53edo: Difference between revisions
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== Theory == | |||
=Theory= | |||
The famous ''53 equal division'' divides the octave into 53 equal comma-sized parts of 22.642 cents each. It is notable as a [[5-limit|5-limit]] system, a fact apparently first noted by Isaac Newton, tempering out the schisma, 32805/32768, the kleisma, 15625/15552, the amity comma, 1600000/1594323 and the semicomma, 2109375/2097152. In the 7-limit it tempers out 225/224, 1728/1715 and 3125/3087, the marvel comma, the gariboh, and the orwell comma. In the 11-limit, it tempers out 99/98 and 121/120, and is the [[Optimal_patent_val|optimal patent val]] for [[Nuwell_family|Big Brother]] temperament, which tempers out both, as well as 11-limit [[Semicomma_family|orwell temperament]], which also tempers out the 11-limit comma 176/175. In the 13-limit, it tempers out 169/168 and 245/243, and gives the optimal patent val for [[Marvel_family|athene temperament]]. It is the eighth [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta integral edo]] and the 16th [[prime_numbers|prime]] edo, following [[47edo|47edo]] and coming before [[59edo|59edo]]. | The famous ''53 equal division'' divides the octave into 53 equal comma-sized parts of 22.642 cents each. It is notable as a [[5-limit|5-limit]] system, a fact apparently first noted by Isaac Newton, tempering out the schisma, 32805/32768, the kleisma, 15625/15552, the amity comma, 1600000/1594323 and the semicomma, 2109375/2097152. In the 7-limit it tempers out 225/224, 1728/1715 and 3125/3087, the marvel comma, the gariboh, and the orwell comma. In the 11-limit, it tempers out 99/98 and 121/120, and is the [[Optimal_patent_val|optimal patent val]] for [[Nuwell_family|Big Brother]] temperament, which tempers out both, as well as 11-limit [[Semicomma_family|orwell temperament]], which also tempers out the 11-limit comma 176/175. In the 13-limit, it tempers out 169/168 and 245/243, and gives the optimal patent val for [[Marvel_family|athene temperament]]. It is the eighth [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta integral edo]] and the 16th [[prime_numbers|prime]] edo, following [[47edo|47edo]] and coming before [[59edo|59edo]]. | ||
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It can also be treated as a no-elevens, no-seventeens tuning, on which it is consistent all the way up to the 21-limit. | It can also be treated as a no-elevens, no-seventeens tuning, on which it is consistent all the way up to the 21-limit. | ||
[http://en.wikipedia.org/wiki/53_equal_temperament Wikipeda article about 53edo] | See also [http://en.wikipedia.org/wiki/53_equal_temperament Wikipeda article about 53edo] | ||
=Linear temperaments= | == Linear temperaments == | ||
[[List_of_edo-distinct_53et_rank_two_temperaments|List of edo-distinct 53et rank two temperaments]] | See [[List_of_edo-distinct_53et_rank_two_temperaments|List of edo-distinct 53et rank two temperaments]] | ||
=Just Approximation= | == Just Approximation == | ||
53edo provides excellent approximations for the classic 5-limit [[just|just]] chords and scales, such as the Ptolemy-Zarlino "just major" scale. | 53edo provides excellent approximations for the classic 5-limit [[just|just]] chords and scales, such as the Ptolemy-Zarlino "just major" scale. | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! | ! interval | ||
! | ! ratio | ||
! | ! size | ||
! | ! difference | ||
|- | |- | ||
| perfect fifth | |||
| 3/2 | |||
| style="text-align:center;" | 31 | | style="text-align:center;" | 31 | ||
| −0.07 cents | |||
|- | |- | ||
| major third | |||
| 5/4 | |||
| style="text-align:center;" | 17 | | style="text-align:center;" | 17 | ||
| −1.40 cents | |||
|- | |- | ||
| minor third | |||
| 6/5 | |||
| style="text-align:center;" | 14 | | style="text-align:center;" | 14 | ||
| +1.34 cents | |||
|- | |- | ||
| major tone | |||
| 9/8 | |||
| style="text-align:center;" | 9 | | style="text-align:center;" | 9 | ||
| −0.14 cents | |||
|- | |- | ||
| minor tone | |||
| 10/9 | |||
| style="text-align:center;" | 8 | | style="text-align:center;" | 8 | ||
