Collection of EDO impressions: Difference between revisions
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: '''MisterShafXen:''' Very bland, not worth using. | : '''MisterShafXen:''' Very bland, not worth using. | ||
: '''Budjarn Lambeth:''' Lends itself to meditative, minimalist music: music where rhythm and timbre are the source of most of the interest, while melody and harmony are repetitive and change by small increments, forcing the listener to pay close attention to the most subtle changes. | : '''Budjarn Lambeth:''' Lends itself to meditative, minimalist music: music where rhythm and timbre are the source of most of the interest, while melody and harmony are repetitive and change by small increments, forcing the listener to pay close attention to the most subtle changes. | ||
: '''Zhenlige:''' Equivalent to [[2-limit]] JI | : '''Zhenlige:''' [[2/1|Octaves]]. Equivalent to [[2-limit]] JI, unless you want to temper some other JI intervals into octaves. Not much to talk about. | ||
: '''Eufalesio:''' Octaves. Extremely boring to use still, as octaves are hyperconsonant, so there is no inertia. You really have to get creative to make something cool in this. Ligeti pulled it off. But I won't care to try. F | : '''Eufalesio:''' Octaves. Extremely boring to use still, as octaves are hyperconsonant, so there is no inertia. You really have to get creative to make something cool in this. Ligeti pulled it off. But I won't care to try. F | ||
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: '''MisterShafXen:''' Nowhere near enough notes. | : '''MisterShafXen:''' Nowhere near enough notes. | ||
: '''Budjarn Lambeth:''' Lends itself to meditative, minimalist music: music where rhythm and timbre are the source of most of the interest, while melody and harmony are repetitive and change by small increments, forcing the listener to pay close attention to the most subtle changes. | : '''Budjarn Lambeth:''' Lends itself to meditative, minimalist music: music where rhythm and timbre are the source of most of the interest, while melody and harmony are repetitive and change by small increments, forcing the listener to pay close attention to the most subtle changes. | ||
: '''Zhenlige:''' Half octaves aka symmetric | : '''Zhenlige:''' [[sqrt(2)|Half octaves]] aka symmetric [[tritone]]s. The key to tritone substitution, although sometimes asymmetric tritones or even non-tritone intervals can also be used. Some notable approximations are [[7/5]], [[17/12]] and [[99/70]], the final one giving [[kalismic temperaments|kalismic]]. 2n-edos within 1000 that do not support kalismic are probably bad in [[11-limit]]. | ||
: '''Eufalesio:''' Only ever good as subsets of other edos such as 12edo. Basically just compton. Anywhere else, they stand out, and not positively. D | : '''Eufalesio:''' Only ever good as subsets of other edos such as 12edo. Basically just compton. Anywhere else, they stand out, and not positively. D | ||
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: '''Glitchydarkness:''' You can make chords with this one! I'll name a few: Augmented ... ...Augmented... Yeah you can't really do much, but it's neat! It's still the first EDO to actually have chords, and it's better than whatever 2edo was! | : '''Glitchydarkness:''' You can make chords with this one! I'll name a few: Augmented ... ...Augmented... Yeah you can't really do much, but it's neat! It's still the first EDO to actually have chords, and it's better than whatever 2edo was! | ||
: '''Budjarn Lambeth:''' Lends itself to meditative, minimalist music: music where rhythm and timbre are the source of most of the interest, while melody and harmony are repetitive and change by small increments, forcing the listener to pay close attention to the most subtle changes. | : '''Budjarn Lambeth:''' Lends itself to meditative, minimalist music: music where rhythm and timbre are the source of most of the interest, while melody and harmony are repetitive and change by small increments, forcing the listener to pay close attention to the most subtle changes. | ||
: '''Zhenlige:''' 12edo augmented | : '''Zhenlige:''' [[12edo]] major thirds. 2.5 subgroup [[augmented (temperament)|augmented]]. The smallest EDO with decent 2.5 subgroup. Treating its steps as [[63/50]] gives [[landscape]]. 3n-edos within 1000 that do not support landscape are probably bad in [[7-limit]]. | ||
: '''Eufalesio''': Only ever good as subsets of other edos such as 12edo. Basically just compton. Anywhere else, they stand out, and not positively. Though 3edo has a surprisingly accurate 5. C | : '''Eufalesio''': Only ever good as subsets of other edos such as 12edo. Basically just compton. Anywhere else, they stand out, and not positively. Though 3edo has a surprisingly accurate 5. C | ||
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: '''Glitchydarkness:''' Has some good melodic movement for its size, and can play the diminished chord! Who cares if it's contained within 12edo, you could name any EDO and it's contained in another higher one too, it's a property of numbers! | : '''Glitchydarkness:''' Has some good melodic movement for its size, and can play the diminished chord! Who cares if it's contained within 12edo, you could name any EDO and it's contained in another higher one too, it's a property of numbers! | ||
: '''Budjarn Lambeth:''' Lends itself to meditative, minimalist music: music where rhythm and timbre are the source of most of the interest, while melody and harmony are repetitive and change by small increments, forcing the listener to pay close attention to the most subtle changes. | : '''Budjarn Lambeth:''' Lends itself to meditative, minimalist music: music where rhythm and timbre are the source of most of the interest, while melody and harmony are repetitive and change by small increments, forcing the listener to pay close attention to the most subtle changes. | ||
: '''Zhenlige:''' 12edo | : '''Zhenlige:''' [[12edo]] minor thirds. | ||
: '''Eufalesio''': Only ever good as subsets of other edos such as 12edo. Basically just compton. Anywhere else, they stand out, and not positively. D | : '''Eufalesio''': Only ever good as subsets of other edos such as 12edo. Basically just compton. Anywhere else, they stand out, and not positively. D | ||
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: '''Vector:''' This is the best 2.3.7 edo by far for its size. Other than that, it's equipentatonic, and so you get the first hint of [[diatonic]]-style melody in this edo. It's a subset of 15edo. | : '''Vector:''' This is the best 2.3.7 edo by far for its size. Other than that, it's equipentatonic, and so you get the first hint of [[diatonic]]-style melody in this edo. It's a subset of 15edo. | ||
: '''Budjarn Lambeth:''' Lends itself to meditative, minimalist music: music where rhythm and timbre are the source of most of the interest, while melody and harmony are repetitive and change by small increments, forcing the listener to pay close attention to the most subtle changes. | : '''Budjarn Lambeth:''' Lends itself to meditative, minimalist music: music where rhythm and timbre are the source of most of the interest, while melody and harmony are repetitive and change by small increments, forcing the listener to pay close attention to the most subtle changes. | ||
: '''Zhenlige:''' Equalized [[2L 3s|pentatonic]] scale. 3-limit [[blackwood]]. Kinda familiar but everything is warped. To me as a Chinese, it sounds like out-of-tone traditional Chinese music. The smallest EDO | : '''Zhenlige:''' Equalized [[2L 3s|pentatonic]] scale. [[3-limit]] [[blackwood]]. Kinda familiar but everything is warped. To me as a Chinese, it sounds like out-of-tone traditional Chinese music. The smallest EDO that roughly represents [[3-limit]] or 2.3.7 subgroup. | ||
: '''Eufalesio:''' The first usable edo and the first edo to have any semblance of a perfect fifth. It features an extremely simplified 2.3.7, forming a consistent circle of 8/7 and 3/2. Due to its extremely coarse grain, it is extremely simple to use, as each step is large enough that no cluttering will ever occur. It is horrible in all other limits... well... except... 2.3.7.37, but who here cares about that –Also due to its extremely coarse grain, you can play anything, short of bashing keys and sitting on the keyboard, and it will sound good. This is because the edostep is so large that it doesn't cause audible cluttering... unless you're playing too low. The sonic profile of this edo is immediately recognizable. – It greatly benefits from non-harmonic timbres, or bell-like sounds, much like that of slendro. Its melodic capabilities are basically the same as that of all pentatonic scales, which is to say: great! It would be wrong to only call 5edo innacurate. A better descriptor would be: coarse. The coarsest, in fact. And due to the fact that it is so coarse, but it is still quite relatively accurate, it is a great edo. A | : '''Eufalesio:''' The first usable edo and the first edo to have any semblance of a perfect fifth. It features an extremely simplified 2.3.7, forming a consistent circle of 8/7 and 3/2. Due to its extremely coarse grain, it is extremely simple to use, as each step is large enough that no cluttering will ever occur. It is horrible in all other limits... well... except... 2.3.7.37, but who here cares about that –Also due to its extremely coarse grain, you can play anything, short of bashing keys and sitting on the keyboard, and it will sound good. This is because the edostep is so large that it doesn't cause audible cluttering... unless you're playing too low. The sonic profile of this edo is immediately recognizable. – It greatly benefits from non-harmonic timbres, or bell-like sounds, much like that of slendro. Its melodic capabilities are basically the same as that of all pentatonic scales, which is to say: great! It would be wrong to only call 5edo innacurate. A better descriptor would be: coarse. The coarsest, in fact. And due to the fact that it is so coarse, but it is still quite relatively accurate, it is a great edo. A | ||
