Slendric - Revision history

Vector at 02:14, 2 June 2026

2026-06-02T02:14:49Z

← Older revision		Revision as of 02:14, 2 June 2026
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	Melodically, the Slendric generator stack forms a 5-note scale (1L 4s) that is [[equipentatonic]] (nearly 5edo). [[MOS]]es further down the hierarchy (6, 11, 16, ... notes) can be thought of as the notes of a basic pentatonic form, inflected by multiples of a characteristic small interval known as the ''quark'' (representing a third of a [[diatonic semitone]], and the commas [[49/48]] and [[64/63]] tempered together). As a result, these MOS scales tend to be extremely [[hard]].		Melodically, the Slendric generator stack forms a 5-note scale (1L 4s) that is [[equipentatonic]] (nearly 5edo). [[MOS]]es further down the hierarchy (6, 11, 16, ... notes) can be thought of as the notes of a basic pentatonic form, inflected by multiples of a characteristic small interval known as the ''quark'' (representing a third of a [[diatonic semitone]], and the commas [[49/48]] and [[64/63]] tempered together). As a result, these MOS scales tend to be extremely [[hard]].
			[[File:Slendric5.png\|thumb\|Slendric pentatonic MOS]]
	Slendric can exhibit a wide range of tunings, with fifths between those of [[26edo]] (692c) and [[56edo]] (707c), or generators roughly between 231 and 236c, while maintaining the recognizability of the 2.3.7 structure. Notable [[EDO]] tunings are in between these, and include EDOs that end in "1" or "6", i.e. [[31edo]], [[36edo]], [[41edo]], and [[46edo]]. Slendric is also supported by edos with 5edo's 3/2, since it is a [[subtemperament]] of 7-limit [[Blackwood]].		Slendric can exhibit a wide range of tunings, with fifths between those of [[26edo]] (692c) and [[56edo]] (707c), or generators roughly between 231 and 236c, while maintaining the recognizability of the 2.3.7 structure. Notable [[EDO]] tunings are in between these, and include EDOs that end in "1" or "6", i.e. [[31edo]], [[36edo]], [[41edo]], and [[46edo]]. Slendric is also supported by edos with 5edo's 3/2, since it is a [[subtemperament]] of 7-limit [[Blackwood]].

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	This name has been criticized for its lack of relevance, and thus other names such as Wonder may be used instead.		This name has been criticized for its lack of relevance, and thus other names such as Wonder may be used instead.

			Pailiaq suggests "Tricot", after its ploidacot signature, but this runs into problems with continued reference to [[Microtemperament#Alphatricot\|alphatricot]] as "tricot" instead.

	== List of patent vals ==		== List of patent vals ==

Inthar: /* Bame */

2026-04-20T19:07:45Z

Bame

← Older revision		Revision as of 19:07, 20 April 2026
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	<nowiki>*</nowiki> Besides the octave		<nowiki>*</nowiki> Besides the octave

	== ~~Bame~~ ==		== Name ==
	"Slendric" comes from the slendro tuning used in gamelan, which creates a pentatonic framework like Slendric temperament does. (However, slendro tunings vary, often being closer to a very sharp Archy temperament with detuned octaves.) "Gamelic" (from "gamelisma") has a similar origin.		"Slendric" comes from the slendro tuning used in gamelan, which creates a pentatonic framework like Slendric temperament does. (However, slendro tunings vary, often being closer to a very sharp Archy temperament with detuned octaves.) "Gamelic" (from "gamelisma") has a similar origin.