| −1.27 cents | |||
|- | |- | ||
| diat. semitone | |||
| 16/15 | |||
| style="text-align:center;" | 5 | | style="text-align:center;" | 5 | ||
| +1.48 cents | |||
|} | |} | ||
One notable property of 53EDO is that it offers good approximations for both pure and pythagorean major thirds. | One notable property of 53EDO is that it offers good approximations for both pure and pythagorean major thirds. | ||
The perfect fifth is almost perfectly equal to the just interval 3/2, with only a 0.07 cent difference! 53EDO is practically equal to an extended Pythagorean. The 14- and 17- degree intervals are also very close to 6/5 and 5/4 respectively, and so 5-limit tuning can also be closely approximated. In addition, the 43-degree interval is only 4.8 cents away from the just ratio 7/4, so 53EDO can also be used for 7-limit harmony, tempering out the [[ | The perfect fifth is almost perfectly equal to the just interval 3/2, with only a 0.07 cent difference! 53EDO is practically equal to an extended Pythagorean. The 14- and 17- degree intervals are also very close to 6/5 and 5/4 respectively, and so 5-limit tuning can also be closely approximated. In addition, the 43-degree interval is only 4.8 cents away from the just ratio 7/4, so 53EDO can also be used for 7-limit harmony, tempering out the [[septimal kleisma]], 225/224. | ||
=Intervals= | == Intervals == | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! | ! degree | ||
! | ! solfege | ||
! | ! cents | ||
! | ! approximate ratios | ||
! colspan="3" | [[User:PiotrGrochowski/Ups_and_Downs_Notation-a|ups and downs]] [[notation]] | ! colspan="3" | [[User:PiotrGrochowski/Ups_and_Downs_Notation-a|ups and downs]] [[notation]] | ||
! | ! generator for | ||
|- | |- | ||
| style="text-align:center;" | 0 | | style="text-align:center;" | 0 | ||
| Line 78: | Line 76: | ||
| style="text-align:center;" | unison | | style="text-align:center;" | unison | ||
| style="text-align:center;" | C | | style="text-align:center;" | C | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 1 | | style="text-align:center;" | 1 | ||
| Line 87: | Line 85: | ||
| style="text-align:center;" | upmajor unison | | style="text-align:center;" | upmajor unison | ||
| style="text-align:center;" | C^ | | style="text-align:center;" | C^ | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 2 | | style="text-align:center;" | 2 | ||
| Line 93: | Line 91: | ||
| style="text-align:center;" | 45.28 | | style="text-align:center;" | 45.28 | ||
| style="text-align:center;" | 49/48, 36/35, 33/32, 128/125 | | style="text-align:center;" | 49/48, 36/35, 33/32, 128/125 | ||
| style="text-align:center;" | ^^1, | | style="text-align:center;" | ^^1, <br/> vvm2 | ||
| style="text-align:center;" | upupmajor unison, <br/> double-down minor 2nd | |||
vvm2 | | style="text-align:center;" | C^^, <br/> Ebvv | ||
| style="text-align:center;" | upupmajor unison | | [[Quartonic]] | ||
double-down minor 2nd | |||
| style="text-align:center;" | C^^, | |||
Ebvv | |||
|- | |- | ||
| style="text-align:center;" | 3 | | style="text-align:center;" | 3 | ||
| Line 111: | Line 103: | ||
| style="text-align:center;" | downdownaugmented unison | | style="text-align:center;" | downdownaugmented unison | ||
| style="text-align:center;" | C#vv | | style="text-align:center;" | C#vv | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 4 | | style="text-align:center;" | 4 | ||
| Line 120: | Line 112: | ||
| style="text-align:center;" | downaugmented unison | | style="text-align:center;" | downaugmented unison | ||
| style="text-align:center;" | C#v | | style="text-align:center;" | C#v | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 5 | | style="text-align:center;" | 5 | ||
| Line 129: | Line 121: | ||
| style="text-align:center;" | augmented unison | | style="text-align:center;" | augmented unison | ||
| style="text-align:center;" | C# | | style="text-align:center;" | C# | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 6 | | style="text-align:center;" | 6 | ||
| Line 138: | Line 130: | ||
