26edo - Revision history

Lucius Chiaraviglio: /* Modern renderings */ Fix links for last entry

2026-11-07T07:21:05Z

Modern renderings: Fix links for last entry

← Older revision		Revision as of 07:21, 7 November 2026
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	; Traditional		; Traditional
	* [https://www.youtube.com/shorts/PrtGI9l3ktk ''Scarborough Fair''] – arranged by [[Claudi Meneghin]] in [[26edo]] (first half) and 31edo (second half) (2024)		* [https://www.youtube.com/shorts/PrtGI9l3ktk ''Scarborough Fair''] – arranged by [[Claudi Meneghin]] in 26edo (first half) and [[31edo]] (second half) (2024)

	==== 21st century ====		==== 21st century ====

Lucius Chiaraviglio: /* Modern renderings */ Add ''Scarborough Fair'' arranged by Claudi Meneghin in 26edo and 31edo (2024)

2026-11-07T07:20:10Z

Modern renderings: Add ''Scarborough Fair'' arranged by Claudi Meneghin in 26edo and 31edo (2024)

← Older revision		Revision as of 07:20, 7 November 2026
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	; {{W\|Claude Debussy}}		; {{W\|Claude Debussy}}
	* [https://www.bilibili.com/video/BV1SGaW6PED3 "Pagodas"] from ''{{w\|Estampes}}'', L. 100 (1903) – rendered by [[wslaozhu]] (2026)		* [https://www.bilibili.com/video/BV1SGaW6PED3 "Pagodas"] from ''{{w\|Estampes}}'', L. 100 (1903) – rendered by [[wslaozhu]] (2026)

			; Traditional
			* [https://www.youtube.com/shorts/PrtGI9l3ktk ''Scarborough Fair''] – arranged by [[Claudi Meneghin]] in [[26edo]] (first half) and 31edo (second half) (2024)

	==== 21st century ====		==== 21st century ====

FloraC: /* Music */

2026-11-02T09:30:38Z

Music

← Older revision		Revision as of 09:30, 2 November 2026
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	; {{W\|Claude Debussy}}		; {{W\|Claude Debussy}}
	* [https://www.bilibili.com/video/BV1SGaW6PED3 "Pagodas"] from {{w\|Estampes}}, L. 100 (1903) – rendered by [[wslaozhu]] (2026)		* [https://www.bilibili.com/video/BV1SGaW6PED3 "Pagodas"] from ''{{w\|Estampes}}'', L. 100 (1903) – rendered by [[wslaozhu]] (2026)

	==== 21st century ====		==== 21st century ====

FloraC: /* Music */ correct title

2026-11-02T09:30:00Z

Music: correct title

← Older revision		Revision as of 09:30, 2 November 2026
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	==== Modern renderings ====		==== Modern renderings ====
	; {{W\|Johann Sebastian Bach}}		; {{W\|Johann Sebastian Bach}}
	* [https://www.youtube.com/watch?v=LUNOFjiyZ0Y ''Contrapunctus 4'' from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)		* [https://www.youtube.com/watch?v=LUNOFjiyZ0Y ''Contrapunctus 4'' from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by [[Claudi Meneghin]] (2024)
	* ''Contrapunctus 11'' from ''The Art of Fugue'', BWV 1080 (1742–1749) – rendered by Claudi Meneghin		* ''Contrapunctus 11'' from ''The Art of Fugue'', BWV 1080 (1742–1749) – rendered by Claudi Meneghin
	** [https://www.youtube.com/watch?v=dlXFoIoc_uk organ rendition] (2024)		** [https://www.youtube.com/watch?v=dlXFoIoc_uk organ rendition] (2024)
	** [https://www.youtube.com/watch?v=NUo1uvUuOlo harpsichord rendition] (2025)		** [https://www.youtube.com/watch?v=NUo1uvUuOlo harpsichord rendition] (2025)
	* [https://www.youtube.com/watch?v=PcQIojtN-lk ''"Ricercar a 3" from ''The Musical Offering'', BWV 1079] (1747) – rendered by Claudi Meneghin (2025)		* [https://www.youtube.com/watch?v=PcQIojtN-lk "Ricercar a 3" from ''The Musical Offering'', BWV 1079] (1747) – rendered by Claudi Meneghin (2025)

