7edo: Difference between revisions

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| Monotonicity = 5

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'''7 equal divisions of the octave''' ('''7edo''') is the [[tuning system]] derived by dividing the [[octave]] into 7 equal steps of 171.4 [[cent]]s each, or the seventh root of 2. It is the fourth [[prime ~~edo~~]], after [[2edo]], [[3edo]] and [[5edo]]. It is the third [[The Riemann Zeta Function and Tuning #Zeta ~~edo~~ lists|zeta integral ~~edo~~]].

'''7 equal divisions of the octave''' ('''7edo''') is the [[tuning system]] derived by dividing the [[octave]] into 7 equal steps of 171.4 [[cent]]s each, or the seventh root of 2. It is the fourth [[prime EDO]], after [[2edo]], [[3edo]] and [[5edo]]. It is the third [[The Riemann Zeta Function and Tuning #Zeta EDO lists|zeta integral EDO]].

== Theory ==

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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[7]" just as the whole tone scale of [[12edo]] is known as "Hexe[6]".

Typically, 7edo exists as the tuning for pentatonic scales in traditional ~~thai~~ music with the other two pitches acting as auxiliary tones. However, it can be used as an interesting diatonic scale choice as well in tunings such as [[14edo]] or [[21edo]].

Typically, 7edo exists as the tuning for pentatonic scales in traditional Thai music with the other two pitches acting as auxiliary tones. However, it can be used as an interesting diatonic scale choice as well in tunings such as [[14edo]] or [[21edo]].

The seventh of 7edo is almost exactly the 29th harmonic ([[29/16]]), which can have a very agreeable sound with harmonic timbres. However it also finds itself nested between ratios such as 20/11 and 9/5, which gives it considerably higher [[harmonic entropy]] than [[7/4]], a much simpler overtone seventh.

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== Observations ==

Related in a lateral way to traditional Thai music. Subset of [[~~14edo|~~14edo]] and [[~~21edo|~~21edo]].

Related in a lateral way to traditional Thai music. Subset of [[14edo]] and [[21edo]].

There is a neutral feel between whole tone scale and major/minor diatonic scale. The second (171.429¢) works well as a basic step for melodic progression.

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== Temperaments ==

7edo is the first ~~edo~~ in which regular temperament theory starts to make sense as a way of subdividing the steps into [[~~mos~~]] scales, with three different ways of dividing it, although there is still quite a lot of ambiguity as each step can be considered as the sharp extreme of one temperament or the flat end of another. 1/7 can be considered the intersection of sharp [[porcupine]] and flat [[tetracot]] temperaments, as three steps makes a 4th and four a 5th. 2/7 can be interpreted as critically flat [[Mohajira]] or critically sharp [[amity]], and creates MOS's of 322 and 2221. 3/7 is on the intersection of [[meantone]] and [[mavila]], and has MOS's of 331 and 21211, making 7edo the first ~~edo~~ with a non-equalized, non-1Lns pentatonic ~~mos~~. This is in part because 7edo is a [[strict zeta ~~edo~~]] (close to low-complexity JI for its size), and is the second ~~edo~~ with a good fifth for its size (after [[5edo]]), the fifth serving as a generator for the ~~edo~~'s meantone and mavila interpertations.

7edo is the first EDO in which regular temperament theory starts to make sense as a way of subdividing the steps into [[MOS]] scales, with three different ways of dividing it, although there is still quite a lot of ambiguity as each step can be considered as the sharp extreme of one temperament or the flat end of another. 1/7 can be considered the intersection of sharp [[porcupine]] and flat [[tetracot]] temperaments, as three steps makes a 4th and four a 5th. 2/7 can be interpreted as critically flat [[Mohajira]] or critically sharp [[amity]], and creates MOS's of 322 and 2221. 3/7 is on the intersection of [[meantone]] and [[mavila]], and has MOS's of 331 and 21211, making 7edo the first EDO with a non-equalized, non-1Lns pentatonic MOS. This is in part because 7edo is a [[The Riemann zeta function and tuning #Zeta EDO lists|strict zeta EDO]] (close to low-complexity JI for its size), and is the second EDO with a good fifth for its size (after [[5edo]]), the fifth serving as a generator for the EDO's meantone and mavila interpertations.

