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| Step size = 171.429¢
| Step size = 171.429¢
| Fifth = 4\7 = 685.714¢
| Fifth = 4\7 = 685.714¢
| Major 2nd = 1\7 = 171¢
| 2nd = 1\7 = 171¢
| Minor 2nd = 1\7 = 171¢
| Augmented 1sn = 0\7 = 0¢
| Augmented 1sn = 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]].
'''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 ==
==Theory==
{| class="wikitable center-all"
{| class="wikitable center-all"
! colspan="2" | <!-- empty cell -->
! colspan="2" |<!-- empty cell -->
! prime 2
!prime 2
! prime 3
! 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
| -43.5
| +59.7
| +59.7
| -37.0
| -37.0
| +16.6
| +16.6
|-
|-
! [[Relative error|relative]] (%)
![[Relative error|relative]] (%)
| 0
|0
| -9
| -9
| -25
| -25
| +35
| +35
| -22
| -22
| +10
| +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
| +1
| -3
| -3
| -2
| -2
| -1
| -1
| +3
| +3
Line 73: Line 72:
A Thai xylophone measured by Morton (1974) "varied only plus or minus 5 cents," from 7-TET. A Ugandan Chopi xylophone measured by Haddon (1952) was also tuned to this system.
A Thai xylophone measured by Morton (1974) "varied only plus or minus 5 cents," from 7-TET. A Ugandan Chopi xylophone measured by Haddon (1952) was also tuned to this system.


== 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.
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"
{| class="wikitable"
|-
|-
! Interval
!Interval
! Cents
!Cents
! interval name
!interval name
! The "neighborhood" of just intervals
!The "neighborhood" of just intervals
|-
|-
| 0
|0
|0.000
|0.000
| unison / prime
|unison / prime
| exactly [[1/1]]
|exactly [[1/1]]
|-
|-
| 1
|1
| 171.429
|171.429
| second
|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]]
|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]]
|-
|-
| 2
|2
| 342.857
|342.857
| third
|third
| 0.374¢ from neutral third [[39/32]]
|0.374¢ from neutral third [[39/32]]
-4.55¢ from neutral third [[11/9]]
-4.55¢ from neutral third [[11/9]]
|-
|-
| 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]]
|16.241¢ from just fourth [[4/3]] (498.045¢) <br /> -5.265¢ from wide fourth [[27/20]]
|-
|-
| 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¢)
|5.265 ¢ from narrow fifth [[40/27]] <br /> -16.241¢ from just fifth [[3/2]] (701.955¢)
|-
|-
| 5
|5
| 857.143
|857.143
| sixth
|sixth
| 4.551¢ from neutral sixth [[18/11]]
|4.551¢ from neutral sixth [[18/11]]
-0.374¢ from neutral sixth [[64/39]]
-0.374¢ from neutral sixth [[64/39]]


-0.048¢ from (neutral sixth) 105/64
-0.048¢ from (neutral sixth) 105/64
|-
|-
| 6
|6
| 1028.571
| 1028.571
| seventh
|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]]
|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]]
|-
|-
| 7
|7
| 1200
| 1200
| octave
|octave
| exactly [[2/1]]
|exactly [[2/1]]
|}
|}


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[[:File:7ed2-001.svg|7ed2-001.svg]]
[[:File:7ed2-001.svg|7ed2-001.svg]]


== Observations ==
==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 [[14edo|14 EDO]] and [[21edo|21 EDO]].  


Line 138: Line 137:
The step from seventh to octave is too large for the leading tone.
The step from seventh to octave is too large for the leading tone.


== Notation ==
== 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 [[14edo|14 EDO]] or even [[21edo|21 EDO]].


== Commas ==
==Commas==
7 EDO [[tempers out]] the following [[comma]]s. This assumes [[val]] {{val| 7 11 16 20 24 26 }}.  
7 EDO [[tempers out]] the following [[comma]]s. This assumes [[val]] {{val| 7 11 16 20 24 26 }}.  


