25edo: Difference between revisions
Jump to navigation
Jump to search
→Intervals: Removed 7mus column |
updated ups/down notation, added color names to the comma list, general cleanup |
||
| Line 1: | Line 1: | ||
__FORCETOC__ | __FORCETOC__ | ||
= | =Theory= | ||
25EDO divides the [[Octave|octave]] in 25 equal steps of exact size 48 [[cent|cent]]s each. It is a good way to tune the [[Blackwood_temperament|Blackwood temperament]], which takes the very sharp fifths of [[5edo|5EDO]] as a given, tempers out 28/27 and 49/48, and attempts to optimize the tunings for 5 ([[5/4|5/4]]) and 7 ([[7/4|7/4]]). It also tunes sixix temperament with a sharp fifth. It supplies the optimal patent val for the 11-limit 6&25 temperament tempering out 49/48, 77/75 and 605/576, and the 13-limit extension also tempering out 66/65. | 25EDO divides the [[Octave|octave]] in 25 equal steps of exact size 48 [[cent|cent]]s each. It is a good way to tune the [[Blackwood_temperament|Blackwood temperament]], which takes the very sharp fifths of [[5edo|5EDO]] as a given, tempers out 28/27 and 49/48, and attempts to optimize the tunings for 5 ([[5/4|5/4]]) and 7 ([[7/4|7/4]]). It also tunes sixix temperament with a sharp fifth. It supplies the optimal patent val for the 11-limit 6&25 temperament tempering out 49/48, 77/75 and 605/576, and the 13-limit extension also tempering out 66/65. | ||
| Line 7: | Line 7: | ||
If 5/4 and 7/4 aren't good enough, it also does 17/16 and 19/16, just like 12EDO. In fact, on the [[k*N_subgroups|2*25 subgroup]] 2.9.5.7.33.39.17.19 it provides the same tuning and tempers out the same commas as 50et, which makes for a wide range of harmony. | If 5/4 and 7/4 aren't good enough, it also does 17/16 and 19/16, just like 12EDO. In fact, on the [[k*N_subgroups|2*25 subgroup]] 2.9.5.7.33.39.17.19 it provides the same tuning and tempers out the same commas as 50et, which makes for a wide range of harmony. | ||
=Intervals= | =Intervals= | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
| Line 47: | Line 35: | ||
| style="text-align:center;" | ^1, ^m2 | | style="text-align:center;" | ^1, ^m2 | ||
| style="text-align:center;" | up 1sn, upminor 2nd | | style="text-align:center;" | up 1sn, upminor 2nd | ||
| style="text-align:center;" | D^ | | style="text-align:center;" | ^D, ^Eb | ||
|- | |- | ||
| style="text-align:center;" | 2 | | style="text-align:center;" | 2 | ||
| Line 55: | Line 43: | ||
| style="text-align:center;" | ^^m2 | | style="text-align:center;" | ^^m2 | ||
| style="text-align:center;" | double-upminor 2nd | | style="text-align:center;" | double-upminor 2nd | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^Eb | ||
|- | |- | ||
| style="text-align:center;" | 3 | | style="text-align:center;" | 3 | ||
| Line 63: | Line 51: | ||
| style="text-align:center;" | vvM2 | | style="text-align:center;" | vvM2 | ||
| style="text-align:center;" | double-downmajor 2nd | | style="text-align:center;" | double-downmajor 2nd | ||
| style="text-align:center;" | | | style="text-align:center;" | vvE | ||
|- | |- | ||
| style="text-align:center;" | 4 | | style="text-align:center;" | 4 | ||
| Line 71: | Line 59: | ||
| 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;" | 5· | | style="text-align:center;" | 5· | ||
| Line 87: | Line 75: | ||
| 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;" | 7 | | style="text-align:center;" | 7 | ||
| Line 95: | Line 83: | ||
| style="text-align:center;" | ^^m3 | | style="text-align:center;" | ^^m3 | ||
