of [[marveltwin chords\|marveltwin]] and [[squbemic chords\|squbemic]]. [[Hecate hexad]] is a chord peculiar to this temperament. Alternatively, helios enables chords of [[ratwolfsmic chords\|ratwolfsmic]].

← Older revision		Revision as of 10:31, 7 February 2026
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	'''Marvel''' is a [[rank-3 temperament\|rank-3]] [[regular temperament\|temperament]] with the same [[lattice]] structure as [[5-limit]] [[JI]], while identifying the [[7/4\|harmonic seventh (7/4)]] as a stack of two [[15/8\|classical major sevenths (15/8)]] [[octave reduction\|octave-reduced]], [[tempering out]] [[225/224]]. It is the head of the [[marvel family]].		'''Marvel''' is a [[rank-3 temperament\|rank-3]] [[regular temperament\|temperament]] with the same [[lattice]] structure as [[5-limit]] [[JI]], while identifying the [[7/4\|harmonic seventh (7/4)]] as a stack of two [[15/8\|classical major sevenths (15/8)]] [[octave reduction\|octave-reduced]], [[tempering out]] [[225/224]]. It is the head of the [[marvel family]].

	The canonical [[11-limit]] [[extension]], sometimes aliased ''unimarv'', ~~which~~ adds [[385/384]] and [[540/539]] to the comma list makes it a member of both [[keenanismic temperaments\|keenansimic]] and [[swetismic temperaments]].		Marvel tends to tune [[5/4]] flat, such that a stack of two such thirds give a sharp [[14/9]], and a stack of three such thirds give a sub-octave of [[35/18]] just short of the octave by a quartertone of [[36/35]]. The canonical [[11-limit]] [[extension]], sometimes aliased ''unimarv'', identifies the quartertone as [[33/32]], so that [[11/8]] is that plus a [[4/3\|perfect fourth]]. This adds [[385/384]] and [[540/539]] to the comma list and makes it a member of both [[keenanismic temperaments\|keenansimic]] and [[swetismic temperaments]].

	The temperament was named by [[Gene Ward Smith]] in 2002–2003, when the 11-limit version was found first<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5145.html#5184 Yahoo! Tuning Group \| ''Relative complexity and scale construction''] – first mention of ''marvel''.</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5687.html Yahoo! Tuning Group \| ''Top 135 11-limit planar temperaments''] – establishment as an 11-limit temperament.</ref>. Gene carried it to the 7-limit restriction in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_50829.html Yahoo! Tuning Group \| ''Marvel'']</ref>.		The temperament was named by [[Gene Ward Smith]] in 2002–2003, when the 11-limit version was found first<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5145.html#5184 Yahoo! Tuning Group \| ''Relative complexity and scale construction''] – first mention of ''marvel''.</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5687.html Yahoo! Tuning Group \| ''Top 135 11-limit planar temperaments''] – establishment as an 11-limit temperament.</ref>. Gene carried it to the 7-limit restriction in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_50829.html Yahoo! Tuning Group \| ''Marvel'']</ref>.

← Older revision		Revision as of 12:19, 13 December 2025
Line 1:		Line 1:
	'''Marvel''' is a [[rank-3 temperament\|rank-3]] [[regular temperament\|temperament]] with the same [[lattice]] structure as [[5-limit]] [[JI]], while identifying the [[7/4\|harmonic seventh (7/4)]] as a stack of two [[15/8\|classical major sevenths (15/8)]] [[octave reduction\|octave-reduced]], [[tempering out]] [[225/224]]. It is the head of the [[marvel family]]~~, and the~~ canonical [[11-limit]] [[extension]] ~~adding~~ [[385/384]] and [[540/539]] to the comma list makes it a member of both [[keenanismic temperaments\|keenansimic]] and [[swetismic temperaments]].		'''Marvel''' is a [[rank-3 temperament\|rank-3]] [[regular temperament\|temperament]] with the same [[lattice]] structure as [[5-limit]] [[JI]], while identifying the [[7/4\|harmonic seventh (7/4)]] as a stack of two [[15/8\|classical major sevenths (15/8)]] [[octave reduction\|octave-reduced]], [[tempering out]] [[225/224]]. It is the head of the [[marvel family]].

			The canonical [[11-limit]] [[extension]], sometimes aliased ''unimarv'', which adds [[385/384]] and [[540/539]] to the comma list makes it a member of both [[keenanismic temperaments\|keenansimic]] and [[swetismic temperaments]].

	The temperament was named by [[Gene Ward Smith]] in 2002–2003, when the 11-limit version was found first<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5145.html#5184 Yahoo! Tuning Group \| ''Relative complexity and scale construction''] – first mention of ''marvel''.</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5687.html Yahoo! Tuning Group \| ''Top 135 11-limit planar temperaments''] – establishment as an 11-limit temperament.</ref>. Gene carried it to the 7-limit restriction in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_50829.html Yahoo! Tuning Group \| ''Marvel'']</ref>.		The temperament was named by [[Gene Ward Smith]] in 2002–2003, when the 11-limit version was found first<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5145.html#5184 Yahoo! Tuning Group \| ''Relative complexity and scale construction''] – first mention of ''marvel''.</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5687.html Yahoo! Tuning Group \| ''Top 135 11-limit planar temperaments''] – establishment as an 11-limit temperament.</ref>. Gene carried it to the 7-limit restriction in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_50829.html Yahoo! Tuning Group \| ''Marvel'']</ref>.