User:Eboone/EDO Impressions: Difference between revisions
m →Fewer Notes, Easier: updated |
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'''PROGESS REPORT, so you don't have to scroll:''' | '''PROGESS REPORT, so you don't have to scroll:''' | ||
Changed the scope of the project to go only up to 50edo, instead of 72edo | |||
Everything up to 20edo is complete, though is certainly subject to change. The 20edo and 22edo demos also available. Tier placements for every other edo are now accurate, though may change. | |||
''Start date: May 13, 2024. Most recent update: November 19, 2024.'' | |||
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[[File:1-50edo Tier List.png|alt=Ebooone's tier list of edos 1-50. S Tier - 12, 41, 31, 34, 22, 50, 19, 17, 26, 15. A Tier - 10, 27, 16, 21, 46, 20, 36, 37, 14, 18, 9, 7, 29, 43. B Tier - 13, 25, 40, 24, 48, 30, 33, 8, 5, 35. C Tier - 11, 28, 23, 32, 45, 44, 39. D Tier - 42, 47, 38, 49, 6. F Tier - 3, 4, 2, 1.|thumb|Ebooone's tier list of edos 1-50]] | |||
I, at least currently, work strictly in [[EDO|'''edos''']]. I tend not to venture higher than 53edo in my own works, and for reasons that are explained in Overarching Points > Multiples of EDOs, I consider ''' | I, at least currently, work strictly in [[EDO|'''edos''']]. I tend not to venture higher than 53edo in my own works, and for reasons that are explained in Overarching Points > Multiples of EDOs, I consider '''50edo''' to be the largest edo that interests me. So, this page will go over my general thoughts regarding every positive integer edo up to that point. There are also a few '''smackdowns''' between edos that I consider "arch rivals," with the first being between 17edo and 19edo. | ||
A few edos on this page are so intriguing that I (will soon) have entirely separate pages talking about them. These pages are linked directly below the headings of these edos. | A few edos on this page are so intriguing that I (will soon) have entirely separate pages talking about them. These pages are linked directly below the headings of these edos. | ||
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For example, 72edo does a much better job in the 2.3.5.7.11 subgroup than 12edo, but now you have to deal with 72 notes. At that point, why not just use just intonation?* The smallest example of this is 10edo being placed above 20edo. | For example, 72edo does a much better job in the 2.3.5.7.11 subgroup than 12edo, but now you have to deal with 72 notes. At that point, why not just use just intonation?* The smallest example of this is 10edo being placed above 20edo. | ||
''*I understand the rationale behind using very large edos instead of just intonation. It isn't just about approximating ratios; there are also things like mosses to consider. I, however, am not in the crowd that uses very large edos. At a certain point ( | ''*I understand the rationale behind using very large edos instead of just intonation. It isn't just about approximating ratios; there are also things like mosses to consider. I, however, am not in the crowd that uses very large edos. At a certain point (in my opinion, 50 notes to be exact), the sheer amount of notes is enough to tank any other possible advantages of using a particular edo. This segues nicely into the next point:'' | ||
==== The Novelty of Fewer ==== | ==== The Novelty of Fewer ==== | ||
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== Categorization == | == Categorization == | ||
=== The | === The 7 Categories of EDOs === | ||
I have split | I have split edos into 7 distinct categories based on step size: | ||
* 1-4edo — '''Trivial''' (300-1200¢) | * 1-4edo — '''Trivial''' (300-1200¢) | ||
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* 20-29edo — '''Macro-Diesitonal''' (41.38-60¢) | * 20-29edo — '''Macro-Diesitonal''' (41.38-60¢) | ||
* 30-39edo — '''Micro-Diesitonal''' (30.77-40¢) | * 30-39edo — '''Micro-Diesitonal''' (30.77-40¢) | ||
* | * ≥40edo — '''Commatonal''' (≤30¢) | ||
''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.'' | ''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.'' | ||
