109edo - Revision history

Overthink: /* Theory */

2025-10-19T03:56:56Z

Theory

← Older revision		Revision as of 03:56, 19 October 2025
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	109edo [[tempering out\|tempers out]] 20000/19683 ([[tetracot comma]]) in the [[5-limit]]; [[245/243]], [[2401/2400]] and [[65625/65536]] in the [[7-limit]]; [[385/384]], [[1375/1372]], and [[4000/3993]] in the [[11-limit]]. It provides the [[optimal patent val]] for 7-limit [[octacot]] temperament, and 11- and 13-limit [[leapweek]]; plus 109ef provides an excellent tuning for 11- and 13-limit octacot.		109edo [[tempering out\|tempers out]] 20000/19683 ([[tetracot comma]]) in the [[5-limit]]; [[245/243]], [[2401/2400]] and [[65625/65536]] in the [[7-limit]]; [[385/384]], [[1375/1372]], and [[4000/3993]] in the [[11-limit]]. It provides the [[optimal patent val]] for 7-limit [[octacot]] temperament, and 11- and 13-limit [[leapweek]]; plus 109ef provides an excellent tuning for 11- and 13-limit octacot.

	109edo has an excellent [[7/1\|7th harmonic]], being a denominator of [[semiconvergent]] to log<sub>2</sub>7, and it is overall a strong 2.5.7.11.19.23.31.41 [[subgroup]] tuning, with errors of less than 10% on all harmonics. Some commas it tempers out in this subgroup are 575/574, 1331/1330, 1375/1372, 2255/~~2244~~, 2300/2299, 6860/6859, 10241/10240.		109edo has an excellent [[7/1\|7th harmonic]], being a denominator of [[semiconvergent]] to log<sub>2</sub>7, and it is overall a strong 2.5.7.11.19.23.31.41 [[subgroup]] tuning, with errors of less than 10% on all harmonics. Some commas it tempers out in this subgroup are 575/574, 1331/1330, 1375/1372, 2255/2254, 2300/2299, 6860/6859, 10241/10240.

	=== Prime harmonics ===		=== Prime harmonics ===

Francium: /* Music */ +music; +links

2025-06-07T11:35:09Z

Music: +music; +links

← Older revision		Revision as of 11:35, 7 June 2025
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	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* [https://www.youtube.com/watch?v=v_J71U392_k ''~~Teenagerges~~''] (~~2024~~) – ~~tetracot~~[13] ~~in 109edo tuning~~		* "Teenagerges" from ''TOTMC September to December 2024'' (2024) – [https://open.spotify.com/track/4oQglJSEyp6CsL5RNWuiBy Spotify] \| [https://francium223.bandcamp.com/track/teenagerges Bandcamp] \| [https://www.youtube.com/watch?v=v_J71U392_k YouTube] – in Tetracot[13], 109edo tuning
			* "Catbabel" from ''Microtonal Six-Dimensional Cats'' (2025) – [https://open.spotify.com/track/0T7nW3ziEFvjV8c7v1EaMB Spotify] \| [https://francium223.bandcamp.com/track/catbabel Bandcamp] \| [https://www.youtube.com/watch?v=gtnTdPqiTDQ YouTube]

	== See also ==		== See also ==
	* [[109-7-comma]]		* [[109-7-comma]]

ArrowHead294 at 16:48, 18 February 2025

2025-02-18T16:48:42Z

← Older revision		Revision as of 16:48, 18 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|109~~}}		{{ED intro}}

	== Theory ==		== Theory ==

Lériendil at 17:18, 19 September 2024

2024-09-19T17:18:01Z

← Older revision		Revision as of 17:18, 19 September 2024
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|109}}		{{Harmonics in equal\|109\|columns=16}}

	=== Subsets and supersets ===		=== Subsets and supersets ===

BudjarnLambeth: Added link to orphaned page

2024-09-18T23:01:20Z

Added link to orphaned page

← Older revision		Revision as of 23:01, 18 September 2024
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	; [[Francium]]		; [[Francium]]
	* [https://www.youtube.com/watch?v=v_J71U392_k ''Teenagerges''] (2024) – tetracot[13] in 109edo tuning		* [https://www.youtube.com/watch?v=v_J71U392_k ''Teenagerges''] (2024) – tetracot[13] in 109edo tuning

			== See also ==
			* [[109-7-comma]]

Francium: +music

2024-09-17T12:13:00Z

+music

← Older revision		Revision as of 12:13, 17 September 2024
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	== Intervals ==		== Intervals ==
	{{Interval table}}		{{Interval table}}

			== Music ==
			; [[Francium]]
			* [https://www.youtube.com/watch?v=v_J71U392_k ''Teenagerges''] (2024) – tetracot[13] in 109edo tuning

FloraC: Note a notable superset

2024-06-08T08:28:33Z

Note a notable superset

← Older revision		Revision as of 08:28, 8 June 2024
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	109edo is the 29th [[prime edo]], following [[107edo]] and before [[113edo]].		109edo is the 29th [[prime edo]], following [[107edo]] and before [[113edo]]. [[436edo]], which slices each step of 109edo in four, provides correction for the approximation to harmonic 3.