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: '''MisterShafXen:''' Augmented in whole tones. So much missing. | : '''MisterShafXen:''' Augmented in whole tones. So much missing. | ||
: '''Budjarn Lambeth:''' Lends itself to meditative, minimalist music: music where rhythm and timbre are the source of most of the interest, while melody and harmony are repetitive and change by small increments, forcing the listener to pay close attention to the most subtle changes. | : '''Budjarn Lambeth:''' Lends itself to meditative, minimalist music: music where rhythm and timbre are the source of most of the interest, while melody and harmony are repetitive and change by small increments, forcing the listener to pay close attention to the most subtle changes. | ||
: '''Zhenlige:''' | : '''Zhenlige:''' [[12edo]] whole tones. Incomplete 12edo. Also a heavily stretched [[didacus]] chain. | ||
: '''Eufalesio''': Only ever good as subsets of other edos such as 12edo. Basically just compton. Anywhere else, they stand out, and not positively. D | : '''Eufalesio''': Only ever good as subsets of other edos such as 12edo. Basically just compton. Anywhere else, they stand out, and not positively. D | ||
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: '''Vector:''' This... could honestly fit in as a diatonic tuning. It's the first kind of tuning where we have functional harmony, although all the chords are neutral. | : '''Vector:''' This... could honestly fit in as a diatonic tuning. It's the first kind of tuning where we have functional harmony, although all the chords are neutral. | ||
: '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to [[timbre]] to prevent it sounding "out of tune". | : '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to [[timbre]] to prevent it sounding "out of tune". | ||
: '''Zhenlige:''' Equalized [[5L 2s|diatonic]] scale. 3-limit [[whitewood]] | : '''Zhenlige:''' Equalized [[5L 2s|diatonic]] scale. 3-limit [[whitewood]]. It sounds like out-of-tone [[3L 4s|neutral scale]] music. The smallest EDO that roughly represents [[5-limit]]. | ||
: '''Eufalesio:''' The second usable edo. Its fifth is a tad flat, but usable, and it is also the first edo to feature a heptatonic scale, obviously... an equalized diatonic. The edostep is now small enough so that cluttering ''can'' occur, but still somewhat bashable. The sonic profile is also immediately recognizable. While the 5-limit is not there, the melodic coolness you can pull of with this coarse edo are nothing to scoff at. C, not for accuracy, but for ''cool''. | : '''Eufalesio:''' The second usable edo. Its fifth is a tad flat, but usable, and it is also the first edo to feature a heptatonic scale, obviously... an equalized diatonic. The edostep is now small enough so that cluttering ''can'' occur, but still somewhat bashable. The sonic profile is also immediately recognizable. While the 5-limit is not there, the melodic coolness you can pull of with this coarse edo are nothing to scoff at. C, not for accuracy, but for ''cool''. | ||
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: '''Vector:''' The tuning I write most of my music in. It's good enough for writing the kind of music I want to write, as long as that kind of music isn't "[[xenharmonic]]". 12edo theory is my inspiration for my [[15edo]] theory system, and my general approach to [[xenharmonic|xenharmony]]. (It also brought with it a fair share of misconceptions: for a while, I assumed "sharp" just meant "1 edostep", and after I was corrected wtih [[17edo]] I assumed it meant "between whatever intervals are (true) minor and major".) | : '''Vector:''' The tuning I write most of my music in. It's good enough for writing the kind of music I want to write, as long as that kind of music isn't "[[xenharmonic]]". 12edo theory is my inspiration for my [[15edo]] theory system, and my general approach to [[xenharmonic|xenharmony]]. (It also brought with it a fair share of misconceptions: for a while, I assumed "sharp" just meant "1 edostep", and after I was corrected wtih [[17edo]] I assumed it meant "between whatever intervals are (true) minor and major".) | ||
: '''Budjarn Lambeth:''' An excellent [[5-limit]] tuning. It is simple and stays out of the composer's way for two reasons: it works with an impressively wide variety of timbres, and it avoids [[wolf interval]]s better than any larger tuning. I believe this elegant simplicity is the reason for its popularity. | : '''Budjarn Lambeth:''' An excellent [[5-limit]] tuning. It is simple and stays out of the composer's way for two reasons: it works with an impressively wide variety of timbres, and it avoids [[wolf interval]]s better than any larger tuning. I believe this elegant simplicity is the reason for its popularity. | ||
: '''Zhenlige:''' Equalized [[chromatic]] scale. Both [[augmented]] and [[diminished]]. The only reasonable tuning for [[dominant (temperament)|dominant]]. The boundary between [[meantone]] and [[schismatic]]. The smallest [[5L 2s|diatonic]] EDO. | : '''Zhenlige:''' Equalized [[5L 7s|chromatic]] scale. Both [[augmented (temperament)|augmented]] and [[diminished (temperament)|diminished]]. The smallest edo with decent [[7-limit]]. The only reasonable tuning for the [[dominant (temperament)|dominant]] temperament ignoring overall streching. A sharper fifth makes [[garibaldi]] better and a flatter fifth makes [[septimal meantone]] better. The boundary between [[meantone]] and [[schismatic]]. The smallest [[5L 2s|diatonic]] EDO. Efficient at its size. Very excellent [[3/1|3]] as well as [[17/1|17]] and [[19/1|19]] for its size, but inaccurate [[5/1|5]] and worse [[7/1|7]]. Suitable for symmetric scales. Easy to make [[../12neji|accurate NEJIs]]. Its 2.3.17.19 subgroup deserves more exploration (something “xenharmonic” but not “microtonal”). Its thirds do not accurately approximate common JI intervals. A [[well temperament]] can make some of them do better. | ||
: '''Eufalesio:''' It's easily one of the best edos. 12edo is many, many things all at once, and I would say that its place in mainstream music is well earned. It's the first edo that can deal with the 5-limit at all, and it also has an incredibly accurate fifth for its size, making it the only temperament that is both meantone and pythagorean at the same time... Super practical, and very easy to conceptualize. S | : '''Eufalesio:''' It's easily one of the best edos. 12edo is many, many things all at once, and I would say that its place in mainstream music is well earned. It's the first edo that can deal with the 5-limit at all, and it also has an incredibly accurate fifth for its size, making it the only temperament that is both meantone and pythagorean at the same time... Super practical, and very easy to conceptualize. S | ||
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: '''Vector:''' A shining example of why the [[chain of fifths]] is not suitable as a universal model. 15edo has a [[diatonic scale]] (the [[zarlino]] scale of 2313231) that makes for a much more familiar interpretation of the tuning than inflecting the 5edo notes up and down. In terms of just intonation, it approximates simple intervals of the [[11-limit]], and tempers the infamous zarlino [[wolf interval|wolf fifth]] flat enough that it merges with the concordant 11th [[subharmonic]], thereby solving the main problem that zarlino itself has. | : '''Vector:''' A shining example of why the [[chain of fifths]] is not suitable as a universal model. 15edo has a [[diatonic scale]] (the [[zarlino]] scale of 2313231) that makes for a much more familiar interpretation of the tuning than inflecting the 5edo notes up and down. In terms of just intonation, it approximates simple intervals of the [[11-limit]], and tempers the infamous zarlino [[wolf interval|wolf fifth]] flat enough that it merges with the concordant 11th [[subharmonic]], thereby solving the main problem that zarlino itself has. | ||
: '''Budjarn Lambeth:''' Offers exciting melodic shapes. Still requires careful attention to [[timbre]], but it's more forgiving on that front than most similar sized tunings. The smallest equal tuning that approximates the entire [[11-limit]], so it's a great starting point for exploring new consonances which can't be found in 12. | : '''Budjarn Lambeth:''' Offers exciting melodic shapes. Still requires careful attention to [[timbre]], but it's more forgiving on that front than most similar sized tunings. The smallest equal tuning that approximates the entire [[11-limit]], so it's a great starting point for exploring new consonances which can't be found in 12. | ||
: '''Zhenlige:''' Better than it seems to be, tho still rough. [[Blackwood]] [[augmented]]. A heavily stretched [[Carlos Alpha]] scale. The best you can get with blackwood. I don't know why there are "people fond of" such inaccurate temperaments. | : '''Zhenlige:''' Better than it seems to be, tho still rough. [[Blackwood]] [[augmented (temperament)|augmented]]. A heavily stretched [[Carlos Alpha]] scale. The best you can get with blackwood. I don't know why there are "people fond of" such inaccurate temperaments. | ||
== [[16edo]] == | == [[16edo]] == | ||