| style="text-align:center;" | double-upminor 3rd | | style="text-align:center;" | double-upminor 3rd | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^F | ||
|- | |- | ||
| style="text-align:center;" | 8· | | style="text-align:center;" | 8· | ||
| Line 103: | Line 91: | ||
| style="text-align:center;" | vvM3 | | style="text-align:center;" | vvM3 | ||
| style="text-align:center;" | double-downmajor 3rd | | style="text-align:center;" | double-downmajor 3rd | ||
| style="text-align:center;" | | | style="text-align:center;" | vvF# | ||
|- | |- | ||
| style="text-align:center;" | 9 | | style="text-align:center;" | 9 | ||
| Line 111: | Line 99: | ||
| style="text-align:center;" | vM3 | | style="text-align:center;" | vM3 | ||
| style="text-align:center;" | downmajor | | style="text-align:center;" | downmajor | ||
| style="text-align:center;" | | | style="text-align:center;" | vF# | ||
|- | |- | ||
| style="text-align:center;" | 10 | | style="text-align:center;" | 10 | ||
| Line 127: | Line 115: | ||
| style="text-align:center;" | ^4 | | style="text-align:center;" | ^4 | ||
| 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;" | 12 | | style="text-align:center;" | 12 | ||
| Line 137: | Line 125: | ||
double-up dim 5th | double-up dim 5th | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^G, ^^Ab | ||
|- | |- | ||
| style="text-align:center;" | 13 | | style="text-align:center;" | 13 | ||
| Line 147: | Line 135: | ||
double-down 5th | double-down 5th | ||
| style="text-align:center;" | | | style="text-align:center;" | vvG#, vvA | ||
|- | |- | ||
| style="text-align:center;" | 14· | | style="text-align:center;" | 14· | ||
| Line 155: | Line 143: | ||
| style="text-align:center;" | v5 | | style="text-align:center;" | v5 | ||
| style="text-align:center;" | down 5th | | style="text-align:center;" | down 5th | ||
| style="text-align:center;" | | | style="text-align:center;" | vA | ||
|- | |- | ||
| style="text-align:center;" | 15 | | style="text-align:center;" | 15 | ||
| Line 171: | Line 159: | ||
| style="text-align:center;" | ^m6 | | style="text-align:center;" | ^m6 | ||
| 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;" | 17· | | style="text-align:center;" | 17· | ||
| Line 179: | Line 167: | ||
| style="text-align:center;" | ^^m6 | | style="text-align:center;" | ^^m6 | ||
| style="text-align:center;" | double-upminor 6th | | style="text-align:center;" | double-upminor 6th | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^Bb | ||
|- | |- | ||
| style="text-align:center;" | 18 | | style="text-align:center;" | 18 | ||
| Line 187: | Line 175: | ||
| style="text-align:center;" | vvM6 | | style="text-align:center;" | vvM6 | ||
| style="text-align:center;" | double-downmajor 6th | | style="text-align:center;" | double-downmajor 6th | ||
| style="text-align:center;" | | | style="text-align:center;" | vvB | ||
|- | |- | ||
| style="text-align:center;" | 19 | | style="text-align:center;" | 19 | ||
| Line 195: | Line 183: | ||
| 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;" | 20· | | style="text-align:center;" | 20· | ||
| Line 211: | Line 199: | ||
| 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;" | 22 | | style="text-align:center;" | 22 | ||
| Line 219: | Line 207: | ||
| style="text-align:center;" | ^^m7 | | style="text-align:center;" | ^^m7 | ||
| style="text-align:center;" | double-upminor 7th | | style="text-align:center;" | double-upminor 7th | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^C | ||
|- | |- | ||
