7edo - Revision history

Vector at 14:40, 4 April 2026

2026-04-04T14:40:53Z

← Older revision		Revision as of 14:40, 4 April 2026
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	=== Scales ===		=== Scales ===
	7edo is the first edo to distinguish the modes of the [[pentic]] scale. However, it is still small enough that it is well-temperable into scales (specifically, those of the 7-form discussed elsewhere in this article). In real world musical cultures which use near-equal 7-note scales, perfect 7edo is almost never used.		7edo is the first edo to distinguish the modes of the [[pentic]] scale. However, it is still small enough that it is well-temperable into scales (specifically, those of the 7-form discussed elsewhere in this article). In real world musical cultures which use near-equal 7-note scales, perfect 7edo is almost never used.

			=== Derivation ===
			7edo is derived by equalizing an equiheptatonic scale.

	== Notation ==		== Notation ==

Vector at 11:57, 5 March 2026

2026-03-05T11:57:12Z

← Older revision		Revision as of 11:57, 5 March 2026
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	=== JI approximation ===		=== JI approximation ===
	7edo is, very crudely, a 2.3.5 system, and strength in 2.3.5 is generally what carries into other equiheptatonic scales. It can also be viewed in various other subgroups, most notably 2.3.13. The diatonic scale in 7edo is equivalent to every note in the tuning system; sharps and flats are not meaningful and all intervals are perfect.		7edo is, very crudely, a 2.3.5 system, and strength in 2.3.5 is generally what carries into other equiheptatonic scales. It can also be viewed in various other subgroups, most notably 2.3.13 and 2.3.11, and equiheptatonic temperaments can be found that represent those subgroups as well. The diatonic scale in 7edo is equivalent to every note in the tuning system; sharps and flats are not meaningful and all intervals are perfect.
	{{Harmonics in ED\|7\|31}}		{{Harmonics in ED\|7\|31}}
	{\| class="wikitable"		{\| class="wikitable"

Vector at 04:18, 22 February 2026

2026-02-22T04:18:20Z

← Older revision		Revision as of 04:18, 22 February 2026
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	7edo may be interpreted as ''Whitewood'' temperament, which tempers out the Pythagorean [[chromatic semitone]]. The most obvious rank-2 extension is to add a free generator corresponding to 7/4, resulting in a system containing multiple copies of 7edo separated by the interval 7/4. This extension is supported by [[21edo]], which, along with 14edo, supports the [[Diatonic\|omnidiatonic]] ternary diatonic scale.		7edo may be interpreted as ''Whitewood'' temperament, which tempers out the Pythagorean [[chromatic semitone]]. The most obvious rank-2 extension is to add a free generator corresponding to 7/4, resulting in a system containing multiple copies of 7edo separated by the interval 7/4. This extension is supported by [[21edo]], which, along with 14edo, supports the [[Diatonic\|omnidiatonic]] ternary diatonic scale.

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

Inthar at 00:39, 19 February 2026

2026-02-19T00:39:28Z

← Older revision		Revision as of 00:39, 19 February 2026
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			'''7edo''' is the basic equiheptatonic, where all the steps are tuned to be precisely equal. It features steps of (1200/7) ~= 171.4 cents.

	== ~~7edo~~ ==		== Theory ==
	~~7edo is the basic equiheptatonic, where all the steps are tuned to be precisely equal. It features steps of (1200/7) ~= 171.4 cents.~~

	~~=== Theory ===~~		=== Edostep interpretations ===

	===== Edostep interpretations =====
	7edo's edostep has the following interpretations in the 2.3.5 subgroup:		7edo's edostep has the following interpretations in the 2.3.5 subgroup:

Line 12:		Line 10:
	* 16/15 (the interval separating 5/4 and 4/3)		* 16/15 (the interval separating 5/4 and 4/3)

	===== JI approximation =====		=== JI approximation ===
	7edo is, very crudely, a 2.3.5 system, and strength in 2.3.5 is generally what carries into other equiheptatonic scales. It can also be viewed in various other subgroups, most notably 2.3.13. The diatonic scale in 7edo is equivalent to every note in the tuning system; sharps and flats are not meaningful and all intervals are perfect.		7edo is, very crudely, a 2.3.5 system, and strength in 2.3.5 is generally what carries into other equiheptatonic scales. It can also be viewed in various other subgroups, most notably 2.3.13. The diatonic scale in 7edo is equivalent to every note in the tuning system; sharps and flats are not meaningful and all intervals are perfect.
	{{Harmonics in ED\|7\|31}}		{{Harmonics in ED\|7\|31}}
Line 28:		Line 26:
	Diatonic thirds are bolded.		Diatonic thirds are bolded.

	===== Chords =====		=== Chords ===
	7edo features, for tertian triadic harmony, only a neutral chord [0 2 4] and the (rather discordant) sus chords [0 1 4] and [0 3 4]. Regardless, due to its triads and due to representing all seven degrees of the diatonic scale, it is the smallest edo where Western functional harmony works.		7edo features, for tertian triadic harmony, only a neutral chord [0 2 4] and the (rather discordant) sus chords [0 1 4] and [0 3 4]. Regardless, due to its triads and due to representing all seven degrees of the diatonic scale, it is the smallest edo where Western functional harmony works.

	===== Scales =====		=== Scales ===
	7edo is the first edo to distinguish the modes of the [[pentic]] scale. However, it is still small enough that it is well-temperable into scales (specifically, those of the 7-form discussed elsewhere in this article). In real world musical cultures which use near-equal 7-note scales, perfect 7edo is almost never used.		7edo is the first edo to distinguish the modes of the [[pentic]] scale. However, it is still small enough that it is well-temperable into scales (specifically, those of the 7-form discussed elsewhere in this article). In real world musical cultures which use near-equal 7-note scales, perfect 7edo is almost never used.

