7edo: Difference between revisions
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<span style="display: block; text-align: right;">[[7平均律|日本語]]</span> | <span style="display: block; text-align: right;">[[7平均律|日本語]]</span> | ||
7-edo 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]]. | |||
__FORCETOC__ | __FORCETOC__ | ||
="Neutral diatonic" or "Neutron[7]"= | == "Neutral diatonic" or "Neutron[7]" == | ||
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. 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). | ||
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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 ([[ | 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. | ||
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. | 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. | ||
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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 in 7-edo= | == Intervals in 7-edo == | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! Interval | |||
! Cents | |||
! Closest diatonic <br/> interval name | |||
! The "neighborhood" of just intervals | |||
|- | |- | ||
| 0 | |||
| 0 | |||
| unison / prime | |||
| exactly 1/1 | |||
|- | |- | ||
| 1 | |||
| 171.429 | |||
| 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 | |||
3.215¢ from second 54/49 | |||
-1.006¢ from the 29th subharmonic 32/29 | |||
-10. | |||
|- | |- | ||
| 2 | |||
| 342.857 | |||
| third | |||
| -4.55¢ from neutral third 11/9 | |||
|- | |- | ||
| 3 | |||
| 514.286 | |||
| fourth | |||
| 16.24¢ from just fourth 4/3 (498.045¢) <br/> -5.265¢ from wide fourth 27/20 | |||
-5.265¢ from wide fourth 27/20 | |||
|- | |- | ||
| 4 | |||
| 685.714 | |||
| fifth | |||
| 5.265 ¢ from narrow fifth 40/27 <br/> -16.241¢ from just fifth 3/2 (701.955¢) | |||
-16.241¢ | |||
|- | |- | ||
| 5 | |||
| 857.143 | |||
| sixth | |||
| 4.551¢ from neutral sixth 18/11 | |||
|- | |- | ||
| 6 | |||
| 1028.571 | |||
| 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 | |||
-6.424¢ from neutral seventh 20/11 | |||
1.006¢ from the 29th harmonic 29/16 | |||
-3.215¢ from seventh 49/27 | |||
|- | |- | ||
| 7 (0) | |||
| 1200 | |||
| eighth | |||
| exactly 2/1 | |||
|} | |} | ||
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[[:File:7ed2-001.svg|7ed2-001.svg]] | [[:File:7ed2-001.svg|7ed2-001.svg]] | ||
=Related scales= | == Related scales == | ||
* Related in a lateral way to traditional Thai music. Subset of [[14edo|14 EDO]] and [[21edo|21 EDO]]. | |||
==Notation== | |||
=== Notation === | |||
==Harmony== | * Rotatable on a five-line staff without accidentals. | ||
=== Harmony === | |||
There is no distinction between Major or Minor; each pitch class is unique. | There is no distinction between Major or Minor; each pitch class is unique. | ||
==Melody== | === Melody === | ||
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. | 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. | The step from seventh to octave is too large for the leading tone. | ||
==Relative tuning accuracy== | === Relative tuning accuracy === | ||
7-edo is the third [[ | 7-edo is the third [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral edo]]. | ||
=Alphabet= | == Alphabet == | ||
William Lynch proposes using numbers 1 through 7 as the nominals of 7 ET with # signs being possible to expand to 14 EDO or even 21 EDO. | [[William Lynch]] proposes using numbers 1 through 7 as the nominals of 7 ET with # signs being possible to expand to [[14edo|14 EDO]] or even [[21edo|21 EDO]]. | ||
The alphabet can be written in three ways: | The alphabet can be written in three ways: | ||
Plain numbers: 1 2 3 4 5 6 7 | * Plain numbers: 1 2 3 4 5 6 7 | ||
* In Japanese number abbreviations: い に さん し ご ろ な い | |||
In Japanese number abbreviations: い に さん し ご ろ な い | * In Chinese/Kanji numbers: 一 二 三 四 五 六七 | ||
In Chinese/Kanji numbers: 一 二 三 四 五 六七 | |||
=Music= | == Music == | ||
* [https://soundcloud.com/overtoneshock/death-teasing-monolith-7-edo-premiere Death Giving Monolith] by [[Stephen Weigel]] (dulcimer and voice) | |||
* [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] by [http://www.akjmusic.com/works.html Aaron K. Johnson] (electronic swirlies) | |||
* [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://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]]'' | |||
* ''[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|Randy Winchester]] | |||
* [http://media.soundcloud.com/stream/IUcgFYhtu3Rk?stream_token=4QIvd Sävelmä] by [http://soundcloud.com/juhani-nuorvala/s-velm-long-version Juhani Nuorvala] | |||
