21edo - Revision history

Inthar at 04:10, 7 June 2026

2026-06-07T04:10:41Z

← Older revision		Revision as of 04:10, 7 June 2026
Line 9:		Line 9:
	* Slentonic (5L6s, sLsLsLsLsLs), interpreted as [[Slendric]][11], generated by stacking the ~8/7 (4\21)		* Slentonic (5L6s, sLsLsLsLsLs), interpreted as [[Slendric]][11], generated by stacking the ~8/7 (4\21)
	* Oneirotonic (5L3s, LLsLLsLs), generated by stacking 8\21		* Oneirotonic (5L3s, LLsLLsLs), generated by stacking 8\21
			21edo also supports [[Sidewalk]] temperament.
	== Basic theory ==		== Basic theory ==
	=== Intervals and notation ===		=== Intervals and notation ===

Inthar: /* 63edo */

2026-03-05T05:23:36Z

63edo

← Older revision		Revision as of 05:23, 5 March 2026
Line 171:		Line 171:
	== Multiples ==		== Multiples ==
	=== 63edo ===		=== 63edo ===
	63edo provides a good representation of 2.3.5.7.11.13.23.29.31.		63edo provides a good representation of 2.3.5.7.11.13.23.29.31. Its prime 17 is critically inaccurate.

	* The 3 is somewhat sharp, thus supporting [[Parapyth]] temperament, a rank-3 temperament where 32/27 is tuned close to 13/11 and 81/64 is tempered together with 14/11, and where the "spacer" 28/27 is identified with 33/32.		* The 3 is somewhat sharp, thus supporting [[Parapyth]] temperament, a rank-3 temperament where 32/27 is tuned close to 13/11 and 81/64 is tempered together with 14/11, and where the "spacer" 28/27 is identified with 33/32.

Hotcrystal0: Prime harmonic approximation for 63

2026-03-02T13:52:06Z

Prime harmonic approximation for 63

← Older revision		Revision as of 13:52, 2 March 2026
Line 175:		Line 175:
	* The 3 is somewhat sharp, thus supporting [[Parapyth]] temperament, a rank-3 temperament where 32/27 is tuned close to 13/11 and 81/64 is tempered together with 14/11, and where the "spacer" 28/27 is identified with 33/32.		* The 3 is somewhat sharp, thus supporting [[Parapyth]] temperament, a rank-3 temperament where 32/27 is tuned close to 13/11 and 81/64 is tempered together with 14/11, and where the "spacer" 28/27 is identified with 33/32.
	* The 5 is quite flat, thus supporting [[Magic]] temperament where the stack of five 5/4 major thirds becomes one 3/1.		* The 5 is quite flat, thus supporting [[Magic]] temperament where the stack of five 5/4 major thirds becomes one 3/1.

			{{Harmonics in ED\|63\|31\|0}}

	{{Cat\|Edos}}		{{Cat\|Edos}}

	{{Navbox EDO}}		{{Navbox EDO}}

Inthar: /* 63edo */

2026-02-21T23:40:41Z

63edo

← Older revision		Revision as of 23:40, 21 February 2026
Line 173:		Line 173:
	63edo provides a good representation of 2.3.5.7.11.13.23.29.31.		63edo provides a good representation of 2.3.5.7.11.13.23.29.31.

	* The 3 is somewhat sharp, thus supporting [[Parapyth]] temperament, a rank-3 temperament 32/27 is tuned close to 13/11 and 81/64 is tempered together with 14/11, and where the "spacer" 28/27 is identified with 33/32.		* The 3 is somewhat sharp, thus supporting [[Parapyth]] temperament, a rank-3 temperament where 32/27 is tuned close to 13/11 and 81/64 is tempered together with 14/11, and where the "spacer" 28/27 is identified with 33/32.
	* The 5 is quite flat, thus supporting [[Magic]] temperament where the stack of five 5/4 major thirds becomes one 3/1.		* The 5 is quite flat, thus supporting [[Magic]] temperament where the stack of five 5/4 major thirds becomes one 3/1.
	{{Cat\|Edos}}		{{Cat\|Edos}}

	{{Navbox EDO}}		{{Navbox EDO}}

Vector at 01:16, 14 February 2026

2026-02-14T01:16:20Z

← Older revision		Revision as of 01:16, 14 February 2026
Line 172:		Line 172:
	=== 63edo ===		=== 63edo ===
	63edo provides a good representation of 2.3.5.7.11.13.23.29.31.		63edo provides a good representation of 2.3.5.7.11.13.23.29.31.