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: '''Fumica:''': This edo is characterized by its hard [[5L 2s|diatonic]] scale, with more contrasting step sizes than [[12edo]]'s basic diatonic scale. This gives it more intense voice leading and more cathartic resolutions. Traditional tertian harmony works pretty well here, but semiquartal harmony, that is using the contrast between [[7/4]] and [[12/7]] as the basis of tonality, does even better. S-tier. | : '''Fumica:''': This edo is characterized by its hard [[5L 2s|diatonic]] scale, with more contrasting step sizes than [[12edo]]'s basic diatonic scale. This gives it more intense voice leading and more cathartic resolutions. Traditional tertian harmony works pretty well here, but semiquartal harmony, that is using the contrast between [[7/4]] and [[12/7]] as the basis of tonality, does even better. S-tier. | ||
: '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to [[timbre]] to prevent it sounding "out of tune". | : '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to [[timbre]] to prevent it sounding "out of tune". | ||
: '''Zhenlige:''' A circle of fifths in [[34edo]]. Interesting sharp fifths. The smallest diatonic EDO with neutral intervals. The boundary between neogothic and superpyth. Like 12edo, its thirds do not approximate any simple ratios well. | : '''Zhenlige:''' A circle of fifths in [[34edo]]. Interesting sharp fifths. The smallest [[5L 2s|diatonic]] EDO with neutral intervals. The boundary between neogothic and superpyth. Like [[12edo]], its diatonic thirds do not approximate any simple ratios well, and a [[well temperament]] may help. Its [[13/1|13]] is good, and [[11/1|11]] and [[7/1|7]] have a similar precision to 12edo's [[5/1|5]]. It benefits from compression. | ||
: '''Eufalesio''': Despite being the next edo with a usable fifth, the fact that it tempers the interval whose edostep best approximates it is the ultimate irony. I like the slightly sharp fifths and neo-gothic feel, but the lack of 5-limit is a hole I can't easily live without, and no matter how good it is on other limits (and it is ''great''), the lack of 5 is sad. C | : '''Eufalesio''': Despite being the next edo with a usable fifth, the fact that it tempers the interval whose edostep best approximates it is the ultimate irony. I like the slightly sharp fifths and neo-gothic feel, but the lack of 5-limit is a hole I can't easily live without, and no matter how good it is on other limits (and it is ''great''), the lack of 5 is sad. C | ||
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: '''Fumica:''' This edo is where my microtonal journey began. Extremely versatile yet friendly to beginners. Using it as a tuning of meantone, the tuning profile is sort of opposite to 12edo, but with seven more pitch classes, the expressive possibility explodes. Presence of an exact hemitwelfth sets it apart from many other meantone edos. Octave stretch solves the intonational problem to a large extent. S-tier. | : '''Fumica:''' This edo is where my microtonal journey began. Extremely versatile yet friendly to beginners. Using it as a tuning of meantone, the tuning profile is sort of opposite to 12edo, but with seven more pitch classes, the expressive possibility explodes. Presence of an exact hemitwelfth sets it apart from many other meantone edos. Octave stretch solves the intonational problem to a large extent. S-tier. | ||
: '''Budjarn Lambeth:''' The smallest equal tuning that approximates the entire [[43-limit]]. Its melodic similarity to 12edo makes it easier to find your bearings, but harder to break out of that diatonic comfort zone and explore all those intricate high limit harmonies it has to offer. | : '''Budjarn Lambeth:''' The smallest equal tuning that approximates the entire [[43-limit]]. Its melodic similarity to 12edo makes it easier to find your bearings, but harder to break out of that diatonic comfort zone and explore all those intricate high limit harmonies it has to offer. | ||
: '''Zhenlige:''' Very different tradeoffs from 12edo. Usable but imperfect for many temperaments. [[Meantone]] or [[magic]], but with a too flat fifth. Strangely large minor 2nds. A compressed [[Carlos Beta]] scale. For meantone [[31edo]] is more preferable, and for magic [[41edo]]. The lower bound of a good fifth. It benefits from stretching | : '''Zhenlige:''' A stack of [[5/3]]. Very different tradeoffs from [[12edo]]. Usable but imperfect for many temperaments. [[Meantone]] or [[magic]], but with a too flat fifth. Strangely large minor 2nds off from [[16/15]] even more than 12edo's. A compressed [[Carlos Beta]] scale. For meantone [[31edo]] is more preferable, and for magic [[41edo]]. The lower bound of a good fifth. It benefits from stretching. Good as a subset of [[enneadecal]]. | ||
: '''Eufalesio:''' The next most easily accessible edo, and one that offers a change in perspective. It is meantone just like 12edo, but it has a completely different sonic profile, due to the flatter 5-limit, which I find very enjoyable. The near just minor thirds are definitely something to remark, though not as discernible as it is in its supersets. Great stuff! A | : '''Eufalesio:''' The next most easily accessible edo, and one that offers a change in perspective. It is meantone just like 12edo, but it has a completely different sonic profile, due to the flatter 5-limit, which I find very enjoyable. The near just minor thirds are definitely something to remark, though not as discernible as it is in its supersets. Great stuff! A | ||
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: '''Fumica:''' The least evil solution to [[porcupine]] and less so to [[superpyth]]. I happen to have experience working with porcupine and it felt quite alright, except that I often found myself struggling to combat its out-of-tune nature. B-tier. | : '''Fumica:''' The least evil solution to [[porcupine]] and less so to [[superpyth]]. I happen to have experience working with porcupine and it felt quite alright, except that I often found myself struggling to combat its out-of-tune nature. B-tier. | ||
: '''Budjarn Lambeth:''' It is the first EDO bigger than 12 which sounds equally as "in-tune" as 12, in my opinion. Though it does have some [[wolf interval]]s which can startle new composers; with experience one learns how to approach those. Its [[superpyth]] and [[pajara]] scales offer a familiar-but-not-too-familiar melodic structure where prior 12edo training is useful, but where exploration beyond it is rewarded with gorgeous new colours. In this sense, it offers the strengths of both 19 and 20 without the drawbacks of either. | : '''Budjarn Lambeth:''' It is the first EDO bigger than 12 which sounds equally as "in-tune" as 12, in my opinion. Though it does have some [[wolf interval]]s which can startle new composers; with experience one learns how to approach those. Its [[superpyth]] and [[pajara]] scales offer a familiar-but-not-too-familiar melodic structure where prior 12edo training is useful, but where exploration beyond it is rewarded with gorgeous new colours. In this sense, it offers the strengths of both 19 and 20 without the drawbacks of either. | ||
: '''Zhenlige:''' The smallest non-meantone EDO with | : '''Zhenlige:''' The smallest EDO with decent [[11-limit]] and the smallest non-meantone EDO with decent [[5-limit]]. [[Superpyth]] and [[porcupine]]. The only reasonable superpyth EDO. The upper bound of a good fifth. The best you can get with [[50/49]] tempered out. | ||
: '''Eufalesio:''' While the change in perspective that 19edo offers is mixed with familiarity, 22edo is an entirely different beast. It features a very exaggerated non-meantone 5-limit, making it the ultimate porcupine, which is not a temperament known for its accuracy, but it's cool! It also supports magic, featuring a flatter 5, which I enjoy, though the incredibly sharp 6/5 is a tad excessive. – The 7-limit structure inside the diatonic scale is something very sui generis, though it's 11-limit is kinda meh, but what can I say, it's the first edo to be consistent in the 11-odd-limit! C, not for accuracy, but for ''cool''. | : '''Eufalesio:''' While the change in perspective that 19edo offers is mixed with familiarity, 22edo is an entirely different beast. It features a very exaggerated non-meantone 5-limit, making it the ultimate porcupine, which is not a temperament known for its accuracy, but it's cool! It also supports magic, featuring a flatter 5, which I enjoy, though the incredibly sharp 6/5 is a tad excessive. – The 7-limit structure inside the diatonic scale is something very sui generis, though it's 11-limit is kinda meh, but what can I say, it's the first edo to be consistent in the 11-odd-limit! C, not for accuracy, but for ''cool''. | ||
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: '''Fumica:''' Potentially useful as every other step of [[46edo]]. D-tier. | : '''Fumica:''' Potentially useful as every other step of [[46edo]]. D-tier. | ||
: '''Budjarn Lambeth:''' A great EDO to begin experimenting with [[octave stretching]] and squishing. With pure octaves, it sounds out of tune, but stretch it by about 10 [[cents]], and you get access to the full array of pretty no-13s [[59-limit]] harmonies. ''Compress'' it by about 10 cents, and you instead get access to the full array of no-19s [[37-limit]] harmonies. Both tunings punch far above their weight by having lots of consonances in only 23 notes. Experiment with both the stretched and squished versions of 23edo, to get a feeling for how stretching or squishing a scale can shift its underlying harmonies dramatically while preserving its melodic shape. | : '''Budjarn Lambeth:''' A great EDO to begin experimenting with [[octave stretching]] and squishing. With pure octaves, it sounds out of tune, but stretch it by about 10 [[cents]], and you get access to the full array of pretty no-13s [[59-limit]] harmonies. ''Compress'' it by about 10 cents, and you instead get access to the full array of no-19s [[37-limit]] harmonies. Both tunings punch far above their weight by having lots of consonances in only 23 notes. Experiment with both the stretched and squished versions of 23edo, to get a feeling for how stretching or squishing a scale can shift its underlying harmonies dramatically while preserving its melodic shape. | ||
