74edo - Revision history

FloraC: /* Notation */ SZG notation

2026-05-12T14:08:27Z

Notation: SZG notation

← Older revision		Revision as of 14:08, 12 May 2026
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	== Notation ==		== Notation ==
	=== ~~Ups~~ and downs notation ===		=== Stein–Zimmermann–Gould notation ===
	74edo can be notated with [[ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).		[[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows:
			{{Sharpness-sharp5-szg}}

			=== Kite's ups and downs notation ===
			74edo can also be notated with [[Kite's ups and downs notation\|Kite's ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).
	{{Sharpness-sharp5a}}		{{Sharpness-sharp5a}}

	~~Another notation uses [[Alternative symbols for ups and downs notation#Sharp-5\|alternative ups and downs]]. It uses sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:~~
	~~{{Sharpness-sharp5}}~~

	=== Sagittal notation ===		=== Sagittal notation ===

FloraC: + RTT properties

2026-03-15T15:33:56Z

+ RTT properties

@@ Line 11: / Line 11: @@
 === Subsets and supersets ===
-Since 74 factors into {{factorization|74}}, 74edo contains [[2edo]] and [[37edo]] as its subsets; of these, 37edo has the same highly accurate prime harmonics in the no-3s [[13-limit]].
+Since 74 factors into {{nowrap| 2 × 37 }}, 74edo contains [[2edo]] and [[37edo]] as its subsets; of these, 37edo has the same highly accurate prime harmonics in the no-3s [[13-limit]].
 == Intervals ==
@@ Line 17: / Line 17: @@
 == Notation ==
-===Ups and downs notation===
+=== Ups and downs notation ===
 edo can be notated with [[ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).
 {{Sharpness-sharp5a}}
 Another notation uses [[Alternative symbols for ups and downs notation#Sharp-5|alternative ups and downs]]. It uses sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:
 {{Sharpness-sharp5}}
 === Sagittal notation ===
 ==== Evo flavor ====
@@ Line 47: / Line 49: @@
 </imagemap>
-In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.
+In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation #Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this edo.
 == Instruments ==

Lucius Chiaraviglio: /* 21st century */ Add Bryan Deister's ''Resonance - Home (microtonal cover in 74edo)'' (2026)

2026-03-15T00:59:53Z

21st century: Add Bryan Deister's ''Resonance - Home (microtonal cover in 74edo)'' (2026)

← Older revision		Revision as of 00:59, 15 March 2026
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	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://www.youtube.com/shorts/ylOGUb395Gg ''microtonal improvisation in 74edo''] (2025)		* [https://www.youtube.com/shorts/ylOGUb395Gg ''microtonal improvisation in 74edo''] (2025)
			* [https://www.youtube.com/shorts/dB9_3TC3yPo ''Resonance - Home (microtonal cover in 74edo)''] (2026)

	[[Category:Meantone]]		[[Category:Meantone]]
	[[Category:Listen]]		[[Category:Listen]]
	[[Category:Historical]]		[[Category:Historical]]

Lucius Chiaraviglio: /* Theory */ Wording to separate 2 numbers to reduce chance of a misread

2026-01-18T09:46:52Z

Theory: Wording to separate 2 numbers to reduce chance of a misread

← Older revision		Revision as of 09:46, 18 January 2026
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	74edo is most notable as a [[meantone]] tuning, [[tempering out]] [[81/80]] in the [[5-limit]]; [[126/125]] and [[225/224]] in the [[7-limit]]; [[99/98]], [[176/175]] and [[441/440]] in the [[11-limit]]; and [[144/143]] and [[847/845]] in the [[13-limit]]. Discarding 847/845 from that gives the 13-limit meantone extension [[grosstone]], for which 74edo gives the [[optimal patent val]]; and discarding 144/143 gives [[semimeantone]], a 13-limit 62 & 74 temperament with half-octave period and two parallel tracks of meantone.		74edo is most notable as a [[meantone]] tuning, [[tempering out]] [[81/80]] in the [[5-limit]]; [[126/125]] and [[225/224]] in the [[7-limit]]; [[99/98]], [[176/175]] and [[441/440]] in the [[11-limit]]; and [[144/143]] and [[847/845]] in the [[13-limit]]. Discarding 847/845 from that gives the 13-limit meantone extension [[grosstone]], for which 74edo gives the [[optimal patent val]]; and discarding 144/143 gives [[semimeantone]], a 13-limit 62 & 74 temperament with half-octave period and two parallel tracks of meantone.