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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>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Monzo]]
![[Monzo]]
! [[Cent]]s
![[Cent]]s
! [[Color notation/Temperament Names|Color Name]]
![[Color notation/Temperament Names|Color Name]]
! Name(s)
!Name(s)
|-
|-
| 3
|3
| [[2187/2048]]
|[[2187/2048]]
| {{monzo| -11 7 }}
|{{monzo| -11 7 }}
| 113.69
|113.69
| Lawa
|Lawa
| Apotome, Pythagorean chromatic semitone
|Apotome, Pythagorean chromatic semitone
|-
|-
| 5
|5
| [[135/128]]
|[[135/128]]
| {{monzo| -7 3 1 }}
| {{monzo| -7 3 1 }}
| 92.18
|92.18
| Layobi
|Layobi
| Major chroma, major limma, pelogic comma
|Major chroma, major limma, pelogic comma
|-
|-
| 5
| 5
| [[25/24]]
|[[25/24]]
| {{monzo| -3 -1 2 }}
|{{monzo| -3 -1 2 }}
| 70.67
|70.67
| Yoyo
|Yoyo
| Classic chromatic semitone, dicot comma
|Classic chromatic semitone, dicot comma
|-
|-
| 5
|5
| [[250/243]]
|[[250/243]]
| {{monzo| 1 -5 3 }}
|{{monzo| 1 -5 3 }}
| 49.17
|49.17
| Triyo
|Triyo
| Maximal diesis, porcupine comma
|Maximal diesis, porcupine comma
|-
|-
| 5
|5
| [[20000/19683]]
|[[20000/19683]]
| {{monzo| 5 -9 4 }}
|{{monzo| 5 -9 4 }}
| 27.66
|27.66
| Saquadyo
|Saquadyo
| Minimal diesis, tetracot comma
|Minimal diesis, tetracot comma
|-
|-
| 5
|5
| [[81/80]]
| [[81/80]]
| {{monzo| -4 4 -1 }}
|{{monzo| -4 4 -1 }}
| 21.51
|21.51
| Gu
|Gu
| Syntonic comma, Didymus comma, meantone comma
|Syntonic comma, Didymus comma, meantone comma
|-
|-
| 5
|5
| [[1600000/1594323|(14 digits)]]
|[[1600000/1594323|(14 digits)]]
| {{monzo| 9 -13 5 }}
|{{monzo| 9 -13 5 }}
| 6.15
|6.15
| Saquinyo
|Saquinyo
| [[Amity comma]]
|[[Amity comma]]
|-
|-
| 7
| 7
| [[36/35]]
|[[36/35]]
| {{monzo| 2 2 -1 -1 }}
|{{monzo| 2 2 -1 -1 }}
| 48.77
|48.77
| Rugu
| Rugu
| Septimal quartertone
|Septimal quartertone
|-
|-
| 7
|7
| [[525/512]]
|
| {{monzo| -9 1 2 1 }}
[[525/512]]
| 43.41
|{{monzo| -9 1 2 1 }}
| Lazoyoyo
|43.41
| Avicennma, Avicenna's enharmonic diesis
|Lazoyoyo
|Avicennma, Avicenna's enharmonic diesis
|-
|-
| 7
|7
| [[64/63]]
|[[64/63]]
| {{monzo| 6 -2 0 -1 }}
|{{monzo| 6 -2 0 -1 }}
