7edo: Difference between revisions

Line 7:

{{Infobox ET

| Prime factorization = 7 (prime)

| Step size = 171.~~429¢~~

| Step size = 171.42857¢

| ~~Fifth~~ = 4\7 = ~~685.714¢~~

| P5 = 4\7 = 686¢

| ~~2nd~~ = 1\7 = 171¢

| M2 = 1\7 = 171¢

| ~~Augmented 1sn~~ = 0\7 = 0¢

| m2 = 1\7 = 171¢

| A1 = 0\7 = 0¢

}}

'''7-edo''' or "Neutral diatonic" divides the 1200-cent [[octave]] into 7 equal parts, making its smallest interval [[cent|171.428¢]], or the seventh root of 2. It is the fourth [[prime numbers|prime]] edo, after [[2edo]], [[3edo]] and [[5edo]]. It is the third [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral edo]].

==Theory==

'''7 EDO''' or "Neutral diatonic" divides the 1200-cent [[octave]] into 7 equal parts, making its smallest interval [[cent|171.428¢]], or the seventh root of 2. It is the fourth [[prime EDO]], after [[2 EDO]], [[3 EDO]] and [[5 EDO]]. It is the third [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral EDO]].

== Theory ==

{| class="wikitable center-all"

! colspan="2" |

! colspan="2" |

!prime 2

! prime 2

! prime 3

!prime 5

! prime 5

!prime 7

! prime 7

!prime 11

! prime 11

!prime 13

! prime 13

|-

! rowspan="2" |error

! rowspan="2" | error

!absolute (¢)

! absolute (¢)

|0.0

| 0.0

| -16.2

| -43.5

| +59.7

| -37.0

| +16.6

|-

![[Relative error|relative]] (%)

! [[Relative error|relative]] (%)

|0

| 0

| -9

| -25

| +35

| -22

| +10

|-

! colspan="2" |[[nearest edomapping]]

! colspan="2" | [[nearest edomapping]]

|7

| 7

|4

| 4

|2

| 2

|6

| 6

|3

| 3

|5

| 5

|-

! colspan="2" |[[fifthspan]]

! colspan="2" | [[fifthspan]]

|0

| 0

| +1

| -3

| -2

| -1

| +3

|}

Equal-heptatonic scales are used in non-western music in African cultures as well as an integral part of early Thai and early Chinese music. It has been speculated in "Indian music:history and structure", that the Indian three-sruti interval of 165 cents is close enough to be mistaken for 171 cents. (or 1.71 semitones).

Equal-heptatonic scales are used in non-western music in African cultures as well as an integral part of early Thai and early Chinese music. Also Georgian music seems to be based on near-equal 7-step scales. It has been speculated in "Indian music:history and structure", that the Indian three-sruti interval of 165 cents is close enough to be mistaken for 171 cents. (or 1.71 semitones).

7~~-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 12 ET is known as "Hexe[6]".

7 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 12 ET is known as "Hexe[6]".

Typically, 7-~~edo~~ 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 14 EDO or 21 EDO.

Typically, 7-EDO 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 [[14 EDO]] or [[21 EDO]].

The seventh of 7-edo 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|harmonic entropy]] than [[Harmonic seventh|7/4]], a much simpler overtone seventh.

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==Intervals==

~~7edo~~ can be notated on a five-line staff without accidentals. There is no distinction between Major or Minor; each pitch class is unique.

7 EDO can be notated on a five-line staff without accidentals. There is no distinction between Major or Minor; each pitch class is unique.

{| class="wikitable"

|-

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==Observations==

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

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

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

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== Notation==

[[William Lynch]] proposes using numbers 1 through 7 as the nominals of 7 ET with sharp signs being possible to expand to [[~~14edo|~~14 EDO]] or even [[~~21edo|~~21 EDO]].

[[William Lynch]] proposes using numbers 1 through 7 as the nominals of 7 ET with sharp signs being possible to expand to [[14 EDO]] or even [[21 EDO]].

