8edo: Difference between revisions
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{{Harmonics in equal|8|intervals=odd}} | {{Harmonics in equal|8|intervals=odd}} | ||
[[File:8edo scale.mp3|thumb|A chromatic 8edo scale on C.]] | [[File:8edo scale.mp3|thumb|A chromatic 8edo scale on C.]] | ||
8edo forms an odd and even pitch set of two diminished seventh chords, which when used in combination yield dissonance. The system has been described as a "barbaric" harmonic system; even so, it does a good job representing the [[just intonation subgroup]]s 2.11/3.13/5, with good intervals of [[13/10]] and an excellent version of [[11/6]]. Stacking the 450-cent interval can result in some semi-consonant chords such as 0-3-6 | 8edo forms an odd and even pitch set of two diminished seventh chords, which when used in combination yield dissonance. The system has been described as a "barbaric" harmonic system; even so, it does a good job representing the [[just intonation subgroup]]s 2.11/3.13/5, with good intervals of [[13/10]] and an excellent version of [[11/6]]. Stacking the 450-cent interval can result in some semi-consonant chords such as 0-3-6 degrees, although these still are quite dissonant compared to standard root-3rd-P5 triads, which are unavailable in 8edo. | ||
Another way of looking at 8edo is to treat a chord of 0-1-2-3-4 degrees (0-150-300-450-600 cents) as approximating harmonics 10:11:12:13:14 (~0-165-316-454-583 cents), which is not too implausible if you can buy that 12edo is a 5-limit temperament. This interpretation would imply that 121/120, 144/143, 169/168, and hence also 36/35 and 66/65, are tempered out. | Another way of looking at 8edo is to treat a chord of 0-1-2-3-4 degrees (0-150-300-450-600 cents) as approximating harmonics 10:11:12:13:14 (~0-165-316-454-583 cents), which is not too implausible if you can buy that 12edo is a 5-limit temperament. This interpretation would imply that 121/120, 144/143, 169/168, and hence also 36/35 and 66/65, are tempered out. | ||
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! colspan="2" | 24edo subset notation | ! colspan="2" | 24edo subset notation | ||
! colspan="2" | 16edo subset notation | ! colspan="2" | 16edo subset notation | ||
! [[3L 2s]] notation | ! [[3L 2s]] notation (J = 1/1) | ||
!Audio | !Audio | ||
|- | |- | ||
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| D | | D | ||
|[[File:0-0 unison.mp3|frameless]] | |[[File:0-0 unison.mp3|frameless]] | ||
| J | |||
|- | |- | ||
| 1 | | 1 | ||
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| E | | E | ||
|[[File:0-150 (8-EDO).mp3|frameless]] | |[[File:0-150 (8-EDO).mp3|frameless]] | ||
| K | |||
|- | |- | ||
| 2 | | 2 | ||
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| F# | | F# | ||
|[[File:0-300 (12-EDO).mp3|frameless]] | |[[File:0-300 (12-EDO).mp3|frameless]] | ||
| K#, Lb | |||
|- | |- | ||
| 3 | | 3 | ||
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| Fb / G# | | Fb / G# | ||
|[[File:0-450 (8-EDO).mp3|frameless]] | |[[File:0-450 (8-EDO).mp3|frameless]] | ||
| L | |||
|- | |- | ||
| 4 | | 4 | ||
| Line 73: | Line 77: | ||
| Gb / A# | | Gb / A# | ||
|[[File:0-600 (12-EDO).mp3|frameless]] | |[[File:0-600 (12-EDO).mp3|frameless]] | ||
| M | |||
|- | |- | ||
| 5 | | 5 | ||
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| Ab / B# | | Ab / B# | ||
|[[File:0-750 (8-EDO).mp3|frameless]] | |[[File:0-750 (8-EDO).mp3|frameless]] | ||
| M#, Nb | |||
|- | |- | ||
| 6 | | 6 | ||
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| Bb | | Bb | ||
|[[File:0-900 (12-EDO).mp3|frameless]] | |[[File:0-900 (12-EDO).mp3|frameless]] | ||
| N | |||
|- | |- | ||
| 7 | | 7 | ||
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| C | | C | ||
|[[File:0-1050 (8-EDO).mp3|frameless]] | |[[File:0-1050 (8-EDO).mp3|frameless]] | ||
| N#, Jb | |||
|- | |- | ||
| 8 | | 8 | ||
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| D | | D | ||
|[[File:0-1200 octave.mp3|frameless]] | |[[File:0-1200 octave.mp3|frameless]] | ||
| J | |||
|} | |} | ||