User:Eboone/EDO Impressions

I, at least currently, work strictly in edos. I don't tend to go any higher than 72edo in my own works, so here are my impressions of all the positive integer edos up to 72. This page is designed to be read wholly from top to bottom, but you can still read specific entries in isolation.

Of course, the tier list above is subject to change in the future, as are all of the impressions on this page.

All demos are created by me in MuseScore 3. They are all short loops at 120 bpm and are meant to be in a style I think works well in that edo.

EDOs I haven't gotten to yet are marked with "placeholder."

Categorization

I have split these edos into categories based on step size:

1-9edo — Macrotonal (133.33-1200¢)
10-19edo — Semitonal (63.16-120¢)
20-29edo — Macro-Diesitonal (41.38-60¢)
30-39edo — Micro-Diesitonal (30.77-40¢)
40-55edo — Super-syntonic (21.82-30¢)
56-72edo — Sub-syntonic (16.67-21.43¢)

These terms are not standard in any way. I just made them up.

Macrotonal

1edo

Tier: F

1edo metal on E

Honestly, can this one even be called an edo? I mean, "equal divisions of the octave" implies that the octave is divided. Anyway, this edo is pretty lame because the whole point of using different temperaments is to access different melodic and harmonic opportunities, and this edo doesn't allow any of that. The only way to make this edo musical is through rhythm, dynamics, form, etc... stuff that isn't related to tuning.

Although, technically there is some room for "melodic" expression if you allow yourself to use devices such as pitch bend. Or, perhaps you could use timbres that don't exactly settle on one pitch but clearly aren't unpitched either, like an old guitar string with wobbly harmonics. These "cheat codes" are partially what make one-note jazz solos so interesting, but of course the rest of the interest comes from the novelty of playing only one note amidst an electron cloud of dissonance. On its own, there really isn't much this temperament offers.

At least it's better than 0edo.

2edo

Tier: F

2edo mischievous theme on E and B♭

This edo is literally just a tritone. And, in this case, it's a rather interesting one. It's the 600¢ hemioctave tritone, the only one that is its own octave complement. So, while its melodic and harmonic capabilities in isolation are pretty bare, its symmetrical nature allows for some cool gimmicks. If instead it were, say, 11/8, that would open the possibility of using both 11/8 and 16/11, its octave complement. This would allow for greater melodic and harmonic expression, but at the expense of having a neat symmetrical tritone.

To illustrate this tritone's nature, the demo for this edo is completely flipped on its head. If you listen carefully, you will notice that the pizzicato violins and celli play each other's part upside down in the second half of the loop. The gimmick is that this only affects contour, not the harmony. So yeah, that's pretty cool.

Anyway, this edo isn't much. In fact, I can't honestly say it's any better than 1edo. In theory, there should be no reason to choose 1edo over 2edo, but how much does that one extra note really add in practice? At the end of the day, both edos are mere novelties.

3edo

Tier: F+

3edo "brumous" ambience on D augmented

This edo is just an augmented triad, but specifically one that is derived by stacking three 400¢ major thirds. This means it closes the octave and, as such, is its own inversion. So, once again, the melodic and harmonic capabilities of this triad in isolation are pretty slim compared to, say, one derived by stacking 5/4. Yet, the symmetrical nature of this chord allows for quite a "sturdy" sound that helps to keep the temperament together.

The demo for this edo has a foggy, perhaps misty vibe. The uninvertible nature of the augmented triad is illustrated in the synth, as it oscillates between two inversions of the triad yet the quality of the chord remains utterly identical. If it were any other type of augmented triad, the inversions would still sound quite similar but they would each have a different vibe.

Anyway, I'd say this edo is definitely more interesting than 1edo and 2edo, mostly because it is the smallest edo with a triad.

4edo

Tier: F+

4edo fanfare on B diminished

While I wouldn't necessarily say 2edo is a better version of 1edo, I will say 4edo is a better version of 2edo. It's a diminished tetrad, but specifically one that is derived by stacking four 300¢ minor thirds. This means it closes the octave and, as such, is its own inversion. So, as always, the melodic and harmonic capabilities of this tetrad in isolation are pretty slim compared to, say, one derived by stacking 6/5. Yet, the symmetrical nature of this chord allows for quite a, dare I say, "sturdy" sound that helps to keep the temperament together.

