47edo - Revision history

BudjarnLambeth: /* Scales */

2026-04-27T11:43:35Z

Scales

← Older revision		Revision as of 11:43, 27 April 2026
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	* Quasi-equal [[equiheptatonic]] (Mixolydian): 7 7 6 7 7 6 7		* Quasi-equal [[equiheptatonic]] (Mixolydian): 7 7 6 7 7 6 7
	* Quasi-equal [[equipentatonic]]: 9 10 9 10 9		* Quasi-equal [[equipentatonic]]: 9 10 9 10 9
	* Sabertooth hexatonic: 3 9 3 13 12 7 (this is the original/default tuning; [[scalesmith\|designed]] for the "gold" and "platinum" timbres in [[Scale Workshop]])		* Sabertooth hexatonic{{idio}}: 3 9 3 13 12 7 (this is the original/default tuning; [[scalesmith\|designed]] for the "gold" and "platinum" timbres in [[Scale Workshop]])
	** Sabertooth pentatonic: 3 9 3 13 19 (this is the original/default tuning)		** Sabertooth pentatonic{{idio}}: 3 9 3 13 19 (this is the original/default tuning)
	** Sabertooth neutral: 3 11 14 11 8 (this is the original/default tuning)		** Sabertooth neutral{{idio}}: 3 11 14 11 8 (this is the original/default tuning)

	== Instruments ==		== Instruments ==

BudjarnLambeth: Temporary until full version is made

2025-09-16T09:58:18Z

Temporary until full version is made

← Older revision		Revision as of 09:58, 16 September 2025
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	default [[File:47b_Evo-SZ_Sagittal.svg]]		default [[File:47b_Evo-SZ_Sagittal.svg]]
	</imagemap>		</imagemap>

			== Octave stretch or compression ==
			47edo's [[prime]] 11 is very sharp, and its sharp and flat mapping of 3 are about equally bad, it can benefit from slight [[octave shrinking]]. [[APS\|25.5cET]] or [[ed9/8\|8ed9/8]] make good compressed-octave versions of 47edo.

	== Scales ==		== Scales ==

BudjarnLambeth: /* Instrument mappings */ merge

2025-04-27T03:53:41Z

Instrument mappings: merge

← Older revision		Revision as of 03:53, 27 April 2025
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	** Sabertooth neutral: 3 11 14 11 8 (this is the original/default tuning)		** Sabertooth neutral: 3 11 14 11 8 (this is the original/default tuning)

	== ~~Instrument mappings~~ ==		== Instruments ==
			=== Lumatone ===
	* [[Lumatone mapping for 47edo]]		* [[Lumatone mapping for 47edo]]
	* [[Skip fretting system 43 3 11]]
			=== Skip fretting ===
			'''Skip fretting system 47 3 11''' is a [[skip-fretting]] system for [[47edo]] where strings are 11\47 and frets are 3\47. This is effectively 15.6666...-edo. All examples of this system on this page are for 5-string bass.

			; Chords
			Neutral-dominant 7th: 1 0 1 2 2

	== Music ==		== Music ==

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

2025-04-11T10:56:11Z

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

← Older revision		Revision as of 10:56, 11 April 2025
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	{{Harmonics in equal\|47}}		{{Harmonics in equal\|47}}

	47edo does a good job of approximating the 2.9.5.7.33.13.17.57.69 23-limit [[kN subgroups\|247 subgroup]] of the [[23-limit]], on which it tempers out the same commas as [[94edo]]. It provides a good tuning for [[baldy]] and [[silver]] and their relatives. It also provides a good tuning for the [[baseball]] temperament. ~~(''See [[regular temperament]] for more about what all this means and how to use it.'')~~		47edo does a good job of approximating the 2.9.5.7.33.13.17.57.69 23-limit [[kN subgroups\|247 subgroup]] of the [[23-limit]], on which it tempers out the same commas as [[94edo]]. It provides a good tuning for [[baldy]] and [[silver]] and their relatives. It also provides a good tuning for the [[baseball]] temperament.