Vector at 17:00, 20 April 2026

2026-04-20T17:00:36Z

← Older revision		Revision as of 17:00, 20 April 2026
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	'''Slendric''' (also known as "Wonder" or "Gamelic") is the basic harmonic interpretation as a [[regular temperament]] for the structure where the perfect fifth (~[[3/2]]) is split into three equal parts; each of these is taken to represent the interval [[8/7]]. Since the 7th [[harmonic]] is less than 3 [[cent]]s from just when 3/2 is pure, Slendric constitutes an exceptionally good [[rank-2 temperament\|rank-2]] traversal of the [[2.3.7 subgroup\|2.3.7]] tuning space for its simplicity. Its corresponding [[comma]] is the difference between 3/2 and (8/7)<sup>3</sup>, which is 1029/1024.		'''Slendric''' (also known as "Wonder" or "Gamelic") is the basic harmonic interpretation as a [[regular temperament]] for the structure where the perfect fifth (~[[3/2]]) is split into three equal parts; each of these is taken to represent the interval [[8/7]]. Since the 7th [[harmonic]] is less than 3 [[cent]]s from just when 3/2 is pure, Slendric constitutes an exceptionally good [[rank-2 temperament\|rank-2]] traversal of the [[2.3.7 subgroup\|2.3.7]] tuning space for its simplicity. Its corresponding [[comma]] is the difference between 3/2 and (8/7)<sup>3</sup>, which is 1029/1024.

	Melodically, the Slendric generator stack forms a 5-note scale (1L 4s) that is ~~nearly~~ [[equipentatonic]]. [[MOS]]es further down the hierarchy (6, 11, 16, ... notes) can be thought of as the notes of a basic pentatonic form, inflected by multiples of a characteristic small interval known as the ''quark'' (representing a third of a [[diatonic semitone]], and the commas [[49/48]] and [[64/63]] tempered together). As a result, these MOS scales tend to be extremely [[hard]].		Melodically, the Slendric generator stack forms a 5-note scale (1L 4s) that is [[equipentatonic]] (nearly 5edo). [[MOS]]es further down the hierarchy (6, 11, 16, ... notes) can be thought of as the notes of a basic pentatonic form, inflected by multiples of a characteristic small interval known as the ''quark'' (representing a third of a [[diatonic semitone]], and the commas [[49/48]] and [[64/63]] tempered together). As a result, these MOS scales tend to be extremely [[hard]].

	Slendric can exhibit a wide range of tunings, with fifths between those of [[26edo]] (692c) and [[56edo]] (707c), or generators roughly between 231 and 236c, while maintaining the recognizability of the 2.3.7 structure. Notable [[EDO]] tunings are in between these, and include EDOs that end in "1" or "6", i.e. [[31edo]], [[36edo]], [[41edo]], and [[46edo]]. Slendric is also supported by edos with 5edo's 3/2, since it is a [[subtemperament]] of 7-limit [[Blackwood]].		Slendric can exhibit a wide range of tunings, with fifths between those of [[26edo]] (692c) and [[56edo]] (707c), or generators roughly between 231 and 236c, while maintaining the recognizability of the 2.3.7 structure. Notable [[EDO]] tunings are in between these, and include EDOs that end in "1" or "6", i.e. [[31edo]], [[36edo]], [[41edo]], and [[46edo]]. Slendric is also supported by edos with 5edo's 3/2, since it is a [[subtemperament]] of 7-limit [[Blackwood]].
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	\|}		\|}
	<nowiki>*</nowiki> Besides the octave		<nowiki>*</nowiki> Besides the octave

			== Bame ==
			"Slendric" comes from the slendro tuning used in gamelan, which creates a pentatonic framework like Slendric temperament does. (However, slendro tunings vary, often being closer to a very sharp Archy temperament with detuned octaves.) "Gamelic" (from "gamelisma") has a similar origin.

			This name has been criticized for its lack of relevance, and thus other names such as Wonder may be used instead.