	74edo tunes [[harmonic]] [[11/1\|11]] only 1/30 of a cent sharp, and [[13/1\|13]] 2.7 cents sharp, making it a distinctly interesting choice for higher-limit meantone.		74edo tunes [[harmonic]] [[11/1\|11]] only 1/30 of a cent sharp, and [[13/1\|13]] only 2.7 cents sharp, making it a distinctly interesting choice for higher-limit meantone.

	=== Odd harmonics ===		=== Odd harmonics ===

Yourmusic Productions: Add lumatone mapping link.

2025-07-26T06:14:08Z

Add lumatone mapping link.

← Older revision		Revision as of 06:14, 26 July 2025
Line 48:		Line 48:

	In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma\|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.		In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma\|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.

			== Instruments ==
			* [[Lumatone mapping for 74edo]]

	== Music ==		== Music ==

Lucius Chiaraviglio: /* Subsets and supersets */ Same prime harmonics 5 through 13

2025-07-09T08:13:34Z

Subsets and supersets: Same prime harmonics 5 through 13

← Older revision		Revision as of 08:13, 9 July 2025
Line 11:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 74 factors into {{factorization\|74}}, 74edo contains [[2edo]] and [[37edo]] as its subsets.		Since 74 factors into {{factorization\|74}}, 74edo contains [[2edo]] and [[37edo]] as its subsets; of these, 37edo has the same highly accurate prime harmonics in the no-3s [[13-limit]].

	== Intervals ==		== Intervals ==

Lucius Chiaraviglio: /* 21st century */ Add Bryan Deister's ''microtonal improvisation in 74edo'' (2025)

2025-06-12T06:11:41Z

21st century: Add Bryan Deister's ''microtonal improvisation in 74edo'' (2025)

← Older revision		Revision as of 06:11, 12 June 2025
Line 58:		Line 58:
	; [[Claudi Meneghin]]		; [[Claudi Meneghin]]
	* ''Twinkle canon'' (2012) – [https://web.archive.org/web/20171009205013/http://soonlabel.com/xenharmonic/archives/573 detail] \| [https://web.archive.org/web/20201127015514/http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-74-edo.mp3 play]		* ''Twinkle canon'' (2012) – [https://web.archive.org/web/20171009205013/http://soonlabel.com/xenharmonic/archives/573 detail] \| [https://web.archive.org/web/20201127015514/http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-74-edo.mp3 play]

			; [[Bryan Deister]]
			* [https://www.youtube.com/shorts/ylOGUb395Gg ''microtonal improvisation in 74edo''] (2025)

	[[Category:Meantone]]		[[Category:Meantone]]
	[[Category:Listen]]		[[Category:Listen]]
	[[Category:Historical]]		[[Category:Historical]]