| style="text-align:center;" | 23 | | style="text-align:center;" | 23 | ||
| Line 227: | Line 215: | ||
| style="text-align:center;" | vvM7 | | style="text-align:center;" | vvM7 | ||
| style="text-align:center;" | double-downmajor 7th | | style="text-align:center;" | double-downmajor 7th | ||
| style="text-align:center;" | | | style="text-align:center;" | vvC# | ||
|- | |- | ||
| style="text-align:center;" | 24 | | style="text-align:center;" | 24 | ||
| Line 235: | Line 223: | ||
| style="text-align:center;" | vM7 | | style="text-align:center;" | vM7 | ||
| style="text-align:center;" | downmajor 7th | | style="text-align:center;" | downmajor 7th | ||
| style="text-align:center;" | | | style="text-align:center;" | vC# | ||
|- | |- | ||
| style="text-align:center;" | 25 | | style="text-align:center;" | 25 | ||
| Line 256: | Line 244: | ||
=Commas= | =Commas= | ||
25 EDO tempers out the following commas. (Note: This assumes the val < 25 40 58 70 86 93 |.) | 25 EDO tempers out the following [[commas]]. (Note: This assumes the val < 25 40 58 70 86 93 |.) | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! | | ! | [[Ratio]] | ||
! | Monzo | ! | [[Monzo]] | ||
! | | ! | [[Cents]] | ||
![[Color notation/Temperament Names|Color Name]] | |||
! | Name 1 | ! | Name 1 | ||
! | Name 2 | ! | Name 2 | ||
| Line 270: | Line 259: | ||
| |<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 277: | Line 267: | ||
| |<nowiki> | -10 -1 5 </nowiki>> | | |<nowiki> | -10 -1 5 </nowiki>> | ||
| style="text-align:right;" | 29.61 | | style="text-align:right;" | 29.61 | ||
| style="text-align:center;" |Laquinyo | |||
| style="text-align:center;" | Small Diesis | | style="text-align:center;" | Small Diesis | ||
| style="text-align:center;" | Magic Comma | | style="text-align:center;" | Magic Comma | ||
| Line 284: | Line 275: | ||
| |<nowiki> | 38 -2 -15 </nowiki>> | | |<nowiki> | 38 -2 -15 </nowiki>> | ||
| style="text-align:right;" | 1.38 | | style="text-align:right;" | 1.38 | ||
| style="text-align:center;" |Sasa-quintrigu | |||
| style="text-align:center;" | Hemithirds Comma | | style="text-align:center;" | Hemithirds Comma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 291: | Line 283: | ||
| |<nowiki> | -14 0 0 5 </nowiki>> | | |<nowiki> | -14 0 0 5 </nowiki>> | ||
| style="text-align:right;" | 44.13 | | style="text-align:right;" | 44.13 | ||
| style="text-align:center;" |Laquinzo | |||
| | | | | | ||
| | | | | | ||
| Line 298: | Line 291: | ||
| |<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 305: | Line 299: | ||
| |<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 312: | Line 307: | ||
| |<nowiki> | 0 -2 5 -3 </nowiki>> | | |<nowiki> | 0 -2 5 -3 </nowiki>> | ||
| style="text-align:right;" | 21.18 | | style="text-align:right;" | 21.18 | ||
| style="text-align:center;" |Triru-aquinyo | |||
| style="text-align:center;" | Gariboh | | style="text-align:center;" | Gariboh | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 319: | Line 315: | ||
| |<nowiki> | -4 1 -5 5 </nowiki>> | | |<nowiki> | -4 1 -5 5 </nowiki>> | ||
| style="text-align:right;" | 14.52 | | style="text-align:right;" | 14.52 | ||
| style="text-align:center;" |Quinzogu | |||
| style="text-align:center;" | Trimyna | | style="text-align:center;" | Trimyna | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 326: | Line 323: | ||
| |<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 333: | Line 331: | ||
| |<nowiki> | 6 0 -5 2 </nowiki>> | | |<nowiki> | 6 0 -5 2 </nowiki>> | ||
