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| __FORCETOC__
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| =Theory=
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| 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.
| | == Theory == |
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| 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|consistent]]. It therefore makes sense to use it as a 2.5.7 [[Just_intonation_subgroups|subgroup]] tuning. Looking just at 2, 5, and 7, it equates five [[8/7|8/7]]s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a [[128/125|128/125]] [[diesis|diesis]] and two [[septimal_tritones|septimal tritones]] of [[7/5|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|50EDO]]. An alternative fifth, 14\25, which is 672 cents, provides an alternative very flat fifth which can be used for [[Mavila|mavila]] temperament. | | 25EDO divides the [[octave]] in 25 equal steps of exact size 48 [[cent]]s 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. |
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| | 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 [[Just intonation subgroups|subgroup]] tuning. Looking just at 2, 5, and 7, it equates five [[8/7]]s 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. |
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| 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. |
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| =Intervals= | | == Intervals == |
| {| class="wikitable" | | |
| | {| class="wikitable center-all" |
| |- | | |- |
| | style="text-align:center;" | Degrees
| | | Degrees |
| | style="text-align:center;" | Cents
| | | Cents |
| | style="text-align:center;" | Approximate
| | | Approximate <br> Ratios* |
| | | | Armodue <br> Notation |
| Ratios* | | | colspan="3" | [[Ups and Downs notation]] |
| | style="text-align:center;" | Armodue
| |
| | |
| Notation | |
| | colspan="3" style="text-align:center;" | [[Ups_and_Downs_Notation|ups and downs notation]] | |
| |- | | |- |
| | style="text-align:center;" | 0
| | | 0 |
| | style="text-align:center;" | 0
| | | 0 |
| | style="text-align:center;" | 1/1
| | | 1/1 |
| | style="text-align:center;" | 1
| | | 1 |
| | style="text-align:center;" | P1
| | | P1 |
| | style="text-align:center;" | perfect 1sn
| | | perfect 1sn |
| | style="text-align:center;" | D, Eb
| | | D, Eb |
| |- | | |- |
| | style="text-align:center;" | 1
| | | 1 |
| | style="text-align:center;" | 48
| | | 48 |
| | style="text-align:center;" | 33/32, 39/38, 34/33
| | | 33/32, 39/38, 34/33 |
| | style="text-align:center;" | 1#
| | | 1# |
| | style="text-align:center;" | ^1, ^m2
| | | ^1, ^m2 |
| | style="text-align:center;" | up 1sn, upminor 2nd
| | | up 1sn, upminor 2nd |
| | style="text-align:center;" | ^D, ^Eb
| | | ^D, ^Eb |
| |- | | |- |
| | style="text-align:center;" | 2
| | | 2 |
| | style="text-align:center;" | 96
| | | 96 |
| | style="text-align:center;" | 17/16, 20/19, 18/17
| | | 17/16, 20/19, 18/17 |
| | style="text-align:center;" | 2b
| | | 2b |
| | style="text-align:center;" | v~2
| | | v~2 |
| | style="text-align:center;" | downmid 2nd
| | | downmid 2nd |
| | style="text-align:center;" | ^^Eb
| | | ^^Eb |
| |- | | |- |
| | style="text-align:center;" | 3
| | | 3 |
| | style="text-align:center;" | 144
| | | 144 |
| | style="text-align:center;" | 12/11, 38/35
| | | 12/11, 38/35 |
| | style="text-align:center;" | 2
| | | 2 |
| | style="text-align:center;" | ^~2
| | | ^~2 |
| | style="text-align:center;" | upmid 2nd
