5edo - Revision history

Vector at 06:43, 22 October 2026

2026-10-22T06:43:01Z

Vector at 11:30, 21 October 2026

2026-10-21T11:30:24Z

@@ Line 1: / Line 1: @@
 [[File:5edo comparison.png|thumb|5edo compared to other equipentatonic scales. Relative to just intonation, it narrows 7/4, 7/6, and 4/3, and widens 12/7, 8/7, and 3/2.]]
-'''5edo''' is the basic equipentatonic, where all the steps are tuned to be precisely equal. It features steps of (1200/5) = 240 cents.
+'''5edo''', or 5 equal divisions of the octave (sometimes called '''5-TET''' or '''5-tone equal temperament'''), is the [[Equal temperament|equal tuning]] featuring steps of (1200/5) = 240 [[Cent|cents]] exactly, 5 of which stack to the perfect octave [[2/1]].  It is the basic equipentatonic, where all five steps are tuned to be exactly equal.
 == Theory ==
 ==== Edostep interpretations ====
@@ Line 11: / Line 23: @@
 * 9/8
-==== JI approximation ====
+=== Intervals and notation ===
-edo is most obviously a 2.3.7 system (and this property carries to 5-form systems as a whole). although its 3 is audibly sharper than a just 3/2. There is no [[diatonic]] scale in 5edo; there are too few notes. However, 5edo interestingly is simple enough, and at least vaguely accurate enough to just intonation, that essentially any combination of notes taken from it sounds consonant to some extent.{{Harmonics in ED|5|23|edo=5|EDO=5|ET=5}}
+edo may be notated with any diatonic notation, as long as you keep in mind that E and F are the same note, and B and C are also the same note; the note sequence is usually C-D-E-G-A like a major pentatonic scale, and it is preferable to avoid accidentals. (However, it may be useful to some to treat the third step as E and F simultaneously; Kite calls this "eef".)
-==== Derivation ====
+[WIP]
 ==== Chords ====
@@ Line 24: / Line 100: @@
 Every possible octave-equivalent subset of 5edo is a MOS; 5edo is the largest edo with this property. There are seven such scales, up to rotation: 5edo, 1edo, 4-1, 3-2, 3-1-1, 2-2-1, and 2-1-1-1.
 == Blackwood temperament ==

Vector at 02:47, 9 May 2026

2026-05-09T02:47:01Z

← Older revision		Revision as of 02:47, 9 May 2026
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	==== Scales ====		==== Scales ====
	5edo is simple enough that the entire edo is usually used as a scale (although composer Hideya Amano avoids this by using subsets). The construction of scales from 5edo is usually not by taking subsets but by detuning the notes to reach one of the equipentatonic scales discussed elsewhere on the page. In fact, in real world musical cultures that use equipentatonic scales, they are almost never perfect 5edo.		5edo is simple enough that the entire edo is usually used as a scale (although composer Hideya Amano avoids this by using subsets such as [0 2 3 5]). The construction of scales from 5edo is usually not by taking subsets but by detuning the notes to reach one of the equipentatonic scales discussed elsewhere on the page. In fact, in real world musical cultures that use equipentatonic scales, they are almost never perfect 5edo.

			Every possible octave-equivalent subset of 5edo is a MOS; 5edo is the largest edo with this property. There are seven such scales, up to rotation: 5edo, 1edo, 4-1, 3-2, 3-1-1, 2-2-1, and 2-1-1-1.

	== Notation ==		== Notation ==

Vector at 02:54, 7 April 2026

2026-04-07T02:54:23Z

← Older revision		Revision as of 02:54, 7 April 2026
Line 24:		Line 24:

	== Notation ==		== Notation ==
	5edo may be notated with any diatonic notation, as long as you keep in mind that E and F are the same note, and B and C are also the same note; the note sequence is usually C-D-E-G-A like a major pentatonic scale, and it is preferable to avoid accidentals.		5edo may be notated with any diatonic notation, as long as you keep in mind that E and F are the same note, and B and C are also the same note; the note sequence is usually C-D-E-G-A like a major pentatonic scale, and it is preferable to avoid accidentals. (However, it may be useful to some to treat the third step as E and F simultaneously; Kite calls this "eef".)

	== Blackwood temperament ==		== Blackwood temperament ==

Vector at 14:40, 4 April 2026

2026-04-04T14:40:31Z

← Older revision		Revision as of 14:40, 4 April 2026
Line 12:		Line 12:

	==== JI approximation ====		==== JI approximation ====
	5edo is most obviously a 2.3.7 system (and this property carries to 5-form systems as a whole). although its 3 is audibly sharper than a just 3/2. There is no [[diatonic]] scale in 5edo; there are too few notes. However, 5edo interestingly is simple enough, and at least vaguely accurate enough to just intonation, that essentially any combination of notes taken from it sounds consonant to some extent.{{Harmonics in ED\|5\|7\|edo=5\|EDO=5\|ET=5}}		5edo is most obviously a 2.3.7 system (and this property carries to 5-form systems as a whole). although its 3 is audibly sharper than a just 3/2. There is no [[diatonic]] scale in 5edo; there are too few notes. However, 5edo interestingly is simple enough, and at least vaguely accurate enough to just intonation, that essentially any combination of notes taken from it sounds consonant to some extent.{{Harmonics in ED\|5\|23\|edo=5\|EDO=5\|ET=5}}

			==== Derivation ====
			5edo is derived by equalizing an equipentatonic scale.

