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| downminor
| downminor
| zo
| zo
| (a, b, 0, 1)
| style="white-space: nowrap;" | (a, b, 0, 1)
| 7/6, 7/4
| 7/6, 7/4
|-
|-
| rowspan="2" | minor
| rowspan="2" | minor
| fourthward wa
| fourthward wa
| (a, b), b < -1
| style="white-space: nowrap;" | (a, b), b < −1
| 32/27, 16/9
| 32/27, 16/9
|-
|-
| gu
| gu
| (a, b, -1)
| style="white-space: nowrap;" | (a, b, −1)
| 6/5, 9/5
| 6/5, 9/5
|-
|-
| rowspan="2" | mid
| rowspan="2" | mid
| ilo
| ilo
| (a, b, 0, 0, 1)
| style="white-space: nowrap;" | (a, b, 0, 0, 1)
| 11/9, 11/6
| 11/9, 11/6
|-
|-
| lu
| lu
| (a, b, 0, 0, -1)
| style="white-space: nowrap;" | (a, b, 0, 0, −1)
| 12/11, 18/11
| 12/11, 18/11
|-
|-
| rowspan="2" | major
| rowspan="2" | major
| yo
| yo
| (a, b, 1)
| style="white-space: nowrap;" | (a, b, 1)
| 5/4, 5/3
| 5/4, 5/3
|-
|-
| fifthward wa
| fifthward wa
| (a, b), b > 1
| style="white-space: nowrap;" | (a, b), b > 1
| 9/8, 27/16
| 9/8, 27/16
|-
|-
| upmajor
| upmajor
| ru
| ru
| (a, b, 0, -1)
| style="white-space: nowrap;" | (a, b, 0, −1)
| 9/7, 12/7
| 9/7, 12/7
|}
|}
Line 541: Line 541:
| 81/80, 121/120, 128/125
| 81/80, 121/120, 128/125
| [{{val| 24 38 56 83 }}]
| [{{val| 24 38 56 83 }}]
| −1.08
| −1.08
| 2.82
| 2.82
| 5.63
| 5.63
Line 548: Line 548:
| 66/65, 81/80, 128/125, 144/143
| 66/65, 81/80, 128/125, 144/143
| [{{val| 24 38 56 83 89 }}]
| [{{val| 24 38 56 83 89 }}]
| −1.37
| −1.37
| 2.59
| 2.59
| 5.19
| 5.19
Line 555: Line 555:
| 51/50, 66/65, 81/80, 128/125, 144/143
| 51/50, 66/65, 81/80, 128/125, 144/143
| [{{val| 24 38 56 83 89 98 }}]
| [{{val| 24 38 56 83 89 98 }}]
| −0.94
| −0.94
| 2.55
| 2.55
| 5.11
| 5.11
Line 562: Line 562:
| 51/50, 66/65, 76/75, 81/80, 128/125, 144/143
| 51/50, 66/65, 76/75, 81/80, 128/125, 144/143
| [{{val| 24 38 56 83 89 98 102 }}]
| [{{val| 24 38 56 83 89 98 102 }}]
| −0.89
| −0.89
| 2.37
| 2.37
| 4.74
| 4.74
Line 1,006: Line 1,006:
|-
|-
| 6:7:9, 26:30:39
| 6:7:9, 26:30:39
| {{dash|0, 5, 14|s=hair|d=med}}
| {{dash|0, 5, 14|hair}}
| {{dash|C, E{{sesquiflat2}}, G|s=hair|d=med}}
| {{dash|C, E{{sesquiflat2}}, G|hair}}
| Cvm<br />Cm({{demiflat2}}3), Cmin({{demiflat2}}3)
| Cvm<br />Cm({{demiflat2}}3), Cmin({{demiflat2}}3)
| C subminor<br />C minor semiflat-three
| C subminor<br />C minor semiflat-three
|-
|-
| 10:12:15
| 10:12:15
| {{dash|0, 6, 14|s=hair|d=med}}
| {{dash|0, 6, 14|hair}}
| {{dash|C, E♭, G|s=hair|d=med}}
| {{dash|C, E♭, G|hair}}
| Cm, Cmin
| Cm, Cmin
| C minor
| C minor
Line 1,019: Line 1,019:
| 18:22:27, 22:27:33
| 18:22:27, 22:27:33
| 0-7-14
| 0-7-14
| {{dash|C, E{{demiflat2}}, G|s=hair|d=med}}
| {{dash|C, E{{demiflat2}}, G|hair}}
| C~, Cneu
| C~, Cneu
| C neutral
| C neutral
|-
|-
| 4:5:6
| 4:5:6
| {{dash|0, 8, 14|s=hair|d=med}}
| {{dash|0, 8, 14|hair}}
| {{dash|C, E, G|s=hair|d=med}}
| {{dash|C, E, G|hair}}
| C, Cmaj
| C, Cmaj
| C, C major
| C, C major
|-
|-
| 14:18:21, 10:13:15
| 14:18:21, 10:13:15
| {{dash|0, 9, 14|s=hair|d=med}}
| {{dash|0, 9, 14|hair}}
| {{dash|C, E{{demisharp2}}, G|s=hair|d=med}}
| {{dash|C, E{{demisharp2}}, G|hair}}
| C^<br />C({{demisharp2}}3), Cmaj({{demisharp2}}3)
| C^<br />C({{demisharp2}}3), Cmaj({{demisharp2}}3)
| C supermajor<br />C major semisharp-three
| C supermajor<br />C major semisharp-three
|}
|}


These chords tend to lack the forcefulness to sound like resolved, tonal sonorities, but can be resolved of that issue by using tetrads in place of triads. For example, the neutral triad can have the neutral 7th added to it to make a full neutral tetrad: {{dash|0, 7, 14, 21|s=hair|d=med}}. However, another option is to replace the neutral third with an 11/8 to produce a sort of 11 limit neutral tetrad: {{dash|0, 14, 21, 35|s=hair|d=med}} [[William Lynch]] considers this chord to be the most consonant tetrad in 24edo involving a neutral tonality.  
