User:Eboone/EDO Impressions - Revision history

Eboone: /* Summary of Ranking */changed 53edo to 41edo because 53 is no longer on the tier list

2025-03-12T17:38:17Z

Summary of Ranking: changed 53edo to 41edo because 53 is no longer on the tier list

← Older revision		Revision as of 17:38, 12 March 2025
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	# '''Unique'''		# '''Unique'''

	These are just guidelines that I tend to follow, and they in no way provide a concrete method of objectifying edos. However, knowing 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.		These are just guidelines that I tend to follow, and they in no way provide a concrete method of objectifying edos. However, knowing what I'm looking for will greatly aid in understanding why I place certain edos where I do. For example, 41edo 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 particularly interesting. This is largely subjective, as I really have no way of classifying mosses in any sort of objective way. '''Factors''' are also considered, as the factors of an edo determine a lot about its structure. 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.		Plus, these aren't the only guidelines. '''[[MOS scales]]''' are also considered, especially if they are scales that I find particularly interesting. This is largely subjective, as I really have no way of classifying mosses in any sort of objective way. '''Factors''' are also considered, as the factors of an edo determine a lot about its structure. 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.

Eboone: Updated all tier list placements and uploaded all tier lists

2024-11-19T04:58:46Z

Updated all tier list placements and uploaded all tier lists

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Eboone: /* Fewer Notes, Easier */ updated

2024-06-18T19:15:16Z

Fewer Notes, Easier: updated

← Older revision		Revision as of 19:15, 18 June 2024
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	This isn't always the case, but it generally is. One of the primary appeals of edos in general is their convenience and versatility, especially in comparison to just intonation. The extreme end of this is very small edos, and as you venture into larger edos, their compactness becomes less important as they strive to be closer to just intonation. Essentially, a small edo that works very well in a certain JI subset (such as 12edo) gains less from being multiplied, as the amount of new notes isn't justified by a newfound ability to approximate JI.		This isn't always the case, but it generally is. One of the primary appeals of edos in general is their convenience and versatility, especially in comparison to just intonation. The extreme end of this is very small edos, and as you venture into larger edos, their compactness becomes less important as they strive to be closer to just intonation. Essentially, a small edo that works very well in a certain JI subset (such as 12edo) gains less from being multiplied, as the amount of new notes isn't justified by a newfound ability to approximate JI.

	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?* ~~Smaller examples include 9edo and and~~ 10edo being placed above ~~18edo and~~ 20edo ~~respectively~~.		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 (72edo 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:''		''*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 (72edo 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:''

Eboone: formatting

2024-06-13T18:48:46Z

formatting

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Eboone: General editing across the board

2024-06-11T23:34:57Z

General editing across the board

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Eboone: Edited macrotonal edo descriptions

2024-06-11T17:14:37Z

Edited macrotonal edo descriptions

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Eboone: Edited descriptions of some edos less than 10 and moved 6edo to D tier

2024-06-11T03:25:43Z

Edited descriptions of some edos less than 10 and moved 6edo to D tier

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Eboone: /* Summary of Ranking */wording

2024-06-10T21:37:42Z

Summary of Ranking: wording

← Older revision		Revision as of 21:37, 10 June 2024
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	In general, edos with these qualities will place higher on the tier list:		In general, edos with these qualities will place higher on the tier list:

	# '''Few ~~notes~~'''		# '''Versatile'''
			# '''Few Notes'''
	# '''Consonant'''		# '''Consonant'''
	~~# '''Versatile'''~~
	# '''Unique'''		# '''Unique'''

Eboone: Finished overarching points for now, also placed them above the categorization heading

2024-06-10T21:08:04Z

Finished overarching points for now, also placed them above the categorization heading

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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.
-I may add more overarching points next, then I will go back and edit 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, in hindsight.
+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.''
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 All demos are short loops at 120bpm created by me in [[MuseScore|'''MuseScore 3''']].
 == 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'''.
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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.
-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.
-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.
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 ==== 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.
 == Trivial ==

Eboone: Added overarching point about approximating just intonation

2024-06-10T20:28:57Z

Added overarching point about approximating just intonation

← Older revision		Revision as of 20:28, 10 June 2024
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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.