== Music ==

*[https://soundcloud.com/overtoneshock/death-teasing-monolith-7-edo-premiere Death Giving Monolith] by [https://www.stephenweigelcomposerperformer.com/ Stephen Weigel] (dulcimer and voice)

*[https://xenharmonicgod.bandcamp.com/track/jingle-bells-7-edo Jingle Bells cover!] (recorded by Stephen Weigel)

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[[Category:Equal divisions of the octave]]

[[Category:7-tone scales]]

~~[[Category:Golden]]~~

[[Category:Listen]]

[[Category:Macrotonal]]

[[Category:Prime EDO]]

[[Category:Zeta]]

@@ Line 14: / Line 14: @@
 | Monotonicity = 5
 }}
-'''7 equal divisions of the octave''' ('''7edo''') is the [[tuning system]] derived by dividing the [[octave]] into 7 equal steps of 171.4 [[cent]]s each, or the seventh root of 2. It is the fourth [[prime edo]], after [[2edo]], [[3edo]] and [[5edo]]. It is the third [[The Riemann Zeta Function and Tuning #Zeta edo lists|zeta integral edo]].
+'''7 equal divisions of the octave''' ('''7edo''') is the [[tuning system]] derived by dividing the [[octave]] into 7 equal steps of 171.4 [[cent]]s each, or the seventh root of 2. It is the fourth [[prime EDO]], after [[2edo]], [[3edo]] and [[5edo]]. It is the third [[The Riemann Zeta Function and Tuning #Zeta EDO lists|zeta integral EDO]].
 == Theory ==
@@ Line 23: / Line 23: @@
 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[7]" just as the whole tone scale of [[12edo]] is known as "Hexe[6]".
-Typically, 7edo exists as the tuning for pentatonic scales in traditional thai music with the other two pitches acting as auxiliary tones. However, it can be used as an interesting diatonic scale choice as well in tunings such as [[14edo]] or [[21edo]].
+Typically, 7edo exists as the tuning for pentatonic scales in traditional Thai music with the other two pitches acting as auxiliary tones. However, it can be used as an interesting diatonic scale choice as well in tunings such as [[14edo]] or [[21edo]].
 The seventh of 7edo is almost exactly the 29th harmonic ([[29/16]]), which can have a very agreeable sound with harmonic timbres. However it also finds itself nested between ratios such as 20/11 and 9/5, which gives it considerably higher [[harmonic entropy]] than [[7/4]], a much simpler overtone seventh.
@@ Line 88: / Line 88: @@
 == Observations ==
-Related in a lateral way to traditional Thai music. Subset of [[14edo|14edo]] and [[21edo|21edo]].
+Related in a lateral way to traditional Thai music. Subset of [[14edo]] and [[21edo]].
 There is a neutral feel between whole tone scale and major/minor diatonic scale. The second (171.429¢) works well as a basic step for melodic progression.
@@ Line 296: / Line 296: @@
 == Temperaments ==
-edo is the first edo in which regular temperament theory starts to make sense as a way of subdividing the steps into [[mos]] scales, with three different ways of dividing it, although there is still quite a lot of ambiguity as each step can be considered as the sharp extreme of one temperament or the flat end of another. 1/7 can be considered the intersection of sharp [[porcupine]] and flat [[tetracot]] temperaments, as three steps makes a 4th and four a 5th. 2/7 can be interpreted as critically flat [[Mohajira]] or critically sharp [[amity]], and creates MOS's of 322 and 2221. 3/7 is on the intersection of [[meantone]] and [[mavila]], and has MOS's of 331 and 21211, making 7edo the first edo with a non-equalized, non-1Lns pentatonic mos. This is in part because 7edo is a [[strict zeta edo]] (close to low-complexity JI for its size), and is the second edo with a good fifth for its size (after [[5edo]]), the fifth serving as a generator for the edo's meantone and mavila interpertations.
+edo is the first EDO in which regular temperament theory starts to make sense as a way of subdividing the steps into [[MOS]] scales, with three different ways of dividing it, although there is still quite a lot of ambiguity as each step can be considered as the sharp extreme of one temperament or the flat end of another. 1/7 can be considered the intersection of sharp [[porcupine]] and flat [[tetracot]] temperaments, as three steps makes a 4th and four a 5th. 2/7 can be interpreted as critically flat [[Mohajira]] or critically sharp [[amity]], and creates MOS's of 322 and 2221. 3/7 is on the intersection of [[meantone]] and [[mavila]], and has MOS's of 331 and 21211, making 7edo the first EDO with a non-equalized, non-1Lns pentatonic MOS. This is in part because 7edo is a [[The Riemann zeta function and tuning #Zeta EDO lists|strict zeta EDO]] (close to low-complexity JI for its size), and is the second EDO with a good fifth for its size (after [[5edo]]), the fifth serving as a generator for the EDO's meantone and mavila interpertations.
 == Music ==
 *[https://soundcloud.com/overtoneshock/death-teasing-monolith-7-edo-premiere Death Giving Monolith] by [https://www.stephenweigelcomposerperformer.com/ Stephen Weigel] (dulcimer and voice)
 *[https://xenharmonicgod.bandcamp.com/track/jingle-bells-7-edo Jingle Bells cover!] (recorded by Stephen Weigel)
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 [[Category:Equal divisions of the octave]]
 [[Category:7-tone scales]]
-[[Category:Golden]]
 [[Category:Listen]]
 [[Category:Macrotonal]]
 [[Category:Prime EDO]]
 [[Category:Zeta]]