| style="text-align:center;" | upupminor second | | style="text-align:center;" | upupminor second | ||
| style="text-align:center;" | Db^^ | | style="text-align:center;" | Db^^ | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 7 | | style="text-align:center;" | 7 | ||
| Line 147: | Line 139: | ||
| style="text-align:center;" | downdownmajor second | | style="text-align:center;" | downdownmajor second | ||
| style="text-align:center;" | Dvv | | style="text-align:center;" | Dvv | ||
| [[Hemikleismic]] | |||
|- | |- | ||
| style="text-align:center;" | 8 | | style="text-align:center;" | 8 | ||
| Line 156: | Line 148: | ||
| style="text-align:center;" | downmajor second | | style="text-align:center;" | downmajor second | ||
| style="text-align:center;" | Dv | | style="text-align:center;" | Dv | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 9 | | style="text-align:center;" | 9 | ||
| Line 165: | Line 157: | ||
| style="text-align:center;" | major second | | style="text-align:center;" | major second | ||
| style="text-align:center;" | D | | style="text-align:center;" | D | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 10 | | style="text-align:center;" | 10 | ||
| Line 174: | Line 166: | ||
| style="text-align:center;" | upmajor 2nd | | style="text-align:center;" | upmajor 2nd | ||
| style="text-align:center;" | E^ | | style="text-align:center;" | E^ | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 11 | | style="text-align:center;" | 11 | ||
| Line 180: | Line 172: | ||
| style="text-align:center;" | 249.06 | | style="text-align:center;" | 249.06 | ||
| style="text-align:center;" | 15/13, 144/125 | | style="text-align:center;" | 15/13, 144/125 | ||
| style="text-align:center;" | ^^M2, | | style="text-align:center;" | ^^M2, <br/> vvm3 | ||
| style="text-align:center;" | double-up major 2nd, <br/> double-down minor 3rd | |||
vvm3 | | style="text-align:center;" | E^^, <br/> Fvv | ||
| style="text-align:center;" | double-up major 2nd, | | [[Hemischis]] | ||
double-down minor 3rd | |||
| style="text-align:center;" | E^^, | |||
Fvv | |||
|- | |- | ||
| style="text-align:center;" | 12 | | style="text-align:center;" | 12 | ||
| Line 198: | Line 184: | ||
| style="text-align:center;" | downminor 3rd | | style="text-align:center;" | downminor 3rd | ||
| style="text-align:center;" | Fv | | style="text-align:center;" | Fv | ||
| [[Orwell]] | |||
|- | |- | ||
| style="text-align:center;" | 13 | | style="text-align:center;" | 13 | ||
| Line 207: | Line 193: | ||
| style="text-align:center;" | minor 3rd | | style="text-align:center;" | minor 3rd | ||
| style="text-align:center;" | F | | style="text-align:center;" | F | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 14 | | style="text-align:center;" | 14 | ||
| Line 216: | Line 202: | ||
| style="text-align:center;" | upminor 3rd | | style="text-align:center;" | upminor 3rd | ||
| style="text-align:center;" | F^ | | style="text-align:center;" | F^ | ||
| [[Hanson]]/[[Catakleismic]] | |||
|- | |- | ||
| style="text-align:center;" | 15 | | style="text-align:center;" | 15 | ||
| Line 225: | Line 211: | ||
| style="text-align:center;" | downmid 3rd | | style="text-align:center;" | downmid 3rd | ||
| style="text-align:center;" | F^^ | | style="text-align:center;" | F^^ | ||
| [[Amity]]/[[Hitchcock]] | |||
|- | |- | ||
| style="text-align:center;" | 16 | | style="text-align:center;" | 16 | ||
| Line 234: | Line 220: | ||
| style="text-align:center;" | upmid 3rd | | style="text-align:center;" | upmid 3rd | ||
| style="text-align:center;" | F#vv | | style="text-align:center;" | F#vv | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 17 | | style="text-align:center;" | 17 | ||
| Line 243: | Line 229: | ||
| style="text-align:center;" | downmajor 3rd | | style="text-align:center;" | downmajor 3rd | ||
| style="text-align:center;" | F#v | | style="text-align:center;" | F#v | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 18 | | style="text-align:center;" | 18 | ||
| Line 252: | Line 238: | ||
| style="text-align:center;" | major 3rd | | style="text-align:center;" | major 3rd | ||