| 27.26
|27.26
| Ru
| Ru
| Septimal comma, Archytas' comma, Leipziger Komma
|Septimal comma, Archytas' comma, Leipziger Komma
|-
|-
| 7
|7
| [[875/864]]
| [[875/864]]
| {{monzo| -5 -3 3 1 }}
|{{monzo| -5 -3 3 1 }}
| 21.90
|21.90
| Zotriyo
| Zotriyo
| Keema
|Keema
|-
|-
| 7
|7
| [[5120/5103]]
|[[5120/5103]]
| {{monzo| 10 -6 1 -1 }}
|{{monzo| 10 -6 1 -1 }}
| 5.76
|5.76
| Saruyo
| Saruyo
| Hemifamity
| Hemifamity
|-
|-
| 7
| 7
| [[6144/6125]]
|[[6144/6125]]
| {{monzo| 11 1 -3 -2 }}
|{{monzo| 11 1 -3 -2 }}
| 5.36
|5.36
| Sarurutriyo
| Sarurutriyo
| Porwell
| Porwell
|-
|-
| 7
|7
| [[4375/4374]]
|[[4375/4374]]
| {{monzo| -1 -7 4 1 }}
|{{monzo| -1 -7 4 1 }}
| 0.40
|0.40
| Zoquadyo
|Zoquadyo
| Ragisma
|Ragisma
|-
|-
| 7
|7
| <abbr title="140737488355328/140710042265625">(30 digits)</abbr>
|<abbr title="140737488355328/140710042265625">(30 digits)</abbr>
| {{monzo| 47 -7 -7 -7 }}
|{{monzo| 47 -7 -7 -7 }}
| 0.34
|0.34
| Trisa-rugu
|Trisa-rugu
| [[Akjaysma]], 5\7 octave comma
|[[Akjaysma]], 5\7 octave comma
|-
|-
| 11
|11
| [[100/99]]
|[[100/99]]
| {{monzo| 2 -2 2 0 -1 }}
|{{monzo| 2 -2 2 0 -1 }}
| 17.40
|17.40
| Luyoyo
|Luyoyo
| Ptolemisma
| Ptolemisma
|-
|-
| 11
|11
| [[121/120]]
|
| {{monzo| -3 -1 -1 0 2 }}
[[121/120]]
| 14.37
|{{monzo| -3 -1 -1 0 2 }}
| Lologu
|14.37
|Lologu
| Biyatisma
| Biyatisma
|-
|-
| 11
| 11
| [[176/175]]
|[[176/175]]
| {{monzo| 4 0 -2 -1 1 }}
|{{monzo| 4 0 -2 -1 1 }}
| 9.86
|9.86
| Lurugugu
|Lurugugu
| Valinorsma
|Valinorsma
|-
|-
| 11
|11
| [[65536/65219]]
| [[65536/65219]]
| {{monzo| 16 0 0 -2 -3 }}
|{{monzo| 16 0 0 -2 -3 }}
| 8.39
|8.39
| Satrilu-aruru
|Satrilu-aruru
| Orgonisma
|Orgonisma
|-
|-
| 11
|11
| [[243/242]]
|[[243/242]]
| {{monzo| -1 5 0 0 -2 }}
|{{monzo| -1 5 0 0 -2 }}
| 7.14
|7.14
| Lulu
|Lulu
| Rastma
|Rastma
|-
|-
| 11
|11
| [[385/384]]
|[[385/384]]
| {{monzo| -7 -1 1 1 1 }}
|{{monzo| -7 -1 1 1 1 }}
| 4.50
|4.50
| Lozoyo
|Lozoyo
| Keenanisma
|Keenanisma
|-
|-
| 11
| 11
| [[4000/3993]]
|
| {{monzo| 5 -1 3 0 -3 }}
[[4000/3993]]
| 3.03
|{{monzo| 5 -1 3 0 -3 }}
| Triluyo
|3.03
|Triluyo
| Wizardharry
| Wizardharry
|}
|}
<references/>
<references />
 