: '''Zhenlige:''' Incomplete [[46edo]]. The largest EDO without a diatonic, blackwood or whitewood fifth. | : '''Zhenlige:''' Incomplete [[46edo]]. The largest EDO without a [[5L 2s|diatonic]], [[5edo|blackwood]] or [[7edo|whitewood]] fifth. | ||
: '''Eufalesio:''' Useless. FF | : '''Eufalesio:''' Useless. FF | ||
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: '''Deja Igliashon:''' I just don't have much to say about this one. It's sort of the opposite of [[21edo]] to me: looks like it should be really cool and good on paper, but I just don't really enjoy the sound. Most of what it's good at can be done in smaller EDOs too, and that's usually what I'd rather choose. | : '''Deja Igliashon:''' I just don't have much to say about this one. It's sort of the opposite of [[21edo]] to me: looks like it should be really cool and good on paper, but I just don't really enjoy the sound. Most of what it's good at can be done in smaller EDOs too, and that's usually what I'd rather choose. | ||
: '''Fumica:''' Just as [[19edo]] is the point separating [[meantone]] and [[flattone]], this is the point separating flattone and [[flattertone|a meantone extension that implies an even flatter fifth]]. Therefore it should share all the advantages of 12edo and 19edo, at least theoretically, that is if not for its poor intonation in the [[5-limit]]. C-tier. | : '''Fumica:''' Just as [[19edo]] is the point separating [[meantone]] and [[flattone]], this is the point separating flattone and [[flattertone|a meantone extension that implies an even flatter fifth]]. Therefore it should share all the advantages of 12edo and 19edo, at least theoretically, that is if not for its poor intonation in the [[5-limit]]. C-tier. | ||
: '''Zhenlige:''' A stack of [[7/4]]. Good for 2.7.11 subgroup. Other intervals suck. Since it is relatively small, consistency does not implies high accuracy. Meantone but tuned terribly. Incomplete [[130edo]]. | : '''Zhenlige:''' The fact that [[53edo]] is good indicates that 26- and 27edo are probably bad. A stack of [[7/4]]. Good for 2.7.11 subgroup. Other intervals suck. Since it is relatively small, consistency does not implies high accuracy. [[Meantone]] in [[5-limit]] but tuned terribly. Incomplete [[130edo]]. | ||
: '''Eufalesio:''' Interesting, but unjustifiably inaccurate for me. D | : '''Eufalesio:''' Interesting, but unjustifiably inaccurate for me. D | ||
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: '''Deja Igliashon:''' if this EDO got as much attention as [[31edo]], the world would be a better place. For many EDOs, getting into the particulars of how they [[temper]] extended [[JI]] is kind of unnecessary to really appreciate them, but 27edo is just so disgustingly ELEGANT in how it tempers that it makes it SO MUCH EASIER to navigate extended JI than darn near anything that can approach it in [[accuracy]]. First, consider the [[unison vector]] 64/63: just like {{EDOs|5, 10, 15, 20, 22, and 25edo}} (and I guess 12d?), tempering this out makes it so you can divide [[7/4]] into two equal parts that are each equal to [[4/3]], so even a short [[chain of fifths]] just automagically incorporates a bunch of ratios of 7. Then you've got [[128/125]], aka the Augmented comma, aka the diesis or something, which makes it so three approximate [[5/4]]s span exactly one octave--if you simply follow a chain of 5/4s, you literally can't get lost in the tuning! So far so good but also [[15edo]] can do both of these as well, so what else do we have? How about the holy trinity of 144/143, 169/168, and 196/195, the vanishing of which make it so [[12/11]]=[[13/12]]=[[14/13]]=[[15/14]]? This is the trinity that really gives 9edo its mojo, and in 27edo we have three parallel closed circles of [[9edo]], offset from one another by 1 and 2 steps of 27edo (respectively). Why is this cool? Because if you have a root note on one chain of 9edo, you have a [[5/4]] above it on the same chain, and then you have [[11/8]], [[3/2]], [[13/8]], [[7/4]], and [[15/8]] on the next chain of 9edo that's 1\27 higher. So you can just arpeggiate a bunch of [[harmonic]]s using motion by a single uniform step size, and if you keep moving by that same step size, instead of getting lost or circulating through ALL THE NOTES OF THE TUNING, you end up back at familiar territory after just a few off-kilter notes. Basically 27edo just makes it really easy not to get lost in [[15-odd-limit]] JI, because you have can find your way between harmonics with simple motions on small closed circles. Just AMAZING! | : '''Deja Igliashon:''' if this EDO got as much attention as [[31edo]], the world would be a better place. For many EDOs, getting into the particulars of how they [[temper]] extended [[JI]] is kind of unnecessary to really appreciate them, but 27edo is just so disgustingly ELEGANT in how it tempers that it makes it SO MUCH EASIER to navigate extended JI than darn near anything that can approach it in [[accuracy]]. First, consider the [[unison vector]] 64/63: just like {{EDOs|5, 10, 15, 20, 22, and 25edo}} (and I guess 12d?), tempering this out makes it so you can divide [[7/4]] into two equal parts that are each equal to [[4/3]], so even a short [[chain of fifths]] just automagically incorporates a bunch of ratios of 7. Then you've got [[128/125]], aka the Augmented comma, aka the diesis or something, which makes it so three approximate [[5/4]]s span exactly one octave--if you simply follow a chain of 5/4s, you literally can't get lost in the tuning! So far so good but also [[15edo]] can do both of these as well, so what else do we have? How about the holy trinity of 144/143, 169/168, and 196/195, the vanishing of which make it so [[12/11]]=[[13/12]]=[[14/13]]=[[15/14]]? This is the trinity that really gives 9edo its mojo, and in 27edo we have three parallel closed circles of [[9edo]], offset from one another by 1 and 2 steps of 27edo (respectively). Why is this cool? Because if you have a root note on one chain of 9edo, you have a [[5/4]] above it on the same chain, and then you have [[11/8]], [[3/2]], [[13/8]], [[7/4]], and [[15/8]] on the next chain of 9edo that's 1\27 higher. So you can just arpeggiate a bunch of [[harmonic]]s using motion by a single uniform step size, and if you keep moving by that same step size, instead of getting lost or circulating through ALL THE NOTES OF THE TUNING, you end up back at familiar territory after just a few off-kilter notes. Basically 27edo just makes it really easy not to get lost in [[15-odd-limit]] JI, because you have can find your way between harmonics with simple motions on small closed circles. Just AMAZING! | ||
: '''Fumica:''' The cyberpunk edo. Good sharp-tending tuning profile in the 2.3.5.7.13 [[subgroup]] with the sole exception of harmonic 15 tuned way too sharp, for I prefer a flat tuning of 15 or at least no sharper than 12edo's to improve its stability as a consonant major seventh. Other than that it's pretty good. Octave compression gives better intonation. A-tier. | : '''Fumica:''' The cyberpunk edo. Good sharp-tending tuning profile in the 2.3.5.7.13 [[subgroup]] with the sole exception of harmonic 15 tuned way too sharp, for I prefer a flat tuning of 15 or at least no sharper than 12edo's to improve its stability as a consonant major seventh. Other than that it's pretty good. Octave compression gives better intonation. A-tier. | ||
: '''Zhenlige:''' Worse than both | : '''Zhenlige:''' Worse than both [[12edo]] and [[22edo]] for [[5-limit]]. It generally sounds worse than 22edo. Its fifth sucks and its diatonic scale makes little sense. Its [[7/3]] and [[7/5]] are good, but 3, 5 and 7 are off. When I hear its ~[[10:12:15]] and ~[[6:7:9]] chord I feel the fifth is obviously off. Use [[108edo]] (not [[landscape]]) to make it a true [[7-limit]] EDO, and [[270edo]] is excellent. | ||
== [[28edo]] == | == [[28edo]] == | ||
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: '''Yourmusic Productions:''' [[14edo]], only with a really in tune major 3rd and lots of other really interesting extra intervals. Really want an instrument that can do this one justice, probably an 8-string [[guitar]] tuned in it's slightly stretched 5ths so the top string is 3 octaves up from the bottom, and a 28-30" fanned fret multiscale fretboard that makes all the chords [[isomorphic]]. | : '''Yourmusic Productions:''' [[14edo]], only with a really in tune major 3rd and lots of other really interesting extra intervals. Really want an instrument that can do this one justice, probably an 8-string [[guitar]] tuned in it's slightly stretched 5ths so the top string is 3 octaves up from the bottom, and a 28-30" fanned fret multiscale fretboard that makes all the chords [[isomorphic]]. | ||
: '''Fumica:''' Potentially useful as every other step of [[56edo]]. D-tier. | : '''Fumica:''' Potentially useful as every other step of [[56edo]]. D-tier. | ||
: '''Zhenlige:''' [[Whitewood]] [[diminished]]. Kinda opposite from [[15edo]]. The best you can get with | : '''Zhenlige:''' [[Whitewood]] [[diminished (temperament)|diminished]]. Kinda opposite from [[15edo]]. The best you can get with whitewood. | ||
: '''Eufalesio:''' The hyper-accurate 5/4 alone makes it useless. FF | : '''Eufalesio:''' The hyper-accurate 5/4 alone makes it useless. FF | ||