	47edo can be treated as a [[dual-fifth system]] in the 2.3+.3-.5.7.13 subgroup, or the 3+.3-.5.7.11+.11-.13 subgroup for those who aren’t intimidated by lots of [[basis element]]s. As a dual-fifth system, it really shines, as both of its fifths have low enough [[harmonic entropy]] to sound [[consonant]] to many listeners, giving two consonant intervals for the price of one.		47edo can be treated as a [[dual-fifth system]] in the 2.3+.3-.5.7.13 subgroup, or the 3+.3-.5.7.11+.11-.13 subgroup for those who aren’t intimidated by lots of [[basis element]]s. As a dual-fifth system, it really shines, as both of its fifths have low enough [[harmonic entropy]] to sound [[consonant]] to many listeners, giving two consonant intervals for the price of one.

BudjarnLambeth: /* Odd harmonics */ + ''See regular temperament for more about what all this means and how to use it.''

2025-04-11T07:06:55Z

Odd harmonics: + ''See regular temperament for more about what all this means and how to use it.''

← Older revision		Revision as of 07:06, 11 April 2025
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	{{Harmonics in equal\|47}}		{{Harmonics in equal\|47}}

	47edo does a good job of approximating the 2.9.5.7.33.13.17.57.69 23-limit [[kN subgroups\|247 subgroup]] of the [[23-limit]], on which it tempers out the same commas as [[94edo]]. It provides a good tuning for [[baldy]] and [[silver]] and their relatives. It also provides a good tuning for the [[baseball]] temperament.		47edo does a good job of approximating the 2.9.5.7.33.13.17.57.69 23-limit [[kN subgroups\|247 subgroup]] of the [[23-limit]], on which it tempers out the same commas as [[94edo]]. It provides a good tuning for [[baldy]] and [[silver]] and their relatives. It also provides a good tuning for the [[baseball]] temperament. (''See [[regular temperament]] for more about what all this means and how to use it.'')

	47edo can be treated as a [[dual-fifth system]] in the 2.3+.3-.5.7.13 subgroup, or the 3+.3-.5.7.11+.11-.13 subgroup for those who aren’t intimidated by lots of [[basis element]]s. As a dual-fifth system, it really shines, as both of its fifths have low enough [[harmonic entropy]] to sound [[consonant]] to many listeners, giving two consonant intervals for the price of one.		47edo can be treated as a [[dual-fifth system]] in the 2.3+.3-.5.7.13 subgroup, or the 3+.3-.5.7.11+.11-.13 subgroup for those who aren’t intimidated by lots of [[basis element]]s. As a dual-fifth system, it really shines, as both of its fifths have low enough [[harmonic entropy]] to sound [[consonant]] to many listeners, giving two consonant intervals for the price of one.

FloraC: /* Intervals */ reduce cent values to one decimal place, per discussion on Discord

2025-03-31T09:01:14Z

Intervals: reduce cent values to one decimal place, per discussion on Discord

Show changes

FloraC: /* Theory */ improve wording

2025-03-31T08:58:03Z

Theory: improve wording

← Older revision		Revision as of 08:58, 31 March 2025
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	== Theory ==		== Theory ==
	47edo is the first edo that has two [[5L 2s\|diatonic]] perfect fifths. The fifth closest to [[3/2]] is 12.593-cent flat, unless you use the alternative fifth which is 12.939-cent sharp, similar to [[35edo]]. The soft diatonic scale generated from its flat fifth is so soft, with {{nowrap\|L/s {{=}} 7/6}}, that it stops sounding like [[meantone]] or even a [[flattone]] system like [[26edo]] or [[40edo]], but just sounds like a [[circulating temperament]] of [[7edo]]. It has therefore not aroused much interest, but its best approximation to [[9/8]] is actually quite good, one-third-of-a-cent sharp.		47edo is the first edo that has two [[5L 2s\|diatonic]] perfect fifths, as both fall between {{nowrap\|4\7 {{=}} 686{{c}}}} and {{nowrap\|3\5 {{=}} 720{{c}}}}. The fifth closest to [[3/2]] is 12.593-cent flat, unless you use the alternative fifth which is 12.939-cent sharp, similar to [[35edo]]. The soft diatonic scale generated from its flat fifth is so soft, with {{nowrap\|L:s {{=}} 7:6}}, that it stops sounding like [[meantone]] or even a [[flattone]] system like [[26edo]] or [[40edo]], but just sounds like a [[circulating temperament]] of [[7edo]]. The hard diatonic scale generated from its sharp fifth is extremely hard, with {{nowrap\|L:s {{=}} 9:1}}. It has therefore not aroused much interest, but its best approximation to [[9/8]] is actually quite good, one-third-of-a-cent sharp.