	== List of patent vals ==		== List of patent vals ==

Inthar: /* Prime 5 */

2026-04-12T23:39:55Z

Prime 5

← Older revision		Revision as of 23:39, 12 April 2026
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	Rodan, meanwhile, slightly sharpens the fifth and can be constructed by equating 81/80 to the quark. This thereby tempers out the [[aberschisma]] (5120/5103), and furthermore implies the Sensamagic ([[245/243]]) equivalence, that [[9/7]] forms half of [[5/3]]. From this, it can be seen that 5/4 is found at a perfect fifth (3 generators) above twice 9/7 (7 generators each), or 17 generators in all: this is the downmajor third in [[#Interval categories\|the system described earlier]]. 41edo and 46edo bound the main Rodan tuning range, but their sum, [[87edo]], is essentially optimal with a nearly just 5/4. 36edo using the flat major third of 367{{c}} as 5/4 also qualifies as Rodan.		Rodan, meanwhile, slightly sharpens the fifth and can be constructed by equating 81/80 to the quark. This thereby tempers out the [[aberschisma]] (5120/5103), and furthermore implies the Sensamagic ([[245/243]]) equivalence, that [[9/7]] forms half of [[5/3]]. From this, it can be seen that 5/4 is found at a perfect fifth (3 generators) above twice 9/7 (7 generators each), or 17 generators in all: this is the downmajor third in [[#Interval categories\|the system described earlier]]. 41edo and 46edo bound the main Rodan tuning range, but their sum, [[87edo]], is essentially optimal with a nearly just 5/4. 36edo using the flat major third of 367{{c}} as 5/4 also qualifies as Rodan.

	As regards weak extensions, notable ones include [[Miracle]], which splits 8/7 in two, and [[Valentine]], which splits it in three (therefore dividing the perfect fifth into 6 and 9 parts, respectively). They also include [[Superkleismic]] (15 & 26), which splits 7/4 into three intervals of [[6/5]]; this is supported by 26, 41, and 56edo.		As regards weak extensions, notable ones include [[Miracle]], which splits 8/7 in two, and [[Valentine]], which splits it in three (therefore dividing the perfect fifth into 6 and 9 parts, respectively). They also include [[Superkleismic]] (15 & 26), which splits 7/4 into three intervals of [[6/5]]; this is supported by 26, 41, and 56edo. [[Lemba]] (16 & 26) is a less accurate weak extension that adds 1\2 interpreted as 7/5~10/7.

	Miracle's generator (known as the "secor") represents [[16/15]] and [[15/14]] simultaneously (tempering out [[225/224]], the marvel comma), so that [[8/5]] is placed at 7 secors. As a consequence of splitting 8/7 in half, Miracle also includes an exact [[neutral third]], interpretable in the 7-limit as [[49/40]]. Miracle is 10 & 21, and 31, 41, and [[72edo]] support it.		Miracle's generator (known as the "secor") represents [[16/15]] and [[15/14]] simultaneously (tempering out [[225/224]], the marvel comma), so that [[8/5]] is placed at 7 secors. As a consequence of splitting 8/7 in half, Miracle also includes an exact [[neutral third]], interpretable in the 7-limit as [[49/40]]. Miracle is 10 & 21, and 31, 41, and [[72edo]] support it.

Overthink: /* Prime 11 */ formatting

2026-04-07T16:31:46Z

Prime 11: formatting

← Older revision		Revision as of 16:31, 7 April 2026
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	As mentioned before, extensions to 11 can be created off of these by tempering out 385/384 and 441/440. This works almost perfectly in the 41 & 46 Rodan range, and the diatonic major third is identified with [[14/11]]. This also applies to the 26 & 31 Mothra range, yet the case with Mothra is slightly more complicated, as the interval formed from (sharpened) 7/6 stacked twice can reasonably represent either [[11/8]] or [[15/11]], depending on the tuning (note that in 31edo, it represents both).		As mentioned before, extensions to 11 can be created off of these by tempering out 385/384 and 441/440. This works almost perfectly in the 41 & 46 Rodan range, and the diatonic major third is identified with [[14/11]]. This also applies to the 26 & 31 Mothra range, yet the case with Mothra is slightly more complicated, as the interval formed from (sharpened) 7/6 stacked twice can reasonably represent either [[11/8]] or [[15/11]], depending on the tuning (note that in 31edo, it represents both).