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: '''Yourmusic Productions:''' [[12edo]]'s evil twin, but in an awesome way. About the same amount of error but in opposite directions means similar kinds of psychoacoustic beating, majors and minors are still clearly recognisable, and everything sounds deceptively familiar right up until it does something awesome that 12 can't. When you do focus on xen intervals and chords, it still sounds much better than [[24edo]] Another definite favourite. | : '''Yourmusic Productions:''' [[12edo]]'s evil twin, but in an awesome way. About the same amount of error but in opposite directions means similar kinds of psychoacoustic beating, majors and minors are still clearly recognisable, and everything sounds deceptively familiar right up until it does something awesome that 12 can't. When you do focus on xen intervals and chords, it still sounds much better than [[24edo]] Another definite favourite. | ||
: '''Fumica:''' The first edo that sounds like [[Pythagorean tuning]] with distinct chromatic and diatonic semitones, such that most contemporary 12edo music will sound alright if retempered to this through [[dominant (temperament)|dominant]]. The [[patent val|patent-val]] interpretation is underwhelming. Otherwise it's a good framework as every other step of [[58edo]] and every third step of [[87edo]]. C-tier. | : '''Fumica:''' The first edo that sounds like [[Pythagorean tuning]] with distinct chromatic and diatonic semitones, such that most contemporary 12edo music will sound alright if retempered to this through [[dominant (temperament)|dominant]]. The [[patent val|patent-val]] interpretation is underwhelming. Otherwise it's a good framework as every other step of [[58edo]] and every third step of [[87edo]]. C-tier. | ||
: '''Zhenlige:''' A circle of fifths in [[mystery]], which supports [[pele]] (and is close to its optimal tuning), a convenient temperament with 5, 7, 11 and 13 on the same chain of fifths. The smallest EDO with a better | : '''Zhenlige:''' A circle of fifths in [[mystery]], which supports [[pele]] (and is close to its optimal tuning), a convenient temperament with [[5/1|5]], [[7/1|7]], [[11/1|11]] and [[13/1|13]] on the same chain of fifths. Near pure [[13/11]]. The smallest EDO with a better [[3/2]] than [[12edo]]. | ||
== [[30edo]] == | == [[30edo]] == | ||
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: '''Yourmusic Productions:''' It definitely sounds nice, but I don't hear much actual songwriting going on in it, just people building enormous washes of harmony and luxuriating in them. Maybe it has too LITTLE tension in it, or maybe it's just past the point of complexity that the human mind can fully comprehend. In any case, it definitely hasn't been used to it's full potential yet. | : '''Yourmusic Productions:''' It definitely sounds nice, but I don't hear much actual songwriting going on in it, just people building enormous washes of harmony and luxuriating in them. Maybe it has too LITTLE tension in it, or maybe it's just past the point of complexity that the human mind can fully comprehend. In any case, it definitely hasn't been used to it's full potential yet. | ||
: '''Fumica:''' This is a great edo. Too great it's a little unfun to work with. It has a tuning profile close to what I consider the [[optimal tuning]] of meantone, and [[migration]], the [[meantone]] [[extension]] that maps harmonic 11 to the semi-augmented fourth, works almost perfectly in this system. [[Octave stretch]] gives better intonation. A-tier. | : '''Fumica:''' This is a great edo. Too great it's a little unfun to work with. It has a tuning profile close to what I consider the [[optimal tuning]] of meantone, and [[migration]], the [[meantone]] [[extension]] that maps harmonic 11 to the semi-augmented fourth, works almost perfectly in this system. [[Octave stretch]] gives better intonation. A-tier. | ||
: '''Zhenlige:''' Ideal for pure-octave [[meantone]], combining lots of 11-limit extensions in a single tuning. The meantone flat fifth makes its neutral thirds close to [[11/9]] (tho there is the JI subgroup problem since 11 and 9 themselves are not so | : '''Zhenlige:''' Ideal for pure-octave [[meantone]], combining lots of [[11-limit]] extensions in a single tuning. The meantone flat fifth makes its neutral thirds close to [[11/9]] (tho there is the JI subgroup problem since [[11/1|11]] and [[9/1|9]] themselves are not so good). Also [[valentine]] and [[miracle]]. IMO the best meantone EDO. Nearly the best meantone can give for high limit. For other temperaments its flat fifth may be a drawback, making 9 bad. | ||
: '''Eufalesio:''' The best meantone edo. Manageable grain, incredible 11-limit. You can't get more juice out of meantone without diminishing returns. From this point on, it becomes hard to justify using a finer meantone gamut. SSS | : '''Eufalesio:''' The best meantone edo. Manageable grain, incredible 11-limit. You can't get more juice out of meantone without diminishing returns. From this point on, it becomes hard to justify using a finer meantone gamut. SSS | ||
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: '''Yourmusic Productions:''' Even better for [[5-limit]] music than [[31edo]], with it's gorgeous thirds, actually defined different sizes of whole tone and still sour harmonic 7, yet even more underused. Definitely deserves more attention. Maybe a half-[[kite guitar]], with full frets up to the perfect 4th or 5th, then [[17edo]] above that point, with adjacent strings tuned so the full range of higher notes can still be played would make it feasible. | : '''Yourmusic Productions:''' Even better for [[5-limit]] music than [[31edo]], with it's gorgeous thirds, actually defined different sizes of whole tone and still sour harmonic 7, yet even more underused. Definitely deserves more attention. Maybe a half-[[kite guitar]], with full frets up to the perfect 4th or 5th, then [[17edo]] above that point, with adjacent strings tuned so the full range of higher notes can still be played would make it feasible. | ||
: '''Fumica:''' This is to 17edo what [[24edo]] is to [[12edo]]. While 17edo is often good enough, this offers some more sophisticated solutions such as [[tetracot]]. Even the [[harmonic]]s 7 and 11, which come from 17edo and are commonly cited as relatively poor in this edo, are convincing enough to me, since when I worked with [[modus]] I never had a problem with the intonation at all, unlike with [[porcupine]]. The sound is better than the structure. B-tier. | : '''Fumica:''' This is to 17edo what [[24edo]] is to [[12edo]]. While 17edo is often good enough, this offers some more sophisticated solutions such as [[tetracot]]. Even the [[harmonic]]s 7 and 11, which come from 17edo and are commonly cited as relatively poor in this edo, are convincing enough to me, since when I worked with [[modus]] I never had a problem with the intonation at all, unlike with [[porcupine]]. The sound is better than the structure. B-tier. | ||
: '''Zhenlige:''' 17edo with | : '''Zhenlige:''' [[17edo]] with [[5/1|5]] and [[17/1|17]] added, making a good 2.3.5.13.17 system. A slightly stretched [[Carlos Gamma]] scale. | ||
== [[35edo]] == | == [[35edo]] == | ||
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: '''Fumica:''' Potentially useful as every other step of [[70edo]]. D-tier. | : '''Fumica:''' Potentially useful as every other step of [[70edo]]. D-tier. | ||
: '''Budjarn Lambeth:''' A very good [[dual-fifth]] edo. | : '''Budjarn Lambeth:''' A very good [[dual-fifth]] edo. | ||
: ''Zhenlige:''' The largest non-diatonic EDO. | : ''Zhenlige:''' The largest non-[[5L 2s|diatonic]] EDO. | ||
: '''Eufalesio:''' Useless. FF | : '''Eufalesio:''' Useless. FF | ||
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: '''Fumica:''' The idea of adding sixth tones to plain 12edo music is interesting, but none of my attempts have been successful as I generally find them to sound forced. I think this edo is more difficult to use than it appears. C-tier. | : '''Fumica:''' The idea of adding sixth tones to plain 12edo music is interesting, but none of my attempts have been successful as I generally find them to sound forced. I think this edo is more difficult to use than it appears. C-tier. | ||
: '''Budjarn Lambeth:''' Along with 24edo, it is one of the two possible ways to extend 12edo while preserving equal spacing, and keeping the number of notes somewhat manageable. 36edo is ideal if you want to add intervals involving the 7th harmonic into 12edo, while 24edo is ideal if you want to add intervals involving the 11th harmonic. Comparing and contrasting 24edo and 36edo can help you get a feel for the difference between the "vibe" of the 11th harmonic, and the "vibe" of the 7th harmonic. I recommend dipping your toes into each of the two. — Try using familar 12edo intervals in lower registers of your instrument(s)/mix, while mixing in some of the strange new 36edo intervals in the higher registers. Thus will mimic the shape of the [[harmonic series]] and sound nice and glittery. | : '''Budjarn Lambeth:''' Along with 24edo, it is one of the two possible ways to extend 12edo while preserving equal spacing, and keeping the number of notes somewhat manageable. 36edo is ideal if you want to add intervals involving the 7th harmonic into 12edo, while 24edo is ideal if you want to add intervals involving the 11th harmonic. Comparing and contrasting 24edo and 36edo can help you get a feel for the difference between the "vibe" of the 11th harmonic, and the "vibe" of the 7th harmonic. I recommend dipping your toes into each of the two. — Try using familar 12edo intervals in lower registers of your instrument(s)/mix, while mixing in some of the strange new 36edo intervals in the higher registers. Thus will mimic the shape of the [[harmonic series]] and sound nice and glittery. | ||