	~~47edo is a diatonic edo because its 5th falls between {{nowrap\|4\7 {{=}} 686{{c}}}} and {{nowrap\|3\5 {{=}} 720{{c}}}}, as does its alternate 5th as well.~~ 47edo is one of the most difficult diatonic edos to notate, because no other diatonic ~~edos 5th~~ is as ~~flat (see [[42edo]] for the opposite~~ extreme).		47edo is one of the most difficult diatonic edos to notate in [[native fifth notation\|native fifths]], because no other diatonic edo's fifth is as extreme.

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

FloraC: /* Theory */ expand

2025-03-23T09:50:00Z

Theory: expand

← Older revision		Revision as of 09:50, 23 March 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	47edo has a fifth ~~which~~ is 12.593-cent flat, unless you use the alternative fifth which is 12.939-cent sharp, similar to [[35edo]]. The soft ~~[[5L 2s\|~~diatonic]] scale generated from its flat fifth is so soft, with {{nowrap\|L/s {{=}} 7/6}}, that it stops sounding like [[meantone]] or even a [[flattone]] system like [[26edo]] or [[40edo]], but just sounds like a [[circulating temperament]] of [[7edo]]. It has therefore not aroused much interest, but its best approximation to [[9/8]] is actually quite good, one-third-of-a-cent sharp.		47edo is the first edo that has two [[5L 2s\|diatonic]] perfect fifths. The fifth closest to [[3/2]] is 12.593-cent flat, unless you use the alternative fifth which is 12.939-cent sharp, similar to [[35edo]]. The soft diatonic scale generated from its flat fifth is so soft, with {{nowrap\|L/s {{=}} 7/6}}, that it stops sounding like [[meantone]] or even a [[flattone]] system like [[26edo]] or [[40edo]], but just sounds like a [[circulating temperament]] of [[7edo]]. It has therefore not aroused much interest, but its best approximation to [[9/8]] is actually quite good, one-third-of-a-cent sharp.

	47edo is a diatonic edo because its 5th falls between {{nowrap\|4\7 {{=}} 686{{c}}}} and {{nowrap\|3\5 {{=}} 720{{c}}}}, as does its alternate 5th as well. 47edo is one of the most difficult diatonic edos to notate, because no other diatonic edos 5th is as flat (see [[42edo]] for the opposite extreme).		47edo is a diatonic edo because its 5th falls between {{nowrap\|4\7 {{=}} 686{{c}}}} and {{nowrap\|3\5 {{=}} 720{{c}}}}, as does its alternate 5th as well. 47edo is one of the most difficult diatonic edos to notate, because no other diatonic edos 5th is as flat (see [[42edo]] for the opposite extreme).

	=== Odd harmonics ===		=== Odd harmonics ===
			{{Harmonics in equal\|47}}

	47edo does a good job of approximating the 2.9.5.7.33.13.17.57.69 23-limit [[kN subgroups\|247 subgroup]] of the [[23-limit]], on which it tempers out the same commas as [[94edo]]. It provides a good tuning for [[baldy]] and [[silver]] and their relatives. It also provides a good tuning for the [[baseball]] temperament.		47edo does a good job of approximating the 2.9.5.7.33.13.17.57.69 23-limit [[kN subgroups\|247 subgroup]] of the [[23-limit]], on which it tempers out the same commas as [[94edo]]. It provides a good tuning for [[baldy]] and [[silver]] and their relatives. It also provides a good tuning for the [[baseball]] temperament.

