Slendric - Revision history

Overthink: subtemperament of blackwood

2026-04-04T19:31:56Z

subtemperament of blackwood

← Older revision		Revision as of 19:31, 4 April 2026
Line 14:		Line 14:
	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
Line 520:		Line 520:

	== 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
Line 1:		Line 1:

	{{Infobox regtemp		{{Infobox regtemp
	\| Title = Slendric		\| Title = Slendric

Inthar: /* A-Team */

2026-03-09T05:06:45Z

A-Team

← Older revision		Revision as of 05:06, 9 March 2026
Line 107:		Line 107:
	As a result of the ease of finding 55/32 and 17/13 along the Slendric chain, any extension to the full 7-limit can also find prime 11, and any extension to 2.3.7.13 can also find prime 17. This applies both to strong and weak extensions.		As a result of the ease of finding 55/32 and 17/13 along the Slendric chain, any extension to the full 7-limit can also find prime 11, and any extension to 2.3.7.13 can also find prime 17. This applies both to strong and weak extensions.
	==== A-Team ====		==== A-Team ====
	Taking every other step of Slendric results in a subtemperament generated by this subfourth, which is known as '''A-Team''' (~~2.9.21[~~5 & 18]; the name is from "18"). It is one of the main regular temperaments representing the [[oneirotonic]] (5L 3s) scale - specifically the hard tunings thereof such as in [[18edo\|18]], [[23edo\|23]], and [[31edo]]. The core [[subgroup]] interpretation of A-Team is 2.9.21.55: note that two A-Team generators, representing [[12/7]], come close to [[55/32]] and therefore [[385/384]] and [[441/440]], which again multiply to 1029/1024, can be tempered out. Different A-Team tunings can pick up other harmonic approximations; an interesting one is the 13:17:19 chord found in Mothra (and especially 31edo)'s version of A-Team.		Taking every other step of Slendric results in a subtemperament generated by this subfourth, which is known as '''A-Team''' (5 & 18; the name is from "18"). It is one of the main regular temperaments representing the [[oneirotonic]] (5L 3s) scale - specifically the hard tunings thereof such as in [[18edo\|18]], [[23edo\|23]], and [[31edo]]. The core [[subgroup]] interpretation of A-Team is 2.9.21.55: note that two A-Team generators, representing [[12/7]], come close to [[55/32]] and therefore [[385/384]] and [[441/440]], which again multiply to 1029/1024, can be tempered out. Different A-Team tunings can pick up other harmonic approximations; an interesting one is the 13:17:19 chord found in Mothra (and especially 31edo)'s version of A-Team.

	A-Team may be considered a [[straddle primes\|straddle-3]] temperament; the >3 is the sharp 32/21 generator and the <3 is reached by +4 21/16 generators. Indeed, stacking >3 and <3 reaches 9 at +3 generators.		A-Team may be considered a [[straddle primes\|straddle-3]] temperament; the >3 is the sharp 32/21 generator and the <3 is reached by +4 21/16 generators. Indeed, stacking >3 and <3 reaches 9 at +3 generators.