	=== Notation ===		== Notation ==
	In 7edo, pretty much all reasonable notation schemes collapse to ABCDEFG on A=440Hz. Accidentals are not used.		In 7edo, pretty much all reasonable notation schemes collapse to ABCDEFG on A=440Hz. Accidentals are not used.

	=== Whitewood temperament ===		== Whitewood temperament ==
	7edo may be interpreted as ''Whitewood'' temperament, which tempers out the Pythagorean [[chromatic semitone]]. The most obvious rank-2 extension is to add a free generator corresponding to 7/4, resulting in a system containing multiple copies of 7edo separated by the interval 7/4. This extension is supported by [[21edo]], which, along with 14edo, supports the [[Diatonic\|omnidiatonic]] ternary diatonic scale.		7edo may be interpreted as ''Whitewood'' temperament, which tempers out the Pythagorean [[chromatic semitone]]. The most obvious rank-2 extension is to add a free generator corresponding to 7/4, resulting in a system containing multiple copies of 7edo separated by the interval 7/4. This extension is supported by [[21edo]], which, along with 14edo, supports the [[Diatonic\|omnidiatonic]] ternary diatonic scale.

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

Lériendil: adding cat

2026-02-18T19:24:34Z

adding cat

← Older revision		Revision as of 19:24, 18 February 2026
Line 39:		Line 39:
	=== Whitewood temperament ===		=== Whitewood temperament ===
	7edo may be interpreted as ''Whitewood'' temperament, which tempers out the Pythagorean [[chromatic semitone]]. The most obvious rank-2 extension is to add a free generator corresponding to 7/4, resulting in a system containing multiple copies of 7edo separated by the interval 7/4. This extension is supported by [[21edo]], which, along with 14edo, supports the [[Diatonic\|omnidiatonic]] ternary diatonic scale.		7edo may be interpreted as ''Whitewood'' temperament, which tempers out the Pythagorean [[chromatic semitone]]. The most obvious rank-2 extension is to add a free generator corresponding to 7/4, resulting in a system containing multiple copies of 7edo separated by the interval 7/4. This extension is supported by [[21edo]], which, along with 14edo, supports the [[Diatonic\|omnidiatonic]] ternary diatonic scale.

			{{Cat\|Edos}}

Lériendil: Created page with " == 7edo == 7edo is the basic equiheptatonic, where all the steps are tuned to be precisely equal. It features steps of (1200/7) ~= 171.4 cents. === Theory === ===== Edostep interpretations ===== 7edo's edostep has the following interpretations in the 2.3.5 subgroup: * 9/8 (the diatonic major second) * 10/9 (the interval separating 9/8 and 5/4) * 16/15 (the interval separating 5/4 and 4/3) ===== JI approximation ===== 7edo is, very crudely, a 2.3.5 system, and streng..."

2026-02-18T19:23:52Z

Created page with " == 7edo == 7edo is the basic equiheptatonic, where all the steps are tuned to be precisely equal. It features steps of (1200/7) ~= 171.4 cents. === Theory === ===== Edostep interpretations ===== 7edo's edostep has the following interpretations in the 2.3.5 subgroup: * 9/8 (the diatonic major second) * 10/9 (the interval separating 9/8 and 5/4) * 16/15 (the interval separating 5/4 and 4/3) ===== JI approximation ===== 7edo is, very crudely, a 2.3.5 system, and streng..."

New page

== 7edo ==
7edo is the basic equiheptatonic, where all the steps are tuned to be precisely equal. It features steps of (1200/7) ~= 171.4 cents.

=== Theory ===

===== Edostep interpretations =====
7edo's edostep has the following interpretations in the 2.3.5 subgroup:

* 9/8 (the diatonic major second)
* 10/9 (the interval separating 9/8 and 5/4)
* 16/15 (the interval separating 5/4 and 4/3)

===== JI approximation =====
7edo is, very crudely, a 2.3.5 system, and strength in 2.3.5 is generally what carries into other equiheptatonic scales. It can also be viewed in various other subgroups, most notably 2.3.13. The diatonic scale in 7edo is equivalent to every note in the tuning system; sharps and flats are not meaningful and all intervals are perfect.
{{Harmonics in ED|7|31}}
{| class="wikitable"
|+Thirds in 7edo
!Quality
|'''Neutral'''
|-
!Cents
|'''343'''
|-
!Just interpretation
|'''11/9'''
|}
Diatonic thirds are bolded.

===== Chords =====
7edo features, for tertian triadic harmony, only a neutral chord [0 2 4] and the (rather discordant) sus chords [0 1 4] and [0 3 4]. Regardless, due to its triads and due to representing all seven degrees of the diatonic scale, it is the smallest edo where Western functional harmony works.

===== Scales =====
7edo is the first edo to distinguish the modes of the [[pentic]] scale. However, it is still small enough that it is well-temperable into scales (specifically, those of the 7-form discussed elsewhere in this article). In real world musical cultures which use near-equal 7-note scales, perfect 7edo is almost never used.

=== Notation ===
In 7edo, pretty much all reasonable notation schemes collapse to ABCDEFG on A=440Hz. Accidentals are not used.

=== Whitewood temperament ===
7edo may be interpreted as ''Whitewood'' temperament, which tempers out the Pythagorean [[chromatic semitone]]. The most obvious rank-2 extension is to add a free generator corresponding to 7/4, resulting in a system containing multiple copies of 7edo separated by the interval 7/4. This extension is supported by [[21edo]], which, along with 14edo, supports the [[Diatonic|omnidiatonic]] ternary diatonic scale.