| style="text-align:center;" | F# | | style="text-align:center;" | F# | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 19 | | style="text-align:center;" | 19 | ||
| Line 261: | Line 247: | ||
| style="text-align:center;" | upmajor 3rd | | style="text-align:center;" | upmajor 3rd | ||
| style="text-align:center;" | F#^ | | style="text-align:center;" | F#^ | ||
| [[Hamity]] | |||
|- | |- | ||
| style="text-align:center;" | 20 | | style="text-align:center;" | 20 | ||
| Line 267: | Line 253: | ||
| style="text-align:center;" | 452.83 | | style="text-align:center;" | 452.83 | ||
| style="text-align:center;" | 13/10, 125/96 | | style="text-align:center;" | 13/10, 125/96 | ||
| style="text-align:center;" | ^^M3, | | style="text-align:center;" | ^^M3, <br/> vv4 | ||
| style="text-align:center;" | double-up major 3rd, <br/> double-down 4th | |||
vv4 | | style="text-align:center;" | F#^^, <br/> Gvv | ||
| style="text-align:center;" | double-up major 3rd, | | | ||
double-down 4th | |||
| style="text-align:center;" | F#^^, | |||
Gvv | |||
|- | |- | ||
| style="text-align:center;" | 21 | | style="text-align:center;" | 21 | ||
| Line 285: | Line 265: | ||
| style="text-align:center;" | down 4th | | style="text-align:center;" | down 4th | ||
| style="text-align:center;" | Gv | | style="text-align:center;" | Gv | ||
| [[Vulture]]/[[Buzzard]] | |||
|- | |- | ||
| style="text-align:center;" | 22 | | style="text-align:center;" | 22 | ||
| Line 294: | Line 274: | ||
| style="text-align:center;" | perfect 4th | | style="text-align:center;" | perfect 4th | ||
| style="text-align:center;" | G | | style="text-align:center;" | G | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 23 | | style="text-align:center;" | 23 | ||
| Line 303: | Line 283: | ||
| style="text-align:center;" | up 4th | | style="text-align:center;" | up 4th | ||
| style="text-align:center;" | G^ | | style="text-align:center;" | G^ | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 24 | | style="text-align:center;" | 24 | ||
| Line 312: | Line 292: | ||
| style="text-align:center;" | double-up 4th | | style="text-align:center;" | double-up 4th | ||
| style="text-align:center;" | G^^ | | style="text-align:center;" | G^^ | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 25 | | style="text-align:center;" | 25 | ||
| Line 318: | Line 298: | ||
| style="text-align:center;" | 566.04 | | style="text-align:center;" | 566.04 | ||
| style="text-align:center;" | 18/13 | | style="text-align:center;" | 18/13 | ||
| style="text-align:center;" | vvA4, | | style="text-align:center;" | vvA4, <br/> vd5 | ||
| style="text-align:center;" | double-down aug 4th, <br/> downdim 5th | |||
vd5 | | style="text-align:center;" | G#vv, <br/> Abv | ||
| style="text-align:center;" | double-down aug 4th, | | [[Tricot]] | ||
downdim 5th | |||
| style="text-align:center;" | G#vv, | |||
Abv | |||
|- | |- | ||
| style="text-align:center;" | 26 | | style="text-align:center;" | 26 | ||
| Line 333: | Line 307: | ||
| style="text-align:center;" | 588.68 | | style="text-align:center;" | 588.68 | ||
| style="text-align:center;" | 7/5, 45/32 | | style="text-align:center;" | 7/5, 45/32 | ||
| style="text-align:center;" | vA4, | | style="text-align:center;" | vA4, <br/> d5 | ||
| style="text-align:center;" | downaug 4th, <br/> dim 5th | |||
d5 | | style="text-align:center;" | G#v, <br/> Ab | ||
| style="text-align:center;" | downaug 4th, | | | ||
dim 5th | |||
| style="text-align:center;" | G#v, | |||
Ab | |||
|- | |- | ||
| style="text-align:center;" | 27 | | style="text-align:center;" | 27 | ||
| Line 348: | Line 316: | ||
| style="text-align:center;" | 611.32 | | style="text-align:center;" | 611.32 | ||
| style="text-align:center;" | 10/7, 64/45 | | style="text-align:center;" | 10/7, 64/45 | ||
| style="text-align:center;" | A4, | | style="text-align:center;" | A4, <br/> ^d5 | ||
| style="text-align:center;" | aug 4th, <br/> updim 5th | |||
^d5 | | style="text-align:center;" | G#, <br/> Ab^ | ||
| style="text-align:center;" | aug 4th, | | | ||
updim 5th | |||
| style="text-align:center;" | G#, | |||
Ab^ | |||
|- | |- | ||
| style="text-align:center;" | 28 | | style="text-align:center;" | 28 | ||