	; {{W\|Nicolaus Bruhns}}		; {{W\|Nicolaus Bruhns}}
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	* [https://www.youtube.com/watch?v=-EVO5ntuoSM ''Prelude in E Minor "The Little"''] – rendered by Claudi Meneghin (2024)		* [https://www.youtube.com/watch?v=-EVO5ntuoSM ''Prelude in E Minor "The Little"''] – rendered by Claudi Meneghin (2024)

	; {{W\|~~Claude_Debussy\|Achille-~~Claude Debussy}}		; {{W\|Claude Debussy}}
	* ''[https://www.bilibili.com/video/BV1SGaW6PED3 ~~Tower~~]~~'' —~~ rendered by wslaozhu (2026)		* [https://www.bilibili.com/video/BV1SGaW6PED3 "Pagodas"] from {{w\|Estampes}}, L. 100 (1903) – rendered by [[wslaozhu]] (2026)

	==== 21st century ====		==== 21st century ====

Lucius Chiaraviglio: /* Modern renderings */ Fix formatting (including obsolete Wikipedia link format)

2026-11-02T05:46:42Z

Modern renderings: Fix formatting (including obsolete Wikipedia link format)

← Older revision		Revision as of 05:46, 2 November 2026
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	* [https://www.youtube.com/watch?v=K7oTEXgmdKY ''Prelude in E Minor "The Great"''] – rendered by Claudi Meneghin (2023)		* [https://www.youtube.com/watch?v=K7oTEXgmdKY ''Prelude in E Minor "The Great"''] – rendered by Claudi Meneghin (2023)
	* [https://www.youtube.com/watch?v=-EVO5ntuoSM ''Prelude in E Minor "The Little"''] – rendered by Claudi Meneghin (2024)		* [https://www.youtube.com/watch?v=-EVO5ntuoSM ''Prelude in E Minor "The Little"''] – rendered by Claudi Meneghin (2024)
	~~'''[[wikipedia:Claude_Debussy\|Achille-Claude Debussy]]'''~~

	:* ''[https://www.bilibili.com/video/BV1SGaW6PED3 Tower]'' - rendered by wslaozhu (2026)		; {{W\|Claude_Debussy\|Achille-Claude Debussy}}
			* ''[https://www.bilibili.com/video/BV1SGaW6PED3 Tower]'' — rendered by wslaozhu (2026)

	==== 21st century ====		==== 21st century ====

Haidilao at 02:50, 2 November 2026

2026-11-02T02:50:14Z

← Older revision		Revision as of 02:50, 2 November 2026
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	* [https://www.youtube.com/watch?v=K7oTEXgmdKY ''Prelude in E Minor "The Great"''] – rendered by Claudi Meneghin (2023)		* [https://www.youtube.com/watch?v=K7oTEXgmdKY ''Prelude in E Minor "The Great"''] – rendered by Claudi Meneghin (2023)
	* [https://www.youtube.com/watch?v=-EVO5ntuoSM ''Prelude in E Minor "The Little"''] – rendered by Claudi Meneghin (2024)		* [https://www.youtube.com/watch?v=-EVO5ntuoSM ''Prelude in E Minor "The Little"''] – rendered by Claudi Meneghin (2024)
	'''[[Achille-Claude Debussy]]'''		'''[[wikipedia:Claude_Debussy\|Achille-Claude Debussy]]'''

	:* ''[https://www.bilibili.com/video/BV1SGaW6PED3 Tower]'' - rendered by wslaozhu (2026)		:* ''[https://www.bilibili.com/video/BV1SGaW6PED3 Tower]'' - rendered by wslaozhu (2026)

Haidilao at 02:48, 2 November 2026

2026-11-02T02:48:17Z

← Older revision		Revision as of 02:48, 2 November 2026
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	* [https://www.youtube.com/watch?v=K7oTEXgmdKY ''Prelude in E Minor "The Great"''] – rendered by Claudi Meneghin (2023)		* [https://www.youtube.com/watch?v=K7oTEXgmdKY ''Prelude in E Minor "The Great"''] – rendered by Claudi Meneghin (2023)
	* [https://www.youtube.com/watch?v=-EVO5ntuoSM ''Prelude in E Minor "The Little"''] – rendered by Claudi Meneghin (2024)		* [https://www.youtube.com/watch?v=-EVO5ntuoSM ''Prelude in E Minor "The Little"''] – rendered by Claudi Meneghin (2024)
			'''[[Achille-Claude Debussy]]'''