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As you can see, that falls apart quickly (as does attempting to group edos by factors or 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. | As you can see, that falls apart quickly (as does attempting to group edos by factors or 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 4 overarching categories: macrotonal, semitonal, diesitonal, and | 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 4 overarching categories: macrotonal, semitonal, diesitonal, and commatonal, but these still feel too large and contain vastly different edos within themselves. So, I basically just split each category down the middle. | ||
== Trivial == | == Trivial == | ||
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''Prime, 1° = 240¢, Fifth = 720¢ (3\5)'' | ''Prime, 1° = 240¢, Fifth = 720¢ (3\5)'' | ||
''Tier: '''B''''' | ''Tier: '''B-''''' | ||
[[File:5edo groove.mp3|none|thumb|5edo tribal groove in A equipentatonic]] | [[File:5edo groove.mp3|none|thumb|5edo tribal groove in A equipentatonic]] | ||
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. It 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. It has quite a desirable "uplifting" quality that brings it out amidst the texture of the rest of the scale. | ||
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''Prime, 1° = 171.43¢, Fifth = 685.71¢ (4\7)'' | ''Prime, 1° = 171.43¢, Fifth = 685.71¢ (4\7)'' | ||
''Tier: '''A''''' | ''Tier: '''A-''''' | ||
[[File:7edo demo.mp3|none|thumb|7edo disco in B neutral]] | [[File:7edo demo.mp3|none|thumb|7edo disco in B neutral]] | ||
This is the first edo with a perfect fifth and a third. The fifth is pretty flat, coming in 16.25¢ flat of 3/2, and the third is a supraminor third of 342.86¢. In a way, 7edo is the polar opposite of 5edo, containing a fifth that is almost equally off in the opposite direction. This gives 7edo a noticeably less uplifting sound, and more of a "crying out in pain" sound as one of my subscribers put it. Quartal and quintal structures have a distinct "underwater" quality, as opposed to the skyward energy of such structures in 5edo. | This is the first edo with a perfect fifth and a third. The fifth is pretty flat, coming in 16.25¢ flat of 3/2, and the third is a supraminor third of 342.86¢. In a way, 7edo is the polar opposite of 5edo, containing a fifth that is almost equally off in the opposite direction. This gives 7edo a noticeably less uplifting sound, and more of a "crying out in pain" sound as one of my subscribers put it. Quartal and quintal structures have a distinct "underwater" quality, as opposed to the skyward energy of such structures in 5edo. | ||
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''2³, 1° = 150¢, "Fifth" = 750¢ (5\8)'' | ''2³, 1° = 150¢, "Fifth" = 750¢ (5\8)'' | ||
''Tier: '''B''''' | ''Tier: '''B-''''' | ||
[[File:8edo demo 3.mp3|none|thumb|8edo march in E minor (?)]] | [[File:8edo demo 3.mp3|none|thumb|8edo march in E minor (?)]] | ||
This is... an interesting one. Honestly, I really didn't used to like 8edo, but eventually I came to see how powerful it is when used in certain contexts. It doesn't have a perfect fifth or a whole tone, but it is extremely close to '''[[12/11]] equal step tuning''', meaning it responds well to '''[[octave stretching]]'''. It also features a good approximation of [[13/10]], a rather ambiguous "third-fourth" that can either be used as an ultramajor third or a very flat fourth. | This is... an interesting one. Honestly, I really didn't used to like 8edo, but eventually I came to see how powerful it is when used in certain contexts. It doesn't have a perfect fifth or a whole tone, but it is extremely close to '''[[12/11]] equal step tuning''', meaning it responds well to '''[[octave stretching]]'''. It also features a good approximation of [[13/10]], a rather ambiguous "third-fourth" that can either be used as an ultramajor third or a very flat fourth. | ||
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''Prime, 1° = 109.09¢, Fifth = 654.55¢ (6\11)'' | ''Prime, 1° = 109.09¢, Fifth = 654.55¢ (6\11)'' | ||
