30edo: Difference between revisions
→Intervals: Removed 7mus column |
updated ups/down notation, added color names to the comma list, general cleanup |
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__FORCETOC__ | |||
= Theory = | |||
The ''30 equal division'' divides the octave into 30 equal steps of precisely 40 cents each. Its [[Patent_val|patent val]] is a doubled version of the patent val for [[15edo|15edo]] through the 11-limit, so 30 can be viewed as a [[contorted|contorted]] version of 15. In the 13-limit it supplies the optimal patent val for [[Trienstonic_clan#Quindecic|quindecic temperament]]. | The ''30 equal division'' divides the octave into 30 equal steps of precisely 40 cents each. Its [[Patent_val|patent val]] is a doubled version of the patent val for [[15edo|15edo]] through the 11-limit, so 30 can be viewed as a [[contorted|contorted]] version of 15. In the 13-limit it supplies the optimal patent val for [[Trienstonic_clan#Quindecic|quindecic temperament]]. | ||
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[[File:plot30.png|alt=plot30.png|plot30.png]] | [[File:plot30.png|alt=plot30.png|plot30.png]] | ||
=Intervals= | |||
{| class="wikitable" | {| class="wikitable" | ||
| Line 25: | Line 27: | ||
| style="text-align:center;" | ^1, ^m2 | | style="text-align:center;" | ^1, ^m2 | ||
| style="text-align:center;" | up unison, upminor 2nd | | style="text-align:center;" | up unison, upminor 2nd | ||
| style="text-align:center;" | D^ | | style="text-align:center;" | ^D, ^Eb | ||
|- | |- | ||
| style="text-align:center;" | 2 | | style="text-align:center;" | 2 | ||
| Line 31: | Line 33: | ||
| style="text-align:center;" | ^^1, v~2 | | style="text-align:center;" | ^^1, v~2 | ||
| style="text-align:center;" | double-up unison, downmid 2nd | | style="text-align:center;" | double-up unison, downmid 2nd | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^D, ^^Eb | ||
|- | |- | ||
| style="text-align:center;" | 3 | | style="text-align:center;" | 3 | ||
| Line 37: | Line 39: | ||
| style="text-align:center;" | ~2 | | style="text-align:center;" | ~2 | ||
| style="text-align:center;" | mid 2nd | | style="text-align:center;" | mid 2nd | ||
| style="text-align:center;" | | | style="text-align:center;" | v<span style="font-size: 90%; vertical-align: super;">3</span>E | ||
|- | |- | ||
| style="text-align:center;" | 4 | | style="text-align:center;" | 4 | ||
| Line 43: | Line 45: | ||
| style="text-align:center;" | ^~2 | | style="text-align:center;" | ^~2 | ||
| style="text-align:center;" | upmid 2nd | | style="text-align:center;" | upmid 2nd | ||
| style="text-align:center;" | | | style="text-align:center;" | vvE | ||
|- | |- | ||
| style="text-align:center;" | 5 | | style="text-align:center;" | 5 | ||
| Line 49: | Line 51: | ||
| style="text-align:center;" | vM2 | | style="text-align:center;" | vM2 | ||
| style="text-align:center;" | downmajor 2nd | | style="text-align:center;" | downmajor 2nd | ||
| style="text-align:center;" | | | style="text-align:center;" | vE | ||
|- | |- | ||
| style="text-align:center;" | 6 | | style="text-align:center;" | 6 | ||
| Line 61: | Line 63: | ||
| style="text-align:center;" | ^m3 | | style="text-align:center;" | ^m3 | ||
| style="text-align:center;" | upminor 3rd | | style="text-align:center;" | upminor 3rd | ||
| style="text-align:center;" | F | | style="text-align:center;" | ^F | ||
|- | |- | ||
| style="text-align:center;" | 8 | | style="text-align:center;" | 8 | ||
| Line 67: | Line 69: | ||
| style="text-align:center;" | v~3 | | style="text-align:center;" | v~3 | ||
| style="text-align:center;" | downmid 3rd | | style="text-align:center;" | downmid 3rd | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^F | ||
|- | |- | ||
| style="text-align:center;" | 9 | | style="text-align:center;" | 9 | ||
| Line 73: | Line 75: | ||
| style="text-align:center;" | ~3 | | style="text-align:center;" | ~3 | ||
| style="text-align:center;" | mid 3rd | | style="text-align:center;" | mid 3rd | ||