	* The 3 is somewhat sharp, thus supporting [[Parapyth]] temperament, a rank-3 temperament 32/27 is tuned close to 13/11 and 81/64 is tempered together with 14/11, and where the "spacer" 28/27 is identified with 33/32.		* The 3 is somewhat sharp, thus supporting [[Parapyth]] temperament, a rank-3 temperament 32/27 is tuned close to 13/11 and 81/64 is tempered together with 14/11, and where the "spacer" 28/27 is identified with 33/32.
	* The 5 is quite flat, thus supporting [[Magic]] temperament where the stack of five 5/4 major thirds becomes one 3/1.		* The 5 is quite flat, thus supporting [[Magic]] temperament where the stack of five 5/4 major thirds becomes one 3/1.
	{{Cat\|Edos}}{{Navbox EDO}}		{{Cat\|Edos}}

			{{Navbox EDO}}

Vector at 01:07, 14 February 2026

2026-02-14T01:07:22Z

← Older revision		Revision as of 01:07, 14 February 2026
Line 174:		Line 174:
	* The 3 is somewhat sharp, thus supporting [[Parapyth]] temperament, a rank-3 temperament 32/27 is tuned close to 13/11 and 81/64 is tempered together with 14/11, and where the "spacer" 28/27 is identified with 33/32.		* The 3 is somewhat sharp, thus supporting [[Parapyth]] temperament, a rank-3 temperament 32/27 is tuned close to 13/11 and 81/64 is tempered together with 14/11, and where the "spacer" 28/27 is identified with 33/32.
	* The 5 is quite flat, thus supporting [[Magic]] temperament where the stack of five 5/4 major thirds becomes one 3/1.		* The 5 is quite flat, thus supporting [[Magic]] temperament where the stack of five 5/4 major thirds becomes one 3/1.
	{{Cat\|Edos}}		{{Cat\|Edos}}{{Navbox EDO}}

Vector: switched to ADIN for interval regions, feel free to revert if you don't like it

2026-02-14T01:06:55Z

switched to ADIN for interval regions, feel free to revert if you don't like it

← Older revision		Revision as of 01:06, 14 February 2026
Line 16:		Line 16:
	\|+		\|+
	! \| Edostep !! \| Cents !! \| Notation (Ups and downs) !! \| Interval name (ups/downs)		! \| Edostep !! \| Cents !! \| Notation (Ups and downs) !! \| Interval name (ups/downs)
	!Interval region		!Interval region (ADIN)
	\|-		\|-
	\|0		\|0
Line 28:		Line 28:
	\|^C		\|^C
	\|Up unison		\|Up unison
	\|~~Diesis~~		\|Farmajor unison
	\|-		\|-
	\|2		\|2
Line 34:		Line 34:
	\|vD		\|vD
	\|Down second		\|Down second
	\|~~Minor 2nd~~		\|Farminor second
	\|-		\|-
	\|3		\|3
Line 40:		Line 40:
	\|D		\|D
	\|Perfect second		\|Perfect second
	\|~~Submajor 2nd~~		\|Neutral second
	\|-		\|-
	\|4		\|4
Line 46:		Line 46:
	\|^D		\|^D
	\|Up second		\|Up second
	\|~~Supermajor 2nd~~		\|Farmajor second
	\|-		\|-
	\|5		\|5
Line 52:		Line 52:
	\|vE		\|vE
	\|Down third		\|Down third
	\|~~Minor 3rd~~		\|Farminor third
	\|-		\|-
	\|6		\|6
Line 58:		Line 58:
	\|E		\|E
	\|Perfect third		\|Perfect third
	\|Neutral ~~3rd~~		\|Neutral third
	\|-		\|-
	\|7		\|7
Line 64:		Line 64:
	\|^E		\|^E
	\|Up third		\|Up third
	\|~~Major 3rd~~		\|Farmajor third
	\|-		\|-
	\|8		\|8
Line 70:		Line 70:
	\|vF		\|vF
	\|Down fourth		\|Down fourth
	\|~~Infra4th/Sub4th~~		\|Farminor fourth
	\|-		\|-
	\|9		\|9
Line 76:		Line 76:
	\|F		\|F
	\|Perfect fourth		\|Perfect fourth
	\|Perfect ~~4th~~		\|Perfect fourth
	\|-		\|-
	\|10		\|10
Line 82:		Line 82:
	\|^F		\|^F
	\|Up fourth		\|Up fourth
	\|~~Lesser tritone~~		\|Farmajor fourth
	\|-		\|-
	\|11		\|11
Line 88:		Line 88:
	\|vG		\|vG
	\|Down fifth		\|Down fifth
	\|~~Greater tritone~~		\|Farminor fifth
	\|-		\|-
	\|12		\|12
Line 94:		Line 94:
	\|G		\|G
	\|Perfect fifth		\|Perfect fifth
	\|Perfect ~~5th~~		\|Perfect fifth
	\|-		\|-
	\|13		\|13
Line 100:		Line 100:
	\|^G		\|^G
	\|Up fifth		\|Up fifth
	\|~~Ultra5th/Super5th~~		\|Farmajor fifth
	\|-		\|-
	\|14		\|14
Line 106:		Line 106:
	\|vA		\|vA
	\|Down sixth		\|Down sixth
	\|~~Minor 6th~~		\|Farminor sixth
	\|-		\|-
	\|15		\|15
Line 112:		Line 112:
	\|A		\|A
	\|Perfect sixth		\|Perfect sixth
	\|Neutral ~~6th~~		\|Neutral sixth
	\|-		\|-
	\|16		\|16
Line 118:		Line 118:
	\|^A		\|^A
	\|Up sixth		\|Up sixth
	\|~~Major 6th~~		\|Farmajor sixth
	\|-		\|-
	\|17		\|17
Line 124:		Line 124:
	\|vB		\|vB
	\|Down seventh		\|Down seventh
	\|~~Subminor 7th~~		\|Farminor seventh
	\|-		\|-
	\|18		\|18
Line 130:		Line 130:
	\|B		\|B
	\|Perfect seventh		\|Perfect seventh
	\|~~Superminor 7th~~		\|Neutral seventh
	\|-		\|-
	\|19		\|19
Line 136:		Line 136:
	\|^B		\|^B
	\|Up seventh		\|Up seventh
	\|~~Major 7th~~		\|Farmajor seventh
	\|-		\|-
	\|20		\|20
Line 142:		Line 142:
	\|vC		\|vC
	\|Down octave		\|Down octave
	\|~~Octave - diesis~~		\|Farminor octave
	\|-		\|-
	\|21		\|21

