User:Eboone/EDO Impressions: Difference between revisions
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The first draft of everything up to 20edo is now complete, with the 20edo and 22edo demos also currently available. Tier placements of 20-29edo are also accurate, and all tier placements after that are outdated. | The first draft of everything up to 20edo is now complete, with the 20edo and 22edo demos also currently available. Tier placements of 20-29edo are also accurate, and all tier placements after that are outdated. | ||
I | I am currently going back and editing what I've already written thus far, making sure to maximize the efficiency of the reading experience. The 17edo vs 19edo smackdown may also be completely switched up in favor of 19edo, so stay tuned. | ||
''Start date: May 13, 2024. Most recent update: June 10, 2024. '''28 days''' have been spent.'' | ''Start date: May 13, 2024. Most recent update: June 10, 2024. '''28 days''' have been spent.'' | ||
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All demos are short loops at 120bpm created by me in [[MuseScore|'''MuseScore 3''']]. | All demos are short loops at 120bpm created by me in [[MuseScore|'''MuseScore 3''']]. | ||
== Overarching Points == | == Overarching Points == | ||
After working on this project for about a month, I realized there were many points I found myself repeating. This isn't inherently an issue, but I thought it would make more sense if I sectioned off a few points that apply to multiple edos. I will be referencing these points directly in the descriptions of many edos, so it may be wise to '''read them before continuing'''. | After working on this project for about a month, I realized there were many points I found myself repeating. This isn't inherently an issue, but I thought it would make more sense if I sectioned off a few points that apply to multiple edos. I will be referencing these points directly in the descriptions of many edos, so it may be wise to '''read them before continuing'''. | ||
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Keep in mind, I'm using quotation marks a lot because all of this is largely subjective. If you want to use extreme intervals with no shred of consonance, feel free to do that. It's just generally desirable to have access to consonant intervals because of their beauty and versatility. | Keep in mind, I'm using quotation marks a lot because all of this is largely subjective. If you want to use extreme intervals with no shred of consonance, feel free to do that. It's just generally desirable to have access to consonant intervals because of their beauty and versatility. | ||
Intervals of certain [[Prime limit|'''prime limits''']] have their own flavors of resonance, like how [[5/4]] and [[6/5]] "lock in" in a similar fashion that is recognizable as 5-limit resonance. This, among other reasons, is why it is useful to analyze edos in terms of their abilities to approximate certain prime limits. | Intervals of certain [[Prime limit|'''prime limits''']] have their own flavors of resonance, like how [[5/4]] and [[6/5]] "lock in" in a similar fashion that is recognizable as [[5-limit]] resonance. This, among other reasons, is why it is useful to analyze edos in terms of their abilities to approximate certain prime limits. | ||
I say "approximate" because it is impossible for any [[regular temperament]] to perfectly represent more than one prime limit exactly (due to the fact that all prime numbers are coprime with each other). In the case of edos, the only prime limit that is uncompromised is the [[2-limit]], which grants the substantial ability to make use of perfect octaves. Maintaining the perfect octave is seen as a first priority in most cases due to the concept of [[octave equivalence]], so any other prime limit can only ever be approximated when using edos. | I say "approximate" because it is impossible for any [[regular temperament]] to perfectly represent more than one prime limit exactly (due to the fact that all prime numbers are coprime with each other). In the case of edos, the only prime limit that is uncompromised is the [[2-limit]], which grants the substantial ability to make use of perfect octaves. Maintaining the perfect octave is seen as a first priority in most cases due to the concept of [[octave equivalence]], so any other prime limit can only ever be approximated when using edos. | ||
Lower prime limits are generally seen as more important, especially the 3-limit. The perfect fifth is absolutely paramount to the structure of Western music because 1) it is very well approximated in 12edo and 2) it is the [[generator]] for the [[diatonic scale]]. So, edos with poor approximations of the 3rd harmonic are generally at a disadvantage in terms of versatility and resonance. 5-limit systems are also very desirable, as are 7-limit, 11-limit, and 13-limit systems. I don't usually care for an edo's ability to approximate anything past that. | Lower prime limits are generally seen as more important, especially the [[3-limit]]. The perfect fifth is absolutely paramount to the structure of Western music because 1) it is very well approximated in 12edo and 2) it is the [[generator]] for the [[diatonic scale]]. So, edos with poor approximations of the [[3/1|3rd harmonic]] are generally at a disadvantage in terms of versatility and resonance. 5-limit systems are also very desirable, as are [[7-limit]], [[11-limit]], and [[13-limit]] systems. I don't usually care for an edo's ability to approximate anything past that. | ||
In short, edos with more consonant intervals are at a distinct advantage compared to other edos. That certainly doesn't mean there won't be any exceptions, but it is true in many cases. | In short, edos with more consonant intervals are at a distinct advantage compared to other edos. That certainly doesn't mean there won't be any exceptions, but it is true in many cases. | ||
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==== All You Need ==== | ==== All You Need ==== | ||
At the end of the day, use whatever tuning you need to achieve your musical vision. It just happens that I basically never consider very large edos to be necessary. If all I need is 12, then all I need is 12. No need to use 24 or 36 or whatever if those extra notes won't help me hone in on the emotions I plan to engender in the listener. | At the end of the day, use whatever tuning you need to achieve your musical vision. It just happens that I basically never consider very large edos to be necessary. If all I need is 12, then all I need is 12. No need to use 24 or 36 or whatever if those extra notes won't help me hone in on the emotions I plan to engender in the listener. | ||
=== Summary of Ranking === | |||
In general, edos with these qualities will place higher on the tier list: | |||
# '''Few notes''' | |||
# '''Consonant''' | |||
# '''Versatile''' | |||
# '''Unique''' | |||
These are just guidelines that I tend to follow, and they in no way provide a concrete method of objectifying edos. However, understanding what I'm looking for will greatly aid in understanding why I place certain edos where I do. For example, 53edo is certainly on the larger side, yet it still resides in S tier because it's just so consonant. It really puts into perspective just how consonant it is if I'm willing to place it that high in spite of the amount of notes. | |||
Plus, these aren't the only guidelines. '''[[MOS scales]]''' are also considered, especially if they are scales that I find interesting. This is largely subjective, as I really have no way of classifying mosses in any sort of objective way. Certain intervals that are technically dissonant may also greatly contribute to an edo's high rating, such as the major third in 17edo (foreshadowing). At the end of the day, everything on this page is based on my own recreational research and opinions, so I'm sorry if your favorite edo is in D tier simply because it doesn't meet my criteria for what makes an edo desirable. | |||
== 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 (which ended up happening anyway, but oh well). 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 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 septimal systems, and 72edo would be grouped with 24edo and 26edo as undecimal systems... | |||
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 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 == | == Trivial == | ||