| style="text-align:right;" | 6.08 | | style="text-align:right;" | 6.08 | ||
| style="text-align:center;" |Zozoquingu | |||
| style="text-align:center;" | Hemimean | | style="text-align:center;" | Hemimean | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 340: | Line 339: | ||
| |<nowiki> | -16 1 5 1 </nowiki>> | | |<nowiki> | -16 1 5 1 </nowiki>> | ||
| style="text-align:right;" | 2.35 | | style="text-align:right;" | 2.35 | ||
| style="text-align:center;" |Lazoquinyo | |||
| style="text-align:center;" | Horwell | | style="text-align:center;" | Horwell | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 347: | Line 347: | ||
| |<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 354: | Line 355: | ||
| |<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 361: | Line 363: | ||
| |<nowiki> | -1 -2 -1 1 0 1 </nowiki>> | | |<nowiki> | -1 -2 -1 1 0 1 </nowiki>> | ||
| style="text-align:right;" | 19.13 | | style="text-align:right;" | 19.13 | ||
| style="text-align:center;" |Thozogu | |||
| style="text-align:center;" | Superleap | | style="text-align:center;" | Superleap | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 368: | Line 371: | ||
| |<nowiki> | 2 -3 -2 0 0 2 </nowiki>> | | |<nowiki> | 2 -3 -2 0 0 2 </nowiki>> | ||
| style="text-align:right;" | 2.56 | | style="text-align:right;" | 2.56 | ||
| style="text-align:center;" |Bithogu | |||
| style="text-align:center;" | Parizeksma | | style="text-align:center;" | Parizeksma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 375: | Line 379: | ||
=A 25edo keyboard= | =A 25edo keyboard= | ||
[[File:mm25.PNG|alt=mm25.PNG|mm25.PNG]] | [[File:mm25.PNG|alt=mm25.PNG|mm25.PNG]] | ||
=Music= | |||
''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Rapoport/StudyInFives.mp3 Study in Fives]'' by [http://en.wikipedia.org/wiki/Paul_Rapoport_%28music_critic%29 Paul Rapoport] | |||
[http://chrisvaisvil.com/?p=2377 Fantasy for Piano in 25 Note per Octave Tuning] ''[http://micro.soonlabel.com/25edo/fantasy_for_piano_in_25_edo.mp3 play]'' by Chris Vaisvil | |||
''[http://micro.soonlabel.com/gene_ward_smith/Others/Fiale/flat%20fourth%20blues.mp3 Flat fourth blues]'' by Fabrizio Fulvio Fausto Fiale | |||
[[File:25edochorale.mid]] [[:File:25edochorale.mid|25edochorale.mid]] Peter Kosmorsky (10/14/10, 2.5.7 subgroup, a friend responded "The <span style="">25edo</span> canon has a nice theme, but all the harmonizations from there are laughably dissonant. I showed them to my roomie and he found it disturbing, hahaha. He had an unintentional physical reaction to it with his mouth in which his muscles did a smirk sort of thing, without him even trying to, hahaha. So, my point; this I think this 25 edo idea was an example of where tonal thinking doesn't suit the sound of the scale.") | |||
[[File:25_edo_prelude_largo.mid]] [[:File:25_edo_prelude_largo.mid|25 edo prelude largo.mid]] Peter Kosmorsky (2011, Blackwood) | |||
[[Category:25edo]] | [[Category:25edo]] | ||
[[Category:edo]] | [[Category:edo]] | ||
Revision as of 08:11, 14 December 2019
Theory
25EDO divides the octave in 25 equal steps of exact size 48 cents each. It is a good way to tune the Blackwood temperament, which takes the very sharp fifths of 5EDO as a given, tempers out 28/27 and 49/48, and attempts to optimize the tunings for 5 (5/4) and 7 (7/4). It also tunes sixix temperament with a sharp fifth. It supplies the optimal patent val for the 11-limit 6&25 temperament tempering out 49/48, 77/75 and 605/576, and the 13-limit extension also tempering out 66/65.
