User:Overthink/EDO impressions - Revision history

Overthink: new opinion on meantone

2026-01-19T00:51:02Z

new opinion on meantone

← Older revision		Revision as of 00:51, 19 January 2026
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	This is a page about my thoughts on various EDOs.		This is a page about my thoughts on various EDOs. An asterisk means my opinion has changed, and I may potentially rewrite this.

	== Ideas ==		== Ideas ==
	In my opinion, an interval is melodically represented well if it is within ~15 cents, but harmonically represented decently only if within ~5-6 cents, the more accurate the better. It is absolutely essential for any system to approximate the perfect fifth within this 5-6 cent bound. ~~(Opinion changed, planning rewrite)~~ Octave stretch may help improve the perfect fifth, though the octave itself is even more important, so it shouldn't be stretched too much.		In my opinion, an interval is melodically represented well if it is within ~15 cents, but harmonically represented decently only if within ~5-6 cents, the more accurate the better. It is absolutely essential for any system to approximate the perfect fifth within this 5-6 cent bound*. Octave stretch may help improve the perfect fifth, though the octave itself is even more important, so it shouldn't be stretched too much.
	<br>		<br>

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	22: The diatonic scale sounds even brighter than in 17, with thirds and sixths having a more obvious septimal flavor. The diatonic semitone is a little smaller than ideal, but still usable. I haven't looked too much into it harmonically. A possibly interesting property is that it supports [[pajara]]. The fifth is not very good though, though a compressed octave may help. For example, [[57ed6]] has the fifth less sharp at 707.5 cents compared to 22edo's 709.1, and sounds noticeably more consonant. This also improves intervals like 6/5 and 7/4, though 6/5 still feels too off.		22: The diatonic scale sounds even brighter than in 17, with thirds and sixths having a more obvious septimal flavor. The diatonic semitone is a little smaller than ideal, but still usable. I haven't looked too much into it harmonically. A possibly interesting property is that it supports [[pajara]]. The fifth is not very good though, though a compressed octave may help. For example, [[57ed6]] has the fifth less sharp at 707.5 cents compared to 22edo's 709.1, and sounds noticeably more consonant. This also improves intervals like 6/5 and 7/4, though 6/5 still feels too off.

	31: A meantone tuning with near-pure 5/4 and 7/4. ~~With pure octaves~~, the ~~error of~~ the fifth is ~~problematic~~, ~~though~~ a stretched-octave version around [[111ed12]] mitigates this as much as possible.		31: A meantone tuning with near-pure 5/4 and 7/4. I don't like the fact that, in the major triad, the major third stands out more than the fifth. There are ''two'' ways to solve this; one is to sharpen the fifth to around [[55edo]], while another is to flatten the fifth close to 695.63{{c}} to get [[DR]] 4:5:6. Personally, the second option sounds much more in tune, while the first sounds 12edo-ish but somewhat less out of tune. However, these tunings don't approximate septimal meantone as well, so if that's your goal, use a stretched-octave version around [[111ed12]], which mitigates this as much as possible.

	41: While this EDO has be cited as good for approximating JI, it has quite a few problems. For example, 5/4 is quite flat, making 5-limit chords sound less concordant, which isn't good for an EDO this size. 7/4 is also a bit flat, making septimal intervals sound more ambiguous and less concordant. In general pental and septimal intervals are too far from their nearest pythagorean intervals, as the comma step is over 29 cents. I prefer 53edo instead.		41: While this EDO has be cited as good for approximating JI, it has quite a few problems. For example, 5/4 is quite flat, making 5-limit chords sound less concordant, which isn't good for an EDO this size. 7/4 is also a bit flat, making septimal intervals sound more ambiguous and less concordant. In general pental and septimal intervals are too far from their nearest pythagorean intervals, as the comma step is over 29 cents. I prefer 53edo instead.