Inthar: /* A-Team */

2026-03-09T05:06:15Z

A-Team

← Older revision		Revision as of 05:06, 9 March 2026
Line 107:		Line 107:
	As a result of the ease of finding 55/32 and 17/13 along the Slendric chain, any extension to the full 7-limit can also find prime 11, and any extension to 2.3.7.13 can also find prime 17. This applies both to strong and weak extensions.		As a result of the ease of finding 55/32 and 17/13 along the Slendric chain, any extension to the full 7-limit can also find prime 11, and any extension to 2.3.7.13 can also find prime 17. This applies both to strong and weak extensions.
	==== A-Team ====		==== A-Team ====
	Taking every other step of Slendric results in a subtemperament generated by this subfourth, which is known as '''A-Team''' (2.9.21[13 & 18]; the name is from "18"). It is one of the main regular temperaments representing the [[oneirotonic]] (5L 3s) scale - specifically the hard tunings thereof such as in [[18edo\|18]], [[23edo\|23]], and [[31edo]]. The core [[subgroup]] interpretation of A-Team is 2.9.21.55: note that two A-Team generators, representing [[12/7]], come close to [[55/32]] and therefore [[385/384]] and [[441/440]], which again multiply to 1029/1024, can be tempered out. Different A-Team tunings can pick up other harmonic approximations; an interesting one is the 13:17:19 chord found in Mothra (and especially 31edo)'s version of A-Team.		Taking every other step of Slendric results in a subtemperament generated by this subfourth, which is known as '''A-Team''' (2.9.21[5 & 18]; the name is from "18"). It is one of the main regular temperaments representing the [[oneirotonic]] (5L 3s) scale - specifically the hard tunings thereof such as in [[18edo\|18]], [[23edo\|23]], and [[31edo]]. The core [[subgroup]] interpretation of A-Team is 2.9.21.55: note that two A-Team generators, representing [[12/7]], come close to [[55/32]] and therefore [[385/384]] and [[441/440]], which again multiply to 1029/1024, can be tempered out. Different A-Team tunings can pick up other harmonic approximations; an interesting one is the 13:17:19 chord found in Mothra (and especially 31edo)'s version of A-Team.

	A-Team may be considered a [[straddle primes\|straddle-3]] temperament; the >3 is the sharp 32/21 generator and the <3 is reached by +4 21/16 generators. Indeed, stacking >3 and <3 reaches 9 at +3 generators.		A-Team may be considered a [[straddle primes\|straddle-3]] temperament; the >3 is the sharp 32/21 generator and the <3 is reached by +4 21/16 generators. Indeed, stacking >3 and <3 reaches 9 at +3 generators.

Inthar: /* A-Team */

2026-03-09T05:05:47Z

A-Team

← Older revision		Revision as of 05:05, 9 March 2026
Line 107:		Line 107:
	As a result of the ease of finding 55/32 and 17/13 along the Slendric chain, any extension to the full 7-limit can also find prime 11, and any extension to 2.3.7.13 can also find prime 17. This applies both to strong and weak extensions.		As a result of the ease of finding 55/32 and 17/13 along the Slendric chain, any extension to the full 7-limit can also find prime 11, and any extension to 2.3.7.13 can also find prime 17. This applies both to strong and weak extensions.
	==== A-Team ====		==== A-Team ====
	Taking every other step of Slendric results in a subtemperament generated by this subfourth, which is known as '''A-Team''' (from "18"). It is one of the main regular temperaments representing the [[oneirotonic]] (5L 3s) scale - specifically the hard tunings thereof such as in [[18edo\|18]], [[23edo\|23]], and [[31edo]]. The core [[subgroup]] interpretation of A-Team is 2.9.21.55: note that two A-Team generators, representing [[12/7]], come close to [[55/32]] and therefore [[385/384]] and [[441/440]], which again multiply to 1029/1024, can be tempered out. Different A-Team tunings can pick up other harmonic approximations; an interesting one is the 13:17:19 chord found in Mothra (and especially 31edo)'s version of A-Team.		Taking every other step of Slendric results in a subtemperament generated by this subfourth, which is known as '''A-Team''' (2.9.21[13 & 18]; the name is from "18"). It is one of the main regular temperaments representing the [[oneirotonic]] (5L 3s) scale - specifically the hard tunings thereof such as in [[18edo\|18]], [[23edo\|23]], and [[31edo]]. The core [[subgroup]] interpretation of A-Team is 2.9.21.55: note that two A-Team generators, representing [[12/7]], come close to [[55/32]] and therefore [[385/384]] and [[441/440]], which again multiply to 1029/1024, can be tempered out. Different A-Team tunings can pick up other harmonic approximations; an interesting one is the 13:17:19 chord found in Mothra (and especially 31edo)'s version of A-Team.