| | | upmid 2nd |
| | style="text-align:center;" | vvE
| | | vvE |
| |- | | |- |
| | style="text-align:center;" | 4
| | | 4 |
| | style="text-align:center;" | 192
| | | 192 |
| | style="text-align:center;" | 9/8, 10/9, 19/17
| | | 9/8, 10/9, 19/17 |
| | style="text-align:center;" | 2#
| | | 2# |
| | style="text-align:center;" | vM2
| | | vM2 |
| | style="text-align:center;" | downmajor 2nd
| | | downmajor 2nd |
| | style="text-align:center;" | vE
| | | vE |
| |- | | |- |
| | style="text-align:center;" | 5·
| | | 5· |
| | style="text-align:center;" | 240
| | | 240 |
| | style="text-align:center;" | 8/7
| | | 8/7 |
| | style="text-align:center;" | 3b
| | | 3b |
| | style="text-align:center;" | M2, m3
| | | M2, m3 |
| | style="text-align:center;" | major 2nd, minor 3rd
| | | major 2nd, minor 3rd |
| | style="text-align:center;" | E, F
| | | E, F |
| |- | | |- |
| | style="text-align:center;" | 6
| | | 6 |
| | style="text-align:center;" | 288
| | | 288 |
| | style="text-align:center;" | 19/16, 20/17
| | | 19/16, 20/17 |
| | style="text-align:center;" | 3
| | | 3 |
| | style="text-align:center;" | ^m3
| | | ^m3 |
| | style="text-align:center;" | upminor 3rd
| | | upminor 3rd |
| | style="text-align:center;" | ^F
| | | ^F |
| |- | | |- |
| | style="text-align:center;" | 7
| | | 7 |
| | style="text-align:center;" | 336
| | | 336 |
| | style="text-align:center;" | 39/32, 17/14, 40/33
| | | 39/32, 17/14, 40/33 |
| | style="text-align:center;" | 3#
| | | 3# |
| | style="text-align:center;" | v~3
| | | v~3 |
| | style="text-align:center;" | downmid 3rd
| | | downmid 3rd |
| | style="text-align:center;" | ^^F
| | | ^^F |
| |- | | |- |
| | style="text-align:center;" | 8·
| | | 8· |
| | style="text-align:center;" | 384
| | | 384 |
| | style="text-align:center;" | 5/4
| | | 5/4 |
| | style="text-align:center;" | 4b
| | | 4b |
| | style="text-align:center;" | ^~3
| | | ^~3 |
| | style="text-align:center;" | upmid 3rd
| | | upmid 3rd |
| | style="text-align:center;" | vvF#
| | | vvF# |
| |- | | |- |
| | style="text-align:center;" | 9
| | | 9 |
| | style="text-align:center;" | 432
| | | 432 |
| | style="text-align:center;" | 9/7, 32/25, 50/39
| | | 9/7, 32/25, 50/39 |
| | style="text-align:center;" | 4
| | | 4 |
| | style="text-align:center;" | vM3
| | | vM3 |
| | style="text-align:center;" | downmajor
| | | downmajor |
| | style="text-align:center;" | vF#
| | | vF# |
| |- | | |- |
| | style="text-align:center;" | 10
| | | 10 |
| | style="text-align:center;" | 480
| | | 480 |
| | style="text-align:center;" | 33/25, 25/19
| | | 33/25, 25/19 |
| | style="text-align:center;" | 4#/5b
| | | 4#/5b |
| | style="text-align:center;" | M3, P4
| | | M3, P4 |
| | style="text-align:center;" | major 3rd, perfect 4th
| | | major 3rd, perfect 4th |
| | style="text-align:center;" | F#, G
| | | F#, G |
| |- | | |- |
| | style="text-align:center;" | 11·
| | | 11· |
| | style="text-align:center;" | 528
| | | 528 |
| | style="text-align:center;" | 31/21, 34/25
| | | 31/21, 34/25 |
| | style="text-align:center;" | 5
| | | 5 |
| | style="text-align:center;" | ^4
| | | ^4 |
| | style="text-align:center;" | up 4th
| | | up 4th |
| | style="text-align:center;" | ^G
| | | ^G |
| |- | | |- |
| | style="text-align:center;" | 12
| | | 12 |
| | style="text-align:center;" | 576
| | | 576 |
| | style="text-align:center;" | 7/5, 39/28
| | | 7/5, 39/28 |
| | style="text-align:center;" | 5#
| | | 5# |
| | style="text-align:center;" | v~4,v~5
| | | v~4,v~5 |
| | style="text-align:center;" | downmid 4th,