	==== Chords ====		==== Chords ====
	Essentially any combination of notes in 5edo is a chord of some kind. Up to inversion and modulation, there are a total of 5 chords in 5edo, not counting a single note or the whole scale. Predictably, triadic harmony is rare in 5edo, and most harmonic systems in this tuning rely on drones or modulation.		Essentially any combination of notes in 5edo is a chord of some kind. Up to inversion and modulation, there are a total of 5 chords in 5edo, not counting a single note or the whole scale. Predictably, triadic harmony is rare in 5edo, and most harmonic systems in this tuning rely on drones or modulation.

Vector at 11:37, 26 March 2026

2026-03-26T11:37:10Z

← Older revision		Revision as of 11:37, 26 March 2026
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	[[File:5edo comparison.png\|thumb\|5edo compared to other equipentatonic scales.]]		[[File:5edo comparison.png\|thumb\|5edo compared to other equipentatonic scales. Relative to just intonation, it narrows 7/4, 7/6, and 4/3, and widens 12/7, 8/7, and 3/2.]]
	'''5edo''' is the basic equipentatonic, where all the steps are tuned to be precisely equal. It features steps of (1200/5) = 240 cents.		'''5edo''' is the basic equipentatonic, where all the steps are tuned to be precisely equal. It features steps of (1200/5) = 240 cents.

Vector at 11:36, 26 March 2026

2026-03-26T11:36:23Z

← Older revision		Revision as of 11:36, 26 March 2026
Line 1:		Line 1:
			[[File:5edo comparison.png\|thumb\|5edo compared to other equipentatonic scales.]]
	'''5edo''' is the basic equipentatonic, where all the steps are tuned to be precisely equal. It features steps of (1200/5) = 240 cents.		'''5edo''' is the basic equipentatonic, where all the steps are tuned to be precisely equal. It features steps of (1200/5) = 240 cents.

Vector at 04:18, 22 February 2026

2026-02-22T04:18:04Z

← Older revision		Revision as of 04:18, 22 February 2026
Line 24:		Line 24:
	Owing to 5edo's accuracy in 2.3.7 but failure to represent 5, a perfectly tuned 5edo can be taken as the 2.3.7 structure in a rank-2 temperament, with 5 (or any other prime) added as a [[generator]]. This is called blackwood temperament, and is supported by, most notably, [[15edo]]. Blackwood tempers out the [[diatonic semitone]], meaning that the 3-limit diatonic MOS scale is degenerate, collapsing to a 5-note scale. However, intervals of 5 are distinct, and may be used to generate the Zarlino [[diatonic]].		Owing to 5edo's accuracy in 2.3.7 but failure to represent 5, a perfectly tuned 5edo can be taken as the 2.3.7 structure in a rank-2 temperament, with 5 (or any other prime) added as a [[generator]]. This is called blackwood temperament, and is supported by, most notably, [[15edo]]. Blackwood tempers out the [[diatonic semitone]], meaning that the 3-limit diatonic MOS scale is degenerate, collapsing to a 5-note scale. However, intervals of 5 are distinct, and may be used to generate the Zarlino [[diatonic]].

	{{Cat\|Edos}}		{{Cat\|Edos}}{{Navbox EDO}}

Inthar at 00:38, 19 February 2026

2026-02-19T00:38:34Z

← Older revision		Revision as of 00:38, 19 February 2026
Line 1:		Line 1:
	~~== 5edo ==~~		'''5edo''' is the basic equipentatonic, where all the steps are tuned to be precisely equal. It features steps of (1200/5) = 240 cents.
	5edo is the basic equipentatonic, where all the steps are tuned to be precisely equal. It features steps of (1200/5) = 240 cents.