Inthar: /* Intervals and notation */

2026-02-13T22:07:03Z

Intervals and notation

← Older revision		Revision as of 22:07, 13 February 2026
Line 11:		Line 11:
	== Basic theory ==		== Basic theory ==
	=== Intervals and notation ===		=== Intervals and notation ===
	Since 21edo's best fifth is from 7edo, 21edo is notated with CDEFGAB representing 7edo and up/down representing 1\21. This allows all intervals to have a "minor", "neutral/perfect", and "major" ~~variant~~.		Since 21edo's best fifth is from 7edo, 21edo is notated with CDEFGAB representing 7edo and up/down representing 1\21. This allows all intervals to have a "minor", "neutral/perfect", and "major" variants.

	{\| class="wikitable"		{\| class="wikitable"
	\|+		\|+
	! \| Edostep !! \| Cents !! \| Notation (Ups and downs) !! \| Interval name		! \| Edostep !! \| Cents !! \| Notation (Ups and downs) !! \| Interval name (ups/downs)
			!Interval region
	\|-		\|-
	\|0		\|0
Line 21:		Line 22:
	\|C		\|C
	\|Perfect unison		\|Perfect unison
			\|Unison
	\|-		\|-
	\|1		\|1
Line 26:		Line 28:
	\|^C		\|^C
	\|Up unison		\|Up unison
			\|Diesis
	\|-		\|-
	\|2		\|2
Line 31:		Line 34:
	\|vD		\|vD
	\|Down second		\|Down second
			\|Minor 2nd
	\|-		\|-
	\|3		\|3
Line 36:		Line 40:
	\|D		\|D
	\|Perfect second		\|Perfect second
			\|Submajor 2nd
	\|-		\|-
	\|4		\|4
Line 41:		Line 46:
	\|^D		\|^D
	\|Up second		\|Up second
			\|Supermajor 2nd
	\|-		\|-
	\|5		\|5
Line 46:		Line 52:
	\|vE		\|vE
	\|Down third		\|Down third
			\|Minor 3rd
	\|-		\|-
	\|6		\|6
Line 51:		Line 58:
	\|E		\|E
	\|Perfect third		\|Perfect third
			\|Neutral 3rd
	\|-		\|-
	\|7		\|7
Line 56:		Line 64:
	\|^E		\|^E
	\|Up third		\|Up third
			\|Major 3rd
	\|-		\|-
	\|8		\|8
Line 61:		Line 70:
	\|vF		\|vF
	\|Down fourth		\|Down fourth
			\|Infra4th/Sub4th
	\|-		\|-
	\|9		\|9
Line 66:		Line 76:
	\|F		\|F
	\|Perfect fourth		\|Perfect fourth
			\|Perfect 4th
	\|-		\|-
	\|10		\|10
Line 71:		Line 82:
	\|^F		\|^F
	\|Up fourth		\|Up fourth
			\|Lesser tritone
	\|-		\|-
	\|11		\|11
Line 76:		Line 88:
	\|vG		\|vG
	\|Down fifth		\|Down fifth
			\|Greater tritone
	\|-		\|-
	\|12		\|12
Line 81:		Line 94:
	\|G		\|G
	\|Perfect fifth		\|Perfect fifth
			\|Perfect 5th
	\|-		\|-
	\|13		\|13
Line 86:		Line 100:
	\|^G		\|^G
	\|Up fifth		\|Up fifth
			\|Ultra5th/Super5th
	\|-		\|-
	\|14		\|14
Line 91:		Line 106:
	\|vA		\|vA
	\|Down sixth		\|Down sixth
			\|Minor 6th
	\|-		\|-
	\|15		\|15
Line 96:		Line 112:
	\|A		\|A
	\|Perfect sixth		\|Perfect sixth
			\|Neutral 6th
	\|-		\|-
	\|16		\|16
Line 101:		Line 118:
	\|^A		\|^A
	\|Up sixth		\|Up sixth
			\|Major 6th
	\|-		\|-
	\|17		\|17
Line 106:		Line 124:
	\|vB		\|vB
	\|Down seventh		\|Down seventh
			\|Subminor 7th
	\|-		\|-
	\|18		\|18
Line 111:		Line 130:
	\|B		\|B
	\|Perfect seventh		\|Perfect seventh
			\|Superminor 7th
	\|-		\|-
	\|19		\|19
Line 116:		Line 136:
	\|^B		\|^B
	\|Up seventh		\|Up seventh
			\|Major 7th
	\|-		\|-
	\|20		\|20
Line 121:		Line 142:
	\|vC		\|vC
	\|Down octave		\|Down octave
			\|Octave - diesis
	\|-		\|-
	\|21		\|21
	\|1200		\|1200
	\|C		\|C
			\|Octave
	\|Octave		\|Octave
	\|}		\|}

