15edo: Difference between revisions
a little cleanup, updated ups/downs chords |
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[[File:15_tone_keyboard.png|alt=15 tone keyboard.png| | [[File:15_tone_keyboard.png|alt=15 tone keyboard.png|400x400px|15 tone keyboard.png]] | ||
== | ==Theory== | ||
15 Equal or 15 EDO is a tuning which divides the octave into 15 equally spaced pitches. It can be thought of as three sets of 5-EDO which do not connect by fifths. The fifth at 720 cents is quite wide yet still useable as a perfect fifth. Some would describe the fifth as more shimmery and pungent than anything closer to a just 3/2. The perfect fifth of 15 EDO returns to the octave if stacked five times which is radically different than a meantone system. | 15 Equal or 15 EDO is a tuning which divides the octave into 15 equally spaced pitches. It can be thought of as three sets of 5-EDO which do not connect by fifths. The fifth at 720 cents is quite wide yet still useable as a perfect fifth. Some would describe the fifth as more shimmery and pungent than anything closer to a just 3/2. The perfect fifth of 15 EDO returns to the octave if stacked five times which is radically different than a meantone system. | ||
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0-3-9-12 = D F A C = Dm7 = "D minor seven", or D F A B = Dm6 = "D minor six" | 0-3-9-12 = D F A C = Dm7 = "D minor seven", or D F A B = Dm6 = "D minor six" | ||
0-4-9-12 = D ^F A C = | 0-4-9-12 = D ^F A C = D^m,7 = "D upminor, add seven", or D ^F A B = D^m,6 = "D upminor add-six" | ||
0-5-9-12 = D vF# A C = | 0-5-9-12 = D vF# A C = Dv,7 = "D down add-seven", or D vF# A B = Dv,6 = "D down add-six" | ||
0-6-9-12 = D F# A C = D7 = "D seven", or D F# A B = D6 = "D six" | 0-6-9-12 = D F# A C = D7 = "D seven", or D F# A B = D6 = "D six" | ||
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| style="text-align:center;" | 7.741 | | style="text-align:center;" | 7.741 | ||
|- | |- | ||
| style="text-align:center;" | [[11/8|11/8]], [[16/11|16/11]] | | style="text-align:center;" | '''[[11/8|11/8]], [[16/11|16/11]]''' | ||
| style="text-align:center;" | 8.682 | | style="text-align:center;" | '''8.682''' | ||
|- | |- | ||
| style="text-align:center;" | [[8/7|8/7]], [[7/4|7/4]] | | style="text-align:center;" | '''[[8/7|8/7]], [[7/4|7/4]]''' | ||
| style="text-align:center;" | 8.826 | | style="text-align:center;" | '''8.826''' | ||
|- | |- | ||
| style="text-align:center;" | [[12/11|12/11]], [[11/6|11/6]] | | style="text-align:center;" | [[12/11|12/11]], [[11/6|11/6]] | ||
| style="text-align:center;" | 9.363 | | style="text-align:center;" | 9.363 | ||
|- | |- | ||
| style="text-align:center;" | [[5/4|5/4]], [[8/5|8/5]] | | style="text-align:center;" | '''[[5/4|5/4]], [[8/5|8/5]]''' | ||
| style="text-align:center;" | 13.686 | | style="text-align:center;" | '''13.686''' | ||
|- | |- | ||
| style="text-align:center;" | [[14/11|14/11]], [[11/7|11/7]] | | style="text-align:center;" | [[14/11|14/11]], [[11/7|11/7]] | ||
| style="text-align:center;" | 17.508 | | style="text-align:center;" | 17.508 | ||
|- | |- | ||
| style="text-align:center;" | [[4/3|4/3]], [[3/2|3/2]] | | style="text-align:center;" | '''[[4/3|4/3]], [[3/2|3/2]]''' | ||
| style="text-align:center;" | 18.045 | | style="text-align:center;" | '''18.045''' | ||
|- | |- | ||
| style="text-align:center;" | [[13/12|13/12]], [[24/13|24/13]] | | style="text-align:center;" | [[13/12|13/12]], [[24/13|24/13]] | ||
