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| Step size = 171.429¢
| Step size = 171.429¢
| Fifth = 4\7 = 685.714¢
| Fifth = 4\7 = 685.714¢
| 2nd = 1\7 = 171¢
| Major 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 72: Line 73:
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 137: Line 138:
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]]
[[525/512]]
| {{monzo| -9 1 2 1 }}
|{{monzo| -9 1 2 1 }}
| 43.41
|43.41
| Lazoyoyo
|Lazoyoyo
| Avicennma, Avicenna's enharmonic diesis
|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]]
[[121/120]]
| {{monzo| -3 -1 -1 0 2 }}
|{{monzo| -3 -1 -1 0 2 }}
| 14.37
|14.37
| Lologu
|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]]
[[4000/3993]]
| {{monzo| 5 -1 3 0 -3 }}
|{{monzo| 5 -1 3 0 -3 }}
| 3.03
|3.03
| Triluyo
|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]]''
* [http://www.seraph.it/dep/det/7edo%20dance.mp3 7edo Dance] ''by [[Carlo_Serafini|Carlo Serafini]]''
*''[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])
* ''[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])
*[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/06%20-%206.%207%20octave.mp3 Comets Over Flatland 6] by [[Randy Winchester]]
* [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://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/puVWio6755c Clockworkian] by [[User:Userminusone|Userminusone]]
* [https://youtu.be/cBSXRZUwWoQ 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]]

Revision as of 05:50, 14 April 2021

← 6edo 7edo 8edo →
Prime factorization 7 (prime)
Step size 171.429 ¢ 
Fifth 4\7 (685.714 ¢)
(semiconvergent)
Semitones (A1:m2) 0:1 (0 ¢ : 171.4 ¢)
Consistency limit 5
Distinct consistency limit 3

7-edo or "Neutral diatonic" divides the 1200-cent octave into 7 equal parts, making its smallest interval 171.428¢, or the seventh root of 2. It is the fourth prime edo, after 2edo, 3edo and 5edo. It is the third zeta integral edo.

Theory

prime 2 prime 3 prime 5 prime 7 prime 11 prime 13
error absolute (¢) 0.0 -16.2 -43.5 +59.7 -37.0 +16.6
relative (%) 0 -9 -25 +35 -22 +10
nearest edomapping 7 4 2 6 3 5
fifthspan 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).

7-tet can be thought of as result of stacking seven 11/9s on top of each other, and then tempering to remove the comma (2^-2 3^-14 11^7). 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.

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 than 7/4, a much simpler overtone seventh.

Similarly, in equi-heptatonic systems the desire for harmonic sound may dictate constant adjustments of intonation away from the theoretical interval of 171 cents. One of the most impressive areas in Africa in which a pen-equidistant heptatonic scale is combined with a distinctively harmonic style based on singing in intervals of thirds plus fifths, or thirds plus fourths, is the eastern Angolan culture area. This music is heptatonic and non-modal; i.e., there is no concept of major or minor thirds as distinctive intervals. In principle all the thirds are neutral, but in practice the thirds rendered by the singers often approximate natural major thirds (386 cents), especially at points of rest. In this manner, the principles of equidistance and harmonic euphony are accommodated within one tonal-harmonic system. For the notation of such music, a seven-line stave is most appropriate, with each horizontal line representing one pitch level.

("African music." Encyclopædia Britannica. 2009. Encyclopædia Britannica Online. 05 Jul. 2009)

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

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

Interval Cents interval name The "neighborhood" of just intervals
0 0.000 unison / prime exactly 1/1
1 171.429 second 6.424¢ from Ptolemy (neutral) second 11/10
3.215¢ from second 54/49
-1.006¢ from the 29th subharmonic 32/29
-10.975¢ from major second (small whole tone) 10/9
2 342.857 third 0.374¢ from neutral third 39/32

-4.55¢ from neutral third 11/9

3 514.286 fourth 16.241¢ from just fourth 4/3 (498.045¢)
-5.265¢ from wide fourth 27/20
4 685.714 fifth 5.265 ¢ from narrow fifth 40/27
-16.241¢ from just fifth 3/2 (701.955¢)
5 857.143 sixth 4.551¢ from neutral sixth 18/11

-0.374¢ from neutral sixth 64/39

-0.048¢ from (neutral sixth) 105/64

6 1028.571 seventh 10.975¢ from (Didymus) minor seventh 9/5
-6.424¢ from neutral seventh 20/11
-1.006¢ from the 29th harmonic 29/16
-3.215¢ from seventh 49/27
7 1200 octave exactly 2/1

alt : Your browser has no SVG support.

7ed2-001.svg

Observations

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.

The step from seventh to octave is too large for the leading tone.

Notation

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

7 EDO tempers out the following commas. This assumes val ⟨7 11 16 20 24 26].

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

Music

Ear Training

7 EDO ear-training exercises by Alex Ness available here.

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