	43: A meantone tuning around 1/5-comma. The thirds are slightly more off than in 31, and the fifth is closer, but the error still feels problematic. Septimal meantone tunes 7/4 too sharp here.		43: A meantone tuning around 1/5-comma. The thirds are slightly more off than in 31, and the fifth is closer, but the error still feels problematic*. Septimal meantone tunes 7/4 too sharp here.

	53: Excellent 5- and 7-limit harmonies. 5/4 is now only slightly flat, compared to nearly 6 cents in 41edo. The 7/4 is a bit sharp, but this makes septimal harmonies more concordant compared to 41. The 49/48 interval is also more noticeable at 45 cents, compared to 29 cents in 41edo. Chords are significantly more consonant than in 41. Definitely would recommend.		53: Excellent 5- and 7-limit harmonies. 5/4 is now only slightly flat, compared to nearly 6 cents in 41edo. The 7/4 is a bit sharp, but this makes septimal harmonies more concordant compared to 41. The 49/48 interval is also more noticeable at 45 cents, compared to 29 cents in 41edo. Chords are significantly more consonant than in 41. Definitely would recommend.

	55: Around the best meantone tuning for most music. The fifth is slightly out of tune, but would probably sound normal to most people. Any sharper and the error of the thirds becomes problematic.		55: Around the best meantone tuning for most music*. The fifth is slightly out of tune, but would probably sound normal to most people. Any sharper and the error of the thirds becomes problematic.

	72: Haven't really tried. This edo seems to approximate the 11-limit well. The 7th harmonic is a little flat like in 41edo, though due to the slightly flat fifth 7/6 and 9/7 may be a bit more concordant than in 41.		72: Haven't really tried. This edo seems to approximate the 11-limit well. The 7th harmonic is a little flat like in 41edo, though due to the slightly flat fifth 7/6 and 9/7 may be a bit more concordant than in 41.

Overthink: /* EDO Impressions */ + a few meantone tunings

2026-01-11T05:22:10Z

EDO Impressions: + a few meantone tunings

← Older revision		Revision as of 05:22, 11 January 2026
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	22: The diatonic scale sounds even brighter than in 17, with thirds and sixths having a more obvious septimal flavor. The diatonic semitone is a little smaller than ideal, but still usable. I haven't looked too much into it harmonically. A possibly interesting property is that it supports [[pajara]]. The fifth is not very good though, though a compressed octave may help. For example, [[57ed6]] has the fifth less sharp at 707.5 cents compared to 22edo's 709.1, and sounds noticeably more consonant. This also improves intervals like 6/5 and 7/4, though 6/5 still feels too off.		22: The diatonic scale sounds even brighter than in 17, with thirds and sixths having a more obvious septimal flavor. The diatonic semitone is a little smaller than ideal, but still usable. I haven't looked too much into it harmonically. A possibly interesting property is that it supports [[pajara]]. The fifth is not very good though, though a compressed octave may help. For example, [[57ed6]] has the fifth less sharp at 707.5 cents compared to 22edo's 709.1, and sounds noticeably more consonant. This also improves intervals like 6/5 and 7/4, though 6/5 still feels too off.

	31: ~~Haven't really tried. Seems like a good 5- and 7-limit~~ meantone tuning, with ~~possible 11~~-~~limit as well~~. ~~The~~ fifth ~~sounds just close enough to be usable~~, ~~but noticeably off. A little~~ octave ~~stretch may help here~~ as ~~well~~.		31: A meantone tuning with near-pure 5/4 and 7/4. With pure octaves, the error of the fifth is problematic, though a stretched-octave version around [[111ed12]] mitigates this as much as possible.

