21edo
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=21 equal divisions of the octave= Twenty one equal divisions of the octave provides the sonic fingerprint of the augmented and 7-edo family, while also giving a some higher harmony possibilities and fun intervals like the apotome, and the medium magic diesis. The system can be treated as three intertwining 7-edo or "equi-heptatonic" scales, or as seven 3-edo ''augmented'' triads. Some other cool things about 21-edo: it has an 11-limit minor third/wide sixth, 7-limit neutral third and sixth, a 7/4 harmonic seventh or grave minor seventh 1280/729 approximation (whichever you please). The harmonic occurs at 968.826 cents while the 21-tone 7/4 approximation is 971.4286 cents, or 2.6 cents off. Twenty-one has a period of 1/3 of the octave as opposed to 1/4 found in diminished families like 12-tet and 16-tet. Some sources claim that cultures in North and South Africa ( Zambezi / Angola / Chopi, etc), as well as ancient traditional Chinese music used 7-edo (or slight alterations within the pitch sets). 0. 1/1 C 1. 57.143 cents C^ Dvv 2. 114.286 cents C^^ Dv 3. 171.429 cents D 4. 228.571 cents D^ Evv 5. 285.714 cents D^^ Ev 6. 342.857 cents E 7. 400.000 cents E^ Fvv 8. 457.143 cents E^^ Fv 9. 514.286 cents F 10. 571.429 cents F^ Gvv 11. 628.571 cents F^^ Gv 12. 685.714 cents G 13. 742.857 cents G^ Avv 14. 800.000 cents G^^ Av 15. 857.143 cents A 16. 914.286 cents A^ Bvv 17. 971.429 cents A^^ Bv 18. 1028.571 cents B 19. 1085.714 cents B^ Cvv 20. 1142.857 cents B^^ Cv 21. 2/1 C Some 21-tone scales: 21-edo Narrow (minor) whole tone 21-edo Undecimal minor 21-edo Septimal neutral major 21-edo Quasi-equal major 21-edo Undecimal minor 21-edo Septimal neutral major 21-edo Quasi-equal major [[image:http://www.ronsword.com/images/ron1.jpg width="254" height="188"]][[image:http://www.swordguitars.com/21tetsm.JPG width="363" height="191"]] **//21-edo Icosihenaphonic Acoustic Guitar (Ron Sword)//** ==**Progressions / Chords / Pitch Space Divisions:**== 2 octaves into 7 parts = 6 6 6 6 6 6 3 octaves into 7 parts = 9 9 9 9 9 9 4 octaves into 7 parts = 12 12 12 12 12 12 12 5 octaves into 7 parts = 15 15 15 15 15 15 15 6 octaves into 7 parts = 18 18 18 18 18 18 18 7 octaves into 7 parts = 21 21 21 21 21 21 21 = octaves 8 octaves into 7 parts = 24 24 24 24 24 24 24 9 octaves into 7 parts = 27 27 27 27 27 27 27 10 octaves into 7 parts = 30 30 30 30 30 30 30 2 octaves into 3 parts = 14 14 14 3 octaves into 3 parts = 21 21 21 = octave 4 octaves into 3 parts = 28 28 28 5 octaves into 3 parts = 35 35 35 6 octaves into 3 parts = 42 42 42 = 2 octaves 7 octaves into 3 parts = 49 49 49 8 octaves into 3 parts = 56 56 56 9 octaves into 3 parts = 63 63 63 = 3 octaves 10 octaves into 3 parts = 70 70 70 =**Books / Literature:**= Sword, Ron. "Icosihenaphonic Scales for Guitar". IAAA Press. 1st ed: July 2009. =**Compositions/Listening:**= [[@http://www.ronsword.com/sounds/21_improv.mp3|Short Clip of 21-edo Acoustic]] by Ron Sword [[@http://www.ronsword.com/sounds/Ron_Sword_21_Tone_improv.mp3|Open tuning Drone Improvisation in 21-edo]] by Ron Sword
Original HTML content:
<html><head><title>21edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x21 equal divisions of the octave"></a><!-- ws:end:WikiTextHeadingRule:0 -->21 equal divisions of the octave</h1> <br /> Twenty one equal divisions of the octave provides the sonic fingerprint of the augmented and 7-edo family, while also giving a some higher harmony possibilities and fun intervals like the apotome, and the medium magic diesis. The system can be treated as three intertwining 7-edo or "equi-heptatonic" scales, or as seven 3-edo ''augmented'' triads. Some other cool things about 21-edo: it has an 11-limit minor third/wide sixth, 7-limit neutral third and sixth, a 7/4 harmonic seventh or grave minor seventh 1280/729 approximation (whichever you please). The harmonic occurs at 968.826 cents while the 21-tone 7/4 approximation is 971.4286 cents, or 2.6 cents off.