Sounding familiar? Yeah, I'd say this edo is on equal footing with 3edo. You could certainly argue that it's better than 3edo, considering it contains two interlocked instances of 2edo, as well as an extra note. This seems like a convincing case for 4edo, but I personally think that augmented triads are more interesting than diminished tetrads in isolation. It's really all about taste, as is everything in the world of xenharmony.

By the way, you won't be seeing F tier for a while after this. These first four edos are honestly just memes, so no amount of good things I say about them can eke them out of F tier. Now, on to the edos people actually care about.

5edo

Tier: B-

This is the first edo with a perfect fifth, but it's pretty sharp, coming in at 720¢ (18.04¢ sharp of 3/2). This means 5edo works best in timbres with quick decay, like a marimba, so that the dissonance of the fifth is softened. Although, the sharp fifth when used melodically has quite a desirable "uplifting" quality that brings it out amidst the texture of the rest of the scale. This edo also features interseptimal intervals, giving melodies an "open" quality. It's a bit reminiscent of the minor pentatonic scale of 12edo, making it quite familiar to unaccustomed ears, but still with a tang of xen. Overall, this is a fun edo to work in, it's just that it suffers from the same problem that all very small edos have; there just aren't enough notes. It isn't a very versatile edo, so you usually have to rely on nontonal musical factors such as rhythm, dynamics, and form to create an interesting piece.

6edo

Tier: C-

Of the subsets of 12edo, I'd say this is the most interesting because it contains a whole tone. There are many pieces that make use of the whole tone scale, but very few that strictly exist in 6edo. Claude Debussy is well known for his use of the scale, and it's a very interesting color to use while working in 6n-edos, but a very limiting scale to use in isolation. The best 6edo pieces I could find are the prelude and invention from Aaron Andrew Hunt's "The Equal Tempered Keyboard," and honestly they are pretty interesting for what they are.

7edo

Tier: A

7edo disco in B neutral

This is the first edo with a perfect fifth and a third. The fifth is pretty flat, coming in at 685.71¢ (16.25¢ flat of 3/2), and the third is a supraminor third of 342.86¢. It's a bit reminiscent of the dorian scale of 12edo, but not really. The 2nd, 3rd, 6th, and 7th are all neutral, so this edo has a very distinct xen sound. It may seem quite limiting to only have one third, but honestly this is a very fun edo to work in. Quartal and quintal structures have a distinct "underwater" quality to them, which I really like. Overall, a very nice edo and one that is trivially easy to notate.

8edo

Tier: B-

This edo does not have a perfect fifth, but it does have 2 flavors of thirds... kind of. Because 8 is divisible by 4, it contains the 300¢ minor third, but it also includes a 450¢ interval that could be used either as an ultramajor third or a very flat fourth. This dual purpose actually makes it a pretty interesting interval to work with harmonically. This edo also has a neutral second, but one that much more closely approximates 12/11 than 7edo, giving melodies a pretty distinct neutral sound. This edo actually works surprisingly well on organ, producing a very sinister, foreboding sound. Overall, a decent edo to work in but one that I don't find myself using often.

9edo

Tier: B-

9edo tango in A harmonic anti-minor

This edo, while I put it in low B tier, is actually a very fun edo. It is, what most people would say, the first edo with 2 flavors of thirds, featuring the familiar 400¢ major third because it's divisible by 3, but also a scarily close approximation of 7/6. In fact, this edo approximates many septimal intervals down to the decimal point, which is quite strange, but definitely contributes to its sound. The fifth is heinously flat (over 30¢ flat of 3/2), but I've found that even this fifth can be softened via the use of a honky-tonk piano timbre. The distinct septimal resonance of the subminor third juxtaposed with the abhorrently flat fifth is an almost ineffable combination, but one that creates some of the most beautiful harmonies. The only reason I put this temperament so low is because the fifth is so flat, so it really is pretty difficult to listen to if you're not using a timbre that is literally out of tune. Plus, there are other edos that support Mavila with much better fifths. Overall, while the tuning isn't very versatile, the sounds it makes are utterly phantasmagoric, and I highly recommend you try this temperament in a harmonic context.