: '''Zhenlige:''' Good for 2.3.7.13.17.19.23.29 subroup. Avoid [[5/1|5]] here because it is almost completely missed. Otherwise incomplete 72edo. | : '''Zhenlige:''' Good for 2.3.7.13.17.19.23.29 subroup. Avoid [[5/1|5]] here because it is almost completely missed. Otherwise incomplete [[72edo]]. | ||
== [[37edo]] == | == [[37edo]] == | ||
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: '''Fumica:''' Potentially useful as every other step of [[74edo]] or every third step of [[111edo]]. Besides that, it has a good 2.5.7.11.13 [[subgroup]] interpretation, tho I have no idea how harmony in this subgroup is supposed to work. D-tier. | : '''Fumica:''' Potentially useful as every other step of [[74edo]] or every third step of [[111edo]]. Besides that, it has a good 2.5.7.11.13 [[subgroup]] interpretation, tho I have no idea how harmony in this subgroup is supposed to work. D-tier. | ||
: '''Budjarn Lambeth:''' A very good [[dual-fifth]] edo. | : '''Budjarn Lambeth:''' A very good [[dual-fifth]] edo. | ||
: '''Zhenlige:''' | : '''Zhenlige:''' A strong no-[[3/1|3]] system, which is kinda hard to use since the only isoharmonic chords are subsets of the 3n+1 and 3n+2 series, and there are not many useful scales. | ||
== [[38edo]] == | == [[38edo]] == | ||
: '''Bozu:''' [[19edo]] slashed into halves. | : '''Bozu:''' [[19edo]] slashed into halves. | ||
: '''Fumica:''' This is to 19edo what [[24edo]] is to [[12edo]]. On paper it adds decent approximation to [[harmonic]]s 11, 17, and 19, but in practice I never had a situation where I felt I needed these additional notes when working with 19edo. C-tier. | : '''Fumica:''' This is to 19edo what [[24edo]] is to [[12edo]]. On paper it adds decent approximation to [[harmonic]]s 11, 17, and 19, but in practice I never had a situation where I felt I needed these additional notes when working with 19edo. C-tier. | ||
: '''Zhenlige:''' 19edo with neutrals. Near pure [[11/9]]. | : '''Zhenlige:''' [[19edo]] with neutrals. Near pure [[11/9]]. Doubling such a coarse EDO won't give anything very notable, and the acceptable error of 19edo really becomes a problem at this size. | ||
== [[39edo]] == | == [[39edo]] == | ||
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: '''Nicolai:''' Smaller version of [[53edo|53EDO]]. | : '''Nicolai:''' Smaller version of [[53edo|53EDO]]. | ||
: '''Fumica:''' The first of the five essential comma-level edos, and the first edo to achieve [[9-odd-limit]] [[distinction]] and [[consistency]]. This is most significant for providing three flavors for each [[chromatic]] category: classical, Pythagorean, and septimal. In this case it is a [[schismic]] and [[garischismic]] system, so that all three kinds are separated by the same [[comma]] step and can be found on a stack of fifths. The comma step is somewhat larger than just, making the differences more pronounced, which is part of why I think this edo is pretty deep – the step isn't only a comma, but many things at once, including but not limited to the septimal dieses, as well as the chroma of the [[archaeotonic]] scale, the scale of [[Tetracot]][7]. The best [[subgroup]] of this edo is, actually, 2.3.5.7.11.19. [[Prime]] 13 is certainly plausible, but prime 19 fits way better. There's a unique uniform tuning for the [[harmonic segment]] 18::22, a fact related to the vanish of s10 = 100/99 and s9/s11 = 243/242. The beauty of this edo goes even beyond the structure, but also to the intonation: it has a very slightly sharp 3 and a more noticeably flat 5, making a flat, more stable 15; that is ideal for my music. Finally, it's an ideal tuning for the [[magic]] temperament. I can't compliment it enough. S-tier. | : '''Fumica:''' The first of the five essential comma-level edos, and the first edo to achieve [[9-odd-limit]] [[distinction]] and [[consistency]]. This is most significant for providing three flavors for each [[chromatic]] category: classical, Pythagorean, and septimal. In this case it is a [[schismic]] and [[garischismic]] system, so that all three kinds are separated by the same [[comma]] step and can be found on a stack of fifths. The comma step is somewhat larger than just, making the differences more pronounced, which is part of why I think this edo is pretty deep – the step isn't only a comma, but many things at once, including but not limited to the septimal dieses, as well as the chroma of the [[archaeotonic]] scale, the scale of [[Tetracot]][7]. The best [[subgroup]] of this edo is, actually, 2.3.5.7.11.19. [[Prime]] 13 is certainly plausible, but prime 19 fits way better. There's a unique uniform tuning for the [[harmonic segment]] 18::22, a fact related to the vanish of s10 = 100/99 and s9/s11 = 243/242. The beauty of this edo goes even beyond the structure, but also to the intonation: it has a very slightly sharp 3 and a more noticeably flat 5, making a flat, more stable 15; that is ideal for my music. Finally, it's an ideal tuning for the [[magic]] temperament. I can't compliment it enough. S-tier. | ||
: '''Zhenlige:''' Prime octave and highly composite fifth, opposite from [[12edo]], thus good for fifth-dividing temperaments. Containing [[Bohlen-Pierce scale]]. Good for [[magic]]. The [[Kite guitar]] shows its elegance, with many simple intervals | : '''Zhenlige:''' Prime octave and highly composite fifth, opposite from [[12edo]], thus good for fifth-dividing temperaments. Containing [[Bohlen-Pierce scale]]. Good for [[magic]]. The [[Kite guitar]] shows its elegance, with many simple intervals evenly spaced. Also [[garibaldi]] and [[miracle]]. The largest problem is its relatively inaccurate [[5/1|5]]. From here on, most EDOs with good [[13-limit]] support [[akea]]. | ||
: '''Eufalesio:''' The first usable schismic edo (29edo and 17edo don't count because their 5/4's are wack). Still manageable grain, hyperaccurate fifths and the non-meantoneness is definitely welcome. It is the first edo to introduce a comma accidental framework, which in my opinion is one of the best frameworks for composition. The 11-limit is marvelous (pun intended) but the 13-limit is... lacking. However, since it tempers so many things together, it is extremely useful. – Still, even if the 5-limit is not that accurate, since the innacuracy is flatwards, I think it's much more enjoyable, as I like wide minor thirds. Also supports Bohlen Pierce, which is also incredibly cool. AC, not for air conditioner, but for ''accuracy'' and ''cool''. | : '''Eufalesio:''' The first usable schismic edo (29edo and 17edo don't count because their 5/4's are wack). Still manageable grain, hyperaccurate fifths and the non-meantoneness is definitely welcome. It is the first edo to introduce a comma accidental framework, which in my opinion is one of the best frameworks for composition. The 11-limit is marvelous (pun intended) but the 13-limit is... lacking. However, since it tempers so many things together, it is extremely useful. – Still, even if the 5-limit is not that accurate, since the innacuracy is flatwards, I think it's much more enjoyable, as I like wide minor thirds. Also supports Bohlen Pierce, which is also incredibly cool. AC, not for air conditioner, but for ''accuracy'' and ''cool''. | ||
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: '''Bozu:''' [[Amphipent]] [[augmented (temperament)|augmented]]. | : '''Bozu:''' [[Amphipent]] [[augmented (temperament)|augmented]]. | ||
: '''Nicolai:''' You either get [[7edo|7EDO]] or [[superpyth]], there is no middle. | : '''Nicolai:''' You either get [[7edo|7EDO]] or [[superpyth]], there is no middle. | ||
: '''Zhenlige:''' Incomplete [[84edo]]. | |||
: '''Eufalesio:''' Useless. FF | : '''Eufalesio:''' Useless. FF | ||
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: '''Fumica:''' [[1/5-comma meantone]], not a bad meantone tuning in the [[5-limit]]. The 3 and 5 are equally off, making up a beautifully pure 15. Unfortunately the diesis is too small to achieve good [[7-limit|septimal]] and [[11-limit|undecimal]] harmony. B-tier. | : '''Fumica:''' [[1/5-comma meantone]], not a bad meantone tuning in the [[5-limit]]. The 3 and 5 are equally off, making up a beautifully pure 15. Unfortunately the diesis is too small to achieve good [[7-limit|septimal]] and [[11-limit|undecimal]] harmony. B-tier. | ||
: '''Budjarn Lambeth''': Better than [[12edo]] for most pop or earlier classical music that doesn't have lots of key changes in the one piece. The fifths are still pretty good, but the thirds and sixths sound so much warmer and more expressively. But, it is unsuitable if you want to use lots of key changes (like in jazz, later classical, or prog rock). Japanese pentatonic scales with semitones in them sound gorgeous in 43edo. I recommend the [[meantone]][19] [[MOS scale]] in 43edo to composers who want to dip their toes into [[microtonal|microtonality]] without getting in too deep. | : '''Budjarn Lambeth''': Better than [[12edo]] for most pop or earlier classical music that doesn't have lots of key changes in the one piece. The fifths are still pretty good, but the thirds and sixths sound so much warmer and more expressively. But, it is unsuitable if you want to use lots of key changes (like in jazz, later classical, or prog rock). Japanese pentatonic scales with semitones in them sound gorgeous in 43edo. I recommend the [[meantone]][19] [[MOS scale]] in 43edo to composers who want to dip their toes into [[microtonal|microtonality]] without getting in too deep. | ||
: '''Zhenlige:''' Close to 1/5-comma [[meantone]] which gives pure [[15/8]]. Not very notable besides that. Its fifth is too sharp for [[septimal meantone]]. | |||
== [[44edo]] == | == [[44edo]] == | ||
: '''Bozu:''' [[Amphipent]] [[diminished (temperament)|diminished]]. | : '''Bozu:''' [[Amphipent]] [[diminished (temperament)|diminished]]. | ||