	41: While this EDO has be cited as good for approximating JI, it has quite a few problems. For example, 5/4 is quite flat, making 5-limit chords sound less concordant, which isn't good for an EDO this size. 7/4 is also a bit flat, making septimal intervals sound more ambiguous and less concordant. In general pental and septimal intervals are too far from their nearest pythagorean intervals, as the comma step is over 29 cents. I prefer 53edo instead.		41: While this EDO has be cited as good for approximating JI, it has quite a few problems. For example, 5/4 is quite flat, making 5-limit chords sound less concordant, which isn't good for an EDO this size. 7/4 is also a bit flat, making septimal intervals sound more ambiguous and less concordant. In general pental and septimal intervals are too far from their nearest pythagorean intervals, as the comma step is over 29 cents. I prefer 53edo instead.

			43: A meantone tuning around 1/5-comma. The thirds are slightly more off than in 31, and the fifth is closer, but the error still feels problematic. Septimal meantone tunes 7/4 too sharp here.

	53: Excellent 5- and 7-limit harmonies. 5/4 is now only slightly flat, compared to nearly 6 cents in 41edo. The 7/4 is a bit sharp, but this makes septimal harmonies more concordant compared to 41. The 49/48 interval is also more noticeable at 45 cents, compared to 29 cents in 41edo. Chords are significantly more consonant than in 41. Definitely would recommend.		53: Excellent 5- and 7-limit harmonies. 5/4 is now only slightly flat, compared to nearly 6 cents in 41edo. The 7/4 is a bit sharp, but this makes septimal harmonies more concordant compared to 41. The 49/48 interval is also more noticeable at 45 cents, compared to 29 cents in 41edo. Chords are significantly more consonant than in 41. Definitely would recommend.

			55: Around the best meantone tuning for most music. The fifth is slightly out of tune, but would probably sound normal to most people. Any sharper and the error of the thirds becomes problematic.

	72: Haven't really tried. This edo seems to approximate the 11-limit well. The 7th harmonic is a little flat like in 41edo, though due to the slightly flat fifth 7/6 and 9/7 may be a bit more concordant than in 41.		72: Haven't really tried. This edo seems to approximate the 11-limit well. The 7th harmonic is a little flat like in 41edo, though due to the slightly flat fifth 7/6 and 9/7 may be a bit more concordant than in 41.

Overthink: /* Ideas */ new opinion

2025-11-22T21:58:51Z

Ideas: new opinion

← Older revision		Revision as of 21:58, 22 November 2025
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	This is a page about my thoughts on various EDOs.		This is a page about my thoughts on various EDOs.
	== Ideas ==		== Ideas ==
	In my opinion, an interval is melodically represented well if it is within ~15 cents, but harmonically represented decently only if within ~5-6 cents, the more accurate the better. It is absolutely essential for any system to approximate the perfect fifth within this 5-6 cent bound. Octave stretch may help improve the perfect fifth, though the octave itself is even more important, so it shouldn't be stretched too much.		In my opinion, an interval is melodically represented well if it is within ~15 cents, but harmonically represented decently only if within ~5-6 cents, the more accurate the better. It is absolutely essential for any system to approximate the perfect fifth within this 5-6 cent bound. (Opinion changed, planning rewrite) Octave stretch may help improve the perfect fifth, though the octave itself is even more important, so it shouldn't be stretched too much.
	<br>		<br>

Overthink: /* EDO Impressions */ 6/5 is quite off in 22edo

2025-11-02T18:15:37Z

EDO Impressions: 6/5 is quite off in 22edo

← Older revision		Revision as of 18:15, 2 November 2025
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	19: Due to the flat tendency of the system, melody seems to have a melancholy feeling that you can't replicate with 12edo. Unfortunately, this includes the perfect fifth, which I feel is too off, though it may be mitigated by octave stretch. Another issue is that the minor seconds are too wide melodically.		19: Due to the flat tendency of the system, melody seems to have a melancholy feeling that you can't replicate with 12edo. Unfortunately, this includes the perfect fifth, which I feel is too off, though it may be mitigated by octave stretch. Another issue is that the minor seconds are too wide melodically.