	A-Team may be considered a [[straddle primes\|straddle-3]] temperament; the >3 is the sharp 32/21 generator and the <3 is reached by +4 21/16 generators. Indeed, stacking >3 and <3 reaches 9 at +3 generators.		A-Team may be considered a [[straddle primes\|straddle-3]] temperament; the >3 is the sharp 32/21 generator and the <3 is reached by +4 21/16 generators. Indeed, stacking >3 and <3 reaches 9 at +3 generators.

Inthar: /* A-Team */

2026-03-06T04:31:03Z

A-Team

← Older revision		Revision as of 04:31, 6 March 2026
Line 107:		Line 107:
	As a result of the ease of finding 55/32 and 17/13 along the Slendric chain, any extension to the full 7-limit can also find prime 11, and any extension to 2.3.7.13 can also find prime 17. This applies both to strong and weak extensions.		As a result of the ease of finding 55/32 and 17/13 along the Slendric chain, any extension to the full 7-limit can also find prime 11, and any extension to 2.3.7.13 can also find prime 17. This applies both to strong and weak extensions.
	==== A-Team ====		==== A-Team ====
	Taking every other step of Slendric results in a subtemperament generated by this subfourth, which is known as '''A-Team''' (from "18"). It is one of the main regular temperaments representing the [[oneirotonic]] (5L 3s) scale - specifically the hard tunings thereof such as in [[18edo\|18]], [[23edo\|23]], and [[31edo]]. The core [[subgroup]] interpretation of A-Team is 2.9.21.55: note that two A-Team generators, representing [[12/7]], come close to [[55/32]] and therefore [[385/384]] and [[441/440]], which again multiply to 1029/1024, can be tempered out. Different A-Team tunings can pick up other harmonic approximations; an interesting one is the 13:17:19 chord found in Mothra (and especially 31edo)'s version of A-~~team~~.		Taking every other step of Slendric results in a subtemperament generated by this subfourth, which is known as '''A-Team''' (from "18"). It is one of the main regular temperaments representing the [[oneirotonic]] (5L 3s) scale - specifically the hard tunings thereof such as in [[18edo\|18]], [[23edo\|23]], and [[31edo]]. The core [[subgroup]] interpretation of A-Team is 2.9.21.55: note that two A-Team generators, representing [[12/7]], come close to [[55/32]] and therefore [[385/384]] and [[441/440]], which again multiply to 1029/1024, can be tempered out. Different A-Team tunings can pick up other harmonic approximations; an interesting one is the 13:17:19 chord found in Mothra (and especially 31edo)'s version of A-Team.

	A-Team may be considered a [[straddle primes\|straddle-3]] temperament; the >3 is the sharp 32/21 generator and the <3 is reached by +4 21/16 generators. Indeed, stacking >3 and <3 reaches 9 at +3 generators.		A-Team may be considered a [[straddle primes\|straddle-3]] temperament; the >3 is the sharp 32/21 generator and the <3 is reached by +4 21/16 generators. Indeed, stacking >3 and <3 reaches 9 at +3 generators.