==Commas==

@@ Line 7: / Line 7: @@
 {{Infobox ET
 | Prime factorization = 7 (prime)
-| Step size = 171.429¢
+| Step size = 171.42857¢
-| Fifth = 4\7 = 685.714¢
+| P5 = 4\7 = 686¢
-| 2nd = 1\7 = 171¢
+| M2 = 1\7 = 171¢
-| Augmented 1sn = 0\7 = 0¢
+| m2 = 1\7 = 171¢
+| A1 = 0\7 = 0¢
 }}
-'''7-edo''' or "Neutral diatonic" divides the 1200-cent [[octave]] into 7 equal parts, making its smallest interval [[cent|171.428¢]], or the seventh root of 2. It is the fourth [[prime numbers|prime]] edo, after [[2edo]], [[3edo]] and [[5edo]]. It is the third [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral edo]].
-==Theory==
+'''7 EDO''' or "Neutral diatonic" divides the 1200-cent [[octave]] into 7 equal parts, making its smallest interval [[cent|171.428¢]], or the seventh root of 2. It is the fourth [[prime EDO]], after [[2 EDO]], [[3 EDO]] and [[5 EDO]]. It is the third [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral EDO]].
+== Theory ==
 {| class="wikitable center-all"
-! colspan="2" |<!-- empty cell -->
+! colspan="2" | <!-- empty cell -->
-!prime 2
+! prime 2
 ! prime 3
-!prime 5
+! prime 5
-!prime 7
+! prime 7
-!prime 11
+! prime 11
-!prime 13
+! prime 13
 |-
-! rowspan="2" |error
+! rowspan="2" | error
-!absolute (¢)
+! absolute (¢)
-|0.0
+| 0.0
-|  -16.2
+| -16.2
 | -43.5
 | +59.7
 | -37.0
-|  +16.6
+| +16.6
 |-
-![[Relative error|relative]] (%)
+! [[Relative error|relative]] (%)
-|0
+| 0
 | -9
-|  -25
+| -25
 | +35
 | -22
 | +10
 |-
-! colspan="2" |[[nearest edomapping]]
+! colspan="2" | [[nearest edomapping]]
-|7
+| 7
-|4
+| 4
-|2
+| 2
-|6
+| 6
-|3
+| 3
-|5
+| 5
 |-
-! colspan="2" |[[fifthspan]]
+! colspan="2" | [[fifthspan]]
-|0
+| 0
 | +1
 | -3
-|  -2
+| -2
 | -1
 | +3
 |}
-Equal-heptatonic scales are used in non-western music in African cultures as well as an integral part of early Thai and early Chinese music. It has been speculated in "Indian music:history and structure", that the Indian three-sruti interval of 165 cents is close enough to be mistaken for 171 cents. (or 1.71 semitones).
+Equal-heptatonic scales are used in non-western music in African cultures as well as an integral part of early Thai and early Chinese music. Also Georgian music seems to be based on near-equal 7-step scales. It has been speculated in "Indian music:history and structure", that the Indian three-sruti interval of 165 cents is close enough to be mistaken for 171 cents. (or 1.71 semitones).
--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 12 ET is known as "Hexe[6]".
+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 12 ET is known as "Hexe[6]".
-Typically, 7-edo 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 14 EDO or 21 EDO.
+Typically, 7-EDO 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 [[14 EDO]] or [[21 EDO]].
 The seventh of 7-edo 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|harmonic entropy]] than [[Harmonic seventh|7/4]], a much simpler overtone seventh.
@@ Line 73: / Line 76: @@
 ==Intervals==
-edo can be notated on a five-line staff without accidentals. There is no distinction between Major or Minor; each pitch class is unique.
+EDO can be notated on a five-line staff without accidentals. There is no distinction between Major or Minor; each pitch class is unique.
 {| class="wikitable"
 |-
@@ Line 131: / Line 134: @@
 ==Observations==
-Related in a lateral way to traditional Thai music. Subset of [[14edo|14 EDO]] and [[21edo|21 EDO]].
+Related in a lateral way to traditional Thai music. Subset of [[14 EDO]] and [[21 EDO]].
 There is a neutral feel between whole tone scale and major/minor diatonic scale. The second (171.429 c) works well as a basic step for melodic progression.
@@ Line 138: / Line 141: @@
 == Notation==
-[[William Lynch]] proposes using numbers 1 through 7 as the nominals of 7 ET with sharp signs being possible to expand to [[14edo|14 EDO]] or even [[21edo|21 EDO]].
+[[William Lynch]] proposes using numbers 1 through 7 as the nominals of 7 ET with sharp signs being possible to expand to [[14 EDO]] or even [[21 EDO]].
 ==Commas==