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== Theory ==
== Theory ==
[[File:7edo scale.mp3|thumb|A chromatic 7edo scale on C.]]
[[File:7edo scale.mp3|thumb|A chromatic 7edo scale on C.]]
Equal-heptatonic scales are used in non-western music in African cultures as well as an integral part of early Chinese music<ref>[https://www.britannica.com/art/African-music Donald Keith Robotham and Gerhard Kubik, ''African music'', Encyclopedia Britannica]</ref>. 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).
Equal-heptatonic scales are used in non-western music in African cultures as well as an integral part of early Chinese music<ref>Robotham, Donald Keith and Gerhard Kubik. [https://www.britannica.com/art/African-music ''African music'', Encyclopedia Britannica.]</ref>. 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).


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]".
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]".
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{{Harmonics in equal|7}}
{{Harmonics in equal|7}}


<references/>
=== Observations ===
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.
 
The step from seventh to octave is too large for the leading tone.
 
It has often been stated that 7edo approximates tunings used in Thai classical music. This is a myth unsupported by empirical studies of the instruments.<ref>Garzoli, John. [http://iftawm.org/journal/oldsite/articles/2015b/Garzoli_AAWM_Vol_4_2.pdf "The Myth of Equidistance in Thai Tuning."]</ref>


== Intervals ==
== 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.
{| class="wikitable center-all"
{| class="wikitable"
|+ Intervals of 7edo
! rowspan="2" | [[Degree]]
! rowspan="2" | [[Cent]]s
! rowspan="2" | [[Interval region]]
! colspan="4" | Approximated [[JI]] intervals ([[error]] in [[¢]])
! rowspan="2" | Audio
|-
|-
!Interval
! [[3-limit]]
!Cents
! [[5-limit]]
!interval name
! [[7-limit]]
!The "neighborhood" of just intervals
! Other
!Audio
|-
|-
|0
| 0
|0.000
| 0
|unison / prime
| Unison (prime)
|exactly [[1/1]]
| [[1/1]] (just)
|[[File:0-0 unison.mp3|frameless]]
|
|
|
| [[File:0-0 unison.mp3|frameless]]
|-
|-
|1
| 1
|171.429
| 171.429
|second
| Submajor second
|6.424¢ from Ptolemy (neutral) second [[11/10]] <br> 3.215¢ from second [[54/49]] <br> -1.006¢ from the 29th subharmonic [[32/29]] <br> -10.975¢ from major second (small whole tone) [[10/9]]
|  
|[[File:0-171,43 second (7-EDO).mp3|frameless]]
| [[10/9]] (-10.975)
| [[54/49]] (+3.215)
| [[11/10]] (+6.424)<br>[[32/29]] (-1.006)
| [[File:0-171,43 second (7-EDO).mp3|frameless]]
|-
|-
|2
| 2
|342.857
| 342.857
|third
| Neutral third
|0.374¢ from neutral third [[39/32]]<br>-4.55¢ from neutral third [[11/9]]
|  
|[[File:piano_2_7edo.mp3]]
|
| [[128/105]] (+0.048)
| [[39/32]] (+0.374)<br>[[11/9]] (-4.551)
| [[File:piano_2_7edo.mp3]]
|-
|-
|3
| 3
|514.286
| 514.286
|fourth
| Fourth
|16.241¢ from just fourth [[4/3]] (498.045¢) <br> -5.265¢ from wide fourth [[27/20]]
| [[4/3]] (+16.241)
|[[File:0-514,29 fourth (7-EDO).mp3|frameless]]
| [[27/20]] (-5.265)
|
| [[35/26]] (-0.326)
| [[File:0-514,29 fourth (7-EDO).mp3|frameless]]
|-
|-
|4
| 4
|685.714
| 685.714
|fifth
| Fifth
|5.265 ¢ from narrow fifth [[40/27]] <br> -16.241¢ from just fifth [[3/2]] (701.955¢)
| [[3/2]] (-16.241)
|[[File:0-685,71 fifth (7-EDO).mp3|frameless]]
| [[40/27]] (+5.265)
|
| [[52/35]] (+0.326)
| [[File:0-685,71 fifth (7-EDO).mp3|frameless]]
|-
|-
|5
| 5
|857.143
| 857.143
|sixth
| Neutral sixth
|4.551¢ from neutral sixth [[18/11]]<br>-0.374¢ from neutral sixth [[64/39]]<br>-0.048¢ from (neutral sixth) 105/64
|  
|[[File:0-857,14 sixth (7-EDO).mp3|frameless]]
|
| [[105/64]] (-0.048)
| [[18/11]] (+4.551)<br>[[64/39]] (-0.374)
| [[File:0-857,14 sixth (7-EDO).mp3|frameless]]
|-
|-
|6
| 6
|1028.571
| 1028.571
|seventh
| Supraminor seventh
|10.975¢ from (Didymus) minor seventh [[9/5]] <br> -6.424¢ from neutral seventh [[20/11]] <br> -1.006¢ from the 29th harmonic [[29/16]] <br> -3.215¢ from seventh [[49/27]]
|  
| [[9/5]] (+10.975)
| [[49/27]] (-3.215)
| [[29/16]] (-1.006)<br>[[20/11]] (-6.424)
|[[File:0-1028,57 seventh (7-EDO).mp3|frameless]]
|[[File:0-1028,57 seventh (7-EDO).mp3|frameless]]
|-
|-
|7
| 7
| 1200
| 1200
|octave
| Octave
|exactly [[2/1]]
| [[2/1]] (just)
|[[File:0-1200 octave.mp3|frameless]]
|
|
|
| [[File:0-1200 octave.mp3|frameless]]
|}
|}