25EDO has fifths 18 cents sharp, but its major thirds are excellent and its 7/4 is acceptable. Moreover, in full 7-limit including the 3, it is not consistent. It therefore makes sense to use it as a 2.5.7 subgroup tuning. Looking just at 2, 5, and 7, it equates five 8/7s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a 128/125 diesis and two septimal tritones of 7/5 with the octave, and hence tempers out 3136/3125. If we want to temper out both of these and also have decent fifths, the obvious solution is 50EDO. An alternative fifth, 14\25, which is 672 cents, provides an alternative very flat fifth which can be used for mavila temperament.
If 5/4 and 7/4 aren't good enough, it also does 17/16 and 19/16, just like 12EDO. In fact, on the 2*25 subgroup 2.9.5.7.33.39.17.19 it provides the same tuning and tempers out the same commas as 50et, which makes for a wide range of harmony.
Intervals
| Degrees | Cents | Approximate
Ratios* |
Armodue
Notation |
ups and downs notation | ||
| 0 | 0 | 1/1 | 1 | P1 | perfect 1sn | D, Eb |
| 1 | 48 | 33/32, 39/38, 34/33 | 1# | ^1, ^m2 | up 1sn, upminor 2nd | ^D, ^Eb |
| 2 | 96 | 17/16, 20/19, 18/17 | 2b | ^^m2 | double-upminor 2nd | ^^Eb |
| 3 | 144 | 12/11, 38/35 | 2 | vvM2 | double-downmajor 2nd | vvE |
| 4 | 192 | 9/8, 10/9, 19/17 | 2# | vM2 | downmajor 2nd | vE |
| 5· | 240 | 8/7 | 3b | M2, m3 | major 2nd, minor 3rd | E, F |
| 6 | 288 | 19/16, 20/17 | 3 | ^m3 | upminor 3rd | ^F |
| 7 | 336 | 39/32, 17/14, 40/33 | 3# | ^^m3 | double-upminor 3rd | ^^F |
| 8· | 384 | 5/4 | 4b | vvM3 | double-downmajor 3rd | vvF# |
| 9 | 432 | 9/7, 32/25, 50/39 | 4 | vM3 | downmajor | vF# |
| 10 | 480 | 33/25, 25/19 | 4#/5b | M3, P4 | major 3rd, perfect 4th | F#, G |
| 11· | 528 | 31/21, 34/25 | 5 | ^4 | up 4th | ^G |
| 12 | 576 | 7/5, 39/28 | 5# | ^^4,^^d5 | double-up 4th,
double-up dim 5th |
^^G, ^^Ab |
| 13 | 624 | 10/7, 56/39 | 6b | vvA4,vv5 | double-down aug 4th,
double-down 5th |
vvG#, vvA |
| 14· | 672 | 42/31, 25/17 | 6 | v5 | down 5th | vA |
| 15 | 720 | 50/33, 38/25 | 6# | P5, m6 | perfect 5th, minor 6th | A, Bb |
| 16 | 768 | 14/9, 25/16, 39/25 | 7b | ^m6 | upminor 6th | ^Bb |
| 17· | 816 | 8/5 | 7 | ^^m6 | double-upminor 6th | ^^Bb |
| 18 | 864 | 64/39, 28/17, 33/20 | 7# | vvM6 | double-downmajor 6th | vvB |
| 19 | 912 | 32/19, 17/10 | 8b | vM6 | downmajor 6th | vB |
| 20· | 960 | 7/4 | 8 | M6, m7 | major 6th, minor 7th | B, C |
| 21 | 1008 | 16/9, 9/5, 34/19 | 8# | ^m7 | upminor 7th | ^C |
| 22 | 1056 | 11/6, 35/19 | 9b | ^^m7 | double-upminor 7th | ^^C |
| 23 | 1104 | 32/17, 17/9, 19/10 | 9 | vvM7 | double-downmajor 7th | vvC# |
| 24 | 1152 | 33/17, 64/33, 76/39 | 9#/1b | vM7 | downmajor 7th | vC# |
| 25 | 1200 | 2/1 | 1 | P8 | perfect 8ve | C#, D |
- based on treating 25-EDO as a 2.9.5.7.33.39.17.19 subgroup; other approaches are possible.