* [https://soundcloud.com/santiagocosentino/rock-in-7edo Rock in 7edo by Santiago Cosentino] | |||
=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]. | ||
=Commas= | == Commas == | ||
7 EDO tempers out the following commas. (Note: This assumes val < 7 11 16 20 24 26 |.) | 7 EDO tempers out the following commas. (Note: This assumes val < 7 11 16 20 24 26 |.) | ||
{| class="wikitable" | {| class="wikitable" style="text-align:center;" | ||
|- | |- | ||
! | ! Comma | ||
! | ! Monzo | ||
! | ! Cents | ||
! | ! Name 1 | ||
! | ! Name 2 | ||
! | ! Name 3 | ||
|- | |- | ||
| 2187/2048 | |||
| | | {{Monzo| -11 7 }} | ||
| style="text-align:right;" | 113.69 | | style="text-align:right;" | 113.69 | ||
| Apotome | |||
| | |||
| | |||
|- | |- | ||
| 135/128 | |||
| | | {{Monzo| -7 3 1 }} | ||
| style="text-align:right;" | 92.18 | | style="text-align:right;" | 92.18 | ||
| Major Chroma | |||
| Major Limma | |||
| Pelagic Comma | |||
|- | |- | ||
| 25/24 | |||
| | | {{Monzo| -3 -1 2 }} | ||
| style="text-align:right;" | 70.67 | | style="text-align:right;" | 70.67 | ||
| Chromatic semitone | |||
| Chroma | |||
| | |||
|- | |- | ||
| 250/243 | |||
| | | {{Monzo| 1 -5 3 }} | ||
| style="text-align:right;" | 49.17 | | style="text-align:right;" | 49.17 | ||
| Maximal Diesis | |||
| Porcupine Comma | |||
| | |||
|- | |- | ||
| 20000/19683 | |||
| | | {{Monzo| 5 -9 4 }} | ||
| style="text-align:right;" | 27.66 | | style="text-align:right;" | 27.66 | ||
| Minimal Disease | |||
| Tricot Comma | |||
| | |||
|- | |- | ||
| 81/80 | |||
| | | {{Monzo| -4 4 -1 }} | ||
| style="text-align:right;" | 21.51 | | style="text-align:right;" | 21.51 | ||
| Syntonic Comma | |||
| Didymos Comma | |||
| Meantone Comma | |||
|- | |- | ||
| 1600000/1594323 | |||
| | | {{Monzo| 9 -13 5 }} | ||
| style="text-align:right;" | 6.15 | | style="text-align:right;" | 6.15 | ||
| Amity Comma | |||
| | |||
| | |||
|- | |- | ||
| 36/35 | |||
| | | {{Monzo| 2 2 -1 -1 }} | ||
| style="text-align:right;" | 48.77 | | style="text-align:right;" | 48.77 | ||
| Septimal Quarter Tone | |||
| | |||
| | |||
|- | |- | ||
| 525/512 | |||
| | | {{Monzo| -9 1 2 1 }} | ||
| style="text-align:right;" | 43.41 | | style="text-align:right;" | 43.41 | ||
| Avicenna | |||
| Avicenna's Enharmonic Diesis | |||
| | |||
|- | |- | ||
| 64/63 | |||
| | | {{Monzo| 6 -2 0 -1 }} | ||
| style="text-align:right;" | 27.26 | | style="text-align:right;" | 27.26 | ||
| Septimal Comma | |||
| Archytas' Comma | |||
| Leipziger Komma | |||
|- | |- | ||
| 875/864 | |||
| | | {{Monzo| -5 -3 3 1 }} | ||
| style="text-align:right;" | 21.90 | | style="text-align:right;" | 21.90 | ||
| Keema | |||
| | |||
| | |||
|- | |- | ||
| 5120/5103 | |||
| | | {{Monzo| 10 -6 1 -1 }} | ||
| style="text-align:right;" | 5.76 | | style="text-align:right;" | 5.76 | ||
| Hemi Family | |||
| | |||
| | |||
|- | |- | ||
| 6144/6125 | |||
| | | {{Monzo| 11 1 -3 -2 }} | ||
| style="text-align:right;" | 5.36 | | style="text-align:right;" | 5.36 | ||
| Cornwell | |||
| | |||
| | |||
|- | |- | ||
| 4375/4374 | |||
| | | {{Monzo| -1 -7 4 1 }} | ||
| style="text-align:right;" | 0.40 | | style="text-align:right;" | 0.40 | ||
| Ragisma | |||
| | |||
| | |||
|- | |- | ||
| 394839/394762 | |||
| | | {{Monzo| 47 -7 -7 -7 }} | ||
| style="text-align:right;" | 0.34 | | style="text-align:right;" | 0.34 | ||
| Akjaysma | |||
| 5\7 Octave Comma | |||
| | |||
|- | |- | ||
| 100/99 | |||
| | | {{Monzo| 2 -2 2 0 -1 }} | ||
| style="text-align:right;" | 17.40 | | style="text-align:right;" | 17.40 | ||
| Ptolemies | |||
| | |||
| | |||
|- | |- | ||
| 121/120 | |||
| | | {{Monzo| -3 -1 -1 0 2 }} | ||
| style="text-align:right;" | 14.37 | | style="text-align:right;" | 14.37 | ||
| Batista | |||
| | |||
| | |||
|- | |- | ||
| 176/175 | |||
| | | {{Monzo| 4 0 -2 -1 1 }} | ||
| style="text-align:right;" | 9.86 | | style="text-align:right;" | 9.86 | ||
| Valinorsma | |||
| | |||
| | |||
|- | |- | ||
| 65536/65219 | |||
| | | {{Monzo| 16 0 0 -2 -3 }} | ||
| style="text-align:right;" | 8.39 | | style="text-align:right;" | 8.39 | ||
| Organisma | |||
| | |||
| | |||
|- | |- | ||
| 243/242 | |||
| | | {{Monzo| -1 5 0 0 -2 }} | ||
| style="text-align:right;" | 7.14 | | style="text-align:right;" | 7.14 | ||
| Rasta | |||
| | |||
| | |||
|- | |- | ||
| 385/384 | |||
| | | {{Monzo| -7 -1 1 1 1 }} | ||
| style="text-align:right;" | 4.50 | | style="text-align:right;" | 4.50 | ||
| Keenanisma | |||
| | |||
| | |||
|- | |- | ||
| 4000/3993 | |||
| | | {{Monzo| 5 -1 3 0 -3 }} | ||
| style="text-align:right;" | 3.03 | | style="text-align:right;" | 3.03 | ||
| Wizard Harry | |||
| | |||
| | |||
|} | |} | ||