105edo - Revision history

Lériendil at 19:44, 30 April 2025

2025-04-30T19:44:12Z

← Older revision		Revision as of 19:44, 30 April 2025
Line 11:		Line 11:
	105 is the product of 3 × 5 × 7, the three smallest odd primes, with other divisors being 15, 21 and 35.		105 is the product of 3 × 5 × 7, the three smallest odd primes, with other divisors being 15, 21 and 35.

	As such, the val [105 165 245 294], which is contorted in 2.n for each prime n in the subgroup, may be used to extend the concept of ~~15edo~~'s 5-limit harmony to the 7-limit, producing an independent dimension for each prime.		As such, the val [105 165 245 294], which is contorted in 2.n for each prime n in the subgroup, may be used to extend the concept of 21edo's 5-limit harmony to the 7-limit, producing an independent dimension for each prime.

	== Intervals ==		== Intervals ==

VectorGraphics at 19:26, 30 April 2025

2025-04-30T19:26:53Z

← Older revision		Revision as of 19:26, 30 April 2025
Line 10:		Line 10:
	=== Subsets and supersets ===		=== Subsets and supersets ===
	105 is the product of 3 × 5 × 7, the three smallest odd primes, with other divisors being 15, 21 and 35.		105 is the product of 3 × 5 × 7, the three smallest odd primes, with other divisors being 15, 21 and 35.

			As such, the val [105 165 245 294], which is contorted in 2.n for each prime n in the subgroup, may be used to extend the concept of 15edo's 5-limit harmony to the 7-limit, producing an independent dimension for each prime.

	== Intervals ==		== Intervals ==

ArrowHead294 at 16:47, 18 February 2025

2025-02-18T16:47:03Z

← Older revision		Revision as of 16:47, 18 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|105~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Theory */ cleanup

2025-01-17T15:16:42Z

Theory: cleanup

← Older revision		Revision as of 15:16, 17 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	105edo is most notable as a tuning of [[meantone]] and in particular higher-limit extensions of meantone, such as [[grosstone]] and [[~~Huygens~~]]. It [[tempers out]] [[81/80]] in the [[5-limit]]; 81/80, [[126/125]] and hence 225/224 in the [[7-limit]]; 99/98, 176/175 and 441/440 in the [[11-limit]]; and if we want to push that far, 144/143 in the [[13-limit]]. This is the sharper fifth mapping of 11-limit meantone (~~aka~~ huygens rather than meanpop), for which it gives the [[optimal patent val]], and provides a good tuning for the 13-limit extension, though [[74edo]] is in that case the optimal patent val. 105edo's meantone fifth is nearly identical to the [[CTE tuning\|CTE generator]] for meantone.		105edo is most notable as a tuning of [[meantone]] and in particular higher-limit extensions of meantone, such as [[grosstone]] and [[huygens]]. It [[tempering out\|tempers out]] [[81/80]] in the [[5-limit]]; 81/80, [[126/125]] and hence 225/224 in the [[7-limit]]; 99/98, 176/175 and 441/440 in the [[11-limit]]; and if we want to push that far, 144/143 in the [[13-limit]]. This is the sharper fifth mapping of 11-limit meantone (a.k.a. huygens rather than meanpop), for which it gives the [[optimal patent val]], and provides a good tuning for the 13-limit extension, though [[74edo]] is in that case the optimal patent val. 105edo's meantone fifth is nearly identical to the [[CTE tuning\|CTE generator]] for meantone.

	=== Odd harmonics ===		=== Odd harmonics ===
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	105 is the product of 3 × 5 × 7, the three smallest odd primes, with other divisors being 15, 21 and 35.		105 is the product of 3 × 5 × 7, the three smallest odd primes, with other divisors being 15, 21 and 35.

	== Intervals ==		== Intervals ==

BudjarnLambeth: Link to lumatone mapping page

2025-01-09T14:04:54Z

Link to lumatone mapping page

← Older revision		Revision as of 14:04, 9 January 2025
Line 15:		Line 15:
	=== 15-odd-limit interval mappings ===		=== 15-odd-limit interval mappings ===
	{{Q-odd-limit intervals\|105}}		{{Q-odd-limit intervals\|105}}

			== Instruments ==
			=== Lumatone ===
			The [[lumatone]] can be used to play 105edo. For key mappings, see: [[Lumatone mapping for 105edo]].

