145edo - Revision history

FloraC: Note OPV for mabila

2026-06-23T02:24:47Z

Note OPV for mabila

← Older revision		Revision as of 02:24, 23 June 2026
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	{{Nowrap\| 145 {{=}} 5 × 29 }}, and 145edo shares the same perfect fifth with [[29edo]]. It is generally a sharp-tending system, with [[prime harmonic]]s 3 to 23 all tuned sharp except for [[7/1\|7]], which is slightly flat. It is [[consistent]] to the [[11-odd-limit]], or the no-13 no-15 [[23-odd-limit]], with [[13/7]], [[15/14]], [[15/8]] and their [[octave complement]]s being the only intervals going over the line.		{{Nowrap\| 145 {{=}} 5 × 29 }}, and 145edo shares the same perfect fifth with [[29edo]]. It is generally a sharp-tending system, with [[prime harmonic]]s 3 to 23 all tuned sharp except for [[7/1\|7]], which is slightly flat. It is [[consistent]] to the [[11-odd-limit]], or the no-13 no-15 [[23-odd-limit]], with [[13/7]], [[15/14]], [[15/8]] and their [[octave complement]]s being the only intervals going over the line.

	As an equal temperament, 145et [[tempering out\|tempers out]] [[1600000/1594323]] in the [[5-limit]]; [[~~4375~~/~~4374~~]] and [[~~5120/5103~~]] in the [[7-limit]]; [[441/440]] and [[896/891]] in the [[11-limit]]; [[196/195]], [[352/351]], [[364/363]], [[676/675]], [[847/845]], and [[1001/1000]] in the [[13-limit]]; [[595/594]] in the [[17-limit]]; [[343/342]] and [[476/475]] in the [[19-limit]].		As an equal temperament, 145et [[tempering out\|tempers out]] 1600000/1594323 ([[amity comma]]) and {{monzo\| 28 -3 -10 }} ([[mabila comma]]) in the [[5-limit]]; 4375/4374 ([[ragisma]]), 5120/5103 ([[aberschisma]]), and 50421/50000 ([[trimyna comma]]) in the [[7-limit]]; [[441/440]] and [[896/891]] in the [[11-limit]]; [[196/195]], [[352/351]], [[364/363]], [[676/675]], [[847/845]], and [[1001/1000]] in the [[13-limit]]; [[595/594]] in the [[17-limit]]; [[343/342]] and [[476/475]] in the [[19-limit]].

	It ~~is the~~ [[optimal patent val]] for the 11-limit [[mystery]] temperament and the 11-limit rank-3 [[pele]] temperament. It also [[support]]s and provides a good tuning for 13-limit mystery~~, and because~~ it tempers out 441/440 it allows [[werckismic chords]], because it tempers out 196/195 it allows [[mynucumic chords]], because it tempers out 352/351 it allows [[major minthmic chords]], because it tempers out 364/363 it allows [[minor minthmic chords]], and because it tempers out 847/845 it allows the [[cuthbert chords]], making it a very flexible harmonic system. The same is true of [[232edo]], the optimal patent val for 13-limit mystery.		It provides an excellent [[optimal patent val]] for the 5-limit [[mabila]] temperament, the 11-limit [[mystery]] temperament and the 11-limit rank-3 [[pele]] temperament. It also [[support]]s and provides a good tuning for 13-limit mystery. Because it tempers out 441/440 it allows [[werckismic chords]], because it tempers out 196/195 it allows [[mynucumic chords]], because it tempers out 352/351 it allows [[major minthmic chords]], because it tempers out 364/363 it allows [[minor minthmic chords]], and because it tempers out 847/845 it allows the [[cuthbert chords]], making it a very flexible harmonic system. The same is true of [[232edo]], the optimal patent val for 13-limit mystery.

	The 145c val provides a tuning for [[magic]] which is nearly identical to the [[POTE tuning]].		The 145c val provides a tuning for [[magic]] which is nearly identical to the [[POTE tuning]].
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	== Music ==		== Music ==
	; [[Chris Vaisvil]] ([http://www.chrisvaisvil.com/ site])		; [[Chris Vaisvil]] ([http://www.chrisvaisvil.com/ site])
	* [http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3 ''Chromatic piece in magic 16''] – ~~magic~~[16] in 145edo tuning		* [http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3 ''Chromatic piece in magic 16''] – Magic[16] in 145edo tuning

			[[Category:Mabila]]
	[[Category:Mystery]]		[[Category:Mystery]]
	[[Category:Pele]]		[[Category:Pele]]
	[[Category:Magic]]		[[Category:Magic]]
	[[Category:Listen]]		[[Category:Listen]]