	22: The diatonic scale sounds even brighter than in 17, with thirds and sixths having a more obvious septimal flavor. The diatonic semitone is a little smaller than ideal, but still usable. I haven't looked too much into it harmonically. A possibly interesting property is that it supports [[pajara]]. The fifth is not very good though, though a compressed octave may help. For example, [[57ed6]] has the fifth less sharp at 707.5 cents compared to 22edo's 709.1, and sounds ~~significantly~~ more consonant. This also improves intervals like 6/5 and 7/4.		22: The diatonic scale sounds even brighter than in 17, with thirds and sixths having a more obvious septimal flavor. The diatonic semitone is a little smaller than ideal, but still usable. I haven't looked too much into it harmonically. A possibly interesting property is that it supports [[pajara]]. The fifth is not very good though, though a compressed octave may help. For example, [[57ed6]] has the fifth less sharp at 707.5 cents compared to 22edo's 709.1, and sounds noticeably more consonant. This also improves intervals like 6/5 and 7/4, though 6/5 still feels too off.

	31: Haven't really tried. Seems like a good 5- and 7-limit meantone tuning, with possible 11-limit as well. The fifth sounds just close enough to be usable, but noticeably off. A little octave stretch may help here as well.		31: Haven't really tried. Seems like a good 5- and 7-limit meantone tuning, with possible 11-limit as well. The fifth sounds just close enough to be usable, but noticeably off. A little octave stretch may help here as well.

Overthink: /* EDO Impressions */ I should try 29edo

2025-11-01T05:36:18Z

EDO Impressions: I should try 29edo

← Older revision		Revision as of 05:36, 1 November 2025
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	Note: They are by no means final!		Note: They are by no means final!

	EDOs I should try: 27, 31, 34, 43, 46, 50, 55?, 56?, 58, 62?, 72, 84, 87?, 94, 111		EDOs I should try: 27, 29, 31, 34, 43, 46, 50, 55?, 56?, 58, 62?, 72, 84, 87?, 94, 111

	12: We've all heard this system thousands of times before. It has a good perfect fifth, which is essential. In my opinion, this system sounds much more like pythagorean tuning than 5-limit, though the slight tempering of the fifth reduces the dissonance of the thirds by pushing them towards the 5-limit ones, but they still don't really show 5-limit flavor. If you want true 5-limit use 53edo (or possibly a more tempered meantone system) instead. Still, the expressive possibilities are vast, though that doesn't mean you shouldn't use other systems.		12: We've all heard this system thousands of times before. It has a good perfect fifth, which is essential. In my opinion, this system sounds much more like pythagorean tuning than 5-limit, though the slight tempering of the fifth reduces the dissonance of the thirds by pushing them towards the 5-limit ones, but they still don't really show 5-limit flavor. If you want true 5-limit use 53edo (or possibly a more tempered meantone system) instead. Still, the expressive possibilities are vast, though that doesn't mean you shouldn't use other systems.

Overthink: /* EDO Impressions */

2025-10-31T03:21:20Z

EDO Impressions

← Older revision		Revision as of 03:21, 31 October 2025
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	EDOs I should try: 27, 31, 34, 43, 46, 50, 55?, 56?, 58, 62?, 72, 84, 87?, 94, 111		EDOs I should try: 27, 31, 34, 43, 46, 50, 55?, 56?, 58, 62?, 72, 84, 87?, 94, 111

	12: We've all heard this system thousands of times before. It has a good perfect fifth, which is essential. In my opinion, this system sounds much more like pythagorean tuning than 5-limit, though the slight tempering of the fifth reduces the dissonance of the thirds by pushing them towards the 5-limit ones, but they still ~~hardly~~ show 5-limit flavor. If you want true 5-limit use 53edo (or possibly a more tempered meantone system) instead. Still, the expressive possibilities are vast, though that doesn't mean you shouldn't use other systems.		12: We've all heard this system thousands of times before. It has a good perfect fifth, which is essential. In my opinion, this system sounds much more like pythagorean tuning than 5-limit, though the slight tempering of the fifth reduces the dissonance of the thirds by pushing them towards the 5-limit ones, but they still don't really show 5-limit flavor. If you want true 5-limit use 53edo (or possibly a more tempered meantone system) instead. Still, the expressive possibilities are vast, though that doesn't mean you shouldn't use other systems.