| Line 363: | Line 325: | ||
| style="text-align:center;" | 633.96 | | style="text-align:center;" | 633.96 | ||
| style="text-align:center;" | 13/9 | | style="text-align:center;" | 13/9 | ||
| style="text-align:center;" | ^A4, | | style="text-align:center;" | ^A4, <br/> ^^d5 | ||
| style="text-align:center;" | upaug 4th, <br/> double-up dim 5th | |||
^^d5 | | style="text-align:center;" | G#^, <br/> Ab^^ | ||
| style="text-align:center;" | upaug 4th, | | | ||
double-up dim 5th | |||
| style="text-align:center;" | G#^, | |||
Ab^^ | |||
|- | |- | ||
| style="text-align:center;" | 29 | | style="text-align:center;" | 29 | ||
| Line 381: | Line 337: | ||
| style="text-align:center;" | double-down 5th | | style="text-align:center;" | double-down 5th | ||
| style="text-align:center;" | Avv | | style="text-align:center;" | Avv | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 30 | | style="text-align:center;" | 30 | ||
| Line 390: | Line 346: | ||
| style="text-align:center;" | down 5th | | style="text-align:center;" | down 5th | ||
| style="text-align:center;" | Av | | style="text-align:center;" | Av | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 31 | | style="text-align:center;" | 31 | ||
| Line 399: | Line 355: | ||
| style="text-align:center;" | perfect 5th | | style="text-align:center;" | perfect 5th | ||
| style="text-align:center;" | A | | style="text-align:center;" | A | ||
| [[Helmholtz]]/[[Garibaldi]] | |||
|- | |- | ||
| style="text-align:center;" | 32 | | style="text-align:center;" | 32 | ||
| Line 408: | Line 364: | ||
| style="text-align:center;" | up 5th | | style="text-align:center;" | up 5th | ||
| style="text-align:center;" | A^ | | style="text-align:center;" | A^ | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 33 | | style="text-align:center;" | 33 | ||
| Line 414: | Line 370: | ||
| style="text-align:center;" | 747.17 | | style="text-align:center;" | 747.17 | ||
| style="text-align:center;" | 20/13, 192/125 | | style="text-align:center;" | 20/13, 192/125 | ||
| style="text-align:center;" | ^^5, | | style="text-align:center;" | ^^5, <br/> vvm6 | ||
| style="text-align:center;" | double-up 5th, <br/> double-down minor 6th | |||
vvm6 | | style="text-align:center;" | A^^, <br/> Bbvv | ||
| style="text-align:center;" | double-up 5th, | | | ||
double-down minor 6th | |||
| style="text-align:center;" | A^^, | |||
Bbvv | |||
|- | |- | ||
| style="text-align:center;" | 34 | | style="text-align:center;" | 34 | ||
| Line 432: | Line 382: | ||
| style="text-align:center;" | downminor 6th | | style="text-align:center;" | downminor 6th | ||
| style="text-align:center;" | Bbv | | style="text-align:center;" | Bbv | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 35 | | style="text-align:center;" | 35 | ||
| Line 441: | Line 391: | ||
| style="text-align:center;" | minor 6th | | style="text-align:center;" | minor 6th | ||
| style="text-align:center;" | Bb | | style="text-align:center;" | Bb | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 36 | | style="text-align:center;" | 36 | ||
| Line 450: | Line 400: | ||
| style="text-align:center;" | upminor 6th | | style="text-align:center;" | upminor 6th | ||
| style="text-align:center;" | Bb^ | | style="text-align:center;" | Bb^ | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 37 | | style="text-align:center;" | 37 | ||
| Line 459: | Line 409: | ||
| style="text-align:center;" | downmid 6th | | style="text-align:center;" | downmid 6th | ||
| style="text-align:center;" | Bb^^ | | style="text-align:center;" | Bb^^ | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 38 | | style="text-align:center;" | 38 | ||
| Line 468: | Line 418: | ||
| style="text-align:center;" | upmid 6th | | style="text-align:center;" | upmid 6th | ||
| style="text-align:center;" | Bvv | | style="text-align:center;" | Bvv | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 39 | | style="text-align:center;" | 39 | ||
| Line 477: | Line 427: | ||
| style="text-align:center;" | downmajor 6th | | style="text-align:center;" | downmajor 6th | ||