FloraC: /* Regular temperament properties */ note

2026-06-22T20:01:55Z

Regular temperament properties: note

← Older revision		Revision as of 20:01, 22 June 2026
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	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
	! rowspan="2" \| [[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \| [[Comma list~~\|Comma List~~]]		! rowspan="2" \| [[Comma list]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal<br>8ve ~~Stretch~~ (¢)		! rowspan="2" \| Optimal<br>8ve stretch (¢)
	! colspan="2" \| Tuning ~~Error~~		! colspan="2" \| Tuning error
	\|-		\|-
	! [[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
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	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>~~Ratio~~*		! Associated<br>ratio*
	! Temperaments		! Temperaments
	\|-		\|-
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	\| [[Mystery]]		\| [[Mystery]]
	\|}		\|}
			<nowiki/>* In [[Normal forms #Minimal-generator form\|minimal-generator form]]

	== Scales ==		== Scales ==

FloraC: /* Regular temperament properties */ + mabila and hemimabila

2026-06-22T19:59:33Z

Regular temperament properties: + mabila and hemimabila

← Older revision		Revision as of 19:59, 22 June 2026
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	\| 77/72		\| 77/72
	\| [[Countermiracle]]		\| [[Countermiracle]]
			\|-
			\| 1
			\| 32\145
			\| 264.83
			\| 7/6
			\| [[Hemimabila]]
	\|-		\|-
	\| 1		\| 1
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	\| 128/105		\| 128/105
	\| [[Amity]] / stalagmite		\| [[Amity]] / stalagmite
			\|-
			\| 1
			\| 64\145
			\| 529.66
			\| 512/375
			\| [[Mabila]]
	\|-		\|-
	\| 5		\| 5
	\| ~~67\145<br>(~~9\145)		\| 9\145
	\| ~~554.48<br>(~~74.48)		\| 74.48
	\| ~~11/8<br>(~~25/24)		\| 25/24
	\| [[Trisedodge]] / [[countdown]]		\| [[Trisedodge]] / [[countdown]]
	\|-		\|-
	\| 29		\| 29
	\| ~~60\145<br>(~~2\145)		\| 2\145
	\| ~~496.55<br>(~~16.55)		\| 16.55
	\| ~~4/3<br>(~~100/99)		\| 100/99
	\| [[Mystery]]		\| [[Mystery]]
	\|}		\|}

Overthink: /* Rank-2 temperaments */ temperament has been renamed

2025-11-19T08:13:35Z

Rank-2 temperaments: temperament has been renamed

← Older revision		Revision as of 08:13, 19 November 2025
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	\| 339.31		\| 339.31
	\| 128/105		\| 128/105
	\| [[Amity]] / ~~catamite~~		\| [[Amity]] / stalagmite
	\|-		\|-
	\| 5		\| 5

Overthink: /* Octave stretch */ Pointed 375edo to 375ed6 rather than ed6 (though page not yet created)

2025-11-19T08:11:42Z

Octave stretch: Pointed 375edo to 375ed6 rather than ed6 (though page not yet created)

← Older revision		Revision as of 08:11, 19 November 2025
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	=== Octave stretch ===		=== Octave stretch ===
	145edo's approximated harmonics 3, 5, 11, 13, 17, 19, and 23 can be improved at the cost of a little worse 7, and moreover the approximated harmonic 13 can be brought to consistency, if slightly [[stretched and compressed tuning\|compressing the octave]] is acceptable. [[~~ed6\|~~375ed6]] is about at the sweet spot for this.		145edo's approximated harmonics 3, 5, 11, 13, 17, 19, and 23 can be improved at the cost of a little worse 7, and moreover the approximated harmonic 13 can be brought to consistency, if slightly [[stretched and compressed tuning\|compressing the octave]] is acceptable. [[375ed6]] is about at the sweet spot for this.

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

BudjarnLambeth: /* Octave stretch */

2025-09-17T10:39:53Z

Octave stretch

← Older revision		Revision as of 10:39, 17 September 2025
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	=== Octave stretch ===		=== Octave stretch ===
	145edo's approximated harmonics 3, 5, 11, 13, 17, 19, and 23 can be improved at the cost of a little worse 7, and moreover the approximated harmonic 13 can be brought to consistency, if slightly [[stretched and compressed tuning\|compressing the octave]] is acceptable. [[375ed6]] is about at the sweet spot for this.		145edo's approximated harmonics 3, 5, 11, 13, 17, 19, and 23 can be improved at the cost of a little worse 7, and moreover the approximated harmonic 13 can be brought to consistency, if slightly [[stretched and compressed tuning\|compressing the octave]] is acceptable. [[ed6\|375ed6]] is about at the sweet spot for this.