	~~There is currently only one~~ overarching ~~point~~, ~~and my next task is to add more.~~ I will ~~then~~ go back and edit what I've already written thus far, making sure to maximize the efficiency of the reading experience.		I may add more overarching points next, then I will go back and edit 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, in hindsight.

	''Start date: May 13, 2024. Most recent update: June 8, 2024. '''26 days''' have been spent.''		''Start date: May 13, 2024. Most recent update: June 10, 2024. '''28 days''' have been spent.''

	—————————[[File:EDO Tier List.png\|alt=A tier list of EDOs. S Tier - 12, 34, 31, 53, 72, 50, 22, 17, 15, 26, 19. A Tier - 27, 10, 46, 21, 20, 7, 16, 41, 55. B Tier - 18, 24, 36, 48, 65, 58, 25, 63, 13, 11, 56, 29, 23, 9, 5, 8. C Tier - 40, 43, 28, 14, 70, 68, 57, 37, 30, 60, 54, 49, 47, 44, 38, 67, 59, 35, 6. F Tier - 52, 62, 66, 71, 64, 39, 51, 61, 32, 39, 42, 45, 33.\|thumb\|['''''OUTDATED''', will be updated when I'm finished with this page''] Ebooone's tier list of edos 5-72]]		—————————[[File:EDO Tier List.png\|alt=A tier list of EDOs. S Tier - 12, 34, 31, 53, 72, 50, 22, 17, 15, 26, 19. A Tier - 27, 10, 46, 21, 20, 7, 16, 41, 55. B Tier - 18, 24, 36, 48, 65, 58, 25, 63, 13, 11, 56, 29, 23, 9, 5, 8. C Tier - 40, 43, 28, 14, 70, 68, 57, 37, 30, 60, 54, 49, 47, 44, 38, 67, 59, 35, 6. F Tier - 52, 62, 66, 71, 64, 39, 51, 61, 32, 39, 42, 45, 33.\|thumb\|['''''OUTDATED''', will be updated when I'm finished with this page''] Ebooone's tier list of edos 5-72]]
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	== 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'''.

			=== Approximating [[Just intonation\|Just Intonation]] ===
			My introduction to microtonality was the '''[[harmonic series]]'''. One of the properties of the harmonic series is that intervals found closer to the fundamental tend to be more '''resonant''', i.e. they are '''consonant''' by definition. Consonance is a very desirable property for any given temperament to have, as it is the basis for making music sound "pleasant." Of course, there are plenty of mathematically consonant intervals that can be treated as dissonances — such as [[7/5]] and [[16/15]] — but even these intervals have that unmistakable resonant quality that makes them "easier" to listen to.

			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.

			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.

			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.

	=== Multiples of EDOs ===		=== Multiples of EDOs ===
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	==== Fewer Notes, Easier ====		==== Fewer Notes, Easier ====
	This isn't always the case, but it generally is. One of the primary appeals of edos in general is their convenience and versatility, especially in comparison to just intonation. The extreme end of this is very small edos, and as you venture into larger edos, their compactness becomes less important as they strive to be closer to [[just intonation]]. Essentially, a small edo that works very well in a certain JI subset (such as 12edo) gains less from being multiplied, as the amount of new notes isn't justified by a newfound ability to approximate JI.		This isn't always the case, but it generally is. One of the primary appeals of edos in general is their convenience and versatility, especially in comparison to just intonation. The extreme end of this is very small edos, and as you venture into larger edos, their compactness becomes less important as they strive to be closer to just intonation. Essentially, a small edo that works very well in a certain JI subset (such as 12edo) gains less from being multiplied, as the amount of new notes isn't justified by a newfound ability to approximate JI.