[[File:7ed2-001.svg|alt=alt : Your browser has no SVG support.]]
== Notation ==
The usual [[Musical notation|notation system]] for 7edo is the [[chain-of-fifths notation]], which is directly derived from the standard notation used in [[12edo]].
 
Sharps (#) and flats (b) have no effect in 7edo, because the apotome ([[2187/2048]]) is [[tempered out]]. Therefore, 7edo can be notated on a five-line staff without accidentals. There is no distinction between major or minor, so every interval has the [[interval quality]] "perfect" instead.


[[:File:7ed2-001.svg|7ed2-001.svg]]
{| class="wikitable center-all"
|+ Notation of 7edo
! rowspan="2" | [[Degree]]
! rowspan="2" | [[Cent]]s
! colspan="2" | [[Chain-of-fifths notation]]
|-
! [[5L 2s|Diatonic]] interval names
! Note names (on D)
|-
| 0
| 0
| '''Perfect unison (P1)'''
| '''D'''
|-
| 1
| 171.429
| '''Perfect second (P2)'''
| '''E'''
|-
| 2
| 342.857
| '''Perfect third (P3)'''
| '''F'''
|-
| 3
| 514.286
| '''Perfect fourth (P4)'''
| '''G'''
|-
| 4
| 685.714
| '''Perfect fifth (P5)'''
| '''A'''
|-
| 5
| 857.143
| '''Perfect sixth (P6)'''
| '''B'''
|-
| 6
| 1028.571
| '''Perfect seventh (P7)'''
| '''C'''
|-
| 7
| 1200
| '''Perfect octave (P8)'''
| '''D'''
|}


== Observations ==
In 7edo:
Subset of [[14edo]] and [[21edo]].  
* [[ups and downs notation]] is identical to circle-of-fifths notation;
* mixed and pure [[sagittal notation]] are identical to circle-of-fifths notation.


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


The step from seventh to octave is too large for the leading tone.
== Solfege ==
{| class="wikitable center-all"
|+ Solfege of 7edo
! [[Degree]]
! [[Cents]]
! Standard [[solfege]]<br>(movable do)
! [[Uniform solfege]]<br>(1 vowel)
|-
| 0
| 0
| Do
| Da
|-
| 1
| 171.429
| Re
| Ra
|-
| 2
| 342.857
| Mi
| Ma
|-
| 3
| 514.286
| Fa
| Fa
|-
| 4
| 685.714
| So
| Sa
|-
| 5
| 857.143
| La
| La
|-
| 6
| 1028.571
| Ti
| Ta
|-
| 7
| 1200
| Do
| Da
|}


It has often been stated that 7edo approximates tunings used in Thai classical music. This is a myth unsupported by empirical studies of the instruments.<ref>Garzoli, John. [http://iftawm.org/journal/oldsite/articles/2015b/Garzoli_AAWM_Vol_4_2.pdf "The Myth of Equidistance in Thai Tuning."]</ref>
== JI approximation ==
[[File:7ed2-001.svg|alt=alt : Your browser has no SVG support.]]


== Notation==
[[:File:7ed2-001.svg|7ed2-001.svg]]
[[William Lynch]] proposes using numbers 1 through 7 as the nominals of 7edo with sharp signs being possible to expand to 14edo or even 21edo.


== Regular temperament properties ==
== Regular temperament properties ==
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|-
|-
! [[Harmonic limit|Prime<br>Limit]]
! [[Harmonic limit|Prime<br>Limit]]
![[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
![[Ratio]]<ref group="note">Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
![[Monzo]]
![[Monzo]]
![[Cent]]s
![[Cent]]s
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|
|
|}
|}
<references />
<references group="note"/>


== Temperaments ==
== Temperaments ==
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== Ear training ==
== Ear training ==
7edo ear-training exercises by Alex Ness available [https://drive.google.com/folderview?id=0BwsXD8q2VCYUT3VEZUVmeVZUcmc&usp=drive_web#list here].
7edo ear-training exercises by Alex Ness available [https://drive.google.com/folderview?id=0BwsXD8q2VCYUT3VEZUVmeVZUcmc&usp=drive_web#list here].
== References ==
<references/>


[[Category:7-tone scales]]
[[Category:7-tone scales]]
[[Category:Macrotonal]]
[[Category:Macrotonal]]
Retrieved from "https://en.xen.wiki/w/7edo"