| | | downmid 4th, <br> downmid 5th |
| | | | ^^G, ^^Ab |
| downmid 5th | |
| | style="text-align:center;" | ^^G, ^^Ab
| |
| |- | | |- |
| | style="text-align:center;" | 13
| | | 13 |
| | style="text-align:center;" | 624
| | | 624 |
| | style="text-align:center;" | 10/7, 56/39
| | | 10/7, 56/39 |
| | style="text-align:center;" | 6b
| | | 6b |
| | style="text-align:center;" | ^~4,^~5
| | | ^~4,^~5 |
| | style="text-align:center;" | upmid 4th,
| | | upmid 4th, <br> upmid 5th |
| | | | vvG#, vvA |
| upmid 5th | |
| | style="text-align:center;" | vvG#, vvA
| |
| |- | | |- |
| | style="text-align:center;" | 14·
| | | 14· |
| | style="text-align:center;" | 672
| | | 672 |
| | style="text-align:center;" | 42/31, 25/17
| | | 42/31, 25/17 |
| | style="text-align:center;" | 6
| | | 6 |
| | style="text-align:center;" | v5
| | | v5 |
| | style="text-align:center;" | down 5th
| | | down 5th |
| | style="text-align:center;" | vA
| | | vA |
| |- | | |- |
| | style="text-align:center;" | 15
| | | 15 |
| | style="text-align:center;" | 720
| | | 720 |
| | style="text-align:center;" | 50/33, 38/25
| | | 50/33, 38/25 |
| | style="text-align:center;" | 6#
| | | 6# |
| | style="text-align:center;" | P5, m6
| | | P5, m6 |
| | style="text-align:center;" | perfect 5th, minor 6th
| | | perfect 5th, minor 6th |
| | style="text-align:center;" | A, Bb
| | | A, Bb |
| |- | | |- |
| | style="text-align:center;" | 16
| | | 16 |
| | style="text-align:center;" | 768
| | | 768 |
| | style="text-align:center;" | 14/9, 25/16, 39/25
| | | 14/9, 25/16, 39/25 |
| | style="text-align:center;" | 7b
| | | 7b |
| | style="text-align:center;" | ^m6
| | | ^m6 |
| | style="text-align:center;" | upminor 6th
| | | upminor 6th |
| | style="text-align:center;" | ^Bb
| | | ^Bb |
| |- | | |- |
| | style="text-align:center;" | 17·
| | | 17· |
| | style="text-align:center;" | 816
| | | 816 |
| | style="text-align:center;" | 8/5
| | | 8/5 |
| | style="text-align:center;" | 7
| | | 7 |
| | style="text-align:center;" | v~6
| | | v~6 |
| | style="text-align:center;" | downmid 6th
| | | downmid 6th |
| | style="text-align:center;" | ^^Bb
| | | ^^Bb |
| |- | | |- |
| | style="text-align:center;" | 18
| | | 18 |
| | style="text-align:center;" | 864
| | | 864 |
| | style="text-align:center;" | 64/39, 28/17, 33/20
| | | 64/39, 28/17, 33/20 |
| | style="text-align:center;" | 7#
| | | 7# |
| | style="text-align:center;" | ^~6
| | | ^~6 |
| | style="text-align:center;" | upmid 6th
| | | upmid 6th |
| | style="text-align:center;" | vvB
| | | vvB |
| |- | | |- |
| | style="text-align:center;" | 19
| | | 19 |
| | style="text-align:center;" | 912
| | | 912 |
| | style="text-align:center;" | 32/19, 17/10
| | | 32/19, 17/10 |
| | style="text-align:center;" | 8b
| | | 8b |
| | style="text-align:center;" | vM6
| | | vM6 |
| | style="text-align:center;" | downmajor 6th
| | | downmajor 6th |
| | style="text-align:center;" | vB
| | | vB |
| |- | | |- |
| | style="text-align:center;" | 20·
| | | 20· |
| | style="text-align:center;" | 960
| | | 960 |
| | style="text-align:center;" | 7/4
| | | 7/4 |
| | style="text-align:center;" | 8
| | | 8 |
| | style="text-align:center;" | M6, m7
| | | M6, m7 |
| | style="text-align:center;" | major 6th, minor 7th
| | | major 6th, minor 7th |
| | style="text-align:center;" | B, C
| | | B, C |
| |- | | |- |
| | style="text-align:center;" | 21
| | | 21 |
| | style="text-align:center;" | 1008
| | | 1008 |
| | style="text-align:center;" | 16/9, 9/5, 34/19
| | | 16/9, 9/5, 34/19 |
| | style="text-align:center;" | 8#
| | | 8# |
| | style="text-align:center;" | ^m7
| | | ^m7 |
| | style="text-align:center;" | upminor 7th
| | | upminor 7th |
| | style="text-align:center;" | ^C
| | | ^C |
| |- | | |- |
| | style="text-align:center;" | 22
| | | 22 |
| | style="text-align:center;" | 1056
| | | 1056 |
| | style="text-align:center;" | 11/6, 35/19
| | | 11/6, 35/19 |
| | style="text-align:center;" | 9b
| | | 9b |
| | style="text-align:center;" | v~7
| | | v~7 |
| | style="text-align:center;" | downmid 7th
| | | downmid 7th |
| | style="text-align:center;" | ^^C
| | | ^^C |
| |- | | |- |
| | style="text-align:center;" | 23
| | | 23 |
| | style="text-align:center;" | 1104
| | | 1104 |
| | style="text-align:center;" | 32/17, 17/9, 19/10
| | | 32/17, 17/9, 19/10 |
| | style="text-align:center;" | 9
| | | 9 |
| | style="text-align:center;" | ^~7
| | | ^~7 |
| | style="text-align:center;" | upmid 7th
| | | upmid 7th |
| | style="text-align:center;" | vvC#
| | | vvC# |
| |- | | |- |
| | style="text-align:center;" | 24
| | | 24 |
| | style="text-align:center;" | 1152
| | | 1152 |
| | style="text-align:center;" | 33/17, 64/33, 76/39
| | | 33/17, 64/33, 76/39 |
| | style="text-align:center;" | 9#/1b
| | | 9#/1b |
| | style="text-align:center;" | vM7
| | | vM7 |
| | style="text-align:center;" | downmajor 7th
| | | downmajor 7th |
| | style="text-align:center;" | vC#
| | | vC# |
| |- | | |- |
| | style="text-align:center;" | 25
| | | 25 |
| | style="text-align:center;" | 1200
| | | 1200 |
| | style="text-align:center;" | 2/1
| | | 2/1 |
| | style="text-align:center;" | 1
| | | 1 |
| | style="text-align:center;" | P8
| | | P8 |
| | style="text-align:center;" | perfect 8ve
| | | perfect 8ve |
| | style="text-align:center;" | C#, D
| | | C#, D |
| |} | | |} |
| *based on treating 25-EDO as a 2.9.5.7.33.39.17.19 subgroup; other approaches are possible. | | *based on treating 25-EDO as a 2.9.5.7.33.39.17.19 subgroup; other approaches are possible. |
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| [[:File:25ed2-001.svg|25ed2-001.svg]] | | [[:File:25ed2-001.svg|25ed2-001.svg]] |
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| =Relationship to Armodue= | | == Relationship to Armodue == |
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| Like [[16edo|16-EDO]] and [[23edo|23-EDO]], 25-EDO contains the 9-note "Superdiatonic" scale of [[7L_2s|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_theory|Armodue]] notation system in much the same way that [[19edo|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. | | Like [[16edo|16-EDO]] and [[23edo|23-EDO]], 25-EDO contains the 9-note "Superdiatonic" scale of [[7L_2s|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_theory|Armodue]] notation system in much the same way that [[19edo|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. |
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| =Commas= | | == Commas == |
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| 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 |.) |
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| {| class="wikitable" | | {| class="wikitable center-all left-2 right-3" |
| |- | | |- |
| ! | [[Ratio]] | | ! [[Ratio]] |
| ! | [[Monzo]] | | ! [[Monzo]] |
| ! | [[Cents]] | | ! [[Cents]] |
| ![[Color notation/Temperament Names|Color Name]] | | ! [[Color name]] |
| ! | Name 1 | | ! Name 1 |
| ! | Name 2 | | ! Name 2 |
| ! | Name 3 | | ! Name 3 |
| |- | | |- |
| | style="text-align:center;" | 256/243
| | | 256/243 |
| | |<nowiki> | 8 -5 </nowiki>> | | | {{Monzo| 8 -5 }} |
| | style="text-align:right;" | 90.22
| | | 90.22 |
| | style="text-align:center;" |Sawa
| | | Sawa |
| | style="text-align:center;" | Limma
| | | Limma |
| | style="text-align:center;" | Pythagorean Minor 2nd
| | | Pythagorean Minor 2nd |
| | style="text-align:center;" |
| | | |
| |- | | |- |
| | style="text-align:center;" | 3125/3072
| | | 3125/3072 |
| | |<nowiki> | -10 -1 5 </nowiki>> | | | {{Monzo| -10 -1 5 }} |
| | style="text-align:right;" | 29.61
| | | 29.61 |
| | style="text-align:center;" |Laquinyo
| | | Laquinyo |
| | style="text-align:center;" | Small Diesis
| | | Small Diesis |
| | style="text-align:center;" | Magic Comma
| | | Magic Comma |
| | style="text-align:center;" |
| | | |
| |- | | |- |
| | style="text-align:center;" |
| | | |
| | |<nowiki> | 38 -2 -15 </nowiki>> | | | {{Monzo| 38 -2 -15 }} |
| | style="text-align:right;" | 1.38
| | | 1.38 |
| | style="text-align:center;" |Sasa-quintrigu
| | | Sasa-quintrigu |
| | style="text-align:center;" | Hemithirds Comma
| | | Hemithirds Comma |
| | style="text-align:center;" |
| | | |
| | style="text-align:center;" |
| | | |
| |- | | |- |
| | style="text-align:center;" | 16807/16384
| | | 16807/16384 |
| | |<nowiki> | -14 0 0 5 </nowiki>> | | | {{Monzo| -14 0 0 5 }} |
| | style="text-align:right;" | 44.13
| | | 44.13 |
| | style="text-align:center;" |Laquinzo
| | | Laquinzo |
| | |
| | | |
| | |
| | | |
| | |
| | | |
| |- | | |- |
| | style="text-align:center;" | 49/48
| | | 49/48 |
| | |<nowiki> | -4 -1 0 2 </nowiki>> | | | {{Monzo| -4 -1 0 2 }} |
| | style="text-align:right;" | 35.70
| | | 35.70 |
| | style="text-align:center;" |Zozo
| | | Zozo |
| | style="text-align:center;" | Slendro Diesis
| | | Slendro Diesis |
| | style="text-align:center;" |
| | | |
| | style="text-align:center;" |
| | | |
| |- | | |- |
| | style="text-align:center;" | 64/63
| | | 64/63 |
| | |<nowiki> | 6 -2 0 -1 </nowiki>> | | | {{Monzo| 6 -2 0 -1 }} |
| | style="text-align:right;" | 27.26
| | | 27.26 |
| | style="text-align:center;" |Ru
| | | Ru |
| | style="text-align:center;" | Septimal Comma
| | | Septimal Comma |
| | style="text-align:center;" | Archytas' Comma
| | | Archytas' Comma |
| | style="text-align:center;" | Leipziger Komma
| | | Leipziger Komma |
| |- | | |- |
| | style="text-align:center;" | 3125/3087
| | | 3125/3087 |
| | |<nowiki> | 0 -2 5 -3 </nowiki>> | | | {{Monzo| 0 -2 5 -3 }} |
| | style="text-align:right;" | 21.18
| | | 21.18 |
| | style="text-align:center;" |Triru-aquinyo
| | | Triru-aquinyo |
| | style="text-align:center;" | Gariboh
| | | Gariboh |
| | style="text-align:center;" |
| | | |
| | style="text-align:center;" |
| | | |
| |- | | |- |
| | style="text-align:center;" | 50421/50000
| | | 50421/50000 |
| | |<nowiki> | -4 1 -5 5 </nowiki>> | | | {{Monzo| -4 1 -5 5 }} |
| | style="text-align:right;" | 14.52
| | | 14.52 |
| | style="text-align:center;" |Quinzogu
| | | Quinzogu |
| | style="text-align:center;" | Trimyna
| | | Trimyna |
| | style="text-align:center;" |
| | | |
| | style="text-align:center;" |
| | | |
| |- | | |- |
| | style="text-align:center;" | 1029/1024
| | | 1029/1024 |
| | |<nowiki> | -10 1 0 3 </nowiki>> | | | {{Monzo| -10 1 0 3 }} |
| | style="text-align:right;" | 8.43
| | | 8.43 |
| | style="text-align:center;" |Latrizo
| | | Latrizo |
| | style="text-align:center;" | Gamelisma
| | | Gamelisma |
| | style="text-align:center;" |
| | | |
| | style="text-align:center;" |
| | | |
| |- | | |- |
| | style="text-align:center;" | 3136/3125
| | | 3136/3125 |
| | |<nowiki> | 6 0 -5 2 </nowiki>> | | | {{Monzo| 6 0 -5 2 }} |
| | style="text-align:right;" | 6.08
| | | 6.08 |
| | style="text-align:center;" |Zozoquingu
| | | Zozoquingu |
| | style="text-align:center;" | Hemimean
| | | Hemimean |
| | style="text-align:center;" |
| | | |
| | style="text-align:center;" |
| | | |
| |- | | |- |
| | style="text-align:center;" | 65625/65536
| | | 65625/65536 |
| | |<nowiki> | -16 1 5 1 </nowiki>> | | | {{Monzo| -16 1 5 1 }} |
| | style="text-align:right;" | 2.35
| | | 2.35 |
| | style="text-align:center;" |Lazoquinyo
| | | Lazoquinyo |
| | style="text-align:center;" | Horwell
| | | Horwell |
| | style="text-align:center;" |
| | | |
| | style="text-align:center;" |
| | | |
| |- | | |- |
| | style="text-align:center;" | 100/99
| | | 100/99 |
| | |<nowiki> | 2 -2 2 0 -1 </nowiki>> | | | {{Monzo| 2 -2 2 0 -1 }} |
| | style="text-align:right;" | 17.40
| | | 17.40 |
| | style="text-align:center;" |Luyoyo
| | | Luyoyo |
| | style="text-align:center;" | Ptolemisma
| | | Ptolemisma |
| | style="text-align:center;" |
| | | |
| | style="text-align:center;" |
| | | |
| |- | | |- |
| | style="text-align:center;" | 176/175
| | | 176/175 |
| | |<nowiki> | 4 0 -2 -1 1 </nowiki>> | | | {{Monzo| 4 0 -2 -1 1 }} |
| | style="text-align:right;" | 9.86
| | | 9.86 |
| | style="text-align:center;" |Lorugugu
| | | Lorugugu |
| | style="text-align:center;" | Valinorsma
| | | Valinorsma |
| | style="text-align:center;" |
| | | |
| | style="text-align:center;" |
| | | |
| |- | | |- |
| | style="text-align:center;" | 91/90
| | | 91/90 |
| | |<nowiki> | -1 -2 -1 1 0 1 </nowiki>> | | | {{Monzo| -1 -2 -1 1 0 1 }} |
| | style="text-align:right;" | 19.13
| | | 19.13 |
| | style="text-align:center;" |Thozogu
| | | Thozogu |
| | style="text-align:center;" | Superleap
| | | Superleap |
| | style="text-align:center;" |
| | | |
| | style="text-align:center;" |
| | | |
| |- | | |- |
| | style="text-align:center;" | 676/675
| | | 676/675 |
| | |<nowiki> | 2 -3 -2 0 0 2 </nowiki>> | | | {{Monzo| 2 -3 -2 0 0 2 }} |
| | style="text-align:right;" | 2.56
| | | 2.56 |
| | style="text-align:center;" |Bithogu
| | | Bithogu |
| | style="text-align:center;" | Parizeksma
| | | Parizeksma |
| | style="text-align:center;" |
| | | |
| | style="text-align:center;" |
| | | |
| |} | | |} |
|
| |
|
| =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]
| |
|
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| [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
| |
|
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| ''[http://micro.soonlabel.com/gene_ward_smith/Others/Fiale/flat%20fourth%20blues.mp3 Flat fourth blues]'' by Fabrizio Fulvio Fausto Fiale
| | == Music == |
|
| |
|
| [[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.") | | * [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]] by [[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]] by Peter Kosmorsky (2011, Blackwood) |
|
| |
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| [[File:25_edo_prelude_largo.mid]] [[:File:25_edo_prelude_largo.mid|25 edo prelude largo.mid]] Peter Kosmorsky (2011, Blackwood)
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| [[Category:25edo]] | | [[Category:25edo]] |
| [[Category:edo]] | | [[Category:Edo]] |
| [[Category:keyboard]] | | [[Category:Keyboard]] |
| [[Category:listen]] | | [[Category:Listen]] |
| [[Category:subgroup]] | | [[Category:Subgroup]] |
| [[Category:todo:unify_precision]] | | [[Category:Twentuning]] |
| [[Category:twentuning]]
| |