	The former is supported by 26 & 31, and the latter by 31 & 36; the resulting extensions are called "~~undecimal~~ Mothra" and "Mosura" respectively. Undecimal Mothra equates 14/11 to 9/7 (tempering out [[99/98]]), and Mosura equates 14/11 to [[32/25]] (tempering out [[176/175]]). Of the two, the former is taken to be canonical primarily as 11/8 itself is reached by far fewer generators (-8, compared to 23).		The former is supported by 26 & 31, and the latter by 31 & 36; the resulting extensions are called "Undecimal Mothra" and "Mosura" respectively. Undecimal Mothra equates 14/11 to 9/7 (tempering out [[99/98]]), and Mosura equates 14/11 to [[32/25]] (tempering out [[176/175]]). Of the two, the former is taken to be canonical primarily as 11/8 itself is reached by far fewer generators (-8, compared to +23).

	Miracle, Valentine, and Superkleismic all receive extensions to 11 in this manner as well. In Miracle's case, the neutral third is mapped to [[11/9]]~[[27/22]], while in Valentine's, the [[neutral second]] formed by two steps represents [[12/11]]~[[11/10]]. Superkleismic, in fact, tempers out [[100/99]], whereby [[16/11]] is reached at only two of its 6/5 generators, which produces the notable 2.7.11 subgroup structure known as [[Orgone]].		Miracle, Valentine, and Superkleismic all receive extensions to 11 in this manner as well. In Miracle's case, the neutral third is mapped to [[11/9]]~[[27/22]], while in Valentine's, the [[neutral second]] formed by two steps represents [[12/11]]~[[11/10]]. Superkleismic, in fact, tempers out [[100/99]], whereby [[16/11]] is reached at only two of its 6/5 generators, which produces the notable 2.7.11 subgroup structure known as [[Orgone]].

Overthink: /* The pentatonic framework */ make color scheme fit better

2026-04-06T20:44:38Z

The pentatonic framework: make color scheme fit better

← Older revision		Revision as of 20:44, 6 April 2026
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	The intervals of Slendric can be organized according to how many steps of [[5edo]], or equivalently the 5-note MOS, they correspond to, since the MOS scales of Slendric up to at least 26 notes have 5 large steps and many small steps, each the size of a quark. The "major" interval of a class here is the one just larger than the corresponding 5edo interval, and the "minor" interval is just smaller. Below are the intervals of the symmetric mode of Slendric[21] (5L 16s). The generator tuning here is 3/10-comma, where the quark is exactly sqrt([[28/27]]), or about 31.5 cents.		The intervals of Slendric can be organized according to how many steps of [[5edo]], or equivalently the 5-note MOS, they correspond to, since the MOS scales of Slendric up to at least 26 notes have 5 large steps and many small steps, each the size of a quark. The "major" interval of a class here is the one just larger than the corresponding 5edo interval, and the "minor" interval is just smaller. Below are the intervals of the symmetric mode of Slendric[21] (5L 16s). The generator tuning here is 3/10-comma, where the quark is exactly sqrt([[28/27]]), or about 31.5 cents.