	47edo can be treated as a [[dual-fifth system]] in the 2.3+.3-.5.7.13 subgroup, or the 3+.3-.5.7.11+.11-.13 subgroup for those who aren’t intimidated by lots of [[basis element]]s. As a dual-fifth system, it really shines, as both of its fifths have low enough [[harmonic entropy]] to sound [[consonant]] to many listeners, giving two consonant intervals for the price of one.		47edo can be treated as a [[dual-fifth system]] in the 2.3+.3-.5.7.13 subgroup, or the 3+.3-.5.7.11+.11-.13 subgroup for those who aren’t intimidated by lots of [[basis element]]s. As a dual-fifth system, it really shines, as both of its fifths have low enough [[harmonic entropy]] to sound [[consonant]] to many listeners, giving two consonant intervals for the price of one.
	~~{{Harmonics in equal\|47}}~~

	=== Subsets and supersets ===		=== Subsets and supersets ===
	47edo is the 15th [[prime edo]], following [[43edo]] and preceding [[53edo]].		47edo is the 15th [[prime edo]], following [[43edo]] and preceding [[53edo]], so it does not contain any nontrivial subset edos, though it contains [[47ed4]]. [[94edo]], which doubles it, corrects its approximations of harmonics 3 and 11 to near-just qualities.

	== Intervals ==		== Intervals ==

BudjarnLambeth: /* Scales */

2025-03-03T09:05:36Z

Scales

← Older revision		Revision as of 09:05, 3 March 2025
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	== Scales ==		== Scales ==
	* [[Negri in zeta-stretched 47edo]]		* [[Negri in zeta-stretched 47edo]]
	* Quasi-equal [[equiheptatonic]]: 7 6 7 7 7 6 7		* Quasi-equal [[equiheptatonic]] (Dorian): 7 6 7 7 7 6 7
	** Quasi-equiheptatonic minor pentatonic: 13 7 7 13 7		** Quasi-equiheptatonic minor pentatonic: 13 7 7 13 7
			* Quasi-equal [[equiheptatonic]] (Mixolydian): 7 7 6 7 7 6 7
	* Quasi-equal [[equipentatonic]]: 9 10 9 10 9		* Quasi-equal [[equipentatonic]]: 9 10 9 10 9
	* Sabertooth hexatonic: 3 9 3 13 12 7 (this is the original/default tuning; [[scalesmith\|designed]] for the "gold" and "platinum" timbres in [[Scale Workshop]])		* Sabertooth hexatonic: 3 9 3 13 12 7 (this is the original/default tuning; [[scalesmith\|designed]] for the "gold" and "platinum" timbres in [[Scale Workshop]])

BudjarnLambeth: /* Scales */

2025-03-03T08:48:21Z

Scales

← Older revision		Revision as of 08:48, 3 March 2025
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	** Quasi-equiheptatonic minor pentatonic: 13 7 7 13 7		** Quasi-equiheptatonic minor pentatonic: 13 7 7 13 7
	* Quasi-equal [[equipentatonic]]: 9 10 9 10 9		* Quasi-equal [[equipentatonic]]: 9 10 9 10 9
	* Sabertooth hexatonic: 3 9 3 13 12 7 (this is the original/default tuning; [[scalesmith\|designed]] for the "gold" ~~timbre~~ in [[Scale Workshop]])		* Sabertooth hexatonic: 3 9 3 13 12 7 (this is the original/default tuning; [[scalesmith\|designed]] for the "gold" and "platinum" timbres in [[Scale Workshop]])
	** Sabertooth pentatonic: 3 9 3 13 19 (this is the original/default tuning)		** Sabertooth pentatonic: 3 9 3 13 19 (this is the original/default tuning)
	** Sabertooth neutral: 3 11 14 11 8 (this is the original/default tuning)		** Sabertooth neutral: 3 11 14 11 8 (this is the original/default tuning)