	17: The diatonic scale has a septimal flavor to it, with major thirds sounding nothing like 12edo ones. The minor second is the perfect size melodically, though it may take a while to get used to it. Haven't really experimented with harmony in this system.		17: The diatonic scale has a septimal flavor to it, with major thirds sounding nothing like 12edo ones. The minor second is the perfect size melodically, though it may take a while to get used to it. Haven't really experimented with harmony in this system.
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	19: Due to the flat tendency of the system, melody seems to have a melancholy feeling that you can't replicate with 12edo. Unfortunately, this includes the perfect fifth, which I feel is too off, though it may be mitigated by octave stretch. Another issue is that the minor seconds are too wide melodically.		19: Due to the flat tendency of the system, melody seems to have a melancholy feeling that you can't replicate with 12edo. Unfortunately, this includes the perfect fifth, which I feel is too off, though it may be mitigated by octave stretch. Another issue is that the minor seconds are too wide melodically.

	22: The diatonic scale sounds even brighter than in 17, with thirds and sixths having a more obvious septimal flavor. The diatonic semitone is a little smaller than ideal, but still usable. I haven't looked too much into it harmonically. A possibly interesting property is that it supports [[pajara]]. The fifth is not very good though, though a compressed octave may help.		22: The diatonic scale sounds even brighter than in 17, with thirds and sixths having a more obvious septimal flavor. The diatonic semitone is a little smaller than ideal, but still usable. I haven't looked too much into it harmonically. A possibly interesting property is that it supports [[pajara]]. The fifth is not very good though, though a compressed octave may help. For example, [[57ed6]] has the fifth less sharp at 707.5 cents compared to 22edo's 709.1, and sounds significantly more consonant. This also improves intervals like 6/5 and 7/4.

	31: Haven't really tried. Seems like a good 5- and 7-limit meantone tuning, with possible 11-limit as well. The fifth sounds just close enough to be usable, but noticeably off. A little octave stretch may help here as well.		31: Haven't really tried. Seems like a good 5- and 7-limit meantone tuning, with possible 11-limit as well. The fifth sounds just close enough to be usable, but noticeably off. A little octave stretch may help here as well.

	41: While this EDO has be cited as good for approximating JI, it has quite a few problems. For example, 5/4 is quite flat, making 5-limit chords sound ~~out-of-tune~~, which isn't good for an EDO this size. 7/4 is also a bit flat, making septimal intervals sound more ambiguous and less concordant~~. Octave stretch might help, but that worsens intervals like 6/5, 9/5, 8/7, and 12/7, as well as 3/2, so it doesn't feel like a solution~~. In general pental and septimal intervals are too far from their nearest pythagorean intervals, as the comma step is over 29 cents. ~~It's better to use~~ 53edo instead.		41: While this EDO has be cited as good for approximating JI, it has quite a few problems. For example, 5/4 is quite flat, making 5-limit chords sound less concordant, which isn't good for an EDO this size. 7/4 is also a bit flat, making septimal intervals sound more ambiguous and less concordant. In general pental and septimal intervals are too far from their nearest pythagorean intervals, as the comma step is over 29 cents. I prefer 53edo instead.

	53: Excellent 5- and 7-limit harmonies. 5/4 is now only slightly flat, compared to nearly 6 cents in 41edo. The 7/4 is a bit sharp, but this makes septimal harmonies more concordant compared to 41. The 49/48 interval is also more noticeable at 45 cents, compared to 29 cents in 41edo. Chords are significantly more consonant than in 41. Definitely would recommend.		53: Excellent 5- and 7-limit harmonies. 5/4 is now only slightly flat, compared to nearly 6 cents in 41edo. The 7/4 is a bit sharp, but this makes septimal harmonies more concordant compared to 41. The 49/48 interval is also more noticeable at 45 cents, compared to 29 cents in 41edo. Chords are significantly more consonant than in 41. Definitely would recommend.

