User:Eboone/EDO Impressions: Difference between revisions
m wording Tags: Visual edit Mobile edit Mobile web edit |
Added content to Categorization heading, added two more edo categories, added recaps |
||
| Line 1: | Line 1: | ||
{{DISPLAYTITLE:Ebooone's EDO Impressions}} | {{DISPLAYTITLE:Ebooone's EDO Impressions}} | ||
[[File:EDO Tier List.png|alt=A tier list of EDOs. S Tier - 12, 34, 31, 53, 72, 50, 22, 17, 15, 26, 19. A Tier - 27, 10, 46, 21, 20, 7, 16, 41, 55. B Tier - 18, 24, 36, 48, 65, 58, 25, 63, 13, 11, 56, 29, 23, 9, 5, 8. C Tier - 40, 43, 28, 14, 70, 68, 57, 37, 30, 60, 54, 49, 47, 44, 38, 67, 59, 35, 6. F Tier - 52, 62, 66, 71, 64, 39, 51, 61, 32, 39, 42, 45, 33.|thumb|[OUTDATED, soon to be updated] Ebooone's tier list of EDOs 5-72, available at https://tiermaker.com/list/personal/numbers-0-100-15569788/3966935.]] | [[File:EDO Tier List.png|alt=A tier list of EDOs. S Tier - 12, 34, 31, 53, 72, 50, 22, 17, 15, 26, 19. A Tier - 27, 10, 46, 21, 20, 7, 16, 41, 55. B Tier - 18, 24, 36, 48, 65, 58, 25, 63, 13, 11, 56, 29, 23, 9, 5, 8. C Tier - 40, 43, 28, 14, 70, 68, 57, 37, 30, 60, 54, 49, 47, 44, 38, 67, 59, 35, 6. F Tier - 52, 62, 66, 71, 64, 39, 51, 61, 32, 39, 42, 45, 33.|thumb|[OUTDATED, soon to be updated] Ebooone's tier list of EDOs 5-72, available at https://tiermaker.com/list/personal/numbers-0-100-15569788/3966935.]] | ||
I, at least currently, work strictly in [[EDO|'''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. | I, at least currently, work strictly in [[EDO|'''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. Additionally, each edo category also has its own tier list and recap. | ||
Of course, | Of course, all tier lists and impressions on this page are subject to change in the future. | ||
All demos are created by me in [[MuseScore|MuseScore 3]]. | All demos are short loops at 120bpm created by me in [[MuseScore|MuseScore 3]]. | ||
== Categorization == | |||
=== The 8 Categories of EDOs 1-72 === | |||
I have split the edos 1-72 into 8 distinct categories based on step size: | |||
* 1-4edo — '''Trivial''' (300-1200¢) | |||
* 5-9edo — '''Macrotonal''' (133.33-240¢) | |||
* 10-14edo — '''Macro-Semitonal''' (85.71-120¢) | |||
* 15-19edo — '''Micro-Semitonal''' (63.16-80¢) | |||
* 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. Also, I am aware that "macrotonal" generally refers to any temperament whose step size is larger than 100¢. That is not necessarily the meaning here.'' | |||
=== Why Categorize EDOs? === | |||
The main reason I wanted to split these edos into categories was so that this wiki page wouldn't be an absolutely mammoth wall of text on mobile. Plus, it just felt like a fun challenge. | |||
But why by step size? EDOs are generally distinguished by their intervals, so wouldn't it make sense to group edos by similar interval content? Sure, but how would you actually do that? There would be so much overlap that any and all meaningful distinction between categories would be lost. 29edo, 41edo, and 53edo would be grouped together as [[3-limit|Pythagorean]] systems, but 41edo and 53edo would also be grouped with 31edo and 50edo as [[5-limit]] systems, and 31edo and 50edo would be grouped with 36edo and 72edo as [[7-limit|septimal]] systems, and 72edo would be grouped with 24edo and 26edo as [[11-limit|undecimal]] systems... | |||
As you can see, that falls apart quickly (as does attempting to group edos by factors or [[MOS scale|mosses]] or anything else, for the same reason), meaning the only other option is to categorize edos by step size. This is a great option because the size of an edo's step is what dictates its voice leading capabilities. For example, chromatic motion in 12edo is limited to semitones, whereas 31edo allows for movement by diesis. Also, no more extreme overlap between categories; 12 is similar to 11 and 13, and 31 is similar to 30 and 32. The borders between categories may be fuzzy, but that's to be expected when categorizing tuning systems anyway, since harmony itself is fuzzy by nature. | |||
In terms of the actual categories themselves, I essentially divided them by significantly different [[Interval region|interval regions]], and then into smaller subcategories. There are really 4 overarching categories: macrotonal, semitonal, diesitonal, and syntonic, but these still feel too large and contain vastly different edos within themselves. So, I basically just split each category down the middle. | |||
== | == Trivial EDOs == | ||
=== [[1edo]] === | === [[1edo]] === | ||
| Line 62: | Line 73: | ||
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... how familiar. | 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... how familiar. | ||
The minor third is sat between 6/5 and [[32/27]], giving it a mildly dark sound that is quite apt for the diminished tetrad. It's a powerful minor third, but without the | The minor third is sat between 6/5 and [[32/27]], giving it a mildly dark sound that is quite apt for the diminished tetrad. It's a powerful minor third, but without the 5-limit resonance of 6/5. Overall, a great minor third. | ||