| style="text-align:center;" | Bv | | style="text-align:center;" | Bv | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 40 | | style="text-align:center;" | 40 | ||
| Line 486: | Line 436: | ||
| style="text-align:center;" | major 6th | | style="text-align:center;" | major 6th | ||
| style="text-align:center;" | B | | style="text-align:center;" | B | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 41 | | style="text-align:center;" | 41 | ||
| Line 495: | Line 445: | ||
| style="text-align:center;" | upmajor 6th | | style="text-align:center;" | upmajor 6th | ||
| style="text-align:center;" | B^ | | style="text-align:center;" | B^ | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 42 | | style="text-align:center;" | 42 | ||
| Line 501: | Line 451: | ||
| style="text-align:center;" | 950.94 | | style="text-align:center;" | 950.94 | ||
| style="text-align:center;" | 26/15, 125/72 | | style="text-align:center;" | 26/15, 125/72 | ||
| style="text-align:center;" | ^^M6 | | style="text-align:center;" | ^^M6, <br/> vvm7 | ||
| style="text-align:center;" | double-up major 6th, <br/> double-down minor 7th | |||
vvm7 | | style="text-align:center;" | B^^, <br/> Cvv | ||
| style="text-align:center;" | double-up major 6th, | | | ||
double-down minor 7th | |||
| style="text-align:center;" | B^^, | |||
Cvv | |||
|- | |- | ||
| style="text-align:center;" | 43 | | style="text-align:center;" | 43 | ||
| Line 519: | Line 463: | ||
| style="text-align:center;" | downminor 7th | | style="text-align:center;" | downminor 7th | ||
| style="text-align:center;" | Cv | | style="text-align:center;" | Cv | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 44 | | style="text-align:center;" | 44 | ||
| Line 528: | Line 472: | ||
| style="text-align:center;" | minor 7th | | style="text-align:center;" | minor 7th | ||
| style="text-align:center;" | C | | style="text-align:center;" | C | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 45 | | style="text-align:center;" | 45 | ||
| Line 537: | Line 481: | ||
| 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;" | 46 | | style="text-align:center;" | 46 | ||
| Line 546: | Line 490: | ||
| style="text-align:center;" | downmid 7th | | style="text-align:center;" | downmid 7th | ||
| style="text-align:center;" | C^^ | | style="text-align:center;" | C^^ | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 47 | | style="text-align:center;" | 47 | ||
| Line 555: | Line 499: | ||
| style="text-align:center;" | upmid 7th | | style="text-align:center;" | upmid 7th | ||
| style="text-align:center;" | C#vv | | style="text-align:center;" | C#vv | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 48 | | style="text-align:center;" | 48 | ||
| Line 564: | Line 508: | ||
| style="text-align:center;" | downmajor 7th | | style="text-align:center;" | downmajor 7th | ||
| style="text-align:center;" | C#v | | style="text-align:center;" | C#v | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 49 | | style="text-align:center;" | 49 | ||
| Line 573: | Line 517: | ||
| style="text-align:center;" | major 7th | | style="text-align:center;" | major 7th | ||
| style="text-align:center;" | C# | | style="text-align:center;" | C# | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 50 | | style="text-align:center;" | 50 | ||
| Line 582: | Line 526: | ||
| style="text-align:center;" | upmajor 7th | | style="text-align:center;" | upmajor 7th | ||
| style="text-align:center;" | C#^ | | style="text-align:center;" | C#^ | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 51 | | style="text-align:center;" | 51 | ||
| Line 588: | Line 532: | ||
| style="text-align:center;" | 1154.72 | | style="text-align:center;" | 1154.72 | ||
| style="text-align:center;" | 125/64 | | style="text-align:center;" | 125/64 | ||
| style="text-align:center;" | ^^M7, | | style="text-align:center;" | ^^M7, <br/> vv8 | ||
| style="text-align:center;" | double-up major 7th, <br/> double-down 8ve | |||
vv8 | | style="text-align:center;" | C#^^, <br/> Dvv | ||
| style="text-align:center;" | double-up major 7th, | | | ||
double-down 8ve | |||
| style="text-align:center;" | C#^^, | |||