''Tier: '''C''''' | ''Tier: '''C+''''' | ||
[[File:11edo demo.mp3|none|thumb|11edo casino swing in A altered lydian (?)]] | [[File:11edo demo.mp3|none|thumb|11edo casino swing in A altered lydian (?)]] | ||
This is a... fun one. It suffers from being '''almost 12edo''', giving it a somewhat similar vibe to 9edo, but without the whole "battle between consonance and dissonance" thing since nearly everything here is dissonant. The fifth is more like [[16/11]] than anything close to 3/2, meaning it actually has the worst fifth since 6edo, though 8edo comes close. This edo is notable for its approximation of [[9/7]], being just 1.28¢ sharp, making it the first edo with a '''supermajor third'''. It also has a pretty good approximation of the '''[[11/8|11th harmonic]]''', being 5.87¢ flat. | This is a... fun one. It suffers from being '''almost 12edo''', giving it a somewhat similar vibe to 9edo, but without the whole "battle between consonance and dissonance" thing since nearly everything here is dissonant. The fifth is more like [[16/11]] than anything close to 3/2, meaning it actually has the worst fifth since 6edo, though 8edo comes close. This edo is notable for its approximation of [[9/7]], being just 1.28¢ sharp, making it the first edo with a '''supermajor third'''. It also has a pretty good approximation of the '''[[11/8|11th harmonic]]''', being 5.87¢ flat. | ||
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I could say many things about 12edo, but I don't think you need to hear it. It's the first edo with the '''diatonic mos''', the first edo with a decent approximation of 3/2 (1.96¢ flat), and the first edo that can claim to be a '''5-limit system'''. It's a '''[[meantone temperament]]''', but only a little. This means the thirds are closer to pure 5-limit ratios, but not enough to sacrifice the edo's ability to support '''Pythagorean''' melodies. It contains symmetrical augmented and diminished structures, as well as the whole-tone scale. It's essentially a perfect temperament that works well in basically any style, so I cannot honestly put it anywhere but the top of the tier list. | I could say many things about 12edo, but I don't think you need to hear it. It's the first edo with the '''diatonic mos''', the first edo with a decent approximation of 3/2 (1.96¢ flat), and the first edo that can claim to be a '''5-limit system'''. It's a '''[[meantone temperament]]''', but only a little. This means the thirds are closer to pure 5-limit ratios, but not enough to sacrifice the edo's ability to support '''Pythagorean''' melodies. It contains symmetrical augmented and diminished structures, as well as the whole-tone scale. It's essentially a perfect temperament that works well in basically any style, so I cannot honestly put it anywhere but the top of the tier list. | ||
Yeah, that's all I'm going to say about 12edo. The purpose of this page is | Yeah, that's all I'm going to say about 12edo. The purpose of this page is really to delve into the other edos. | ||
=== [[13edo]] === | === [[13edo]] === | ||
''Prime, 1° = 92.31¢, Dual Fifths = 738.46¢ (7\13), 646.15¢ (6\13)'' | ''Prime, 1° = 92.31¢, Dual Fifths = 738.46¢ (7\13), 646.15¢ (6\13)'' | ||
''Tier: '''B''''' | ''Tier: '''B+''''' | ||
[[File:13edo demo 2.mp3|none|thumb|13edo baroque fantasia in A minor (?)]] | [[File:13edo demo 2.mp3|none|thumb|13edo baroque fantasia in A minor (?)]] | ||
This is just a better 11edo. It has a better approximation of 11/8 (2.53¢ sharp), and is honestly much better at pulling off the "almost 12edo" effect. It also has 2 fifths, and even though they're both terrible it's still better than having whatever 11edo has. | This is just a better 11edo. It has a better approximation of 11/8 (2.53¢ sharp), and is honestly much better at pulling off the "almost 12edo" effect. It also has 2 fifths, and even though they're both terrible it's still better than having whatever 11edo has. | ||
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====Verdict==== | ====Verdict==== | ||