I'd say this edo is on equal footing with 3edo, maybe slightly behind. You could certainly argue that it's better than 3edo, considering it contains 2 interlocked instances of 2edo, as well as an extra note. This seems like a convincing case for 4edo, but I personally think augmented triads are more interesting than diminished tetrads in isolation. It's really all about taste, as is everything in the world of music. | I'd say this edo is on equal footing with 3edo, maybe slightly behind. You could certainly argue that it's better than 3edo, considering it contains 2 interlocked instances of 2edo, as well as an extra note. This seems like a convincing case for 4edo, but I personally think augmented triads are more interesting than diminished tetrads in isolation. It's really all about taste, as is everything in the world of music. | ||
=== Trivial EDO Recap === | |||
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. I can't really hear them as anything other than subsets of 12edo, which really makes them seem pointless. They work best as additional colors in larger edos that contain them, not as temperaments on their own. | |||
== Macrotonal EDOs == | |||
=== [[5edo]] === | === [[5edo]] === | ||
| Line 75: | Line 89: | ||
This is the first edo with a perfect fifth, coming in 18.04¢ sharp of [[3/2]]. Because of how sharp the fifth is, 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 is the first edo with a perfect fifth, coming in 18.04¢ sharp of [[3/2]]. Because of how sharp the fifth is, 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 interval|interseptimal intervals]], a very interesting class of intervals characterized by toeing the lines between extreme | This edo also features [[Interseptimal interval|interseptimal intervals]], a very interesting class of intervals characterized by toeing the lines between extreme septimal intervals. There's the 240¢ "second-third," which lies between [[8/7]] and [[7/6]], and the 960¢ "seventh-sixth," which lies between [[7/4]] and [[12/7]]. I'd say 240¢ definitely sounds more like a supermajor second than an inframinor third in most cases, and I find it almost impossible to hear 960¢ as a sixth since it's so close to the 7th harmonic, but it is interesting how these intervals are technically ambiguous. | ||
Oh yeah, did I just mention it has a decent approximation of the 7th harmonic? It's only 8.83¢ flat of 7/4, which is cool because this approximation extends to all 5n-edos. Anyway, the equipentatonic scale that this edo sports is a bit reminiscent of the minor pentatonic scale of 12edo (or, dare I say, the dorian pentatonic scale), making it quite familiar to unaccustomed ears, but still with a tang of xen. In many cases, it is rather difficult to notice if a piece is in this edo if you aren't familiar with it. Because of this, I'd say 5edo is a good starting edo when venturing into xen territory. | Oh yeah, did I just mention it has a decent approximation of the 7th harmonic? It's only 8.83¢ flat of 7/4, which is cool because this approximation extends to all 5n-edos. Anyway, the equipentatonic scale that this edo sports is a bit reminiscent of the minor pentatonic scale of 12edo (or, dare I say, the dorian pentatonic scale), making it quite familiar to unaccustomed ears, but still with a tang of xen. In many cases, it is rather difficult to notice if a piece is in this edo if you aren't familiar with it. Because of this, I'd say 5edo is a good starting edo when venturing into xen territory. | ||
| Line 135: | Line 149: | ||
Overall, a very solid edo. You can choose to avoid the dissonant fifth or embrace it, with both approaches leading to an incredible sound. It's surprisingly versatile, more so than any edo smaller than it, putting it above 7edo. | Overall, a very solid edo. You can choose to avoid the dissonant fifth or embrace it, with both approaches leading to an incredible sound. It's surprisingly versatile, more so than any edo smaller than it, putting it above 7edo. | ||
== Semitonal == | === Macrotonal EDO Recap === | ||
placeholder | |||
== Macro-Semitonal EDOs == | |||
=== [[10edo]] === | === [[10edo]] === | ||
| Line 158: | Line 175: | ||
''Tier: '''C+'''''[[File:14edo groove.mp3|none|thumb|14edo noir swing in A minor (?)]] | ''Tier: '''C+'''''[[File:14edo groove.mp3|none|thumb|14edo noir swing in A minor (?)]] | ||
placeholder | placeholder | ||
=== Macro-Semitonal EDO Recap === | |||
placeholder | |||
== Micro-Semitonal EDOs == | |||
=== [[15edo]] === | === [[15edo]] === | ||
| Line 184: | Line 206: | ||
placeholder | placeholder | ||
== Macro- | === Micro-Semitonal EDO Recap === | ||
placeholder | |||
== Macro-Diesitonal EDOs == | |||
=== [[20edo]] === | === [[20edo]] === | ||
| Line 236: | Line 261: | ||
placeholder | placeholder | ||
== Micro- | === Macro-Diesitonal EDO Recap === | ||
placeholder | |||
== Micro-Diesitonal EDOs == | |||
=== [[30edo]] === | === [[30edo]] === | ||
| Line 288: | Line 316: | ||
placeholder | placeholder | ||
== Super- | === Micro-Diesitonal EDO Recap === | ||
placeholder | |||
== Super-Syntonic EDOs == | |||
=== [[40edo]] === | === [[40edo]] === | ||
| Line 370: | Line 401: | ||
placeholder | placeholder | ||
== Sub- | === Super-Syntonic EDO Recap === | ||
placeholder | |||
== Sub-Syntonic EDOs == | |||
=== [[56edo]] === | === [[56edo]] === | ||
| Line 455: | Line 489: | ||
''Tier: '''S''''' | ''Tier: '''S''''' | ||
placeholder | |||
=== Sub-Syntonic EDO Recap === | |||
placeholder | placeholder | ||