User:Zhenlige/EDO impressions: Difference between revisions

Line 7:

In terms of accuracy, assuming harmonic overtone.

*[[0edo|0]]: A fancy way to say “pitchless”. The only tuning of the [[Single-pitch tuning|Om]] temperament. Important in theory, useless in practice.

*[[1edo|1]]: Equivalent to [[2-limit]] JI. Not much about harmony. Possibly useful for a transition between different tunings.

*[[1edo|1]]: Equivalent to [[2-limit]] JI (unless you want to temper some higher-rank JI subgroups into octaves, which I think nobody will do). Not much about harmony. Possibly useful for a transition between different tunings.

*[[2edo|2]]: ~~Equally~~-~~divided tritones~~.

*[[2edo|2]]: Half octaves aka symmetric tritones. The key to tritone substitution, although sometimes asymmetric tritones or even non-tritone intervals can also be used.

*[[3edo|3]]: 12edo augmented chords.

*[[4edo|4]]: 12edo diminished seventh chords.

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*[[10edo|10]]: A stack of [[13/8]]. A subset of [[130edo]] and [[270edo]].

*[[11edo|11]]: Incomplete [[22edo]].

*[[12edo|12]]: Equalized [[chromatic]] scale. It deserves its position. A good tuning for almost all types of music, tho sometimes not perfect. Very excellent [[3/2]] as well as prime [[17/1|17]] and [[19/1|19]] for its size, but inaccurate [[5/4]] and worse [[7/4]]. Suitable for symmetric scales. Easy to make [[../12neji|accurate NEJIs]]. Its 2.3.17.19 subgroup really deserves more exploration (something “xenharmonic” but not “microtonal”).

*[[12edo|12]]: Equalized [[chromatic]] scale. The boundary between [[meantone]] and [[schismatic]]. It deserves its position. A good tuning for almost all types of music, tho sometimes not perfect. Very excellent [[3/2]] as well as prime [[17/1|17]] and [[19/1|19]] for its size, but inaccurate [[5/4]] and worse [[7/4]]. Suitable for symmetric scales. Easy to make [[../12neji|accurate NEJIs]]. Its 2.3.17.19 subgroup really deserves more exploration (something “xenharmonic” but not “microtonal”).

*...

*[[15edo|15]]: Better than it seems to be, tho still rough. A heavily stretched [[Carlos Alpha]] scale.

*...

*[[17edo|17]]: A circle of fifths in [[34edo]]. Interesting sharp fifths. The fact that its thirds do not approximate any simple ratios well is a pity. (or benefit? I don't know) I don't know how to write harmonies here.

*[[17edo|17]]: A circle of fifths in [[34edo]]. Interesting sharp fifths. The boundary between neogothic and superpyth. The fact that its thirds do not approximate any simple ratios well is a pity. (or benefit? I don't know) I don't know how to write harmonies here.

*[[18edo|18]]: Incomplete [[36edo]].

*[[19edo|19]]: Very different tradeoffs from 12edo. Usable but imperfect for many temperaments. [[Meantone]] or [[magic]], but with a too flat fifth. Strangely large minor 2nds. Also a compressed [[Carlos Beta]]. 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]].

*[[20edo|20]]: The fact that [[41edo]] is good indicates that 20- and 21edo are probably bad. Does anyone really think an inconsistent 27 can be used with a 3 or 9?

*...

*[[22edo|22]]: The simplest non-meantone EDO with reasonable 5-limit. Good [[superpyth]] and [[porcupine]] tuning. The upper bound of a good fifth.

*[[22edo|22]]: The simplest non-meantone EDO with reasonable 5-limit. Good [[superpyth]] and [[porcupine]] tuning. The only reasonable superpyth EDO. The upper bound of a good fifth.

*[[23edo|23]]: Incomplete [[46edo]].

*[[24edo|24]]: 12edo with neutrals. Good for prime [[11/1|11]]. Accurate in subgroup 2.3.11.17.19.

*[[24edo|24]]: What many non-microtonalists think microtonality is. 12edo with neutrals. Good for prime [[11/1|11]]. Accurate in subgroup 2.3.11.17.19.

*...

*[[26edo|26]]: A stack of [[7/4]]. Meantone but tuned terribly. Incomplete [[130edo]].

Line 42:

*[[38edo|38]]: 19edo with neutrals. Near pure [[11/9]]. The acceptable error of 19edo really becomes a problem at this size.

*...