These chords tend to lack the forcefulness to sound like resolved, tonal sonorities, but can be resolved of that issue by using tetrads in place of triads. For example, the neutral triad can have the neutral 7th added to it to make a full neutral tetrad: {{dash|0, 7, 14, 21|hair}}. However, another option is to replace the neutral third with an 11/8 to produce a sort of 11 limit neutral tetrad: {{dash|0, 14, 21, 35|hair}} [[William Lynch]] considers this chord to be the most consonant tetrad in 24edo involving a neutral tonality.  


24edo also is very good at 15 limit and does 13 quite well allowing barbodos 10:13:15 and barbodos minor triad 26:30:39 to be used as an entirely new harmonic system.
24edo also is very good at 15 limit and does 13 quite well allowing barbodos 10:13:15 and barbodos minor triad 26:30:39 to be used as an entirely new harmonic system.
Line 1,042: Line 1,042:
More good chords in 24edo:
More good chords in 24edo:


* {{dash|0, 4, 8, 11, 14|s=hair|d=med}} ("major" chord with a 9:8 and a 11:8 above the root)
* {{dash|0, 4, 8, 11, 14|hair}} ("major" chord with a 9:8 and a 11:8 above the root)
* Its inversion, {{dash|0, 3, 6, 10, 14|s=hair|d=med}} ("minor")
* Its inversion, {{dash|0, 3, 6, 10, 14|hair}} ("minor")
* 0-5-10 (another kind of "neutral", splitting the fourth in two. The {{dash|0, 5, 10|s=hair|d=med}} can be extended into a ([[Godzilla]]) pentatonic scale ({{dash|0, 5, 10, 14, 19, 24|s=hair|d=med}}), that is close to equi-pentatonic and also close to several Indonesian slendro scales. In a similar way {{dash|0, 7, 14|s=hair|d=med}} extends to {{dash|0, 4, 7, 11, 14, 18, 21, 24|s=hair|d=med}} ([[mohajira]]), a heptatonic scale close to several Arabic scales.)
* 0-5-10 (another kind of "neutral", splitting the fourth in two. The {{dash|0, 5, 10|hair}} can be extended into a ([[Godzilla]]) pentatonic scale ({{dash|0, 5, 10, 14, 19, 24|hair}}), that is close to equi-pentatonic and also close to several Indonesian slendro scales. In a similar way {{dash|0, 7, 14|hair}} extends to {{dash|0, 4, 7, 11, 14, 18, 21, 24|hair}} ([[mohajira]]), a heptatonic scale close to several Arabic scales.)