Relationship to Armodue
Like 16-EDO and 23-EDO, 25-EDO contains the 9-note "Superdiatonic" scale of 7L2s (LLLsLLLLs) that is generated by a circle of heavily-flattened 3/2s (ranging in size from 5\9-EDO or 666.67 cents, to 4\7-EDO or 685.71 cents). The 25-EDO generator for this scale is the 672-cent interval. This allows 25-EDO to be used with the Armodue notation system in much the same way that 19-EDO is used with the standard diatonic notation; see the above interval chart for the Armodue names. Because the 25-EDO Armodue 6th is flatter than that of 16-EDO (the middle of the Armodue spectrum), sharps are lower in pitch than enharmonic flats.
Commas
25 EDO tempers out the following commas. (Note: This assumes the val < 25 40 58 70 86 93 |.)
| Ratio | Monzo | Cents | Color Name | Name 1 | Name 2 | Name 3 |
|---|---|---|---|---|---|---|
| 256/243 | | 8 -5 > | 90.22 | Sawa | Limma | Pythagorean Minor 2nd | |
| 3125/3072 | | -10 -1 5 > | 29.61 | Laquinyo | Small Diesis | Magic Comma | |
| | 38 -2 -15 > | 1.38 | Sasa-quintrigu | Hemithirds Comma | |||
| 16807/16384 | | -14 0 0 5 > | 44.13 | Laquinzo | |||
| 49/48 | | -4 -1 0 2 > | 35.70 | Zozo | Slendro Diesis | ||
| 64/63 | | 6 -2 0 -1 > | 27.26 | Ru | Septimal Comma | Archytas' Comma | Leipziger Komma |
| 3125/3087 | | 0 -2 5 -3 > | 21.18 | Triru-aquinyo | Gariboh | ||
| 50421/50000 | | -4 1 -5 5 > | 14.52 | Quinzogu | Trimyna | ||
| 1029/1024 | | -10 1 0 3 > | 8.43 | Latrizo | Gamelisma | ||
| 3136/3125 | | 6 0 -5 2 > | 6.08 | Zozoquingu | Hemimean | ||
| 65625/65536 | | -16 1 5 1 > | 2.35 | Lazoquinyo | Horwell | ||
| 100/99 | | 2 -2 2 0 -1 > | 17.40 | Luyoyo | Ptolemisma | ||
| 176/175 | | 4 0 -2 -1 1 > | 9.86 | Lorugugu | Valinorsma | ||
| 91/90 | | -1 -2 -1 1 0 1 > | 19.13 | Thozogu | Superleap | ||
| 676/675 | | 2 -3 -2 0 0 2 > | 2.56 | Bithogu | Parizeksma |
A 25edo keyboard
Music
Study in Fives by Paul Rapoport
Fantasy for Piano in 25 Note per Octave Tuning play by Chris Vaisvil
Flat fourth blues by Fabrizio Fulvio Fausto Fiale
File:25edochorale.mid 25edochorale.mid Peter Kosmorsky (10/14/10, 2.5.7 subgroup, a friend responded "The 25edo canon has a nice theme, but all the harmonizations from there are laughably dissonant. I showed them to my roomie and he found it disturbing, hahaha. He had an unintentional physical reaction to it with his mouth in which his muscles did a smirk sort of thing, without him even trying to, hahaha. So, my point; this I think this 25 edo idea was an example of where tonal thinking doesn't suit the sound of the scale.")
File:25 edo prelude largo.mid 25 edo prelude largo.mid Peter Kosmorsky (2011, Blackwood)