	72: Haven't really tried. This edo seems to approximate the 11-limit well. The 7th harmonic is a little flat like in 41edo, though due to the slightly flat fifth 7/6 and 9/7 may be a bit more concordant than in 41.		72: Haven't really tried. This edo seems to approximate the 11-limit well. The 7th harmonic is a little flat like in 41edo, though due to the slightly flat fifth 7/6 and 9/7 may be a bit more concordant than in 41.

Overthink: /* Ideas */

2025-10-26T04:04:54Z

Ideas

← Older revision		Revision as of 04:04, 26 October 2025
Line 1:		Line 1:
	This is a page about my thoughts on various EDOs.		This is a page about my thoughts on various EDOs.
	== Ideas ==		== Ideas ==
	In my opinion, an interval is melodically represented well if it is within ~15 cents, but harmonically represented decently only if within ~5-6 cents, the more accurate the better. It is absolutely essential for any system to approximate the perfect fifth within this 5-6 cent bound. Octave stretch may help improve the perfect fifth		In my opinion, an interval is melodically represented well if it is within ~15 cents, but harmonically represented decently only if within ~5-6 cents, the more accurate the better. It is absolutely essential for any system to approximate the perfect fifth within this 5-6 cent bound. Octave stretch may help improve the perfect fifth, though the octave itself is even more important, so it shouldn't be stretched too much.
	<br>		<br>

Overthink: /* Ideas */

2025-10-26T04:03:07Z

Ideas

← Older revision		Revision as of 04:03, 26 October 2025
Line 1:		Line 1:
	This is a page about my thoughts on various EDOs.		This is a page about my thoughts on various EDOs.
	== Ideas ==		== Ideas ==
	In my opinion, an interval is melodically represented well if it is within ~15 cents, but harmonically represented decently only if within ~5-6 cents, the more accurate the better. It is absolutely essential for any system to approximate the perfect fifth within this 5-6 cent bound.		In my opinion, an interval is melodically represented well if it is within ~15 cents, but harmonically represented decently only if within ~5-6 cents, the more accurate the better. It is absolutely essential for any system to approximate the perfect fifth within this 5-6 cent bound. Octave stretch may help improve the perfect fifth
	<br>		<br>

	== EDO Impressions ==		== EDO Impressions ==
	Note: They are by no means final!		Note: They are by no means final!

Overthink: /* EDO Impressions */

2025-10-26T04:01:36Z

EDO Impressions

← Older revision		Revision as of 04:01, 26 October 2025
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	== Ideas ==		== Ideas ==
	In my opinion, an interval is melodically represented well if it is within ~15 cents, but harmonically represented decently only if within ~5-6 cents, the more accurate the better. It is absolutely essential for any system to approximate the perfect fifth within this 5-6 cent bound.		In my opinion, an interval is melodically represented well if it is within ~15 cents, but harmonically represented decently only if within ~5-6 cents, the more accurate the better. It is absolutely essential for any system to approximate the perfect fifth within this 5-6 cent bound.
			<br>
	== EDO Impressions ==		== EDO Impressions ==
	Note: They are by no means final!		Note: They are by no means final!

	12: We've all heard this system thousands of times before. It has a good perfect fifth, which is essential. In my opinion, this system sounds much more like pythagorean tuning than 5-limit, though the slight tempering of the fifth reduces the dissonance of the thirds by pushing them towards the 5-limit ones, but ~~IMO not close enough to harmonically represent them~~. If you want true 5-limit use 53edo instead. Still, the expressive possibilities are vast, though that doesn't mean you shouldn't use other systems.		EDOs I should try: 27, 31, 34, 43, 46, 50, 55?, 56?, 58, 62?, 72, 84, 87?, 94, 111

			12: We've all heard this system thousands of times before. It has a good perfect fifth, which is essential. In my opinion, this system sounds much more like pythagorean tuning than 5-limit, though the slight tempering of the fifth reduces the dissonance of the thirds by pushing them towards the 5-limit ones, but they still hardly show 5-limit flavor. If you want true 5-limit use 53edo (or possibly a more tempered meantone system) instead. Still, the expressive possibilities are vast, though that doesn't mean you shouldn't use other systems.