: '''Fumica:''' This edo adds decent approximation to [[harmonic]] [[13/1|13]] on top of 22edo's [[11-limit]], which is pretty tense to start with. At this point it just all breaks down. D-tier. | : '''Fumica:''' This edo adds decent approximation to [[harmonic]] [[13/1|13]] on top of 22edo's [[11-limit]], which is pretty tense to start with. At this point it just all breaks down. D-tier. | ||
: '''Zhenlige:''' Like [[38edo]], doubling a coarse EDO won't give anything very notable. | |||
== [[45edo]] == | == [[45edo]] == | ||
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: '''Nicolai:''' You either get [[5edo|5EDO]] or [[7edo|7EDO]], but there is a middle. | : '''Nicolai:''' You either get [[5edo|5EDO]] or [[7edo|7EDO]], but there is a middle. | ||
: '''Fumica:''' The second essential comma-level edo. Five more notes than [[41edo]], offering the distinction of two types of [[neutral]] intervals at the cost of a narrower [[septimal diesis]]. As an eighth-tone system, it has a true [[quartertone]]. With that and all the accurate approximations, the expressive possibilities are endless. Best as a 2.3.5.7.11.17.23-[[subgroup]] temperament. A-tier. | : '''Fumica:''' The second essential comma-level edo. Five more notes than [[41edo]], offering the distinction of two types of [[neutral]] intervals at the cost of a narrower [[septimal diesis]]. As an eighth-tone system, it has a true [[quartertone]]. With that and all the accurate approximations, the expressive possibilities are endless. Best as a 2.3.5.7.11.17.23-[[subgroup]] temperament. A-tier. | ||
: '''Zhenlige:''' | : '''Zhenlige:''' [[13-limit]] [[diaschismic]] and [[valentine]]. Near pure [[11/7]]. It has quartertones similar to [[22edo]] but approximates JI intervals more accurately. Its 30::36 are all 2 steps apart. | ||
: '''Eufalesio:''' The best diaschismic. 13-limit stuff, though a bit sharp and not as accurate as 41-edo, it is good. I haven't composed anything with it, however, as I think diaschismic is kinda hard to conceptualize, and the sharpness of the 5 is something that I find less desirable. B | : '''Eufalesio:''' The best diaschismic. 13-limit stuff, though a bit sharp and not as accurate as 41-edo, it is good. I haven't composed anything with it, however, as I think diaschismic is kinda hard to conceptualize, and the sharpness of the 5 is something that I find less desirable. B | ||
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: '''Bozu:''' [[Amphipent]] [[augmented (temperament)|augmented]]. | : '''Bozu:''' [[Amphipent]] [[augmented (temperament)|augmented]]. | ||
: '''Nicolai:''' You either get [[7edo|7EDO]] or [[superpyth]], but there's a nice third. | : '''Nicolai:''' You either get [[7edo|7EDO]] or [[superpyth]], but there's a nice third. | ||
: '''Zhenlige:''' Incomplete [[94edo]]. | |||
: '''Eufalesio:''' Useless. FF | : '''Eufalesio:''' Useless. FF | ||
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: '''Nicolai:''' 12EDO, but more fancy. | : '''Nicolai:''' 12EDO, but more fancy. | ||
: '''Fumica:''' More appropriate as an interval category scheme than anything else. C-tier. | : '''Fumica:''' More appropriate as an interval category scheme than anything else. C-tier. | ||
: '''Zhenlige:''' A not-so-good multiple of [[12edo]]. | |||
== [[49edo]] == | == [[49edo]] == | ||
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: '''Nicolai:''' I consider this an optimal meantone EDO, due to a wealthy collection of notes here. | : '''Nicolai:''' I consider this an optimal meantone EDO, due to a wealthy collection of notes here. | ||
: '''Fumica:''' Close to [[2/7-comma meantone]] so it has a niche. Has the same problem as [[45edo]], though less severe. C-tier. | : '''Fumica:''' Close to [[2/7-comma meantone]] so it has a niche. Has the same problem as [[45edo]], though less severe. C-tier. | ||
: '''Zhenlige:''' | : '''Zhenlige:''' [[Meantone]] with a flatter fifth than [[31edo]], but I usually use [[golden meantone]] (with slight octave stretching) for this range. | ||
: '''Eufalesio:''' Still a good meantone edo, and though it is a much better approximant for golden meantone, I prefer using golden meantone as a rank-2, and not buying the entire gamut. The 19-limit usability is surprising, still. However, having all those new intervals inside a meantone edo feels in my opinion strangely unnatural, as we're stretching the meantone chain-of-fifths beyond what's supposed to. – For bigger edos in this range, meantone ceases to do it for me, but I respect it. C | : '''Eufalesio:''' Still a good meantone edo, and though it is a much better approximant for golden meantone, I prefer using golden meantone as a rank-2, and not buying the entire gamut. The 19-limit usability is surprising, still. However, having all those new intervals inside a meantone edo feels in my opinion strangely unnatural, as we're stretching the meantone chain-of-fifths beyond what's supposed to. – For bigger edos in this range, meantone ceases to do it for me, but I respect it. C | ||
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: '''Nicolai:''' [[JI]]: The Book. | : '''Nicolai:''' [[JI]]: The Book. | ||
: '''Fumica:''' The third essential comma-level edo. This one is kinda overrated. The best thing about it is the distinction of [[15/13]] and [[13/10]] from nearby [[7-limit|septimal]] intervals, which neither 41- nor 46edo does. What bugs me is that the fifth feels undertempered for pretty much every purpose, and while the 5-limit approximation is praiseworthy the rest deserves more love. Compared to [[41edo|41-]] or [[46edo]], it feels slack and doesn't convey a sense of tightly packed well-compromisedness. B-tier. | : '''Fumica:''' The third essential comma-level edo. This one is kinda overrated. The best thing about it is the distinction of [[15/13]] and [[13/10]] from nearby [[7-limit|septimal]] intervals, which neither 41- nor 46edo does. What bugs me is that the fifth feels undertempered for pretty much every purpose, and while the 5-limit approximation is praiseworthy the rest deserves more love. Compared to [[41edo|41-]] or [[46edo]], it feels slack and doesn't convey a sense of tightly packed well-compromisedness. B-tier. | ||
: '''Zhenlige:''' A stack of [[3/2]]. Almost just [[3/1|3]], and | : '''Zhenlige:''' A stack of [[3/2]]. Almost just [[3/1|3]], accurate [[5-limit]], and decent [[7-limit]]. Good for 5-limit [[schismatic]] with occasional [[garibaldi]] [[7/1|7]]. | ||
: '''Eufalesio:''' Pythagorean tuning incarnate, and astounding 5-limit. 2.3.5.13.19 is especially potent, but the .7.23 is still very much usable, even the .11! It doesn't temper as many things together as 41edo, so it feels like a less compromised system, still, I feel bad for the rest of the edos near this one, because this trumps a lot of the competition. But what can I say? Suck it losers! SS | : '''Eufalesio:''' Pythagorean tuning incarnate, and astounding 5-limit. 2.3.5.13.19 is especially potent, but the .7.23 is still very much usable, even the .11! It doesn't temper as many things together as 41edo, so it feels like a less compromised system, still, I feel bad for the rest of the edos near this one, because this trumps a lot of the competition. But what can I say? Suck it losers! SS | ||
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: '''Aura:''' While I don't recall making many songs with this EDO, I did compile a private list of [[JI|Just Intervals]], and I was quite fascinated with it for a time, as this EDO has better [[5-limit]] and [[7-limit]] approximations than both [[12edo]] and [[24edo]], with the latter being inherited from [[36edo]]. However, the fifth is not [[telic]], which is a problem for me in its own right. | : '''Aura:''' While I don't recall making many songs with this EDO, I did compile a private list of [[JI|Just Intervals]], and I was quite fascinated with it for a time, as this EDO has better [[5-limit]] and [[7-limit]] approximations than both [[12edo]] and [[24edo]], with the latter being inherited from [[36edo]]. However, the fifth is not [[telic]], which is a problem for me in its own right. | ||
: '''Fumica:''' The last essential comma-level edo. Has the same problem as [[60edo]]. Even tho it approximates [[JI]] way better and thus qualifies for an essential comma-level edo, most of its structural features have been provided by 41- and 58edo. B-tier. | : '''Fumica:''' The last essential comma-level edo. Has the same problem as [[60edo]]. Even tho it approximates [[JI]] way better and thus qualifies for an essential comma-level edo, most of its structural features have been provided by 41- and 58edo. B-tier. | ||
: '''Zhenlige:''' The ultimate extension of | : '''Zhenlige:''' The ultimate extension of [[12edo]] and [[24edo]]. Its [[11-limit]] is very accurate with a slightly sharp tendency that works well with 12edo's flat [[3/1|3]], and some higher limit intervals are also usable. [[Compton]] which is useful in 12edo-based programs. The only notable [[13-limit]] non-[[akea]] EDO around this size. A powerful tool for modulating quartertones, which can be difficult in 24edo itself. Good for [[miracle]]. Suitable for octave stretching if only [[17-limit]] or below is used. Playable by using three 24edo instruments or six 12edo instruments. | ||
: '''Eufalesio:''' The first compton edo that achieves any semblance of JIoid goodness. This was one of the first finer edos I've composed in. It has an astounding 11-limit, and decent 19-limit! It's also a multiple of 12, so it is very transposing-friendly and building it is trivial! It's a miracle, and it also supports it! SSS | : '''Eufalesio:''' The first compton edo that achieves any semblance of JIoid goodness. This was one of the first finer edos I've composed in. It has an astounding 11-limit, and decent 19-limit! It's also a multiple of 12, so it is very transposing-friendly and building it is trivial! It's a miracle, and it also supports it! SSS | ||