Inthar: /* Intervals and notation */

2026-02-13T18:30:43Z

Intervals and notation

← Older revision		Revision as of 18:30, 13 February 2026
Line 25:		Line 25:
	\|57.1		\|57.1
	\|^C		\|^C
	\|~~Inframinor second~~		\|Up unison
	\|-		\|-
	\|2		\|2
	\|114.3		\|114.3
	\|vD		\|vD
	\|~~Minor~~ second		\|Down second
	\|-		\|-
	\|3		\|3
Line 40:		Line 40:
	\|228.6		\|228.6
	\|^D		\|^D
	\|~~Major~~ second		\|Up second
	\|-		\|-
	\|5		\|5
	\|285.7		\|285.7
	\|vE		\|vE
	\|~~Minor~~ third		\|Down third
	\|-		\|-
	\|6		\|6
Line 55:		Line 55:
	\|400		\|400
	\|^E		\|^E
	\|~~Major~~ third		\|Up third
	\|-		\|-
	\|8		\|8
	\|457.1		\|457.1
	\|^E		\|vF
	\|~~Minor~~ fourth		\|Down fourth
	\|-		\|-
	\|9		\|9
Line 70:		Line 70:
	\|571.4		\|571.4
	\|^F		\|^F
	\|~~Major~~ fourth		\|Up fourth
	\|-		\|-
	\|11		\|11
	\|628.6		\|628.6
	\|vG		\|vG
	\|~~Minor~~ fifth		\|Down fifth
	\|-		\|-
	\|12		\|12
Line 85:		Line 85:
	\|742.9		\|742.9
	\|^G		\|^G
	\|~~Major~~ fifth		\|Up fifth
	\|-		\|-
	\|14		\|14
	\|800		\|800
	\|vA		\|vA
	\|~~Minor~~ sixth		\|Down sixth
	\|-		\|-
	\|15		\|15
	\|857.1		\|857.1
	\|A		\|A
	\|~~Neutral~~ sixth		\|Perfect sixth
	\|-		\|-
	\|16		\|16
	\|914.3		\|914.3
	\|^A		\|^A
	\|~~Major~~ sixth		\|Up sixth
	\|-		\|-
	\|17		\|17
	\|971.4		\|971.4
	\|vB		\|vB
	\|~~Minor~~ seventh		\|Down seventh
	\|-		\|-
	\|18		\|18
Line 115:		Line 115:
	\|1085.7		\|1085.7
	\|^B		\|^B
	\|~~Major~~ seventh		\|Up seventh
	\|-		\|-
	\|20		\|20
	\|1142.9		\|1142.9
	\|vC		\|vC
	\|~~Ultramajor seventh~~		\|Down octave
	\|-		\|-
	\|21		\|21

Inthar: /* Intervals and notation */

2026-02-13T16:10:51Z

Intervals and notation

← Older revision		Revision as of 16:10, 13 February 2026
Line 15:		Line 15:
	{\| class="wikitable"		{\| class="wikitable"
	\|+		\|+
	! \| Edostep !! \| Cents !! \| Notation (Ups and downs) !! \| Interval ~~category <br> (ADIN)~~		! \| Edostep !! \| Cents !! \| Notation (Ups and downs) !! \| Interval name
	\|-		\|-
	\|0		\|0