	=== Nonoctave temperaments ===		=== Nonoctave temperaments ===

FloraC: /* Subsets and supersets */

2024-06-04T13:12:45Z

Subsets and supersets

← Older revision		Revision as of 13:12, 4 June 2024
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	109edo is the 29th [[prime edo]].		109edo is the 29th [[prime edo]], following [[107edo]] and before [[113edo]].

	=== Nonoctave temperaments ===		=== Nonoctave temperaments ===

FloraC: Cleanup and correct typos

2024-06-04T13:12:19Z

Cleanup and correct typos

← Older revision		Revision as of 13:12, 4 June 2024
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|109}}		{{EDO intro\|109}}
	~~==Theory==~~
	109edo [[tempering out\|tempers out]] 20000/19683 in the [[5-limit]]; [[245/243]], 2401/2400 and 65625/65536 in the [[7-limit]]; [[385/384]], 1375/1372, and 4000/3993 in the [[11-limit]]. It provides the [[optimal patent val]] for 7-limit [[octacot]] temperament, and 11 and 13 limit [[leapweek]]; plus 109ef provides an excellent tuning for 11- and 13-limit octacot.

	109edo has an excellent 7th harmonic, being a denominator of [[semiconvergent]] to log<sub>2</sub>7, and it is overall a strong 2.5.7.11.19.23.31.41 subgroup tuning, with errors of less than 10% on all harmonics. Some commas it tempers out in this subgroup are 575/574, 1331/1330, 1375/~~1572~~, 2255/2244, 2300/2299, 6860/6859, 10241/10240.		== Theory ==
			109edo [[tempering out\|tempers out]] 20000/19683 ([[tetracot comma]]) in the [[5-limit]]; [[245/243]], [[2401/2400]] and [[65625/65536]] in the [[7-limit]]; [[385/384]], [[1375/1372]], and [[4000/3993]] in the [[11-limit]]. It provides the [[optimal patent val]] for 7-limit [[octacot]] temperament, and 11- and 13-limit [[leapweek]]; plus 109ef provides an excellent tuning for 11- and 13-limit octacot.

			109edo has an excellent [[7/1\|7th harmonic]], being a denominator of [[semiconvergent]] to log<sub>2</sub>7, and it is overall a strong 2.5.7.11.19.23.31.41 [[subgroup]] tuning, with errors of less than 10% on all harmonics. Some commas it tempers out in this subgroup are 575/574, 1331/1330, 1375/1372, 2255/2244, 2300/2299, 6860/6859, 10241/10240.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{~~harmonics~~ in equal\|109}}		{{Harmonics in equal\|109}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	109edo is the 29th [[prime ~~EDO~~]].		109edo is the 29th [[prime edo]].

	=== Nonoctave temperaments ===		=== Nonoctave temperaments ===
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	== Intervals ==		== Intervals ==
	{{Interval table}}		{{Interval table}}

	~~[[Category:Equal divisions of the octave\|###]]<!-- 3-digit number -->~~
	~~[[Category:Prime EDO]]~~

Eliora: /* Theory */ rework

2024-02-02T15:08:28Z

Theory: rework

← Older revision		Revision as of 15:08, 2 February 2024
Line 4:		Line 4:
	109edo [[tempering out\|tempers out]] 20000/19683 in the [[5-limit]]; [[245/243]], 2401/2400 and 65625/65536 in the [[7-limit]]; [[385/384]], 1375/1372, and 4000/3993 in the [[11-limit]]. It provides the [[optimal patent val]] for 7-limit [[octacot]] temperament, and 11 and 13 limit [[leapweek]]; plus 109ef provides an excellent tuning for 11- and 13-limit octacot.		109edo [[tempering out\|tempers out]] 20000/19683 in the [[5-limit]]; [[245/243]], 2401/2400 and 65625/65536 in the [[7-limit]]; [[385/384]], 1375/1372, and 4000/3993 in the [[11-limit]]. It provides the [[optimal patent val]] for 7-limit [[octacot]] temperament, and 11 and 13 limit [[leapweek]]; plus 109ef provides an excellent tuning for 11- and 13-limit octacot.

	109edo is a strong 2.5.7.11.19.23.31 subgroup tuning, with errors of less than 10% on all harmonics. ~~The error on the 7th harmonic is exceptionally small due to 109 being a denominator of [[semiconvergent]] to log<sub>2<~~/~~sub>7~~.		109edo has an excellent 7th harmonic, being a denominator of [[semiconvergent]] to log<sub>2</sub>7, and it is overall a strong 2.5.7.11.19.23.31.41 subgroup tuning, with errors of less than 10% on all harmonics. Some commas it tempers out in this subgroup are 575/574, 1331/1330, 1375/1572, 2255/2244, 2300/2299, 6860/6859, 10241/10240.

	=== Prime harmonics ===		=== Prime harmonics ===