	[[Category:105edo\| ]] <!-- main article -->		[[Category:105edo\| ]] <!-- main article -->

ArrowHead294: /* Intervals */

2024-05-24T13:21:17Z

Intervals

← Older revision		Revision as of 13:21, 24 May 2024
Line 14:		Line 14:
	{{Main\|Table of 105edo intervals}}		{{Main\|Table of 105edo intervals}}
	=== 15-odd-limit interval mappings ===		=== 15-odd-limit interval mappings ===
	~~{{Q-odd-limit intervals\|105}}~~
	{{Q-odd-limit intervals\|105}}		{{Q-odd-limit intervals\|105}}

ArrowHead294: /* Intervals */

2024-05-24T13:21:03Z

Intervals

← Older revision		Revision as of 13:21, 24 May 2024
Line 13:		Line 13:
	== Intervals ==		== Intervals ==
	{{Main\|Table of 105edo intervals}}		{{Main\|Table of 105edo intervals}}
	~~{{Interval table}}~~
	=== 15-odd-limit interval mappings ===		=== 15-odd-limit interval mappings ===
	{{15-odd-limit\|105}}		{{Q-odd-limit intervals\|105}}
			{{Q-odd-limit intervals\|105}}

	[[Category:105edo\| ]] <!-- main article -->		[[Category:105edo\| ]] <!-- main article -->

CompactStar at 02:10, 28 February 2024

2024-02-28T02:10:28Z

← Older revision		Revision as of 02:10, 28 February 2024
Line 13:		Line 13:
	== Intervals ==		== Intervals ==
	{{Main\|Table of 105edo intervals}}		{{Main\|Table of 105edo intervals}}
			{{Interval table}}
	=== 15-odd-limit interval mappings ===		=== 15-odd-limit interval mappings ===
	{{15-odd-limit\|105}}		{{15-odd-limit\|105}}

Eliora: /* Intervals */

2023-05-30T21:13:13Z

Intervals

Show changes

Fredg999: Add 15-odd-limit table, mention two examples of meantone extensions relevant to this tuning, misc. edits

2023-05-24T21:09:50Z

Add 15-odd-limit table, mention two examples of meantone extensions relevant to this tuning, misc. edits

← Older revision		Revision as of 21:09, 24 May 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	~~'''105edo''' is the [[equal division of the octave]] into~~ 105 ~~equal parts of 11.429 [[cent]]s each.~~		{{EDO intro\|105}}

	== Theory ==		== Theory ==
	105edo is most notable as a tuning of [[meantone]] and in particular higher-limit extensions of meantone. It [[tempers out]] [[81/80]] in the [[5-limit]]; 81/80, [[126/125]] and hence 225/224 in the [[7-limit]]; 99/98, 176/175 and 441/440 in the [[11-limit]]; and if we want to push that far, 144/143 in the [[13-limit]]. This is the sharper fifth mapping of 11-limit meantone (aka huygens rather than meanpop), for which it gives the [[optimal patent val]], and provides a good tuning for the 13-limit extension, though [[74edo]] is in that case the optimal patent val. 105edo's meantone fifth is nearly identical to the [[CTE tuning\|CTE generator]] for meantone.		105edo is most notable as a tuning of [[meantone]] and in particular higher-limit extensions of meantone, such as [[grosstone]] and [[Huygens]]. It [[tempers out]] [[81/80]] in the [[5-limit]]; 81/80, [[126/125]] and hence 225/224 in the [[7-limit]]; 99/98, 176/175 and 441/440 in the [[11-limit]]; and if we want to push that far, 144/143 in the [[13-limit]]. This is the sharper fifth mapping of 11-limit meantone (aka huygens rather than meanpop), for which it gives the [[optimal patent val]], and provides a good tuning for the 13-limit extension, though [[74edo]] is in that case the optimal patent val. 105edo's meantone fifth is nearly identical to the [[CTE tuning\|CTE generator]] for meantone.

	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|105}}		{{Harmonics in equal\|105}}

	=== Intervals ===		== Intervals ==
	[[Table of 105edo intervals]]		{{Main\|Table of 105edo intervals}}

			=== 15-odd-limit interval mappings ===
			{{15-odd-limit\|105}}

	=== Miscellany ===		=== Miscellany ===