| style="text-align:center;" | F | | style="text-align:center;" | ^<span style="font-size: 90%; vertical-align: super;">3</span>F, v<span style="font-size: 90%; vertical-align: super;">3</span>F# | ||
|- | |- | ||
| style="text-align:center;" | 10 | | style="text-align:center;" | 10 | ||
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| style="text-align:center;" | ^~3 | | style="text-align:center;" | ^~3 | ||
| style="text-align:center;" | upmid 3rd | | style="text-align:center;" | upmid 3rd | ||
| style="text-align:center;" | | | style="text-align:center;" | vvF# | ||
|- | |- | ||
| style="text-align:center;" | 11 | | style="text-align:center;" | 11 | ||
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| style="text-align:center;" | vM3, v4 | | style="text-align:center;" | vM3, v4 | ||
| style="text-align:center;" | downmajor 3rd, down 4th | | style="text-align:center;" | downmajor 3rd, down 4th | ||
| style="text-align:center;" | | | style="text-align:center;" | vF#, vG | ||
|- | |- | ||
| style="text-align:center;" | 12 | | style="text-align:center;" | 12 | ||
| Line 97: | Line 99: | ||
| style="text-align:center;" | ^4, ^d5 | | style="text-align:center;" | ^4, ^d5 | ||
| style="text-align:center;" | up 4th, updim 5th | | style="text-align:center;" | up 4th, updim 5th | ||
| style="text-align:center;" | G^ | | style="text-align:center;" | ^G, ^Ab | ||
|- | |- | ||
| style="text-align:center;" | 14 | | style="text-align:center;" | 14 | ||
| style="text-align:center;" | 560 | | style="text-align:center;" | 560 | ||
| style="text-align:center;" | | | style="text-align:center;" | v~4, v~d5 | ||
| style="text-align:center;" | | | style="text-align:center;" | downmid 4th, downmid 5th | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^G, ^^Ab | ||
|- | |- | ||
| style="text-align:center;" | 15 | | style="text-align:center;" | 15 | ||
| style="text-align:center;" | 600 | | style="text-align:center;" | 600 | ||
| style="text-align:center;" | ^<span style="font-size: 90%; vertical-align: super;">3</span> | | style="text-align:center;" | ~4, ~5 | ||
| style="text-align:center;" | mid 4th, mid 5th | |||
| style="text-align:center;" | ^<span style="font-size: 90%; vertical-align: super;">3</span>G, v<span style="font-size: 90%; vertical-align: super;">3</span>A | |||
|- | |- | ||
| style="text-align:center;" | 16 | | style="text-align:center;" | 16 | ||
| style="text-align:center;" | 640 | | style="text-align:center;" | 640 | ||
| style="text-align:center;" | | | style="text-align:center;" | ^~A4, ^~5 | ||
| style="text-align:center;" | | | style="text-align:center;" | upmid 4th, upmid 5th | ||
| style="text-align:center;" | | | style="text-align:center;" | vvG#, vvA | ||
|- | |- | ||
| style="text-align:center;" | 17 | | style="text-align:center;" | 17 | ||
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| style="text-align:center;" | vA4, v5 | | style="text-align:center;" | vA4, v5 | ||
| style="text-align:center;" | downaug 4th, down 5th | | style="text-align:center;" | downaug 4th, down 5th | ||
| style="text-align:center;" | | | style="text-align:center;" | vG#, vA | ||
|- | |- | ||
| style="text-align:center;" | 18 | | style="text-align:center;" | 18 | ||
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| style="text-align:center;" | ^5, ^m6 | | style="text-align:center;" | ^5, ^m6 | ||
| style="text-align:center;" | up 5th, upminor 6th | | style="text-align:center;" | up 5th, upminor 6th | ||
| style="text-align:center;" | A^ | | style="text-align:center;" | ^A, ^Bb | ||
|- | |- | ||
| style="text-align:center;" | 20 | | style="text-align:center;" | 20 | ||
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| style="text-align:center;" | v~6 | | style="text-align:center;" | v~6 | ||
| style="text-align:center;" | downmid 6th | | style="text-align:center;" | downmid 6th | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^Bb | ||
|- | |- | ||