			:* ''[https://www.bilibili.com/video/BV1SGaW6PED3 Tower]'' - rendered by wslaozhu (2026)

	==== 21st century ====		==== 21st century ====

Jdood: /* Theory */ some more minor edits

2026-10-17T18:14:20Z

Theory: some more minor edits

← Older revision		Revision as of 18:14, 17 October 2026
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	# In terms of more traditional chord types we have flattone, a variant of meantone with flat fifths, which provides an interesting structure but unsatisfying intonation due mainly to the poorly tuned thirds. Extending meantone harmony to the 7-limit is quite intuitive; for example, augmented becomes supermajor, and diminished becomes subminor. Simple mappings for harmonics up to 13 are also achieved.		# In terms of more traditional chord types we have flattone, a variant of meantone with flat fifths, which provides an interesting structure but unsatisfying intonation due mainly to the poorly tuned thirds. Extending meantone harmony to the 7-limit is quite intuitive; for example, augmented becomes supermajor, and diminished becomes subminor. Simple mappings for harmonics up to 13 are also achieved.
	# As two chains of meantone fifths half an octave apart, it supports injera temperament. The generator for this is an interval which can be called either 21/20 or 15/14, and which represents two steps of 26, and hence one step of 13. Hence in 26edo (as opposed to [[38edo]]) can be viewed as two parallel 13edo scales, and from that point of view we can consider it as supporting the 13b&26 temperament, allowing the two chains be shifted slightly and which can be used for more atonal melodies. In this way its internal dynamics resemble those of [[14edo]].		# As two chains of meantone fifths half an octave apart, it supports injera temperament. The generator for this is an interval which can be called either 21/20 or 15/14, and which represents two steps of 26, and hence one step of 13. Hence 26edo (as opposed to [[38edo]]) can be viewed as two parallel 13edo scales, and from that point of view we can consider it as supporting the 13b&26 temperament, allowing the two chains be shifted slightly and which can be used for more atonal melodies. In this way its internal dynamics resemble those of [[14edo]].
	# 26edo nearly perfectly approximates the 7th and 11th harmonics, and an entire system may be constructed analogous to that based on the 3rd and 5th harmonics. In terms of subgroups, this is the 2.7.11 subgroup, and on this 26 tempers out the pair of commas [[65536/65219]] and [[117649/117128]]. The 65536/65219 comma, the orgonisma, leads to the [[Orgonia\|orgone temperament]] with an approximate 77/64 generator of 7\26, with mos scales of size 7, 11 and 15. The 117649/117128 comma leads to a half-octave period and an approximate [[49/44]] generator of 4\26, leading to mos of size 8 and 14.		# 26edo nearly perfectly approximates the 7th and 11th harmonics, and an entire system may be constructed analogous to that based on the 3rd and 5th harmonics. In terms of subgroups, this is the 2.7.11 subgroup, and on this 26 tempers out the pair of commas [[65536/65219]] and [[117649/117128]]. The 65536/65219 comma, the orgonisma, leads to the [[Orgonia\|orgone temperament]] with an approximate 77/64 generator of 7\26, with mos scales of size 7, 11 and 15. The 117649/117128 comma leads to a half-octave period and an approximate [[49/44]] generator of 4\26, leading to mos of size 8 and 14.
	# We can also treat 26edo as a full 13-limit temperament, since it is consistent on the 13-odd-limit (unlike all lower edos).		# We can also treat 26edo as a full 13-limit temperament, since it is consistent on the 13-odd-limit (unlike all lower edos).