Inthar: /* A-Team */

2026-03-06T04:29:07Z

A-Team

← Older revision		Revision as of 04:29, 6 March 2026
Line 107:		Line 107:
	As a result of the ease of finding 55/32 and 17/13 along the Slendric chain, any extension to the full 7-limit can also find prime 11, and any extension to 2.3.7.13 can also find prime 17. This applies both to strong and weak extensions.		As a result of the ease of finding 55/32 and 17/13 along the Slendric chain, any extension to the full 7-limit can also find prime 11, and any extension to 2.3.7.13 can also find prime 17. This applies both to strong and weak extensions.
	==== A-Team ====		==== A-Team ====
	Taking every other step of Slendric results in a subtemperament generated by this subfourth, which is known as '''A-Team''' (from "18"). It is one of the main regular temperaments representing the [[oneirotonic]] (5L 3s) scale - specifically the hard tunings thereof such as in [[18edo\|18]], [[23edo\|23]], and 31edo. The core [[subgroup]] interpretation of A-Team is 2.9.21.55: note that two A-Team generators, representing [[12/7]], come close to [[55/32]] and therefore [[385/384]] and [[441/440]], which again multiply to 1029/1024, can be tempered out. Different A-Team tunings can pick up other harmonic approximations; an interesting one is the 13:17:19 chord found in Mothra (and especially 31edo)'s version of A-team.		Taking every other step of Slendric results in a subtemperament generated by this subfourth, which is known as '''A-Team''' (from "18"). It is one of the main regular temperaments representing the [[oneirotonic]] (5L 3s) scale - specifically the hard tunings thereof such as in [[18edo\|18]], [[23edo\|23]], and [[31edo]]. The core [[subgroup]] interpretation of A-Team is 2.9.21.55: note that two A-Team generators, representing [[12/7]], come close to [[55/32]] and therefore [[385/384]] and [[441/440]], which again multiply to 1029/1024, can be tempered out. Different A-Team tunings can pick up other harmonic approximations; an interesting one is the 13:17:19 chord found in Mothra (and especially 31edo)'s version of A-team.

	A-Team may be considered a [[straddle primes\|straddle-3]] temperament; the >3 is the sharp 32/21 generator and the <3 is reached by +4 21/16 generators. Indeed, stacking >3 and <3 reaches 9 at +3 generators.		A-Team may be considered a [[straddle primes\|straddle-3]] temperament; the >3 is the sharp 32/21 generator and the <3 is reached by +4 21/16 generators. Indeed, stacking >3 and <3 reaches 9 at +3 generators.

Inthar: /* A-Team */

2026-03-06T04:27:15Z

A-Team

← Older revision		Revision as of 04:27, 6 March 2026
Line 109:		Line 109:
	Taking every other step of Slendric results in a subtemperament generated by this subfourth, which is known as '''A-Team''' (from "18"). It is one of the main regular temperaments representing the [[oneirotonic]] (5L 3s) scale - specifically the hard tunings thereof such as in [[18edo\|18]], [[23edo\|23]], and 31edo. The core [[subgroup]] interpretation of A-Team is 2.9.21.55: note that two A-Team generators, representing [[12/7]], come close to [[55/32]] and therefore [[385/384]] and [[441/440]], which again multiply to 1029/1024, can be tempered out. Different A-Team tunings can pick up other harmonic approximations; an interesting one is the 13:17:19 chord found in Mothra (and especially 31edo)'s version of A-team.		Taking every other step of Slendric results in a subtemperament generated by this subfourth, which is known as '''A-Team''' (from "18"). It is one of the main regular temperaments representing the [[oneirotonic]] (5L 3s) scale - specifically the hard tunings thereof such as in [[18edo\|18]], [[23edo\|23]], and 31edo. The core [[subgroup]] interpretation of A-Team is 2.9.21.55: note that two A-Team generators, representing [[12/7]], come close to [[55/32]] and therefore [[385/384]] and [[441/440]], which again multiply to 1029/1024, can be tempered out. Different A-Team tunings can pick up other harmonic approximations; an interesting one is the 13:17:19 chord found in Mothra (and especially 31edo)'s version of A-team.

	A-Team may be considered a [[straddle primes\|straddle-3]] temperament; the >3 is the sharp 32/21 generator and the <3 is reached by +4 21/16 generators.		A-Team may be considered a [[straddle primes\|straddle-3]] temperament; the >3 is the sharp 32/21 generator and the <3 is reached by +4 21/16 generators. Indeed, stacking >3 and <3 reaches 9 at +3 generators.

	Two subranges of A-Team are		Two subranges of A-Team are