*[[41edo|41]]: Prime octave and highly composite fifth, opposite from [[12edo]], thus good for fifth-dividing temperaments. Good for [[magic]]. The [[Kite guitar]] shows its elegance, with many simple intervals equidistantly spaced. I have no idea how other similar-sized EDOs (namely 53 and 72) can be applied on a fretted string instrument. Also ~~good~~ [[garibaldi]] and [[neutral]].

*[[41edo|41]]: Prime octave and highly composite fifth, opposite from [[12edo]], thus good for fifth-dividing temperaments. Good for [[magic]]. The [[Kite guitar]] shows its elegance, with many simple intervals equidistantly spaced. I have no idea how other similar-sized EDOs (namely 53 and 72) can be applied on a fretted string instrument. It's a pity that its [[5/1|5]] is not very good. Also [[garibaldi]] and [[neutral]].

*...

*[[46edo|46]]: Efficient [[gentle region|neogothic]] EDO.

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*[[111edo|111]]: [[37edo]] with [[3/1|3]] added.

*...

*[[118edo|118]]: 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 a bit overtempered (outside 5-odd-limit [[diamond tradeoff]]), and 171 and 31 are ideal. So like 19, I won't ~~use~~ it much.

*[[118edo|118]]: 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 a bit overtempered (outside 5-odd-limit [[diamond tradeoff]]), and 171 and 31 are ideal. So like 19, I won't appreciate it much.

*...

*[[171edo|171]]: ~~Ideal~~ for approximating [[7-limit]] JI. Good as [[schismatic]], [[gammic]], [[ennealimmal]] and [[enneadecal]]. 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. For 11-limit maybe [[342edo|doubling]] is a good choice, and for 13-limit [[684edo|quadrupling]].

*[[171edo|171]]: The ultimate EDO for approximating [[7-limit]] JI. If you don't need some ridiculous high precision, there is no need to go any further. Good as [[schismatic]], [[gammic]], [[ennealimmal]] and [[enneadecal]]. 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. For 11-limit maybe [[342edo|doubling]] is a good choice, and for 13-limit [[684edo|quadrupling]].

*...

*[[224edo|224]]: like 171 but with a slightly sharper (and closer to just) fifth, worse 7-limit but better [[13-limit]]. Ideal for free-pitch-like music that emphasizes 13-limit.

[[Category:Impression]]