| style="text-align:center;" | 21 | | style="text-align:center;" | 21 | ||
| Line 145: | Line 147: | ||
| style="text-align:center;" | ~6 | | style="text-align:center;" | ~6 | ||
| style="text-align:center;" | mid 6th | | style="text-align:center;" | mid 6th | ||
| style="text-align:center;" | | | style="text-align:center;" | v<span style="font-size: 90%; vertical-align: super;">3</span>B | ||
|- | |- | ||
| style="text-align:center;" | 22 | | style="text-align:center;" | 22 | ||
| Line 151: | Line 153: | ||
| style="text-align:center;" | ^~6 | | style="text-align:center;" | ^~6 | ||
| style="text-align:center;" | upmid 6th | | style="text-align:center;" | upmid 6th | ||
| style="text-align:center;" | | | style="text-align:center;" | vvB | ||
|- | |- | ||
| style="text-align:center;" | 23 | | style="text-align:center;" | 23 | ||
| Line 157: | Line 159: | ||
| style="text-align:center;" | vM6 | | style="text-align:center;" | vM6 | ||
| style="text-align:center;" | downmajor 6th | | style="text-align:center;" | downmajor 6th | ||
| style="text-align:center;" | | | style="text-align:center;" | vB | ||
|- | |- | ||
| style="text-align:center;" | 24 | | style="text-align:center;" | 24 | ||
| Line 169: | Line 171: | ||
| style="text-align:center;" | ^m7 | | style="text-align:center;" | ^m7 | ||
| style="text-align:center;" | upminor 7th | | style="text-align:center;" | upminor 7th | ||
| style="text-align:center;" | C | | style="text-align:center;" | ^C | ||
|- | |- | ||
| style="text-align:center;" | 26 | | style="text-align:center;" | 26 | ||
| Line 175: | Line 177: | ||
| style="text-align:center;" | v~7 | | style="text-align:center;" | v~7 | ||
| style="text-align:center;" | downmid 7th | | style="text-align:center;" | downmid 7th | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^C | ||
|- | |- | ||
| style="text-align:center;" | 27 | | style="text-align:center;" | 27 | ||
| Line 181: | Line 183: | ||
| style="text-align:center;" | ~7 | | style="text-align:center;" | ~7 | ||
| style="text-align:center;" | mid 7th | | style="text-align:center;" | mid 7th | ||
| style="text-align:center;" | | | style="text-align:center;" | ^<span style="font-size: 90%; vertical-align: super;">3</span>C | ||
|- | |- | ||
| style="text-align:center;" | 28 | | style="text-align:center;" | 28 | ||
| Line 187: | Line 189: | ||
| style="text-align:center;" | ^~7, vv8 | | style="text-align:center;" | ^~7, vv8 | ||
| style="text-align:center;" | upmid 7th, double-down 8ve | | style="text-align:center;" | upmid 7th, double-down 8ve | ||
| style="text-align:center;" | | | style="text-align:center;" | vvC#, vvD | ||
|- | |- | ||
| style="text-align:center;" | 29 | | style="text-align:center;" | 29 | ||
| Line 193: | Line 195: | ||
| style="text-align:center;" | vM7, v8 | | style="text-align:center;" | vM7, v8 | ||
| style="text-align:center;" | downmajor 7th, down 8ve | | style="text-align:center;" | downmajor 7th, down 8ve | ||
| style="text-align:center;" | | | style="text-align:center;" | vC#, vD | ||
|- | |- | ||
| style="text-align:center;" | 30 | | style="text-align:center;" | 30 | ||
| Line 203: | Line 205: | ||
=Commas= | =Commas= | ||
30 EDO tempers out the following commas. (Note: This assumes the val < 30 48 70 84 104 111 | .) | 30 EDO tempers out the following [[commas]]. (Note: This assumes the val < 30 48 70 84 104 111 | .) | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! | | ! | [[Ratio]] | ||
! | Monzo | ! | [[Monzo]] | ||
! | | ! | [[Cents]] | ||
![[Color notation/Temperament Names|Color Name]] | |||
! | Name 1 | ! | Name 1 | ||
! | Name 2 | ! | Name 2 | ||
| Line 217: | Line 220: | ||
| |<nowiki> | 8 -5 </nowiki>> | | |<nowiki> | 8 -5 </nowiki>> | ||
| style="text-align:right;" | 90.22 | | style="text-align:right;" | 90.22 | ||
| style="text-align:center;" |Sawa | |||
| style="text-align:center;" | Limma | | style="text-align:center;" | Limma | ||
| style="text-align:center;" | Pythagorean Minor 2nd | | style="text-align:center;" | Pythagorean Minor 2nd | ||