	17: The diatonic scale has a septimal flavor to it, with major thirds sounding nothing like 12edo ones. The minor second is the perfect size melodically, though it may take a while to get used to it. Haven't really experimented with harmony in this system.		17: The diatonic scale has a septimal flavor to it, with major thirds sounding nothing like 12edo ones. The minor second is the perfect size melodically, though it may take a while to get used to it. Haven't really experimented with harmony in this system.
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	22: The diatonic scale sounds even brighter than in 17, with thirds and sixths having a more obvious septimal flavor. The diatonic semitone is a little smaller than ideal, but still usable. I haven't looked too much into it harmonically. A possibly interesting property is that it supports [[pajara]]. The fifth is not very good though, though a compressed octave may help.		22: The diatonic scale sounds even brighter than in 17, with thirds and sixths having a more obvious septimal flavor. The diatonic semitone is a little smaller than ideal, but still usable. I haven't looked too much into it harmonically. A possibly interesting property is that it supports [[pajara]]. The fifth is not very good though, though a compressed octave may help.

	31: Haven't really tried. The fifth sounds just close enough to be usable, but noticeably off. A little octave stretch may help here as well.		31: Haven't really tried. Seems like a good 5- and 7-limit meantone tuning, with possible 11-limit as well. The fifth sounds just close enough to be usable, but noticeably off. A little octave stretch may help here as well.

	41: While this EDO has be cited as good for approximating JI, it has quite a few problems. For example, 5/4 is ~~very~~ flat, making 5-limit chords sound out-of-tune, ~~and~~ 7/4 is also a bit flat, making septimal intervals sound ambiguous and less concordant. In general pental and septimal intervals are too far from their nearest pythagorean intervals, as the comma step is over 29 cents.		41: While this EDO has be cited as good for approximating JI, it has quite a few problems. For example, 5/4 is quite flat, making 5-limit chords sound out-of-tune, which isn't good for an EDO this size. 7/4 is also a bit flat, making septimal intervals sound more ambiguous and less concordant. Octave stretch might help, but that worsens intervals like 6/5, 9/5, 8/7, and 12/7, as well as 3/2, so it doesn't feel like a solution. In general pental and septimal intervals are too far from their nearest pythagorean intervals, as the comma step is over 29 cents. It's better to use 53edo instead.

	53: Excellent 5- and 7-limit harmonies. 5/4 is now only slightly flat, compared to nearly 6 cents in 41edo. The 7/4 is a bit sharp, but this makes septimal harmonies more concordant compared to 41. The 49/48 interval is also more noticeable at 44 cents, compared to 29 cents in 41edo. Chords are significantly more consonant than in 41. Definitely would recommend.		53: Excellent 5- and 7-limit harmonies. 5/4 is now only slightly flat, compared to nearly 6 cents in 41edo. The 7/4 is a bit sharp, but this makes septimal harmonies more concordant compared to 41. The 49/48 interval is also more noticeable at 45 cents, compared to 29 cents in 41edo. Chords are significantly more consonant than in 41. Definitely would recommend.

	72: Haven't really tried. This edo seems to approximate the 11-limit well. The 7th harmonic is a little flat like in 41edo, though due to the slightly flat fifth 7/6 and 9/7 may be a bit more concordant than in 41.		72: Haven't really tried. This edo seems to approximate the 11-limit well. The 7th harmonic is a little flat like in 41edo, though due to the slightly flat fifth 7/6 and 9/7 may be a bit more concordant than in 41.