@@ Line 7: / Line 7: @@
 In terms of accuracy, assuming harmonic overtone.
 *[[0edo|0]]: A fancy way to say “pitchless”. The only tuning of the [[Single-pitch tuning|Om]] temperament. Important in theory, useless in practice.
-*[[1edo|1]]: Equivalent to [[2-limit]] JI. Not much about harmony. Possibly useful for a transition between different tunings.
+*[[1edo|1]]: Equivalent to [[2-limit]] JI (unless you want to temper some higher-rank JI subgroups into octaves, which I think nobody will do). Not much about harmony. Possibly useful for a transition between different tunings.
-*[[2edo|2]]: Equally-divided tritones.
+*[[2edo|2]]: Half octaves aka symmetric tritones. The key to tritone substitution, although sometimes asymmetric tritones or even non-tritone intervals can also be used.
 *[[3edo|3]]: 12edo augmented chords.
 *[[4edo|4]]: 12edo diminished seventh chords.
@@ Line 18: / Line 18: @@
 *[[10edo|10]]: A stack of [[13/8]]. A subset of [[130edo]] and [[270edo]].
 *[[11edo|11]]: Incomplete [[22edo]].
-*[[12edo|12]]: Equalized [[chromatic]] scale. It deserves its position. A good tuning for almost all types of music, tho sometimes not perfect. Very excellent [[3/2]] as well as prime [[17/1|17]] and [[19/1|19]] for its size, but inaccurate [[5/4]] and worse [[7/4]]. Suitable for symmetric scales. Easy to make [[../12neji|accurate NEJIs]]. Its 2.3.17.19 subgroup really deserves more exploration (something “xenharmonic” but not “microtonal”).
+*[[12edo|12]]: Equalized [[chromatic]] scale. The boundary between [[meantone]] and [[schismatic]]. It deserves its position. A good tuning for almost all types of music, tho sometimes not perfect. Very excellent [[3/2]] as well as prime [[17/1|17]] and [[19/1|19]] for its size, but inaccurate [[5/4]] and worse [[7/4]]. Suitable for symmetric scales. Easy to make [[../12neji|accurate NEJIs]]. Its 2.3.17.19 subgroup really deserves more exploration (something “xenharmonic” but not “microtonal”).
 *...
 *[[15edo|15]]: Better than it seems to be, tho still rough. A heavily stretched [[Carlos Alpha]] scale.
 *...
-*[[17edo|17]]: A circle of fifths in [[34edo]]. Interesting sharp fifths. The fact that its thirds do not approximate any simple ratios well is a pity. (or benefit? I don't know) I don't know how to write harmonies here.
+*[[17edo|17]]: A circle of fifths in [[34edo]]. Interesting sharp fifths. The boundary between neogothic and superpyth. The fact that its thirds do not approximate any simple ratios well is a pity. (or benefit? I don't know) I don't know how to write harmonies here.
 *[[18edo|18]]: Incomplete [[36edo]].
 *[[19edo|19]]: Very different tradeoffs from 12edo. Usable but imperfect for many temperaments. [[Meantone]] or [[magic]], but with a too flat fifth. Strangely large minor 2nds. Also a compressed [[Carlos Beta]]. 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]].
 *[[20edo|20]]: The fact that [[41edo]] is good indicates that 20- and 21edo are probably bad. Does anyone really think an inconsistent 27 can be used with a 3 or 9?
 *...
-*[[22edo|22]]: The simplest non-meantone EDO with reasonable 5-limit. Good [[superpyth]] and [[porcupine]] tuning. The upper bound of a good fifth.
+*[[22edo|22]]: The simplest non-meantone EDO with reasonable 5-limit. Good [[superpyth]] and [[porcupine]] tuning. The only reasonable superpyth EDO. The upper bound of a good fifth.
 *[[23edo|23]]: Incomplete [[46edo]].
-*[[24edo|24]]: 12edo with neutrals. Good for prime [[11/1|11]]. Accurate in subgroup 2.3.11.17.19.
+*[[24edo|24]]: What many non-microtonalists think microtonality is. 12edo with neutrals. Good for prime [[11/1|11]]. Accurate in subgroup 2.3.11.17.19.
 *...
 *[[26edo|26]]: A stack of [[7/4]]. Meantone but tuned terribly. Incomplete [[130edo]].
@@ Line 42: / Line 42: @@
 *[[38edo|38]]: 19edo with neutrals. Near pure [[11/9]]. The acceptable error of 19edo really becomes a problem at this size.
 *...
-*[[41edo|41]]: Prime octave and highly composite fifth, opposite from [[12edo]], thus good for fifth-dividing temperaments. Good for [[magic]]. The [[Kite guitar]] shows its elegance, with many simple intervals equidistantly spaced. I have no idea how other similar-sized EDOs (namely 53 and 72) can be applied on a fretted string instrument. Also good [[garibaldi]] and [[neutral]].
+*[[41edo|41]]: Prime octave and highly composite fifth, opposite from [[12edo]], thus good for fifth-dividing temperaments. Good for [[magic]]. The [[Kite guitar]] shows its elegance, with many simple intervals equidistantly spaced. I have no idea how other similar-sized EDOs (namely 53 and 72) can be applied on a fretted string instrument. It's a pity that its [[5/1|5]] is not very good. Also [[garibaldi]] and [[neutral]].
 *...
 *[[46edo|46]]: Efficient [[gentle region|neogothic]] EDO.
@@ Line 64: / Line 64: @@
 *[[111edo|111]]: [[37edo]] with [[3/1|3]] added.
 *...
-*[[118edo|118]]: 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 a bit overtempered (outside 5-odd-limit [[diamond tradeoff]]), and 171 and 31 are ideal. So like 19, I won't use it much.
+*[[118edo|118]]: 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 a bit overtempered (outside 5-odd-limit [[diamond tradeoff]]), and 171 and 31 are ideal. So like 19, I won't appreciate it much.
 *...
-*[[171edo|171]]: Ideal for approximating [[7-limit]] JI. Good as [[schismatic]], [[gammic]], [[ennealimmal]] and [[enneadecal]]. 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. For 11-limit maybe [[342edo|doubling]] is a good choice, and for 13-limit [[684edo|quadrupling]].
+*[[171edo|171]]: The ultimate EDO for approximating [[7-limit]] JI. If you don't need some ridiculous high precision, there is no need to go any further. Good as [[schismatic]], [[gammic]], [[ennealimmal]] and [[enneadecal]]. 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. For 11-limit maybe [[342edo|doubling]] is a good choice, and for 13-limit [[684edo|quadrupling]].
 *...
 *[[224edo|224]]: like 171 but with a slightly sharper (and closer to just) fifth, worse 7-limit but better [[13-limit]]. Ideal for free-pitch-like music that emphasizes 13-limit.
 [[Category:Impression]]