| Line 224: | Line 228: | ||
| |<nowiki> | 1 -5 3 </nowiki>> | | |<nowiki> | 1 -5 3 </nowiki>> | ||
| style="text-align:right;" | 49.17 | | style="text-align:right;" | 49.17 | ||
| style="text-align:center;" |Triyo | |||
| style="text-align:center;" | Maximal Diesis | | style="text-align:center;" | Maximal Diesis | ||
| style="text-align:center;" | Porcupine Comma | | style="text-align:center;" | Porcupine Comma | ||
| Line 231: | Line 236: | ||
| |<nowiki> | 7 0 -3 </nowiki>> | | |<nowiki> | 7 0 -3 </nowiki>> | ||
| style="text-align:right;" | 41.06 | | style="text-align:right;" | 41.06 | ||
| style="text-align:center;" |Trigu | |||
| style="text-align:center;" | Diesis | | style="text-align:center;" | Diesis | ||
| style="text-align:center;" | Augmented Comma | | style="text-align:center;" | Augmented Comma | ||
| Line 238: | Line 244: | ||
| |<nowiki> | -6 -5 6 </nowiki>> | | |<nowiki> | -6 -5 6 </nowiki>> | ||
| style="text-align:right;" | 8.11 | | style="text-align:right;" | 8.11 | ||
| style="text-align:center;" |Tribiyo | |||
| style="text-align:center;" | Kleisma | | style="text-align:center;" | Kleisma | ||
| style="text-align:center;" | Semicomma Majeur | | style="text-align:center;" | Semicomma Majeur | ||
| Line 245: | Line 252: | ||
| |<nowiki> | -3 1 -3 3 </nowiki>> | | |<nowiki> | -3 1 -3 3 </nowiki>> | ||
| style="text-align:right;" | 49.49 | | style="text-align:right;" | 49.49 | ||
| style="text-align:center;" |Trizogu | |||
| style="text-align:center;" | Keega | | style="text-align:center;" | Keega | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 252: | Line 260: | ||
| |<nowiki> | -4 -1 0 2 </nowiki>> | | |<nowiki> | -4 -1 0 2 </nowiki>> | ||
| style="text-align:right;" | 35.70 | | style="text-align:right;" | 35.70 | ||
| style="text-align:center;" |Zozo | |||
| style="text-align:center;" | Slendro Diesis | | style="text-align:center;" | Slendro Diesis | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 259: | Line 268: | ||
| |<nowiki> | 6 -2 0 -1 </nowiki>> | | |<nowiki> | 6 -2 0 -1 </nowiki>> | ||
| style="text-align:right;" | 27.26 | | style="text-align:right;" | 27.26 | ||
| style="text-align:center;" |Ru | |||
| style="text-align:center;" | Septimal Comma | | style="text-align:center;" | Septimal Comma | ||
| style="text-align:center;" | Archytas' Comma | | style="text-align:center;" | Archytas' Comma | ||
| Line 266: | Line 276: | ||
| |<nowiki> | -9 3 -3 4 </nowiki>> | | |<nowiki> | -9 3 -3 4 </nowiki>> | ||
| style="text-align:right;" | 22.23 | | style="text-align:right;" | 22.23 | ||
| style="text-align:center;" |Laquadzo-atrigu | |||
| style="text-align:center;" | Squalentine | | style="text-align:center;" | Squalentine | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 273: | Line 284: | ||
| |<nowiki> | -5 -3 3 1 </nowiki>> | | |<nowiki> | -5 -3 3 1 </nowiki>> | ||
| style="text-align:right;" | 21.90 | | style="text-align:right;" | 21.90 | ||
| style="text-align:center;" |Zotriyo | |||
| style="text-align:center;" | Keema | | style="text-align:center;" | Keema | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 280: | Line 292: | ||
| |<nowiki> | 1 2 -3 1 </nowiki>> | | |<nowiki> | 1 2 -3 1 </nowiki>> | ||
| style="text-align:right;" | 13.79 | | style="text-align:right;" | 13.79 | ||
| style="text-align:center;" |Zotrigu | |||
| style="text-align:center;" | Septimal Semicomma | | style="text-align:center;" | Septimal Semicomma | ||
| style="text-align:center;" | Starling Comma | | style="text-align:center;" | Starling Comma | ||
| Line 287: | Line 300: | ||
| |<nowiki> | 5 -4 3 -2 </nowiki>> | | |<nowiki> | 5 -4 3 -2 </nowiki>> | ||
| style="text-align:right;" | 13.47 | | style="text-align:right;" | 13.47 | ||
| style="text-align:center;" |Rurutriyo | |||
| style="text-align:center;" | Octagar | | style="text-align:center;" | Octagar | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 294: | Line 308: | ||