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

Lériendil at 01:59, 30 August 2025

2025-08-30T01:59:24Z

← Older revision		Revision as of 01:59, 30 August 2025
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	== Theory ==		== Theory ==
	{{Nowrap\| 145 {{=}} 5 × 29 }}, and 145edo shares the same perfect fifth with [[29edo]]. It is generally a sharp-tending system, with [[prime harmonic]]s 3 to 23 all tuned sharp except for [[7/1\|7]], which is slightly flat. It is [[consistent]] to the [[11-odd-limit]], or the no-13 no-15 [[23-odd-limit]], with [[13/7]], [[15/8]] and their [[octave complement]]s being the only intervals going over the line.		{{Nowrap\| 145 {{=}} 5 × 29 }}, and 145edo shares the same perfect fifth with [[29edo]]. It is generally a sharp-tending system, with [[prime harmonic]]s 3 to 23 all tuned sharp except for [[7/1\|7]], which is slightly flat. It is [[consistent]] to the [[11-odd-limit]], or the no-13 no-15 [[23-odd-limit]], with [[13/7]], [[15/14]], [[15/8]] and their [[octave complement]]s being the only intervals going over the line.

	As an equal temperament, 145et [[tempering out\|tempers out]] [[1600000/1594323]] in the [[5-limit]]; [[4375/4374]] and [[5120/5103]] in the [[7-limit]]; [[441/440]] and [[896/891]] in the [[11-limit]]; [[196/195]], [[352/351]], [[364/363]], [[676/675]], [[847/845]], and [[1001/1000]] in the [[13-limit]]; [[595/594]] in the [[17-limit]]; [[343/342]] and [[476/475]] in the [[19-limit]].		As an equal temperament, 145et [[tempering out\|tempers out]] [[1600000/1594323]] in the [[5-limit]]; [[4375/4374]] and [[5120/5103]] in the [[7-limit]]; [[441/440]] and [[896/891]] in the [[11-limit]]; [[196/195]], [[352/351]], [[364/363]], [[676/675]], [[847/845]], and [[1001/1000]] in the [[13-limit]]; [[595/594]] in the [[17-limit]]; [[343/342]] and [[476/475]] in the [[19-limit]].

FloraC: /* Regular temperament properties */ extend to the 23-limit

2025-03-24T13:49:03Z

Regular temperament properties: extend to the 23-limit

← Older revision		Revision as of 13:49, 24 March 2025
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	\| 2.3.5		\| 2.3.5
	\| 1600000/1594323, {{monzo\| 28 -3 -10 }}		\| 1600000/1594323, {{monzo\| 28 -3 -10 }}
	\| {{~~mapping~~\| 145 230 337 }}		\| {{Mapping\| 145 230 337 }}
	\| -0.695		\| -0.695
	\| 0.498		\| 0.498
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	\| 2.3.5.7		\| 2.3.5.7
	\| 4375/4374, 5120/5103, 50421/50000		\| 4375/4374, 5120/5103, 50421/50000
	\| {{~~mapping~~\| 145 230 337 407 }}		\| {{Mapping\| 145 230 337 407 }}
	\| -0.472		\| -0.472
	\| 0.578		\| 0.578
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	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 441/440, 896/891, 3388/3375, 4375/4374		\| 441/440, 896/891, 3388/3375, 4375/4374
	\| {{~~mapping~~\| 145 230 337 407 502 }}		\| {{Mapping\| 145 230 337 407 502 }}
	\| -0.561		\| -0.561
	\| 0.547		\| 0.547
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	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 196/195, 352/351, 364/363, 676/675, 4375/4374		\| 196/195, 352/351, 364/363, 676/675, 4375/4374
	\| {{~~mapping~~\| 145 230 337 407 502 537 }}		\| {{Mapping\| 145 230 337 407 502 537 }}
	\| -0.630		\| -0.630
	\| 0.522		\| 0.522
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	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 196/195, 256/255, 352/351, 364/363, 676/675, 1156/1155		\| 196/195, 256/255, 352/351, 364/363, 676/675, 1156/1155
	\| {{~~mapping~~\| 145 230 337 407 502 537 593 }}		\| {{Mapping\| 145 230 337 407 502 537 593 }}
	\| -0.632		\| -0.632
	\| 0.484		\| 0.484
	\| 5.85		\| 5.85
			\|-
			\| 2.3.5.7.11.13.17.19
			\| 196/195, 256/255, 343/342, 352/351, 361/360, 364/363, 476/475
			\| {{Mapping\| 145 230 337 407 502 537 593 616 }}
			\| -0.565
			\| 0.486
			\| 5.87
			\|-
			\| 2.3.5.7.11.13.17.19.23
			\| 196/195, 256/255, 276/275, 352/351, 361/360, 364/363, 460/459, 476/475
			\| {{Mapping\| 145 230 337 407 502 537 593 616 656 }}
			\| -0.519
			\| 0.476
			\| 5.75
	\|}		\|}