Dvv | |||
|- | |- | ||
| style="text-align:center;" | 52 | | style="text-align:center;" | 52 | ||
| Line 606: | Line 544: | ||
| style="text-align:center;" | down 8ve | | style="text-align:center;" | down 8ve | ||
| style="text-align:center;" | Dv | | style="text-align:center;" | Dv | ||
| | |||
|- | |- | ||
| style="text-align:center;" | 53 | | style="text-align:center;" | 53 | ||
| Line 615: | Line 553: | ||
| style="text-align:center;" | perfect 8ve | | style="text-align:center;" | perfect 8ve | ||
| style="text-align:center;" | D | | style="text-align:center;" | D | ||
| | |||
|} | |} | ||
Combining ups and downs notation with [[Kite's_color_notation|color notation]], qualities can be loosely associated with colors: | Combining ups and downs notation with [[Kite's_color_notation|color notation]], qualities can be loosely associated with colors: | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! | !quality | ||
! | ! [[Kite's color notation|color]] | ||
! | ! monzo format | ||
! | ! examples | ||
|- | |- | ||
| style="text-align:center;" | downminor | | style="text-align:center;" | downminor | ||
| Line 666: | Line 605: | ||
| style="text-align:center;" | 9/7, 12/7 | | style="text-align:center;" | 9/7, 12/7 | ||
|} | |} | ||
All 53edo chords can be named using ups and downs. Here are the zo, gu, lova, yo and ru triads: | All 53edo chords can be named using ups and downs. Here are the zo, gu, lova, yo and ru triads: | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! | ! [[Kite's color notation|color of the 3rd]] | ||
! | ! JI chord | ||
! | ! notes as edosteps | ||
! | ! notes of C chord | ||
! | ! written name | ||
! | ! spoken name | ||
|- | |- | ||
| style="text-align:center;" | zo | | style="text-align:center;" | zo | ||
| Line 712: | Line 652: | ||
| style="text-align:center;" | C upmajor or C dot up | | style="text-align:center;" | C upmajor or C dot up | ||
|} | |} | ||
[ | For a more complete list, see [[Ups and Downs Notation#Chord names in other EDOs|Ups and Downs Notation - Chord names in other EDOs]]. | ||
[http://www.akjmusic.com/audio/desert_prayer.mp3 Desert Prayer] by [http://www.akjmusic.com/ Aaron Krister Johnson] | == Compositions == | ||
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Khramov/prelude1-53.mp3 Bach WTC1 Prelude 1 in 53] by Bach and [[Mykhaylo_Khramov|Mykhaylo Khramov]] | |||
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Khramov/fugue1-53.mp3 Bach WTC1 Fugue 1 in 53] by Bach and Mykhaylo Khramov | |||
* [http://bumpermusic.blogspot.com/2007/05/whisper-song-in-53-edo-now-526-slower.html Whisper Song in 53EDO] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Prent/sing53-c5-slow.mp3 play] by [[Prent Rodgers]] | |||
* [http://www.archive.org/details/TrioInOrwell Trio in Orwell] [http://www.archive.org/download/TrioInOrwell/TrioInOrwell.mp3 play] by [[Gene Ward Smith]] | |||
* [http://www.akjmusic.com/audio/desert_prayer.mp3 Desert Prayer] by [http://www.akjmusic.com/ Aaron Krister Johnson] | |||
* [http://micro.soonlabel.com/gene_ward_smith/Others/Rodgers/sing53-c5-slow.mp3 Whisper Song in 53 EDO] by [[Prent_Rodgers|Prent Rodgers]] | |||
* [http://andrewheathwaite.bandcamp.com/track/elf-dine-on-ho-ho Elf Dine on Ho Ho] ([http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2005%20Elf%20Dine%20on%20Ho%20Ho.mp3 play]) by [[Andrew Heathwaite]] | |||
* [http://andrewheathwaite.bandcamp.com/track/spun Spun] ([http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2008%20Spun.mp3 play]) by Andrew Heathwaite | |||
* [http://chrisvaisvil.com/the-fallen-of-kleismic15/ The Fallen of Kleismic15][http://micro.soonlabel.com/53edo/20130903_Kleismic%5b15%5d.mp3 play] by [[Chris_Vaisvil|Chris Vaisvil]] | |||
* [https://soundcloud.com/cam-taylor-2-1/mothers mothers] by [[Cam Taylor]] | |||
[[Category:amity]] | [[Category:amity]] | ||
[[Category:athene]] | [[Category:athene]] | ||
| Line 746: | Line 681: | ||
[[Category:semicomma]] | [[Category:semicomma]] | ||
[[Category:zeta]] | [[Category:zeta]] | ||
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[[de:53edo]] | |||