| |<nowiki> | -10 1 0 3 </nowiki>> | | |<nowiki> | -10 1 0 3 </nowiki>> | ||
| style="text-align:right;" | 8.43 | | style="text-align:right;" | 8.43 | ||
| style="text-align:center;" |Latrizo | |||
| style="text-align:center;" | Gamelisma | | style="text-align:center;" | Gamelisma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 301: | Line 316: | ||
| |<nowiki> | 11 1 -3 -2 </nowiki>> | | |<nowiki> | 11 1 -3 -2 </nowiki>> | ||
| style="text-align:right;" | 5.36 | | style="text-align:right;" | 5.36 | ||
| style="text-align:center;" |Saruru-atrigu | |||
| style="text-align:center;" | Porwell | | style="text-align:center;" | Porwell | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 308: | Line 324: | ||
| |<nowiki> | -4 6 -6 3 </nowiki>> | | |<nowiki> | -4 6 -6 3 </nowiki>> | ||
| style="text-align:right;" | 0.33 | | style="text-align:right;" | 0.33 | ||
| style="text-align:center;" |Trizogugu | |||
| style="text-align:center;" | Landscape Comma | | style="text-align:center;" | Landscape Comma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 315: | Line 332: | ||
| |<nowiki> | 2 -2 2 0 -1 </nowiki>> | | |<nowiki> | 2 -2 2 0 -1 </nowiki>> | ||
| style="text-align:right;" | 17.40 | | style="text-align:right;" | 17.40 | ||
| style="text-align:center;" |Luyoyo | |||
| style="text-align:center;" | Ptolemisma | | style="text-align:center;" | Ptolemisma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 322: | Line 340: | ||
| |<nowiki> | -3 -1 -1 0 2 </nowiki>> | | |<nowiki> | -3 -1 -1 0 2 </nowiki>> | ||
| style="text-align:right;" | 14.37 | | style="text-align:right;" | 14.37 | ||
| style="text-align:center;" |Lologu | |||
| style="text-align:center;" | Biyatisma | | style="text-align:center;" | Biyatisma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 329: | Line 348: | ||
| |<nowiki> | 4 0 -2 -1 1 </nowiki>> | | |<nowiki> | 4 0 -2 -1 1 </nowiki>> | ||
| style="text-align:right;" | 9.86 | | style="text-align:right;" | 9.86 | ||
| style="text-align:center;" |Lorugugu | |||
| style="text-align:center;" | Valinorsma | | style="text-align:center;" | Valinorsma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 336: | Line 356: | ||
| |<nowiki> | 16 0 0 -2 -3 </nowiki>> | | |<nowiki> | 16 0 0 -2 -3 </nowiki>> | ||
| style="text-align:right;" | 8.39 | | style="text-align:right;" | 8.39 | ||
| style="text-align:center;" |Satrilu-aruru | |||
| style="text-align:center;" | Orgonisma | | style="text-align:center;" | Orgonisma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 343: | Line 364: | ||
| |<nowiki> | -7 -1 1 1 1 </nowiki>> | | |<nowiki> | -7 -1 1 1 1 </nowiki>> | ||
| style="text-align:right;" | 4.50 | | style="text-align:right;" | 4.50 | ||
| style="text-align:center;" |Lozoyo | |||
| style="text-align:center;" | Keenanisma | | style="text-align:center;" | Keenanisma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 350: | Line 372: | ||
| |<nowiki> | -3 2 -1 2 -1 </nowiki>> | | |<nowiki> | -3 2 -1 2 -1 </nowiki>> | ||
| style="text-align:right;" | 3.93 | | style="text-align:right;" | 3.93 | ||
| style="text-align:center;" |Luzozogu | |||
| style="text-align:center;" | Werckisma | | style="text-align:center;" | Werckisma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 357: | Line 380: | ||
| |<nowiki> | 5 -1 3 0 -3 </nowiki>> | | |<nowiki> | 5 -1 3 0 -3 </nowiki>> | ||
| style="text-align:right;" | 3.03 | | style="text-align:right;" | 3.03 | ||
| style="text-align:center;" |Triluyo | |||
| style="text-align:center;" | Wizardharry | | style="text-align:center;" | Wizardharry | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 364: | Line 388: | ||
| |<nowiki> | -4 -3 2 -1 2 </nowiki>> | | |<nowiki> | -4 -3 2 -1 2 </nowiki>> | ||
| style="text-align:right;" | 0.57 | | style="text-align:right;" | 0.57 | ||
| style="text-align:center;" |Loloruyoyo | |||
| style="text-align:center;" | Lehmerisma | | style="text-align:center;" | Lehmerisma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||