Of course, retuning two 8-bar loops isn't going to decide which edo is better. This is just a fun experiment I thought I'd do, and I must say that '''19edo wins this | Of course, retuning two 8-bar loops isn't going to decide which edo is better. This is just a fun experiment I thought I'd do, and I must say that '''19edo wins this smackdown!''' While the lack of neutral intervals is certainly a bit of a tank, the utter beauty and ethereality of 19edo is something that is truly unique. Not even 31edo can sound like it, thanks to the interseptimal intervals. Anyway, there really isn't a way to compare these in any objective sense because they're so different. They are both absolutely amazing edos considering their size! | ||
By the way, this isn't the only showdown. Stay tuned... (pun intended) | By the way, this isn't the only showdown. Stay tuned... (pun intended) | ||
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''2×11, 1° = 54.55¢, Fifth = 709.09¢ (13\22)'' | ''2×11, 1° = 54.55¢, Fifth = 709.09¢ (13\22)'' | ||
''Tier: '''S | ''Tier: '''S''''' | ||
[[File:22edo demo.mp3|none|thumb|22edo crystal cavern theme in G]] | [[File:22edo demo.mp3|none|thumb|22edo crystal cavern theme in G]] | ||
placeholder | placeholder | ||
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''Prime, 1° = 41.38¢, Fifth = 703.45¢ (17\29)'' | ''Prime, 1° = 41.38¢, Fifth = 703.45¢ (17\29)'' | ||
''Tier: ''' | ''Tier: '''A-''''' | ||
placeholder | placeholder | ||
===Macro-Diesitonal EDO Recap=== | ===Macro-Diesitonal EDO Recap=== | ||
[[File:Macro-Diesitonal EDO Tier List.png|thumb|Tier list of edos 20-29]] | |||
placeholder | placeholder | ||
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===[[30edo]]=== | ===[[30edo]]=== | ||
''Tier: ''' | ''Tier: '''B''''' | ||
placeholder | placeholder | ||
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===[[32edo]]=== | ===[[32edo]]=== | ||
''Tier: ''' | ''Tier: '''C''''' | ||
placeholder | placeholder | ||
===[[33edo]]=== | ===[[33edo]]=== | ||
''Tier: ''' | ''Tier: '''B''''' | ||
placeholder | placeholder | ||
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===[[35edo]]=== | ===[[35edo]]=== | ||
''Tier: ''' | ''Tier: '''B-''''' | ||
placeholder | placeholder | ||
===[[36edo]]=== | ===[[36edo]]=== | ||
''Tier: ''' | ''Tier: '''A''''' | ||
placeholder | placeholder | ||
===[[37edo]]=== | ===[[37edo]]=== | ||
''Tier: ''' | ''Tier: '''A''''' | ||
placeholder | placeholder | ||
===[[38edo]]=== | ===[[38edo]]=== | ||
''Tier: ''' | ''Tier: '''D''''' | ||
placeholder | placeholder | ||
===[[39edo]]=== | ===[[39edo]]=== | ||
''Tier: ''' | ''Tier: '''C''''' | ||
placeholder | placeholder | ||
===Micro-Diesitonal EDO Recap=== | ===Micro-Diesitonal EDO Recap=== | ||
[[File:Micro-Diesitonal EDO Tier List.png|thumb|Tier list of edos 30-39]] | |||
placeholder | placeholder | ||
== | ==Commatonal== | ||
===[[40edo]]=== | ===[[40edo]]=== | ||
''Tier: ''' | ''Tier: '''B''''' | ||
placeholder | placeholder | ||
===[[41edo]]=== | ===[[41edo]]=== | ||
''Tier: ''' | ''Tier: '''S+''''' | ||
placeholder | placeholder | ||
===[[42edo]]=== | ===[[42edo]]=== | ||
''Tier: ''' | ''Tier: '''D''''' | ||
placeholder | placeholder | ||
===[[43edo]]=== | ===[[43edo]]=== | ||
''Tier: ''' | ''Tier: '''A-''''' | ||
placeholder | placeholder | ||
===[[44edo]]=== | ===[[44edo]]=== | ||
''Tier: '''C | ''Tier: '''C''''' | ||
placeholder | placeholder | ||
===[[45edo]]=== | ===[[45edo]]=== | ||
''Tier: ''' | ''Tier: '''C''''' | ||
placeholder | placeholder | ||
===[[46edo]]=== | ===[[46edo]]=== | ||
''Tier: '''A | ''Tier: '''A''''' | ||
placeholder | placeholder | ||
===[[47edo]]=== | ===[[47edo]]=== | ||
''Tier: ''' | ''Tier: '''D''''' | ||
placeholder | placeholder | ||
===[[48edo]]=== | ===[[48edo]]=== | ||
''Tier: ''' | ''Tier: '''B''''' | ||
placeholder | placeholder | ||
===[[49edo]]=== | ===[[49edo]]=== | ||
''Tier: ''' | ''Tier: '''D''''' | ||
placeholder | placeholder | ||
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placeholder | placeholder | ||
=== | ===Commatonal EDO Recap=== | ||
[[File:40-50edo Tier List.png|thumb|Tier list of edos 40-50]] | |||
placeholder | placeholder | ||
[[Category:EDO theory pages]] | [[Category:EDO theory pages]] | ||