7edo: Difference between revisions

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== Theory ==

[[File:7edo scale.mp3|thumb|A chromatic 7edo scale on C.]]

7edo ~~can be thought~~ of as the ~~result of stacking seven~~ [[~~11/9~~]]~~'s on top of each other~~, and ~~then tempering to remove the~~ [[~~comma~~]] ~~{{monzo| -2 -14 0 0 7 }}~~. As a ~~temperament,~~ [[~~William Lynch~~]] ~~gives it the name "~~[[~~Neutron~~|~~Neutron[7]]]" just as the~~ whole tone scale ~~of [[12edo~~]] is ~~known~~ as "[[~~Hexe|Hexe[6]~~]]".

7edo unifies the seven modes of the [[5L 2s|diatonic]] scale – Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian – into a single one: 7edo can be used as an interesting diatonic scale choice as well in tunings such as [[14edo]] or [[21edo]]. There is a [[interval quality|neutral]] feel somewhere between a [[6edo|whole tone scale]] and major/minor diatonic scale. The second (171.429¢) works well as a basic step for melodic progression. The step from seventh to octave is too large as a leading tone. Possibly lending itself to a "sevenplus" scale similar to [[elevenplus]].

=== Prime harmonics ===

~~=== As an equalized diatonic scale ===~~

7edo unifies the seven [[5L 2s|diatonic]] scales - Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian - into a single one: 7edo can be used as an interesting diatonic scale choice as well in tunings such as [[14edo]] or [[21edo]].

~~There is a [[interval quality|neutral]] feel somewhere between a [[6edo|whole tone scale]] and major/minor diatonic scale. The second (171.429¢) works well as a basic step for melodic progression.~~

~~The step from seventh to octave is too large as a leading tone. Possibly lending itself to a “sevenplus” scale similar to [[elevenplus]].~~

=== In non-Western traditions ===

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7edo is the unique intersection of the temperaments of [[meantone]] (specifically [[3/4-comma meantone]]) and [[porcupine]].

~~The~~ [[Octave stretch|stretched-octaves]] tuning [[Ed257/128#7ed257/128|7ed257/128]] greatly improves ~~7edo’s~~ approximation of 3/1, 5/1 and 11/1, at the cost of slightly worsening 2/1 and 7/1, and greatly worsening 13/1. If one is hoping to use 7edo for [[11-limit]] harmonies, then 7ed257/128 is a good choice to make that easier.

7edo can be thought of as the result of stacking seven [[11/9]]'s on top of each other, and then tempering to remove the [[comma]] {{monzo| -2 -14 0 0 7 }}. As a temperament, [[William Lynch]] gives it the name "[[neutron|Neutron[7]]]" just as the whole tone scale of [[12edo]] is known as "[[hexe|Hexe[6]]]".

=== Octave stretch ===

The [[stretched and compressed tuning|stretched-octaves]] tuning [[Ed257/128 #7ed257/128|7ed257/128]] greatly improves 7edo's approximation of harmonics 3, 5 and 11, at the cost of slightly worsening 2 and 7, and greatly worsening 13. If one is hoping to use 7edo for [[11-limit]] harmonies, then 7ed257/128 is a good choice to make that easier.

The stretched 7edo tuning [[zpi|15zpi]] can also be used to improve 7edo’s approximation of JI in a similar way.

=== Subsets and supersets ===

7edo is the 4th [[prime edo]], after [[5edo]] and before [[11edo]]. Multiples such as [[14edo]], [[21edo]], … up to [[35edo]], share the same tuning of the perfect fifth as 7edo, while improving on other intervals.

7edo is the 4th [[prime edo]], after [[5edo]] and before [[11edo]]. It contains [[7ed4]]. Multiples such as [[14edo]], [[21edo]], … up to [[35edo]], share the same tuning of the perfect fifth as 7edo, while improving on other intervals.

== Intervals ==

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 == Theory ==
 [[File:7edo scale.mp3|thumb|A chromatic 7edo scale on C.]]
-edo can be thought of as the result of stacking seven [[11/9]]'s on top of each other, and then tempering to remove the [[comma]] {{monzo| -2 -14 0 0 7 }}. As a temperament, [[William Lynch]] gives it the name "[[Neutron|Neutron[7]]]" just as the whole tone scale of [[12edo]] is known as "[[Hexe|Hexe[6]]]".
+edo unifies the seven modes of the [[5L 2s|diatonic]] scale – Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian – into a single one: 7edo can be used as an interesting diatonic scale choice as well in tunings such as [[14edo]] or [[21edo]]. There is a [[interval quality|neutral]] feel somewhere between a [[6edo|whole tone scale]] and major/minor diatonic scale. The second (171.429¢) works well as a basic step for melodic progression. The step from seventh to octave is too large as a leading tone. Possibly lending itself to a "sevenplus" scale similar to [[elevenplus]].
 === Prime harmonics ===
 {{Harmonics in equal|7}}
-=== As an equalized diatonic scale ===
-edo unifies the seven [[5L 2s|diatonic]] scales - Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian - into a single one: 7edo can be used as an interesting diatonic scale choice as well in tunings such as [[14edo]] or [[21edo]].
-There is a [[interval quality|neutral]] feel somewhere between a [[6edo|whole tone scale]] and major/minor diatonic scale. The second (171.429¢) works well as a basic step for melodic progression.
-The step from seventh to octave is too large as a leading tone. Possibly lending itself to a “sevenplus” scale similar to [[elevenplus]].
 === In non-Western traditions ===
@@ Line 40: / Line 34: @@
 edo is the unique intersection of the temperaments of [[meantone]] (specifically [[3/4-comma meantone]]) and [[porcupine]].
-The [[Octave stretch|stretched-octaves]] tuning [[Ed257/128#7ed257/128|7ed257/128]] greatly improves 7edo’s approximation of 3/1, 5/1 and 11/1, at the cost of slightly worsening 2/1 and 7/1, and greatly worsening 13/1. If one is hoping to use 7edo for [[11-limit]] harmonies, then 7ed257/128 is a good choice to make that easier.
+edo can be thought of as the result of stacking seven [[11/9]]'s on top of each other, and then tempering to remove the [[comma]] {{monzo| -2 -14 0 0 7 }}. As a temperament, [[William Lynch]] gives it the name "[[neutron|Neutron[7]]]" just as the whole tone scale of [[12edo]] is known as "[[hexe|Hexe[6]]]".
+=== Octave stretch ===
+The [[stretched and compressed tuning|stretched-octaves]] tuning [[Ed257/128 #7ed257/128|7ed257/128]] greatly improves 7edo's approximation of harmonics 3, 5 and 11, at the cost of slightly worsening 2 and 7, and greatly worsening 13. If one is hoping to use 7edo for [[11-limit]] harmonies, then 7ed257/128 is a good choice to make that easier.
 The stretched 7edo tuning [[zpi|15zpi]] can also be used to improve 7edo’s approximation of JI in a similar way.
 === Subsets and supersets ===
-edo is the 4th [[prime edo]], after [[5edo]] and before [[11edo]]. Multiples such as [[14edo]], [[21edo]], … up to [[35edo]], share the same tuning of the perfect fifth as 7edo, while improving on other intervals.
+edo is the 4th [[prime edo]], after [[5edo]] and before [[11edo]]. It contains [[7ed4]]. Multiples such as [[14edo]], [[21edo]], … up to [[35edo]], share the same tuning of the perfect fifth as 7edo, while improving on other intervals.
 == Intervals ==