William Lynch considers these as some possible good tetrads:
William Lynch considers these as some possible good tetrads:
Line 1,059: Line 1,059:
! Audio example
! Audio example
|-
|-
| {{dash|0, 5, 14, 19|s=hair|d=med}}
| {{dash|0, 5, 14, 19|hair}}
| {{dash|1, vb3, 5, vb7|s=hair|d=med}}
| {{dash|1, vb3, 5, vb7|hair}}
| {{dash|C, E{{sesquiflat2}}, G, B{{sesquiflat2}}|s=hair|d=med}}
| {{dash|C, E{{sesquiflat2}}, G, B{{sesquiflat2}}|hair}}
| smin7<br />min7({{demiflat2}}3, {{demiflat2}}7)
| smin7<br />min7({{demiflat2}}3, {{demiflat2}}7)
| Subminor seven<br />Minor seven semiflat-three semiflat-seven
| Subminor seven<br />Minor seven semiflat-three semiflat-seven
|  
|  
|-
|-
| {{dash|0, 6, 14, 20|s=hair|d=med}}
| {{dash|0, 6, 14, 20|hair}}
| {{dash|1, b3, 5, b7|s=hair|d=med}}
| {{dash|1, b3, 5, b7|hair}}
| {{dash|C, E♭, G, B♭|s=hair|d=med}}
| {{dash|C, E♭, G, B♭|hair}}
| m7, min7
| m7, min7
| Minor seven
| Minor seven
|  
|  
|-
|-
| {{dash|0, 7, 14, 21|s=hair|d=med}}
| {{dash|0, 7, 14, 21|hair}}
| {{dash|1, v3, 5, v7|s=hair|d=med}}
| {{dash|1, v3, 5, v7|hair}}
| {{dash|C, E{{demiflat2}}, G, B{{demiflat2}}|s=hair|d=med}}
| {{dash|C, E{{demiflat2}}, G, B{{demiflat2}}|hair}}
| n7, neu7
| n7, neu7
| Neutral seven
| Neutral seven
| [[File:Neutral Tetrad on C.mp3]]
| [[File:Neutral Tetrad on C.mp3]]
|-
|-
| {{dash|0, 8, 14, 22|s=hair|d=med}}
| {{dash|0, 8, 14, 22|hair}}
| {{dash|1, b3, 5, b7|s=hair|d=med}}
| {{dash|1, b3, 5, b7|hair}}
| {{dash|C, E, G, B|s=hair|d=med}}
| {{dash|C, E, G, B|hair}}
| maj7
| maj7
| Major seven
| Major seven
|  
|  
|-
|-
| {{dash|0, 8, 14, 22|s=hair|d=med}}
| {{dash|0, 8, 14, 22|hair}}
| {{dash|1, b3, 5, b7|s=hair|d=med}}
| {{dash|1, b3, 5, b7|hair}}
| {{dash|C, E{{demisharp2}}, G, B{{demisharp2}}|s=hair|d=med}}
| {{dash|C, E{{demisharp2}}, G, B{{demisharp2}}|hair}}
| smaj7<br />maj7({{demisharp2}}3, {{demisharp2}}7)
| smaj7<br />maj7({{demisharp2}}3, {{demisharp2}}7)
| Supermajor seven<br />Major seven semisharp-three semisharp-seven
| Supermajor seven<br />Major seven semisharp-three semisharp-seven
|  
|  
|-
|-
| {{dash|0, 8, 14, 20|s=hair|d=med}}
| {{dash|0, 8, 14, 20|hair}}
| {{dash|1, 3, 5, b7|s=hair|d=med}}
| {{dash|1, 3, 5, b7|hair}}
| {{dash|C, E, G, B♭|s=hair|d=med}}
| {{dash|C, E, G, B♭|hair}}
| 7, dom7
| 7, dom7
| Dominant seven
| Dominant seven
|  
|  
|-
|-
| {{dash|0, 8, 14, 19|s=hair|d=med}}
| {{dash|0, 8, 14, 19|hair}}
| {{dash|1, 3, 5, vb7|s=hair|d=med}}
| {{dash|1, 3, 5, vb7|hair}}
| {{dash|C, E, G, B{{sesquiflat2}}|s=hair|d=med}}
| {{dash|C, E, G, B{{sesquiflat2}}|hair}}
| h7<br />7({{demiflat2}}7)
| h7<br />7({{demiflat2}}7)
| Harmonic seven<br />Dominant 7 semiflat-seven
| Harmonic seven<br />Dominant 7 semiflat-seven
|  
|  
|-
|-
| {{dash|0, 5, 14, 20|s=hair|d=med}}
| {{dash|0, 5, 14, 20|hair}}
| {{dash|1, vb3, 5, b7|s=hair|d=med}}
| {{dash|1, vb3, 5, b7|hair}}
| {{dash|C, E{{sesquiflat2}}, G, B♭|s=hair|d=med}}
| {{dash|C, E{{sesquiflat2}}, G, B♭|hair}}
| min7({{demiflat2}}3)
| min7({{demiflat2}}3)
| Arto<br />Minor seven semiflat-three
| Arto<br />Minor seven semiflat-three
| [[File:arto tetrad on C.mp3]]
| [[File:arto tetrad on C.mp3]]
|-
|-
| {{dash|0, 9, 14, 19|s=hair|d=med}}
| {{dash|0, 9, 14, 19|hair}}
| {{dash|1, ^3, 5, vb7|s=hair|d=med}}
| {{dash|1, ^3, 5, vb7|hair}}
| {{dash|C, E{{demisharp2}}, G, B{{sesquiflat2}}|s=hair|d=med}}
| {{dash|C, E{{demisharp2}}, G, B{{sesquiflat2}}|hair}}
| h7({{demisharp2}}3)<br />7({{demisharp2}}3, {{demiflat2}}7)
| h7({{demisharp2}}3)<br />7({{demisharp2}}3, {{demiflat2}}7)
| Tendo<br />Harmonic seven semisharp-three<br />Dominant seven semisharp-three semiflat-seven
| Tendo<br />Harmonic seven semisharp-three<br />Dominant seven semisharp-three semiflat-seven
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