	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?* Smaller examples include 9edo and and 10edo being placed above 18edo and 20edo respectively.		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?* Smaller examples include 9edo and and 10edo being placed above 18edo and 20edo respectively.
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	==== The Novelty of Fewer ====		==== The Novelty of Fewer ====
	Yeah, I'm literally just saying smaller edos are cooler (unless they're too small; see F tier). I mean, think about it. Equally dividing the octave seems to clash with the logarithmic nature of the [[harmonic series]], so the fact that this even works at all is already cool enough. Yet, all you need are 12 equal partitions to completely dominate the music industry. Sure, your ears may not care about the novelty factor of using a small number of notes within the uncountably infinite realm of pitch, but conceptually I find it incredibly neat.		Yeah, I'm literally just saying smaller edos are cooler (unless they're too small; see F tier). I mean, think about it. Equally dividing the octave seems to clash with the logarithmic nature of the harmonic series, so the fact that this even works at all is already cool enough. Yet, all you need are 12 equal partitions to completely dominate the music industry. Sure, your ears may not care about the novelty factor of using a small number of notes within the uncountably infinite realm of pitch, but conceptually I find it incredibly neat.

	5edo is a great example. Like, really? Only 5? But it sounds so cute! Then there's 7edo, a surprisingly versatile temperament that often gets me thinking "wait... there's only 7 notes here?" It's kind of like my brain is drawing parallels from the idea of simple ratios being consonant. In a way, small edos are "consonant" and large edos are "dissonant" in terms of their conception.		5edo is a great example. Like, really? Only 5? But it sounds so cute! Then there's 7edo, a surprisingly versatile temperament that often gets me thinking "wait... there's only 7 notes here?" It's kind of like my brain is drawing parallels from the idea of simple ratios being consonant. In a way, small edos are "consonant" and large edos are "dissonant" in terms of their conception.
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	''Tier: '''F+'''''		''Tier: '''F+'''''
	[[File:3edo groove.mp3\|none\|thumb\|3edo foggy ambience on D augmented]]		[[File:3edo groove.mp3\|none\|thumb\|3edo foggy ambience on D augmented]]
	This edo is just an '''augmented triad''', but specifically one that is derived by stacking three 400¢ major thirds. This means it closes the octave and, as such, is its own inversion. So, once again, the melodic and harmonic capabilities of this triad in isolation are pretty slim compared to, say, one derived by stacking [[5/4]]. Yet, the symmetrical nature of this chord allows for quite a "sturdy" sound that helps to keep the temperament together.		This edo is just an '''augmented triad''', but specifically one that is derived by stacking three 400¢ major thirds. This means it closes the octave and, as such, is its own inversion. So, once again, the melodic and harmonic capabilities of this triad in isolation are pretty slim compared to, say, one derived by stacking 5/4. Yet, the symmetrical nature of this chord allows for quite a "sturdy" sound that helps to keep the temperament together.

	The major third itself is 13.79¢ sharp of 5/4, enough for noticeable inharmonicity to occasionally take place in timbres with a prominent 5th harmonic (such as a piano). This contributes to the "foggy" sound of the temperament, as the demo illustrates.		The major third itself is 13.79¢ sharp of 5/4, enough for noticeable inharmonicity to occasionally take place in timbres with a prominent 5th harmonic (such as a piano). This contributes to the "foggy" sound of the temperament, as the demo illustrates.
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	''Tier: '''F+'''''		''Tier: '''F+'''''
	[[File:4edo groove.mp3\|none\|thumb\|4edo fanfare on B diminished]]		[[File:4edo groove.mp3\|none\|thumb\|4edo fanfare on B diminished]]
	While I wouldn't necessarily say 2edo is a better version of 1edo, I will say 4edo is a better version of 2edo. It's a '''diminished tetrad''', but specifically one that is derived by stacking four 300¢ minor thirds. This means it closes the octave and, as such, is its own inversion. So, as always, the melodic and harmonic capabilities of this tetrad in isolation are pretty slim compared to, say, one derived by stacking [[6/5]]. Yet, the symmetrical nature of this chord allows for quite a, dare I say, "sturdy" sound that helps to keep the temperament together... how familiar.		While I wouldn't necessarily say 2edo is a better version of 1edo, I will say 4edo is a better version of 2edo. It's a '''diminished tetrad''', but specifically one that is derived by stacking four 300¢ minor thirds. This means it closes the octave and, as such, is its own inversion. So, as always, the melodic and harmonic capabilities of this tetrad in isolation are pretty slim compared to, say, one derived by stacking 6/5. Yet, the symmetrical nature of this chord allows for quite a, dare I say, "sturdy" sound that helps to keep the temperament together... how familiar.