Jdood: /* Theory */ Fixed some weird issues with grammar

2026-10-17T18:13:51Z

Theory: Fixed some weird issues with grammar

← Older revision		Revision as of 18:13, 17 October 2026
Line 20:		Line 20:

	# In terms of more traditional chord types we have flattone, a variant of meantone with flat fifths, which provides an interesting structure but unsatisfying intonation due mainly to the poorly tuned thirds. Extending meantone harmony to the 7-limit is quite intuitive; for example, augmented becomes supermajor, and diminished becomes subminor. Simple mappings for harmonics up to 13 are also achieved.		# In terms of more traditional chord types we have flattone, a variant of meantone with flat fifths, which provides an interesting structure but unsatisfying intonation due mainly to the poorly tuned thirds. Extending meantone harmony to the 7-limit is quite intuitive; for example, augmented becomes supermajor, and diminished becomes subminor. Simple mappings for harmonics up to 13 are also achieved.
	# As two chains of meantone fifths half an octave apart, it supports injera temperament. The generator for this is an interval which can be called either 21/20 or 15/14, and which represents two steps of 26, and hence one step of 13. Hence in 26edo (as opposed to~~, for instance,~~ [[38edo]]) it can be viewed as two parallel 13edo scales, and from that point of view we can consider it as supporting the 13b&26 temperament, allowing the two chains be shifted slightly and which can be used for more atonal melodies. In this way its internal dynamics resemble those of [[14edo]].		# As two chains of meantone fifths half an octave apart, it supports injera temperament. The generator for this is an interval which can be called either 21/20 or 15/14, and which represents two steps of 26, and hence one step of 13. Hence in 26edo (as opposed to [[38edo]]) can be viewed as two parallel 13edo scales, and from that point of view we can consider it as supporting the 13b&26 temperament, allowing the two chains be shifted slightly and which can be used for more atonal melodies. In this way its internal dynamics resemble those of [[14edo]].
	# 26edo nearly perfectly approximates the 7th and 11th harmonics, and an entire system may be constructed analogous to that based on the 3rd and 5th harmonics. In terms of subgroups, this is the 2.7.11 subgroup, and on this 26 tempers out the pair of commas [[65536/65219]] and [[117649/117128]]. The 65536/65219 comma, the orgonisma, leads to the [[Orgonia\|orgone temperament]] with an approximate 77/64 generator of 7\26, with mos scales of size 7, 11 and 15. The 117649/117128 comma leads to a half-octave period and an approximate [[49/44]] generator of 4\26, leading to mos of size 8 and 14.		# 26edo nearly perfectly approximates the 7th and 11th harmonics, and an entire system may be constructed analogous to that based on the 3rd and 5th harmonics. In terms of subgroups, this is the 2.7.11 subgroup, and on this 26 tempers out the pair of commas [[65536/65219]] and [[117649/117128]]. The 65536/65219 comma, the orgonisma, leads to the [[Orgonia\|orgone temperament]] with an approximate 77/64 generator of 7\26, with mos scales of size 7, 11 and 15. The 117649/117128 comma leads to a half-octave period and an approximate [[49/44]] generator of 4\26, leading to mos of size 8 and 14.
	# We can also treat 26edo as a full 13-limit temperament, since it is consistent on the 13-odd-limit (unlike all lower edos).		# We can also treat 26edo as a full 13-limit temperament, since it is consistent on the 13-odd-limit (unlike all lower edos).

Lucius Chiaraviglio: /* 21st century */ Bryan Deister's ''Caprice in 26edo'' (2026): Add full version

2026-08-26T08:54:12Z

21st century: Bryan Deister's ''Caprice in 26edo'' (2026): Add full version

← Older revision		Revision as of 08:54, 26 August 2026
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	** [https://www.youtube.com/watch?v=XplpKE_Tc38 <nowiki>[full version[</nowiki>] (with animation by WIRED0006)		** [https://www.youtube.com/watch?v=XplpKE_Tc38 <nowiki>[full version[</nowiki>] (with animation by WIRED0006)
	* [https://www.youtube.com/shorts/wHGLOaeAkt8 ''26edo groove''] (2026)		* [https://www.youtube.com/shorts/wHGLOaeAkt8 ''26edo groove''] (2026)
	* [https://www.youtube.com/shorts/WvnJb5VNGj4 ''<nowiki>~~Caprice in 26edo~~ [short clip]</nowiki>''] (~~2026~~)		* ''Caprice in 26edo'' (2026)
			** [https://www.youtube.com/shorts/WvnJb5VNGj4 <nowiki>[short clip]</nowiki>] (Lumatone view)
			** [https://www.youtube.com/watch?v=mMQADmxJkFc <nowiki>[full version]</nowiki>]

	; [[User:Eboone\|Ebooone]]		; [[User:Eboone\|Ebooone]]