FloraC: No need to remind readers of what a regular temperament is everywhere

2025-04-11T11:02:40Z

No need to remind readers of what a regular temperament is everywhere

← Older revision		Revision as of 11:02, 11 April 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	74edo is most notable as a [[meantone]] tuning, [[tempering out]] [[81/80]] in the [[5-limit]]; [[126/125]] and [[225/224]] in the [[7-limit]]; [[99/98]], [[176/175]] and [[441/440]] in the [[11-limit]]; and [[144/143]] and [[847/845]] in the [[13-limit]]. Discarding 847/845 from that gives the 13-limit meantone extension [[grosstone]], for which 74edo gives the [[optimal patent val]]; and discarding 144/143 gives [[semimeantone]], a 13-limit 62 & 74 temperament with half-octave period and two parallel tracks of meantone. ~~(''See [[regular temperament]] for more about what all this means and how to use it.'')~~		74edo is most notable as a [[meantone]] tuning, [[tempering out]] [[81/80]] in the [[5-limit]]; [[126/125]] and [[225/224]] in the [[7-limit]]; [[99/98]], [[176/175]] and [[441/440]] in the [[11-limit]]; and [[144/143]] and [[847/845]] in the [[13-limit]]. Discarding 847/845 from that gives the 13-limit meantone extension [[grosstone]], for which 74edo gives the [[optimal patent val]]; and discarding 144/143 gives [[semimeantone]], a 13-limit 62 & 74 temperament with half-octave period and two parallel tracks of meantone.

	74edo tunes [[harmonic]] [[11/1\|11]] only 1/30 of a cent sharp, and [[13/1\|13]] 2.7 cents sharp, making it a distinctly interesting choice for higher-limit meantone.		74edo tunes [[harmonic]] [[11/1\|11]] only 1/30 of a cent sharp, and [[13/1\|13]] 2.7 cents sharp, making it a distinctly interesting choice for higher-limit meantone.

BudjarnLambeth: /* Theory */ (''See regular temperament for more about what all this means and how to use it.'')

2025-04-11T07:26:09Z

Theory: (''See regular temperament for more about what all this means and how to use it.'')

← Older revision		Revision as of 07:26, 11 April 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	74edo is most notable as a [[meantone]] tuning, [[tempering out]] [[81/80]] in the [[5-limit]]; [[126/125]] and [[225/224]] in the [[7-limit]]; [[99/98]], [[176/175]] and [[441/440]] in the [[11-limit]]; and [[144/143]] and [[847/845]] in the [[13-limit]]. Discarding 847/845 from that gives the 13-limit meantone extension [[grosstone]], for which 74edo gives the [[optimal patent val]]; and discarding 144/143 gives [[semimeantone]], a 13-limit 62 & 74 temperament with half-octave period and two parallel tracks of meantone.		74edo is most notable as a [[meantone]] tuning, [[tempering out]] [[81/80]] in the [[5-limit]]; [[126/125]] and [[225/224]] in the [[7-limit]]; [[99/98]], [[176/175]] and [[441/440]] in the [[11-limit]]; and [[144/143]] and [[847/845]] in the [[13-limit]]. Discarding 847/845 from that gives the 13-limit meantone extension [[grosstone]], for which 74edo gives the [[optimal patent val]]; and discarding 144/143 gives [[semimeantone]], a 13-limit 62 & 74 temperament with half-octave period and two parallel tracks of meantone. (''See [[regular temperament]] for more about what all this means and how to use it.'')

	74edo tunes [[harmonic]] [[11/1\|11]] only 1/30 of a cent sharp, and [[13/1\|13]] 2.7 cents sharp, making it a distinctly interesting choice for higher-limit meantone.		74edo tunes [[harmonic]] [[11/1\|11]] only 1/30 of a cent sharp, and [[13/1\|13]] 2.7 cents sharp, making it a distinctly interesting choice for higher-limit meantone.

Hkm: /* Ups and downs notation */

2025-03-23T20:33:46Z

Ups and downs notation

← Older revision		Revision as of 20:33, 23 March 2025
Line 18:		Line 18:
	== Notation ==		== Notation ==
	===Ups and downs notation===		===Ups and downs notation===
	~~32edo~~ can be notated with [[ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).		74edo can be notated with [[ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).
	{{Sharpness-sharp5a}}		{{Sharpness-sharp5a}}
	Another notation uses [[Alternative symbols for ups and downs notation#Sharp-5\|alternative ups and downs]]. It uses sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:		Another notation uses [[Alternative symbols for ups and downs notation#Sharp-5\|alternative ups and downs]]. It uses sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]: