14edo: Difference between revisions
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| style="text-align:center;" | 22/21, 28/27, 21/20 | | style="text-align:center;" | 22/21, 28/27, 21/20 | ||
| style="text-align:center;" | 67 | | style="text-align:center;" | 67 | ||
| style="text-align:center;" | up-unison, | | style="text-align:center;" | up-unison,<br/>down-2nd | ||
down-2nd | |||
| style="text-align:center;" | ^1, v2 | | style="text-align:center;" | ^1, v2 | ||
| style="text-align:center;" | D^, Ev | | style="text-align:center;" | D^, Ev | ||
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| | 2 | | | 2 | ||
| style="text-align:center;" | 171.429 | | style="text-align:center;" | 171.429 | ||
| style="text-align:center;" | 11/10, 10/9, | | style="text-align:center;" | 11/10, 10/9,<br/>19/17 | ||
| style="text-align:center;" | 9/8, 10/9,<br/>11/10, 12/11 | |||
19/17 | |||
| style="text-align:center;" | 9/8, 10/9, | |||
11/10, 12/11 | |||
| style="text-align:center;" | 71 | | style="text-align:center;" | 71 | ||
| style="text-align:center;" | 2nd | | style="text-align:center;" | 2nd | ||
| style="text-align:center;" | 2 | | style="text-align:center;" | 2 | ||
| style="text-align:center;" | E | | style="text-align:center;" | E | ||
| style="text-align:center;" | Neutral 2nd, or | | style="text-align:center;" | Neutral 2nd, or<br/>Narrow Major 2nd | ||
Narrow Major 2nd | |||
|- | |- | ||
| | 3· | | | 3· | ||
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| style="text-align:center;" | 7/6, 8/7 | | style="text-align:center;" | 7/6, 8/7 | ||
| style="text-align:center;" | 37 | | style="text-align:center;" | 37 | ||
| style="text-align:center;" | up-2nd, | | style="text-align:center;" | up-2nd,<br/>down-3rd | ||
down-3rd | |||
| style="text-align:center;" | ^2, v3 | | style="text-align:center;" | ^2, v3 | ||
| style="text-align:center;" | E^, Fv | | style="text-align:center;" | E^, Fv | ||
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| | 5· | | | 5· | ||
| style="text-align:center;" | 428.571 | | style="text-align:center;" | 428.571 | ||
| style="text-align:center;" | 9/7, 14/11, | | style="text-align:center;" | 9/7, 14/11,<br/>22/17 | ||
22/17 | |||
| style="text-align:center;" | 9/7, 14/11 | | style="text-align:center;" | 9/7, 14/11 | ||
| style="text-align:center;" | 41 | | style="text-align:center;" | 41 | ||
| style="text-align:center;" | up-3rd, | | style="text-align:center;" | up-3rd,<br/>down-4th | ||
down-4th | |||
| style="text-align:center;" | ^3, v4 | | style="text-align:center;" | ^3, v4 | ||
| style="text-align:center;" | F^, Gv | | style="text-align:center;" | F^, Gv | ||
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| style="text-align:center;" | 7/5, 10/7 | | style="text-align:center;" | 7/5, 10/7 | ||
| style="text-align:center;" | 91 | | style="text-align:center;" | 91 | ||
| style="text-align:center;" | up-4th, | | style="text-align:center;" | up-4th,<br/>down-5th | ||
down-5th | |||
| style="text-align:center;" | ^4, v5 | | style="text-align:center;" | ^4, v5 | ||
| style="text-align:center;" | G^, Av | | style="text-align:center;" | G^, Av | ||
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| | 9· | | | 9· | ||
| style="text-align:center;" | 771.429 | | style="text-align:center;" | 771.429 | ||
| style="text-align:center;" | 14/9, 11/7, | | style="text-align:center;" | 14/9, 11/7,<br/>17/11 | ||
17/11 | |||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| style="text-align:center;" | 25 | | style="text-align:center;" | 25 | ||
| style="text-align:center;" | up-5th, | | style="text-align:center;" | up-5th,<br/>down-6th | ||
down-6th | |||
| style="text-align:center;" | ^5, v6 | | style="text-align:center;" | ^5, v6 | ||
| style="text-align:center;" | A^, Bv | | style="text-align:center;" | A^, Bv | ||
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| style="text-align:center;" | 12/7, 7/4 | | style="text-align:center;" | 12/7, 7/4 | ||
| style="text-align:center;" | 55 | | style="text-align:center;" | 55 | ||
| style="text-align:center;" | up-6th, | | style="text-align:center;" | up-6th,<br/>down-7th | ||
down-7th | |||
| style="text-align:center;" | ^6, v7 | | style="text-align:center;" | ^6, v7 | ||
| style="text-align:center;" | B^, Cv | | style="text-align:center;" | B^, Cv | ||
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| | 12 | | | 12 | ||
| style="text-align:center;" | 1028.571 | | style="text-align:center;" | 1028.571 | ||
| style="text-align:center;" | 20/11, 9/5, | | style="text-align:center;" | 20/11, 9/5,<br/>34/19 | ||
| style="text-align:center;" | 16/9, 9/5,<br/>20/11, 11/6 | |||
34/19 | |||
| style="text-align:center;" | 16/9, 9/5, | |||
20/11, 11/6 | |||
| style="text-align:center;" | 29 | | style="text-align:center;" | 29 | ||
| style="text-align:center;" | 7th | | style="text-align:center;" | 7th | ||
| style="text-align:center;" | 7 | | style="text-align:center;" | 7 | ||
| style="text-align:center;" | C | | style="text-align:center;" | C | ||
| style="text-align:center;" | Neutral 7th, or | | style="text-align:center;" | Neutral 7th, or<br/>Wide Minor 7th | ||
Wide Minor 7th | |||
|- | |- | ||
| | 13 | | | 13 | ||
| style="text-align:center;" | 1114.286 | | style="text-align:center;" | 1114.286 | ||
| style="text-align:center;" | 19/10, 36/19, | | style="text-align:center;" | 19/10, 36/19,<br/>17/9 | ||
17/9 | |||
| style="text-align:center;" | 21/11, 27/14, 40/21 | | style="text-align:center;" | 21/11, 27/14, 40/21 | ||
| style="text-align:center;" | 61 | | style="text-align:center;" | 61 | ||
| style="text-align:center;" | up-7th, | | style="text-align:center;" | up-7th,<br/>down-8ve | ||
down-8ve | |||
| style="text-align:center;" | ^7, v8 | | style="text-align:center;" | ^7, v8 | ||
| style="text-align:center;" | C^, Dv | | style="text-align:center;" | C^, Dv | ||
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Ups and downs can be used to name 14edo chords. Because every interval is perfect, the quality can be omitted, and the words major, minor, augmented and diminished are never used. | Ups and downs can be used to name 14edo chords. Because every interval is perfect, the quality can be omitted, and the words major, minor, augmented and diminished are never used. | ||
0-4-8 = C E G = C = C or C perfect | 0-4-8 = C E G = C = C or C perfect<br/> | ||
0-3-8 = C Ev G = C(v3) = C down-three<br/> | |||
0-3-8 = C Ev G = C(v3) = C down-three | 0-5-8 = C E^ G = C(^3) = C up-three<br/> | ||
0-4-7 = C E Gv = C(v5) = C down-five<br/> | |||
0-5-8 = C E^ G = C(^3) = C up-three | 0-5-9 = C E^ G^ = C(^3,^5) = C up-three up-five<br/> | ||
0-4-8-12 = C E G B = C7 = C seven<br/> | |||
0-4-7 = C E Gv = C(v5) = C down-five | 0-4-8-11 = C E G Bv = C(v7) = C down-seven<br/> | ||
0-3-8-12 = C Ev G B = C7(v3) = C seven down-three<br/> | |||
0-5-9 = C E^ G^ = C(^3,^5) = C up-three up-five | 0-3-8-11 = C Ev G Bv = C.v7 = C dot down seven<br/> | ||
0-4-8-12 = C E G B = C7 = C seven | |||
0-4-8-11 = C E G Bv = C(v7) = C down-seven | |||
0-3-8-12 = C Ev G B = C7(v3) = C seven down-three | |||
0-3-8-11 = C Ev G Bv = C.v7 = C dot down seven | |||
For a more complete list, see [[Ups_and_Downs_Notation#Chord names in other EDOs|Ups and Downs Notation - Chord names in other EDOs]]. | For a more complete list, see [[Ups_and_Downs_Notation#Chord names in other EDOs|Ups and Downs Notation - Chord names in other EDOs]]. | ||
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Using titanium[9], we could name the intervals of 14edo as follows. The 3, 5, 6, 8, 9, and 11-step intervals are all consonant, while 1, 2, 4, 7, 10, 12, and 13 steps are dissonant. There is no distinction between "perfect" (modulatory) and "imperfect" (major/minor) consonances here; there are enough chords here that root motion may occur by ''any'' consonant interval, and thus ''all'' six consonances are "perfect" intervals, rather than just two of them as in the diatonic system. As in the diatonic scale, the perfect intervals come in pairs separated by a major second, and with a characteristic dissonance between them; in titanium[9] there are three such pairs rather than just one. | Using titanium[9], we could name the intervals of 14edo as follows. The 3, 5, 6, 8, 9, and 11-step intervals are all consonant, while 1, 2, 4, 7, 10, 12, and 13 steps are dissonant. There is no distinction between "perfect" (modulatory) and "imperfect" (major/minor) consonances here; there are enough chords here that root motion may occur by ''any'' consonant interval, and thus ''all'' six consonances are "perfect" intervals, rather than just two of them as in the diatonic system. As in the diatonic scale, the perfect intervals come in pairs separated by a major second, and with a characteristic dissonance between them; in titanium[9] there are three such pairs rather than just one. | ||
1\14: Minor 2nd<span style="vertical-align: sub;">9</span>: functions similarly to the diatonic minor second, but is more incisive. | 1\14: Minor 2nd<span style="vertical-align: sub;">9</span>: functions similarly to the diatonic minor second, but is more incisive.<br/> | ||
2\14: Major 2nd<span style="vertical-align: sub;">9</span>: functions similarly to the diatonic major second, but is narrower and has a rather different quality.<br/> | |||
2\14: Major 2nd<span style="vertical-align: sub;">9</span>: functions similarly to the diatonic major second, but is narrower and has a rather different quality. | 3\14: Perfect 3rd<span style="vertical-align: sub;">9</span>: the generator, standing in for 8:7, 7:6, ''and'' 6:5, but closest to 7:6.<br/> | ||
4\14: Augmented 3rd<span style="vertical-align: sub;">9</span>/diminished 4th<span style="vertical-align: sub;">9</span>: A dissonance, falling in between two perfect consonances and hence analogous to the tritone.<br/> | |||
3\14: Perfect 3rd<span style="vertical-align: sub;">9</span>: the generator, standing in for 8:7, 7:6, ''and'' 6:5, but closest to 7:6. | 5\14: Perfect 4th<span style="vertical-align: sub;">9</span>: technically represents 5:4 but is quite a bit wider.<br/> | ||
6\14: Perfect 5th<span style="vertical-align: sub;">9</span>: represents 4:3 and 7:5, much closer to the former.<br/> | |||
4\14: Augmented 3rd<span style="vertical-align: sub;">9</span>/diminished 4th<span style="vertical-align: sub;">9</span>: A dissonance, falling in between two perfect consonances and hence analogous to the tritone. | 7\14: Augmented 5th<span style="vertical-align: sub;">9</span>/diminished 6th<span style="vertical-align: sub;">9</span>: The so-called "tritone" (but no longer made up of three whole tones). Like 4\14 and 10\14, this is a characteristic<br/> dissonance separating a pair of perfect consonances.<br/> | ||
8\14: Perfect 6th<span style="vertical-align: sub;">9</span>: represents 10:7 and 3:2, much closer to the latter.<br/> | |||
5\14: Perfect 4th<span style="vertical-align: sub;">9</span>: technically represents 5:4 but is quite a bit wider. | 9\14: Perfect 7th<span style="vertical-align: sub;">9</span>: technically represents 5:8 but noticeably narrower.<br/> | ||
10\14: Augmented 7th<span style="vertical-align: sub;">9</span>/diminished 8th<span style="vertical-align: sub;">9</span>: The third and final characteristic dissonance, analogous to the tritone.<br/> | |||
6\14: Perfect 5th<span style="vertical-align: sub;">9</span>: represents 4:3 and 7:5, much closer to the former. | 11\14: Perfect 8th<span style="vertical-align: sub;">9</span>: Represents 5:3, 12:7 and 7:4.<br/> | ||
12\14: Minor 9th<span style="vertical-align: sub;">9</span>: Analogous to the diatonic minor seventh, but sharper than usual.<br/> | |||
7\14: Augmented 5th<span style="vertical-align: sub;">9</span>/diminished 6th<span style="vertical-align: sub;">9</span>: The so-called "tritone" (but no longer made up of three whole tones). Like 4\14 and 10\14, this is a characteristic dissonance separating a pair of perfect consonances. | 13\14: Major 9th<span style="vertical-align: sub;">9</span>: A high, incisive leading tone.<br/> | ||
8\14: Perfect 6th<span style="vertical-align: sub;">9</span>: represents 10:7 and 3:2, much closer to the latter. | |||
9\14: Perfect 7th<span style="vertical-align: sub;">9</span>: technically represents 5:8 but noticeably narrower. | |||
10\14: Augmented 7th<span style="vertical-align: sub;">9</span>/diminished 8th<span style="vertical-align: sub;">9</span>: The third and final characteristic dissonance, analogous to the tritone. | |||
11\14: Perfect 8th<span style="vertical-align: sub;">9</span>: Represents 5:3, 12:7 and 7:4. | |||
12\14: Minor 9th<span style="vertical-align: sub;">9</span>: Analogous to the diatonic minor seventh, but sharper than usual. | |||
13\14: Major 9th<span style="vertical-align: sub;">9</span>: A high, incisive leading tone. | |||
14\14: The 10th<span style="vertical-align: sub;">9 </span>or "enneatonic decave", (i. e., the octave, 2:1). | 14\14: The 10th<span style="vertical-align: sub;">9 </span>or "enneatonic decave", (i. e., the octave, 2:1). | ||
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=[[modes|Modes]]= | =[[modes|Modes]]= | ||
5 5 4 - [[MOSScales|MOS]] of [[2L_1s|2L1s]] | 5 5 4 - [[MOSScales|MOS]] of [[2L_1s|2L1s]]<br/> | ||
5 4 5 - [[MOSScales|MOS]] of [[2L_1s|2L1s]]<br/> | |||
5 4 5 - [[MOSScales|MOS]] of [[2L_1s|2L1s]] | 4 1 4 4 1 - [[MOSScales|MOS]] of [[3L_2s|3L2s]]<br/> | ||
4 1 4 1 4 - [[MOSScales|MOS]] of [[3L_2s|3L2s]]<br/> | |||
4 1 4 4 1 - [[MOSScales|MOS]] of [[3L_2s|3L2s]] | 3 3 3 3 2 - [[MOSScales|MOS]] of [[4L_1s|4L1s]]<br/> | ||
3 2 3 3 3 - [[MOSScales|MOS]] of [[4L_1s|4L1s]]<br/> | |||
4 1 4 1 4 - [[MOSScales|MOS]] of [[3L_2s|3L2s]] | 3 2 2 2 2 3 - [[MOSScales|MOS]] of [[2L_4s|2L4s]]<br/> | ||
2 2 3 2 2 3 - [[MOSScales|MOS]] of [[2L_4s|2L4s]]<br/> | |||
3 3 3 3 2 - [[MOSScales|MOS]] of [[4L_1s|4L1s]] | '''3 3 1 3 3 1 -''' [[MOSScales|MOS]] of [[4L_2s|4L2s]]<br/> | ||
3 1 3 3 1 3 - [[MOSScales|MOS]] of [[4L_2s|4L2s]]<br/> | |||
3 2 3 3 3 - [[MOSScales|MOS]] of [[4L_1s|4L1s]] | 3 1 3 1 3 3 - [[MOSScales|MOS]] of [[4L_2s|4L2s]]<br/> | ||
2 2 1 2 2 2 2 1 - [[MOSScales|MOS]] of [[6L_2s|6L2s]]<br/> | |||
3 2 2 2 2 3 - [[MOSScales|MOS]] of [[2L_4s|2L4s]] | 2 2 2 1 2 2 2 1 - [[MOSScales|MOS]] of [[6L_2s|6L2s]]<br/> | ||
'''2 2 2 2 1 2 2 1 -''' [[MOSScales|MOS]] of [[6L_2s|6L2s]]<br/> | |||
2 2 3 2 2 3 - [[MOSScales|MOS]] of [[2L_4s|2L4s]] | 2 1 2 2 1 2 2 2 - [[MOSScales|MOS]] of [[6L_2s|6L2s]]<br/> | ||
2 1 2 1 2 1 2 1 2 - [[MOSScales|MOS]] of [[5L_4s|5L4s]]<br/> | |||
'''3 3 1 3 3 1 -''' [[MOSScales|MOS]] of [[4L_2s|4L2s]] | 2 1 2 1 2 1 2 2 1 - [[MOSScales|MOS]] of [[5L_4s|5L4s]]<br/> | ||
2 1 2 1 2 2 1 2 1 - [[MOSScales|MOS]] of [[5L_4s|5L4s]]<br/> | |||
3 1 3 3 1 3 - [[MOSScales|MOS]] of [[4L_2s|4L2s]] | 2 1 1 2 1 2 1 1 2 1 - [[MOSScales|MOS]] of [[4L_6s|4L6s]]<br/> | ||
2 1 1 1 2 1 1 2 1 1 1 - [[MOSScales|MOS]] of [[3L_8s|3L8s]]<br/> | |||
3 1 3 1 3 3 - [[MOSScales|MOS]] of [[4L_2s|4L2s]] | '''1 1 2 1 1 1 2 1 1 1 2''' - [[MOSScales|MOS]] of [[3L_8s|3L8s]]<br/> | ||
2 2 1 2 2 2 2 1 - [[MOSScales|MOS]] of [[6L_2s|6L2s]] | |||
2 2 2 1 2 2 2 1 - [[MOSScales|MOS]] of [[6L_2s|6L2s]] | |||
'''2 2 2 2 1 2 2 1 -''' [[MOSScales|MOS]] of [[6L_2s|6L2s]] | |||
2 1 2 2 1 2 2 2 - [[MOSScales|MOS]] of [[6L_2s|6L2s]] | |||
2 1 2 1 2 1 2 1 2 - [[MOSScales|MOS]] of [[5L_4s|5L4s]] | |||
2 1 2 1 2 1 2 2 1 - [[MOSScales|MOS]] of [[5L_4s|5L4s]] | |||
2 1 2 1 2 2 1 2 1 - [[MOSScales|MOS]] of [[5L_4s|5L4s]] | |||
2 1 1 2 1 2 1 1 2 1 - [[MOSScales|MOS]] of [[4L_6s|4L6s]] | |||
2 1 1 1 2 1 1 2 1 1 1 - [[MOSScales|MOS]] of [[3L_8s|3L8s]] | |||
'''1 1 2 1 1 1 2 1 1 1 2''' - [[MOSScales|MOS]] of [[3L_8s|3L8s]] | |||
=Books= | =Books= | ||