FloraC: /* Theory */ +octave stretch

2025-03-24T13:38:05Z

Theory: +octave stretch

← Older revision		Revision as of 13:38, 24 March 2025
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	== Theory ==		== Theory ==
	145 = 5 × 29, and 145edo shares the same perfect fifth with [[29edo]]. It is generally a sharp-tending system, with [[prime harmonic]]s 3 to 23 all tuned sharp except for 7, which is slightly flat. It is [[consistent]] to the [[11-odd-limit]], or the no-13 no-15 [[23-odd-limit]], with [[13/7]], [[15/8]] and their [[octave complement]]s being the only intervals going over the line.		{{Nowrap\| 145 {{=}} 5 × 29 }}, and 145edo shares the same perfect fifth with [[29edo]]. It is generally a sharp-tending system, with [[prime harmonic]]s 3 to 23 all tuned sharp except for [[7/1\|7]], which is slightly flat. It is [[consistent]] to the [[11-odd-limit]], or the no-13 no-15 [[23-odd-limit]], with [[13/7]], [[15/8]] and their [[octave complement]]s being the only intervals going over the line.

	As an equal temperament, 145et [[tempering out\|tempers out]] [[1600000/1594323]] in the [[5-limit]]; [[4375/4374]] and [[5120/5103]] in the [[7-limit]]; [[441/440]] and [[896/891]] in the 11-limit; [[196/195]], [[352/351]], [[364/363]], [[676/675]], [[847/845]], and [[1001/1000]] in the 13-limit; [[595/594]] in the 17-limit; [[343/342]] and [[476/475]] in the 19-limit.		As an equal temperament, 145et [[tempering out\|tempers out]] [[1600000/1594323]] in the [[5-limit]]; [[4375/4374]] and [[5120/5103]] in the [[7-limit]]; [[441/440]] and [[896/891]] in the [[11-limit]]; [[196/195]], [[352/351]], [[364/363]], [[676/675]], [[847/845]], and [[1001/1000]] in the [[13-limit]]; [[595/594]] in the [[17-limit]]; [[343/342]] and [[476/475]] in the [[19-limit]].

	It is the [[optimal patent val]] for the 11-limit [[mystery]] temperament and the 11-limit rank-3 [[pele]] temperament. It also [[support]]s and provides a good tuning for 13-limit mystery, and because it tempers out 441/440 it allows [[werckismic chords]], because it tempers out 196/195 it allows [[mynucumic chords]], because it tempers out 352/351 it allows [[major minthmic chords]], because it tempers out 364/363 it allows [[minor minthmic chords]], and because it tempers out 847/845 it allows the [[cuthbert chords]], making it a very flexible harmonic system. The same is true of [[232edo]], the optimal patent val for 13-limit mystery.		It is the [[optimal patent val]] for the 11-limit [[mystery]] temperament and the 11-limit rank-3 [[pele]] temperament. It also [[support]]s and provides a good tuning for 13-limit mystery, and because it tempers out 441/440 it allows [[werckismic chords]], because it tempers out 196/195 it allows [[mynucumic chords]], because it tempers out 352/351 it allows [[major minthmic chords]], because it tempers out 364/363 it allows [[minor minthmic chords]], and because it tempers out 847/845 it allows the [[cuthbert chords]], making it a very flexible harmonic system. The same is true of [[232edo]], the optimal patent val for 13-limit mystery.
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|145\|intervals=prime}}		{{Harmonics in equal\|145\|intervals=prime}}

			=== Octave stretch ===
			145edo's approximated harmonics 3, 5, 11, 13, 17, 19, and 23 can be improved at the cost of a little worse 7, and moreover the approximated harmonic 13 can be brought to consistency, if slightly [[stretched and compressed tuning\|compressing the octave]] is acceptable. [[375ed6]] is about at the sweet spot for this.

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

ArrowHead294 at 17:05, 18 February 2025

2025-02-18T17:05:00Z

← Older revision		Revision as of 17:05, 18 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|145~~}}		{{ED intro}}

	== Theory ==		== Theory ==