Overthink at 03:32, 26 October 2025

2025-10-26T03:32:27Z

← Older revision		Revision as of 03:32, 26 October 2025
Line 1:		Line 1:
	This is a page about my thoughts on various EDOs.		This is a page about my thoughts on various EDOs.
			== Ideas ==
			In my opinion, an interval is melodically represented well if it is within ~15 cents, but harmonically represented decently only if within ~5-6 cents, the more accurate the better. It is absolutely essential for any system to approximate the perfect fifth within this 5-6 cent bound.
	== EDO Impressions ==		== EDO Impressions ==
	Note: They are by no means final!		Note: They are by no means final!

	12: We've all heard this system thousands of times before. It has a good perfect fifth, which is essential. In my opinion, this system sounds much more like pythagorean tuning than 5-limit. If you want true 5-limit use 53edo instead. Still, the expressive possibilities are vast, though that doesn't mean you shouldn't use other systems.		12: We've all heard this system thousands of times before. It has a good perfect fifth, which is essential. In my opinion, this system sounds much more like pythagorean tuning than 5-limit, though the slight tempering of the fifth reduces the dissonance of the thirds by pushing them towards the 5-limit ones, but IMO not close enough to harmonically represent them. If you want true 5-limit use 53edo instead. Still, the expressive possibilities are vast, though that doesn't mean you shouldn't use other systems.

	17: The diatonic scale has a septimal flavor to it, with major thirds sounding nothing like 12edo ones. The minor second is the perfect size melodically, though it may take a while to get used to it. Haven't really experimented with harmony in this system.		17: The diatonic scale has a septimal flavor to it, with major thirds sounding nothing like 12edo ones. The minor second is the perfect size melodically, though it may take a while to get used to it. Haven't really experimented with harmony in this system.
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	31: Haven't really tried. The fifth sounds just close enough to be usable, but noticeably off. A little octave stretch may help here as well.		31: Haven't really tried. The fifth sounds just close enough to be usable, but noticeably off. A little octave stretch may help here as well.

	41: While this EDO has be cited as good for approximating JI, it has quite a few problems. For example, 5/4 is ~~too~~ flat, and 7/4 is also ~~quite~~ flat, making septimal intervals sound ambiguous and less concordant. In general pental and septimal intervals are too far from their nearest pythagorean intervals, as the comma step is over 29 cents.		41: While this EDO has be cited as good for approximating JI, it has quite a few problems. For example, 5/4 is very flat, making 5-limit chords sound out-of-tune, and 7/4 is also a bit flat, making septimal intervals sound ambiguous and less concordant. In general pental and septimal intervals are too far from their nearest pythagorean intervals, as the comma step is over 29 cents.

	53: Excellent 5- and 7-limit harmonies. 5/4 is now only slightly flat, compared to nearly 6 cents in 41edo. The 7/4 is a bit sharp, but this makes septimal harmonies more concordant compared to 41. The 49/48 interval is also more noticeable at 44 cents, compared to 29 cents in 41edo. Chords are significantly more consonant than in 41. Definitely would recommend.		53: Excellent 5- and 7-limit harmonies. 5/4 is now only slightly flat, compared to nearly 6 cents in 41edo. The 7/4 is a bit sharp, but this makes septimal harmonies more concordant compared to 41. The 49/48 interval is also more noticeable at 44 cents, compared to 29 cents in 41edo. Chords are significantly more consonant than in 41. Definitely would recommend.

	72: Haven't really tried. This edo seems to approximate the 11-limit well. The 7th harmonic is a little flat like in 41edo, though due to the slightly flat fifth 7/6 and 9/7 may be a bit more concordant than in 41.		72: Haven't really tried. This edo seems to approximate the 11-limit well. The 7th harmonic is a little flat like in 41edo, though due to the slightly flat fifth 7/6 and 9/7 may be a bit more concordant than in 41.