<br /> <br /> Twenty-one has a period of 1/3 of the octave as opposed to 1/4 found in diminished families like 12-tet and 16-tet. Some sources claim that cultures in North and South Africa ( Zambezi / Angola / Chopi, etc), as well as ancient traditional Chinese music used 7-edo (or slight alterations within the pitch sets).<br /> <br /> 0. 1/1 C<br /> 1. 57.143 cents C^ Dvv<br /> 2. 114.286 cents C^^ Dv<br /> 3. 171.429 cents D<br /> 4. 228.571 cents D^ Evv<br /> 5. 285.714 cents D^^ Ev<br /> 6. 342.857 cents E<br /> 7. 400.000 cents E^ Fvv<br /> 8. 457.143 cents E^^ Fv<br /> 9. 514.286 cents F<br /> 10. 571.429 cents F^ Gvv<br /> 11. 628.571 cents F^^ Gv<br /> 12. 685.714 cents G<br /> 13. 742.857 cents G^ Avv<br /> 14. 800.000 cents G^^ Av<br /> 15. 857.143 cents A<br /> 16. 914.286 cents A^ Bvv<br /> 17. 971.429 cents A^^ Bv<br /> 18. 1028.571 cents B<br /> 19. 1085.714 cents B^ Cvv<br /> 20. 1142.857 cents B^^ Cv<br /> 21. 2/1 C<br /> <br /> Some 21-tone scales:<br /> <br /> 21-edo Narrow (minor) whole tone<br /> 21-edo Undecimal minor<br /> 21-edo Septimal neutral major<br /> 21-edo Quasi-equal major<br /> 21-edo Undecimal minor<br /> 21-edo Septimal neutral major<br /> 21-edo Quasi-equal major<br /> <!-- ws:start:WikiTextRemoteImageRule:8:<img src="http://www.ronsword.com/images/ron1.jpg" alt="" title="" style="height: 188px; width: 254px;" /> --><img src="http://www.ronsword.com/images/ron1.jpg" alt="external image ron1.jpg" title="external image ron1.jpg" style="height: 188px; width: 254px;" /><!-- ws:end:WikiTextRemoteImageRule:8 --><!-- ws:start:WikiTextRemoteImageRule:9:<img src="http://www.swordguitars.com/21tetsm.JPG" alt="" title="" style="height: 191px; width: 363px;" /> --><img src="http://www.swordguitars.com/21tetsm.JPG" alt="external image 21tetsm.JPG" title="external image 21tetsm.JPG" style="height: 191px; width: 363px;" /><!-- ws:end:WikiTextRemoteImageRule:9 --><br /> <strong><em>21-edo Icosihenaphonic Acoustic Guitar (Ron Sword)</em></strong><br /> <br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x21 equal divisions of the octave-Progressions / Chords / Pitch Space Divisions:"></a><!-- ws:end:WikiTextHeadingRule:2 --><strong>Progressions / Chords / Pitch Space Divisions:</strong></h2> 2 octaves into 7 parts = 6 6 6 6 6 6<br /> 3 octaves into 7 parts = 9 9 9 9 9 9<br /> 4 octaves into 7 parts = 12 12 12 12 12 12 12<br /> 5 octaves into 7 parts = 15 15 15 15 15 15 15<br /> 6 octaves into 7 parts = 18 18 18 18 18 18 18<br /> 7 octaves into 7 parts = 21 21 21 21 21 21 21 = octaves<br /> 8 octaves into 7 parts = 24 24 24 24 24 24 24<br /> 9 octaves into 7 parts = 27 27 27 27 27 27 27<br /> 10 octaves into 7 parts = 30 30 30 30 30 30 30<br /> <br /> 2 octaves into 3 parts = 14 14 14<br /> 3 octaves into 3 parts = 21 21 21 = octave<br /> 4 octaves into 3 parts = 28 28 28<br /> 5 octaves into 3 parts = 35 35 35<br /> 6 octaves into 3 parts = 42 42 42 = 2 octaves<br /> 7 octaves into 3 parts = 49 49 49<br /> 8 octaves into 3 parts = 56 56 56<br /> 9 octaves into 3 parts = 63 63 63 = 3 octaves<br /> 10 octaves into 3 parts = 70 70 70<br /> <br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="Books / Literature:"></a><!-- ws:end:WikiTextHeadingRule:4 --><strong>Books / Literature:</strong></h1> Sword, Ron. "Icosihenaphonic Scales for Guitar". IAAA Press. 1st ed: July 2009.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Compositions/Listening:"></a><!-- ws:end:WikiTextHeadingRule:6 --><strong>Compositions/Listening:</strong></h1> <a class="wiki_link_ext" href="http://www.ronsword.com/sounds/21_improv.mp3" rel="nofollow" target="_blank">Short Clip of 21-edo Acoustic</a> by Ron Sword<br /> <a class="wiki_link_ext" href="http://www.ronsword.com/sounds/Ron_Sword_21_Tone_improv.mp3" rel="nofollow" target="_blank">Open tuning Drone Improvisation in 21-edo</a> by Ron Sword</body></html>