User:VectorGraphics/intro to 5edo
5edo is the smallest edo. that's technically not true, but it's the smallest one that you didn't just get because you bought 12edo from EA and they ripped you off.
one of the most important musical intervals is the 5th. here is the 5th. [0 720c] sound weird and dissonant? well, tough luck. hey, i remember saying this before. other intervals in 5edo include the fourth [0 480c], the second [0 240c], the seventh [0 960c], the octave [0 1200c], and that's it. there are no other intervals. ok, there's technically the unison but that's an interval in the same way multiplying by 1 is a multiplication. in fact, that's literally what it is. what about thirds and sixths? there are none. well, kind of. you can use other intervals as thirds and sixths. let's call these notes C, D, E, G, and A, because those are the notes of the pentatonic scale, the other main scale that has 5 notes. F and B don't exist because 5edo actually breaks the way we name notes. you see, we name notes by stacking fifths. a fifth above C is, by definition, G. a fifth above G is D, then A, then E, and then B, but when you get to B in 5edo it turns out it is actually exactly the same note as C. similarly, sharps and flats are redundant because adding two more fifths to get to F# and C#, you will find that C# is in fact D. even if you tried to redefine sharps and flats to make sense in this context, the smallest step available IS that from C to D, so you can't.
anyway, back to theory. let's use all five notes of the scale for now, because they kind of sound like a pentatonic scale. remember when I said thirds didn't exist? well, you can still do a kind of triadic harmony by using what are basically sus4 and sus2 chords. i.e. [0 480c 720c] and [0 240c 720c]. note that these are inversions of each other, unlike normal major and minor chords, so it's important that you establish your root note, otherwise you can accidentally use the wrong chord. or is it the same chord in a different context? i dunno. but 5edo is actually small enough that you can actually categorize every single chord or scale spanning up to an octave - there are 16 of them, and 7 up to inversions.
| ID | Notes | Name | Inversion class |
|---|---|---|---|
| 0 | C | unison | unison |
| 1 | C,D | second | second |
| 2 | C,E | fourth | fourth |
| 3 | C,D,E | diminished triad | diminished triad |
| 4 | C,G | fifth | fourth |
| 5 | C,D,G | minor triad | sus triad |
| 6 | C,E,G | major triad | sus triad |
| 7 | C,D,E,G | diminished seventh | diminished seventh |
| 8 | C,A | seventh | second |
| 9 | C,D,A | diminished triad | |
| 10 | C,E,A | augmented triad | sus triad |
| 11 | C,D,E,A | diminished seventh | |
| 12 | C,G,A | diminished triad | |
| 13 | C,D,G,A | diminished seventh | |
| 14 | C,E,G,A | diminished seventh | |
| 15 | C,D,E,G,A | entire scale | scale |
that's it. that's all of them. of course, there are more if you're willing to exceed the octave