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| style="text-align:center;" | 39.443 | | style="text-align:center;" | 39.443 | ||
|- | |- | ||
| style="text-align:center;" | [[16/13|16/13]], [[13/8|13/8]] | | style="text-align:center;" | '''[[16/13|16/13]], [[13/8|13/8]]''' | ||
| style="text-align:center;" | 39.472 | | style="text-align:center;" | '''39.472''' | ||
|} | |} | ||
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| style="text-align:center;" | 7.741 | | style="text-align:center;" | 7.741 | ||
|- | |- | ||
| style="text-align:center;" | [[11/8|11/8]], [[16/11|16/11]] | | style="text-align:center;" | '''[[11/8|11/8]], [[16/11|16/11]]''' | ||
| style="text-align:center;" | 8.682 | | style="text-align:center;" | '''8.682''' | ||
|- | |- | ||
| style="text-align:center;" | [[8/7|8/7]], [[7/4|7/4]] | | style="text-align:center;" | '''[[8/7|8/7]], [[7/4|7/4]]''' | ||
| style="text-align:center;" | 8.826 | | style="text-align:center;" | '''8.826''' | ||
|- | |- | ||
| style="text-align:center;" | [[12/11|12/11]], [[11/6|11/6]] | | style="text-align:center;" | [[12/11|12/11]], [[11/6|11/6]] | ||
| style="text-align:center;" | 9.363 | | style="text-align:center;" | 9.363 | ||
|- | |- | ||
| style="text-align:center;" | [[5/4|5/4]], [[8/5|8/5]] | | style="text-align:center;" | '''[[5/4|5/4]], [[8/5|8/5]]''' | ||
| style="text-align:center;" | 13.686 | | style="text-align:center;" | '''13.686''' | ||
|- | |- | ||
| style="text-align:center;" | [[14/11|14/11]], [[11/7|11/7]] | | style="text-align:center;" | [[14/11|14/11]], [[11/7|11/7]] | ||
| style="text-align:center;" | 17.508 | | style="text-align:center;" | 17.508 | ||
|- | |- | ||
| style="text-align:center;" | [[4/3|4/3]], [[3/2|3/2]] | | style="text-align:center;" | '''[[4/3|4/3]], [[3/2|3/2]]''' | ||
| style="text-align:center;" | 18.045 | | style="text-align:center;" | '''18.045''' | ||
|- | |- | ||
| style="text-align:center;" | [[13/12|13/12]], [[24/13|24/13]] | | style="text-align:center;" | [[13/12|13/12]], [[24/13|24/13]] | ||
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| style="text-align:center;" | 36.090 | | style="text-align:center;" | 36.090 | ||
|- | |- | ||
| style="text-align:center;" | [[16/13|16/13]], [[13/8|13/8]] | | style="text-align:center;" | '''[[16/13|16/13]], [[13/8|13/8]]''' | ||
| style="text-align:center;" | 39.472 | | style="text-align:center;" | '''39.472''' | ||
|- | |- | ||
| style="text-align:center;" | [[15/14|15/14]], [[28/15|28/15]] | | style="text-align:center;" | [[15/14|15/14]], [[28/15|28/15]] | ||
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<ul><li>See the main [[Porcupine_Notation|porcupine notation]] page.</li></ul>Porcupine notation bases porcupine[8] LLLLLLLs scale using eight nominals α β χ δ ε φ γ η. Others have proposed ABCDEFGHA but conflicts with european notation have caused many to reject this approach. Thus greek letters can be used in place with a close resemblance to the spelling of ABCDEFGHA. | <ul><li>See the main [[Porcupine_Notation|porcupine notation]] page.</li></ul>Porcupine notation bases porcupine[8] LLLLLLLs scale using eight nominals α β χ δ ε φ γ η. Others have proposed ABCDEFGHA but conflicts with european notation have caused many to reject this approach. Thus greek letters can be used in place with a close resemblance to the spelling of ABCDEFGHA. | ||
==Interval names for Porcupine[8] | ==Interval names for Porcupine[8]== | ||
{| class="wikitable" | {| class="wikitable" | ||