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== [[77edo]] == | == [[77edo]] == | ||
: '''Fumica:''' This edo is very sophisticated and hard to evaluate. It's an ideal tuning for the [[valentine]] temperament, obviously. It also seems to be capable of somewhat approximating the full [[23-limit]]. Overall, the structure is a tight fit, with lots of quirks, but that's not too troublesome – they may as well be turned into advantages in the right circumstances. B-tier. | : '''Fumica:''' This edo is very sophisticated and hard to evaluate. It's an ideal tuning for the [[valentine]] temperament, obviously. It also seems to be capable of somewhat approximating the full [[23-limit]]. Overall, the structure is a tight fit, with lots of quirks, but that's not too troublesome – they may as well be turned into advantages in the right circumstances. B-tier. | ||
: '''Zhenlige:''' Good for [[valentine]] | : '''Zhenlige:''' Good for [[valentine]]. Its slightly flat [[3/2]] gives a good [[19/1|19]] via [[boethius]]. Containing [[Carlos Alpha]]. [[40/27]] as 4\7 aka [[absurdity]]. Usable for high limit JI. At this size even some inconsistent intervals are usable via val mapping since its step size is only ~16 cents. | ||
== [[79edo]] == | == [[79edo]] == | ||
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== [[81edo]] == | == [[81edo]] == | ||
: '''Zhenlige:''' The [[optimal patent val]] for [[meantone]] and some of its higher-limit extentions, but | : '''Zhenlige:''' The [[optimal patent val]] for [[meantone]] and some of its higher-limit extentions, but I won't use such a large EDO for a temperament with relatively low accuracy, and rather use [[golden meantone]] instead, which is simpler and more elegant mathematically. | ||
: '''Eufalesio:''' Interesting, but rank-2 golden meantone is basically the same. D | : '''Eufalesio:''' Interesting, but rank-2 golden meantone is basically the same. D | ||
== [[84edo]] == | == [[84edo]] == | ||
: '''Yourmusic Productions:''' [[12edo]] only each note is split into a full rainbow, which makes for awesome looking yet still easily comprehensible [[notation]]. The best multiple of 12 for [[5-limit]] music and my personal holy grail of edos to find a way to make playable. | : '''Yourmusic Productions:''' [[12edo]] only each note is split into a full rainbow, which makes for awesome looking yet still easily comprehensible [[notation]]. The best multiple of 12 for [[5-limit]] music and my personal holy grail of edos to find a way to make playable. | ||
: '''Zhenlige:''' An alternate [[compton]] EDO besides [[72edo]], with better [[5/1|5]] and [[13/1|13]] with the expense of [[11/1|11]]. It has a sharp tendency instead of 72edo's flat. | |||
: '''Eufalesio:''' I haven't composed anything in it, but theory tells me that it's a really good compton edo. The bad tuning of the 11 is a bit sad, but it can be useful all the way up to the 31-limit. The 2.3.5.7.13 here is instead a great subgroup, which is a good selling point for me. Had I known about it, I could have probably used this instead of 72edo, but I'm now not that interested in compton anymore. A | : '''Eufalesio:''' I haven't composed anything in it, but theory tells me that it's a really good compton edo. The bad tuning of the 11 is a bit sad, but it can be useful all the way up to the 31-limit. The 2.3.5.7.13 here is instead a great subgroup, which is a good selling point for me. Had I known about it, I could have probably used this instead of 72edo, but I'm now not that interested in compton anymore. A | ||
== [[87edo]] == | == [[87edo]] == | ||
: '''Bozu:''' [[29edo]] with each interval sliced into three. You can do some nifty stuff with it, but the number of notes is too crazy to cover much with midi unless you choose a subset. Pushing a continuum beyond this. | : '''Bozu:''' [[29edo]] with each interval sliced into three. You can do some nifty stuff with it, but the number of notes is too crazy to cover much with midi unless you choose a subset. Pushing a continuum beyond this. | ||
: '''Zhenlige:''' Good [[mystery]] EDO. Useful for high | : '''Zhenlige:''' Good [[mystery]] EDO. Useful for high limit JI. Playable by using three [[29edo]] instruments. | ||
== [[94edo]] == | == [[94edo]] == | ||
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== [[99edo]] == | == [[99edo]] == | ||
: '''Zhenlige:''' Efficient near-[[Logarithmic approximants#Argent | : '''Zhenlige:''' Efficient near-[[Logarithmic approximants#Argent tuning|argent]] EDO. It suggests slight compression. Good for [[hemififths]]. It completely misses [[11/1|11]] and [[13/1|13]]. | ||
== [[111edo]] == | == [[111edo]] == | ||
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== [[118edo]] == | == [[118edo]] == | ||
: '''Zhenlige:''' The relationship of 53-118-171edo for [[schismatic]] is similar to 12-19-31edo for meantone. 53 and 12 are the simplest reasonable EDO with very mildly tempered fifths, 118 and 19 are better over all but | : '''Zhenlige:''' The relationship of [[53edo|53]]-118-[[171edo]] for [[schismatic]] is similar to [[12edo|12]]-[[19edo|19]]-[[31edo]] for meantone. 53 and 12 are the simplest reasonable EDO with very mildly tempered fifths, 118 and 19 are better over all but slightly overtempered (outside 5-odd-limit [[diamond tradeoff]]), and 171 and 31 are ideal. So like 19, I won't appreciate it much. | ||
== [[120edo]] == | == [[120edo]] == | ||
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== [[171edo]] == | == [[171edo]] == | ||
: '''Zhenlige:''' The ultimate EDO for approximating [[7-limit]] JI. If you don't need some ridiculous high precision or specific microtemperaments, there is no need to go any further. | : '''Zhenlige:''' The ultimate EDO for approximating [[7-limit]] JI. It suggests very slight stretching. If you don't need some ridiculous high precision or specific microtemperaments, there is no need to go any further. [[Schismatic]], [[gammic]], [[ennealimmal]] and [[enneadecal]]. Containing a better [[Carlos Gamma]] scale than [[34edo]]. At this size level, EDOs are more like free pitch, rather than either JI or a stable temperament. Ideal for free-pitch-like music that emphasizes 7-limit. | ||
: '''Eufalesio:''' Ennealimmal, personified. I haven't composed in it directly, but since I did compose in 7-limit JI, it'd sound the same. It features a dead-accurate 7-limit that I cannot distinguish from just. It's that good. The great innacuracy of the 11 is a bit sad, though it still has a usable 13, which has that going for it. A | : '''Eufalesio:''' Ennealimmal, personified. I haven't composed in it directly, but since I did compose in 7-limit JI, it'd sound the same. It features a dead-accurate 7-limit that I cannot distinguish from just. It's that good. The great innacuracy of the 11 is a bit sad, though it still has a usable 13, which has that going for it. A | ||
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== [[224edo]] == | == [[224edo]] == | ||
: '''Zhenlige:''' Like 171edo but with a slightly sharper (and closer to just) fifth, worse 7-limit but better [[13-limit]]. | : '''Zhenlige:''' Like [[171edo]] but with a slightly sharper (and closer to just) fifth, worse [[7-limit]] but better [[13-limit]]. | ||
: '''Eufalesio:''' A cousin to 217edo which is still schismic, dare I say the ultimate schismic edo, though still harder to conceptualize. Theory tells me that the 13-limit is extremely accurate, even more than the 217edo, and for that I think it deserves some attention. But 217edo is smaller, and it contains 31edo, so... I think I'll stick with the other one. B | : '''Eufalesio:''' A cousin to 217edo which is still schismic, dare I say the ultimate schismic edo, though still harder to conceptualize. Theory tells me that the 13-limit is extremely accurate, even more than the 217edo, and for that I think it deserves some attention. But 217edo is smaller, and it contains 31edo, so... I think I'll stick with the other one. B | ||
== [[270edo]] == | == [[270edo]] == | ||
: '''Zhenlige:''' Better than 224edo if [[schismatic]] is not required. Ideal for free-pitch-like music that emphasizes 13-limit. | : '''Zhenlige:''' Better than [[224edo]] if [[schismatic]] is not required. Ideal for free-pitch-like music that emphasizes [[13-limit]]. | ||
: '''Eufalesio:''' Ultimate low complexity JIoid edo. Though a tad large now, consistency within its 2.3.5.7.11.13.19 is insane. This trumps a lot of the competition. Using a finer gamut in the same subgroup becomes hard to justify. SSS | : '''Eufalesio:''' Ultimate low complexity JIoid edo. Though a tad large now, consistency within its 2.3.5.7.11.13.19 is insane. This trumps a lot of the competition. Using a finer gamut in the same subgroup becomes hard to justify. SSS | ||
== [[311edo]] == | == [[311edo]] == | ||
: '''Zhenlige:''' Good for very high | : '''Zhenlige:''' Good for very high limit JI. | ||
: '''Eufalesio:''' Ultimate ultra-high-limit JI. Absolute error is a smidge worse than 270edo, but it makes up by being consistent to the goddamn 41-odd-limit. Serendipity personified. Very hard to justify using anything else other than this, as the difference between edosteps from this point on is definitely nigh impossible to hear. I see it as an ultimate tuning of sorts for practicality's sake. SSS | : '''Eufalesio:''' Ultimate ultra-high-limit JI. Absolute error is a smidge worse than 270edo, but it makes up by being consistent to the goddamn 41-odd-limit. Serendipity personified. Very hard to justify using anything else other than this, as the difference between edosteps from this point on is definitely nigh impossible to hear. I see it as an ultimate tuning of sorts for practicality's sake. SSS | ||