==Pathological Modes==
2 1 1 1 1 1 1 [[1L 5s]] MOS


== Music ==
==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://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)
*[https://xenharmonicgod.bandcamp.com/track/jingle-bells-7-edo Jingle Bells cover!] (recorded by Stephen Weigel)
* [http://sethares.engr.wisc.edu/mp3s/PagansRevenge.mp3 Pagan's Revenge] by [[Bill Sethares]] (synthetic gamelan)
*[http://sethares.engr.wisc.edu/mp3s/PagansRevenge.mp3 Pagan's Revenge] by [[Bill Sethares]] (synthetic gamelan)
* [http://www.akjmusic.com/audio/i_dream_of_tibet.mp3 I dream of Tibet] {{dead link}} by [http://www.akjmusic.com/works.html Aaron K. Johnson] (electronic swirlies) {{dead link}}
*[http://www.akjmusic.com/audio/i_dream_of_tibet.mp3 I dream of Tibet] {{dead link}} by [http://www.akjmusic.com/works.html Aaron K. Johnson] (electronic swirlies) {{dead link}}
* [http://micro.soonlabel.com/gene_ward_smith/Others/Walker/Seven%20Equal%20Trio.mp3 Seven Equal Trio] by [http://robertinventor.tripod.com/tunes/tunes.htm#7_equal_trio Robert Walker] ((synth) violin, viola, glockenspiel)
*[http://micro.soonlabel.com/gene_ward_smith/Others/Walker/Seven%20Equal%20Trio.mp3 Seven Equal Trio] by [http://robertinventor.tripod.com/tunes/tunes.htm#7_equal_trio Robert Walker] ((synth) violin, viola, glockenspiel)
* [http://micro.soonlabel.com/gene_ward_smith/Others/Hunt/7ET.mp3 Two-part Invention in 7TET] by [http://www.h-pi.com/musicFiles.html Aaron Hunt]
*[http://micro.soonlabel.com/gene_ward_smith/Others/Hunt/7ET.mp3 Two-part Invention in 7TET] by [http://www.h-pi.com/musicFiles.html Aaron Hunt]
* [http://www.uvnitr.cz/flaoyg/flao_yg/pavouci.html Pavouci], [http://www.uvnitr.cz/flaoyg/flao_yg/kelt.html Kelt] by Milan Guštar
*[http://www.uvnitr.cz/flaoyg/flao_yg/pavouci.html Pavouci], [http://www.uvnitr.cz/flaoyg/flao_yg/kelt.html Kelt] by Milan Guštar
* [http://www.seraph.it/dep/det/7edo%20dance.mp3 7edo Dance] ''by [[Carlo_Serafini|Carlo Serafini]]''
*[http://www.seraph.it/dep/det/7edo%20dance.mp3 7edo Dance] ''by [[Carlo Serafini]]''
* ''[https://www.youtube.com/watch?v=IQ4hY41TvAo&feature=youtu.be Nightfire (video)]'' by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/ac7b7a4c36a28d28f624fc2066b98f3c-236.html blog entry])
*''[https://www.youtube.com/watch?v=IQ4hY41TvAo&feature=youtu.be Nightfire (video)]'' by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/ac7b7a4c36a28d28f624fc2066b98f3c-236.html blog entry])
* [http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/06%20-%206.%207%20octave.mp3 Comets Over Flatland 6] by [[Randy_Winchester|Randy Winchester]]
*[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/06%20-%206.%207%20octave.mp3 Comets Over Flatland 6] by [[Randy Winchester]]
* [http://media.soundcloud.com/stream/IUcgFYhtu3Rk?stream_token=4QIvd Sävelmä] {{dead link}} by [http://soundcloud.com/juhani-nuorvala/s-velm-long-version Sävelmä (long version)] by [[Juhani Nuorvala]]
*[http://media.soundcloud.com/stream/IUcgFYhtu3Rk?stream_token=4QIvd Sävelmä] {{dead link}} by [http://soundcloud.com/juhani-nuorvala/s-velm-long-version Sävelmä (long version)] by [[Juhani Nuorvala]]
* [https://soundcloud.com/santiagocosentino/rock-in-7edo Rock in 7edo by Santiago Cosentino] {{dead link}}
*[https://soundcloud.com/santiagocosentino/rock-in-7edo Rock in 7edo by Santiago Cosentino] {{dead link}}
* [https://soundcloud.com/user-544568549/zhaleyka-7-edo Zhaleyka] by [[Dmitry Bazhenov]]
*[https://soundcloud.com/user-544568549/zhaleyka-7-edo Zhaleyka] by [[Dmitry Bazhenov]]
* [https://youtu.be/cBSXRZUwWoQ Clockworkian] by [[User:Userminusone|Userminusone]]
*[https://youtu.be/puVWio6755c Clockworkian] by [[User:Userminusone|Userminusone]]


== Ear Training ==
==Ear Training==
7 EDO ear-training exercises by Alex Ness available [https://drive.google.com/folderview?id=0BwsXD8q2VCYUT3VEZUVmeVZUcmc&usp=drive_web#list here].
7 EDO ear-training exercises by Alex Ness available [https://drive.google.com/folderview?id=0BwsXD8q2VCYUT3VEZUVmeVZUcmc&usp=drive_web#list here].


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[[Category:Zeta]]
[[Category:Zeta]]


[[Category:todo:unify_precision]]
[[Category:todo:unify precision]]
Retrieved from "https://en.xen.wiki/w/7edo"