	=== Theory ===		== Theory ==

	===== Edostep interpretations =====		==== Edostep interpretations ====
	5edo's edostep has the following interpretations in the 2.3.7 subgroup:		5edo's edostep has the following interpretations in the 2.3.7 subgroup:

Line 11:		Line 10:
	* 9/8		* 9/8

	===== JI approximation =====		==== JI approximation ====
	5edo is most obviously a 2.3.7 system (and this property carries to 5-form systems as a whole). although its 3 is audibly sharper than a just 3/2. There is no [[diatonic]] scale in 5edo; there are too few notes. However, 5edo interestingly is simple enough, and at least vaguely accurate enough to just intonation, that essentially any combination of notes taken from it sounds consonant to some extent.{{Harmonics in ED\|5\|7\|edo=5\|EDO=5\|ET=5}}		5edo is most obviously a 2.3.7 system (and this property carries to 5-form systems as a whole). although its 3 is audibly sharper than a just 3/2. There is no [[diatonic]] scale in 5edo; there are too few notes. However, 5edo interestingly is simple enough, and at least vaguely accurate enough to just intonation, that essentially any combination of notes taken from it sounds consonant to some extent.{{Harmonics in ED\|5\|7\|edo=5\|EDO=5\|ET=5}}
	===== Chords =====		==== Chords ====
	Essentially any combination of notes in 5edo is a chord of some kind. Up to inversion and modulation, there are a total of 5 chords in 5edo, not counting a single note or the whole scale. Predictably, triadic harmony is rare in 5edo, and most harmonic systems in this tuning rely on drones or modulation.		Essentially any combination of notes in 5edo is a chord of some kind. Up to inversion and modulation, there are a total of 5 chords in 5edo, not counting a single note or the whole scale. Predictably, triadic harmony is rare in 5edo, and most harmonic systems in this tuning rely on drones or modulation.

	===== Scales =====		==== Scales ====
	5edo is simple enough that the entire edo is usually used as a scale (although composer Hideya Amano avoids this by using subsets). The construction of scales from 5edo is usually not by taking subsets but by detuning the notes to reach one of the equipentatonic scales discussed elsewhere on the page. In fact, in real world musical cultures that use equipentatonic scales, they are almost never perfect 5edo.		5edo is simple enough that the entire edo is usually used as a scale (although composer Hideya Amano avoids this by using subsets). The construction of scales from 5edo is usually not by taking subsets but by detuning the notes to reach one of the equipentatonic scales discussed elsewhere on the page. In fact, in real world musical cultures that use equipentatonic scales, they are almost never perfect 5edo.

	=== Notation ===		== Notation ==
	5edo may be notated with any diatonic notation, as long as you keep in mind that E and F are the same note, and B and C are also the same note; the note sequence is usually C-D-E-G-A like a major pentatonic scale, and it is preferable to avoid accidentals.		5edo may be notated with any diatonic notation, as long as you keep in mind that E and F are the same note, and B and C are also the same note; the note sequence is usually C-D-E-G-A like a major pentatonic scale, and it is preferable to avoid accidentals.

	=== Blackwood temperament ===		== Blackwood temperament ==
	Owing to 5edo's accuracy in 2.3.7 but failure to represent 5, a perfectly tuned 5edo can be taken as the 2.3.7 structure in a rank-2 temperament, with 5 (or any other prime) added as a [[generator]]. This is called blackwood temperament, and is supported by, most notably, [[15edo]]. Blackwood tempers out the [[diatonic semitone]], meaning that the 3-limit diatonic MOS scale is degenerate, collapsing to a 5-note scale. However, intervals of 5 are distinct, and may be used to generate the Zarlino [[diatonic]].		Owing to 5edo's accuracy in 2.3.7 but failure to represent 5, a perfectly tuned 5edo can be taken as the 2.3.7 structure in a rank-2 temperament, with 5 (or any other prime) added as a [[generator]]. This is called blackwood temperament, and is supported by, most notably, [[15edo]]. Blackwood tempers out the [[diatonic semitone]], meaning that the 3-limit diatonic MOS scale is degenerate, collapsing to a 5-note scale. However, intervals of 5 are distinct, and may be used to generate the Zarlino [[diatonic]].

	{{Cat\|Edos}}		{{Cat\|Edos}}

Lériendil: adding cat

2026-02-18T19:24:22Z

adding cat

← Older revision		Revision as of 19:24, 18 February 2026
Line 24:		Line 24:
	=== Blackwood temperament ===		=== Blackwood temperament ===
	Owing to 5edo's accuracy in 2.3.7 but failure to represent 5, a perfectly tuned 5edo can be taken as the 2.3.7 structure in a rank-2 temperament, with 5 (or any other prime) added as a [[generator]]. This is called blackwood temperament, and is supported by, most notably, [[15edo]]. Blackwood tempers out the [[diatonic semitone]], meaning that the 3-limit diatonic MOS scale is degenerate, collapsing to a 5-note scale. However, intervals of 5 are distinct, and may be used to generate the Zarlino [[diatonic]].		Owing to 5edo's accuracy in 2.3.7 but failure to represent 5, a perfectly tuned 5edo can be taken as the 2.3.7 structure in a rank-2 temperament, with 5 (or any other prime) added as a [[generator]]. This is called blackwood temperament, and is supported by, most notably, [[15edo]]. Blackwood tempers out the [[diatonic semitone]], meaning that the 3-limit diatonic MOS scale is degenerate, collapsing to a 5-note scale. However, intervals of 5 are distinct, and may be used to generate the Zarlino [[diatonic]].

			{{Cat\|Edos}}