	The minor third is sat between 6/5 and [[32/27]], giving it a mildly dark sound that is quite apt for the diminished tetrad. It's a powerful minor third, but without the 5-limit resonance of 6/5. Overall, a great minor third.		The minor third is sat between 6/5 and [[32/27]], giving it a mildly dark sound that is quite apt for the diminished tetrad. It's a powerful minor third, but without the 5-limit resonance of 6/5. Overall, a great minor third.
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	Ah yes, the homeland of [[Mosh\|'''mosh''']]. 10edo is actually my favorite of the edos less than 12, although 9edo does come pretty close. This edo is the largest one with a singular third, that being the 360¢ submajor third which is extremely close to [[16/13]]. That means this temperament also features a stunning approximation of the [[13/8\|'''13th harmonic''']], coming in just 0.53¢ sharp. It also features all of the interseptimal intervals from 5edo, meaning it includes the same approximation of the 7th harmonic, as well as a relatively stable fifth (especially compared to 9edo).		Ah yes, the homeland of [[Mosh\|'''mosh''']]. 10edo is actually my favorite of the edos less than 12, although 9edo does come pretty close. This edo is the largest one with a singular third, that being the 360¢ submajor third which is extremely close to [[16/13]]. That means this temperament also features a stunning approximation of the [[13/8\|'''13th harmonic''']], coming in just 0.53¢ sharp. It also features all of the interseptimal intervals from 5edo, meaning it includes the same approximation of the 7th harmonic, as well as a relatively stable fifth (especially compared to 9edo).

	10edo is a very xen tuning — more so than even 7edo in my opinion — because it doesn't even pretend to represent the [[diatonic scale]] (5L 2s). Instead, as mentioned previously, the heptatonic [[MOS scale\|'''mos''']] of 10edo is 3L 4s, or mosh. This is an incredibly intriguing mos that can be difficult to wrap your head around, but the sounds it produces are quite beautiful. [https://www.youtube.com/watch?v=uOsrbFEC6bQ ''Apartment in the Sky''] by [[HEHEHE I AM A SUPAHSTAR SAGA]] is an example of the brightest mode of mosh, dril.		10edo is a very xen tuning — more so than even 7edo in my opinion — because it doesn't even pretend to represent the diatonic scale (5L 2s). Instead, as mentioned previously, the heptatonic [[MOS scale\|'''mos''']] of 10edo is 3L 4s, or mosh. This is an incredibly intriguing mos that can be difficult to wrap your head around, but the sounds it produces are quite beautiful. [https://www.youtube.com/watch?v=uOsrbFEC6bQ ''Apartment in the Sky''] by [[HEHEHE I AM A SUPAHSTAR SAGA]] is an example of the brightest mode of mosh, dril.

	The demo I wrote for this edo is in the middle mode, bish. It oscilates between "tonic" and "dominant," and it sounds quite reminiscent of such movement in the diatonic mos, until you realize it's totally different. This mode of mosh could be mapped to the [[wikipedia:Double_harmonic_scale\|double harmonic major scale]] in a diatonic system, yet doing that results in a very different sound. I was incredibly surprised when I retuned the demo to be in A♭ double harmonic major, only to be subjected to something the original could only dream of being as weird as. Of course, I probably only say that because I wasn't used to it.		The demo I wrote for this edo is in the middle mode, bish. It oscilates between "tonic" and "dominant," and it sounds quite reminiscent of such movement in the diatonic mos, until you realize it's totally different. This mode of mosh could be mapped to the [[wikipedia:Double_harmonic_scale\|double harmonic major scale]] in a diatonic system, yet doing that results in a very different sound. I was incredibly surprised when I retuned the demo to be in A♭ double harmonic major, only to be subjected to something the original could only dream of being as weird as. Of course, I probably only say that because I wasn't used to it.