	{\| class="wikitable center-all left-1~~" style="color: #000000;~~"		{\| class="wikitable center-all left-1"
	\|-		\|-
	! Steps of 5edo		! Steps of 5edo
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	!4		!4
	!5		!5
	\|- style="background-color: #~~DFDFDF~~;"		\|- style="background-color: #003030;"
	! "Augmented" interval		! "Augmented" interval
	\| 63.0		\| 63.0
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	\| 997.8		\| 997.8
	\|		\|
	\|- ~~style="background-color: #F7F7F7;"~~		\|-
	! JI intervals represented		! JI intervals represented
	\| 28/27		\| 28/27
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	\| 16/9		\| 16/9
	\|		\|
	\|- style="background-color: #~~DFDFDF~~;"		\|- style="background-color: #003030;"
	! "Major" interval		! "Major" interval
	\| 31.5		\| 31.5
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	\| 966.3		\| 966.3
	\| ''1200.0''		\| ''1200.0''
	\|- ~~style="background-color: #F7F7F7;"~~		\|-
	! JI intervals represented		! JI intervals represented
	\| 49/48, 64/63		\| 49/48, 64/63
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	\| 7/4		\| 7/4
	\| ''2/1''		\| ''2/1''
	\|- style="background-color: #~~DFDFDF~~;"		\|- style="background-color: #003030;"
	! "Minor" interval		! "Minor" interval
	\| ''0.0''		\| ''0.0''
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	\| 934.8		\| 934.8
	\| 1168.5		\| 1168.5
	\|- ~~style="background-color: #F7F7F7;"~~		\|-
	! JI intervals represented		! JI intervals represented
	\| ''1/1''		\| ''1/1''
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	\| 12/7		\| 12/7
	\| 63/32, 96/49		\| 63/32, 96/49
	\|- style="background-color: #~~DFDFDF~~;"		\|- style="background-color: #003030;"
	! "Diminished" interval		! "Diminished" interval
	\|		\|
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	\| 903.3		\| 903.3
	\| 1137.0		\| 1137.0
	\|- ~~style="background-color: #F7F7F7;"~~		\|-
	! JI intervals represented		! JI intervals represented
	\|		\|

Overthink: subtemperament of blackwood

2026-04-04T19:31:56Z

subtemperament of blackwood

← Older revision		Revision as of 19:31, 4 April 2026
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	Melodically, the Slendric generator stack forms a 5-note scale (1L 4s) that is nearly [[equipentatonic]]. [[MOS]]es further down the hierarchy (6, 11, 16, ... notes) can be thought of as the notes of a basic pentatonic form, inflected by multiples of a characteristic small interval known as the ''quark'' (representing a third of a [[diatonic semitone]], and the commas [[49/48]] and [[64/63]] tempered together). As a result, these MOS scales tend to be extremely [[hard]].		Melodically, the Slendric generator stack forms a 5-note scale (1L 4s) that is nearly [[equipentatonic]]. [[MOS]]es further down the hierarchy (6, 11, 16, ... notes) can be thought of as the notes of a basic pentatonic form, inflected by multiples of a characteristic small interval known as the ''quark'' (representing a third of a [[diatonic semitone]], and the commas [[49/48]] and [[64/63]] tempered together). As a result, these MOS scales tend to be extremely [[hard]].

	Slendric can exhibit a wide range of tunings, with fifths between those of [[26edo]] (692c) and [[56edo]] (707c), or generators roughly between 231 and 236c, while maintaining the recognizability of the 2.3.7 structure. Notable [[EDO]] tunings are in between these, and include EDOs that end in "1" or "6", i.e. [[31edo]], [[36edo]], [[41edo]], and [[46edo]]. Slendric is also supported by edos with 5edo's 3/2.		Slendric can exhibit a wide range of tunings, with fifths between those of [[26edo]] (692c) and [[56edo]] (707c), or generators roughly between 231 and 236c, while maintaining the recognizability of the 2.3.7 structure. Notable [[EDO]] tunings are in between these, and include EDOs that end in "1" or "6", i.e. [[31edo]], [[36edo]], [[41edo]], and [[46edo]]. Slendric is also supported by edos with 5edo's 3/2, since it is a [[subtemperament]] of 7-limit [[Blackwood]].

	== Structural theory ==		== Structural theory ==

Inthar: /* List of patent vals */

2026-03-16T13:59:00Z

List of patent vals

← Older revision		Revision as of 13:59, 16 March 2026
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	== List of patent vals ==		== List of patent vals ==
	{\| class="wikitable"		{\| class="wikitable sortable"
	\|+		\|+
	!EDO		!EDO

Vector at 02:24, 13 March 2026

2026-03-13T02:24:06Z

Show changes

Lériendil at 20:31, 10 March 2026

2026-03-10T20:31:55Z

← Older revision		Revision as of 20:31, 10 March 2026
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	{{Infobox regtemp		{{Infobox regtemp
	\| Title = Slendric		\| Title = Slendric