33edo: Difference between revisions

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== Theory ==

=== ~~Harmonics~~ ===

=== Structural properties ===

33edo is ~~not especially good at representing all rational intervals in~~ the [[~~7-limit~~]], ~~but~~ it ~~does very~~ well ~~on the 7-limit~~ [[~~k*N subgroups~~|3*33 ~~subgroup~~]] 2.~~27.15.21.~~11.13. ~~On this subgroup it tunes things to~~ the ~~same tuning as~~ [[~~99edo~~]], and as a ~~subgroup patent val it tempers out~~ the ~~same commas. The 99 equal temperaments hemififths~~, ~~amity~~, ~~parakleismic~~, ~~hemiwuerschmidt~~, ~~ennealimmal and hendecatonic can be reduced to this subgroup and give various possibilities for MOS scales~~, ~~etc~~. ~~In particular~~, the [[~~Subgroup temperaments#Terrain|terrain~~]] 2.7/5.9/5 ~~subgroup temperament can be~~ tuned ~~via the 5~~\33 ~~generator. The full system~~ of ~~harmony provides~~ the ~~optimal patent val for~~ [[~~Mint_temperaments#Slurpee|slurpee temperament~~]] ~~in the~~ 5-, 7-, ~~11-~~, and ~~13-limits~~.

While relatively uncommon, 33edo is actually quite an interesting system. As a multiple of [[11edo]], it approximates the 7th and 11th harmonics via [[orgone]] temperament (see [[26edo]]). 33edo also tunes the 13th harmonic slightly flat, allowing it to approximate the 21st and 17th harmonics as well, having a [[3L 7s]] with {{nowrap|L {{=}} 4|s {{=}} 3}}. The 33c ({{val| 33 52 76 93 }}) and 33cd ({{val| 33 52 76 92 }}) mappings temper out [[81/80]] and can be used to represent [[1/2-comma meantone]], a [[Meantone family#Flattertone|"flattertone"]] tuning where the whole tone is [[10/9]] in size. Indeed, the perfect fifth is tuned about 11{{c}} flat, and two stacked fifths fall only 0.6{{c}} flat of 10/9. Leaving the scale be would result in the standard diatonic scale ([[5L 2s]]) having minor seconds of four steps and whole tones of five steps. This also results in common practice minor and major chords becoming more supraminor and submajor in character, making everything sound almost neutral in quality.

Instead of the flat 19-step fifth you may use the 20-step sharp fifth, over 25{{c}} sharp. Two of these lead to a 9/8 of 7\33, which is about 22/19 in size and may be counted as a small third. Between the flat 5\33 version of 9/8 and the sharp 7\33 version there is, of course, a {{nowrap|6\33 {{=}} 2\[[11edo|11]]}} interval of 218{{c}}. Together, these add up to {{nowrap|6\33 + 5\33 {{=}} 11\33 {{=}} 1\3}}, or 400{{c}}, the same major third as 12edo. We also have both a 327{{c}} minor third ({{nowrap|9\33 {{=}} 6\22 {{=}} 3\11}}), the same as that of [[22edo]], and a flatter 8\33 third of 291{{c}}, which if you like could also be called a flat 19th harmonic, but much more accurately a 13/11 sharp by 1.7{{c}} (if you use the patent val it is an extremely inaccurate 6/5). Another talent it has is that 7/5 is tuned quite accurately by 16\33, and we may put two 8\33 versions of 13/11 together to produce the [[cuthbert triad]]. The 8\33 generator, with MOS of size 5, 9, and 13, gives plenty of scope for these, as well as the 11th, 13th, and 19th harmonics (taking the generator as a 19/16) which are relatively well in tune.

~~While it might not be the most harmonically~~ accurate temperament, it is structurally quite interesting, and it approximates the full 19-limit consort in its own way. You could even say it tunes the 23rd and 29th harmonics ten cents flat if you were so inclined; as well as getting within two cents of the ~~37th~~.

33edo contains an accurate approximation of the [[Bohlen–Pierce]] scale with 4\33 near [[13edt|1\13edt]].

~~{{Harmonics in equal|33}}~~

~~=== Structural properties ===~~

Other notable 33edo scales are [[diasem]] with {{nowrap|L:m:s {{=}} 5:3:1}} and [[5L 4s]] with {{nowrap|L:s {{=}} 5:2}}. This step ratio for 5L 4s is great for its semitone size of 72.7{{c}}.

~~While relatively uncommon,~~ 33edo ~~is actually quite an interesting system. As a multiple of [[11edo]], it approximates the 7th and 11th harmonics via~~ [[~~orgone]] temperament (see [[26edo]]). 33edo also tunes the 13th harmonic slightly flat, allowing it to approximate the 21st and 17th harmonics as well, having a [[3L 7s~~]] with {{nowrap|L ~~{{=}} 4|~~s {{=}} 3}}~~. The 33c ({{val| 33 52 76 93 }})~~ and ~~33cd ({{val| 33 52 76 92 }}) mappings temper out~~ [[~~81/80~~]] ~~and can be used to represent [[1/2-comma meantone]], a [[Meantone family#Flattertone~~|~~"flattertone"]] tuning where the whole tone is [[10/9]] in size. Indeed, the perfect fifth is tuned about 11~~{{c}} ~~flat, and two stacked fifths fall only 0.6{{c~~}} ~~flat of 10/9~~. ~~Leaving the scale be would result in the standard diatonic scale ([[~~5L ~~2s]]) having minor seconds of four steps and whole tones~~ of ~~five steps~~. ~~This also results in common practice minor and major chords becoming more supraminor and submajor in character, making everything sound almost neutral in quality~~.

Instead of the flat 19-step fifth you may use the 20-step sharp fifth, over 25{{c}} sharp. Two of these lead to a 9/8 of 7\33, which is about 22/19 in size and may be counted as a small third. Between the flat 5\33 version of 9/8 and the sharp 7\33 version there is, of course, a {{nowrap|6\33 {{=~~}} 2\[[11edo|11]]}} interval of 218{{c}}. Together, these add up to {{nowrap|6\33 + 5\33 {{~~=~~}} 11\33 {{~~=~~}} 1\3}}, or 400~~{{~~c}}, the same major third as 12edo. We also have both a 327¢ minor third ({{nowrap~~|~~9\33 {{=}} 6\22 {{=}} 3\11}}), the same as that of [[22edo]], and a flatter 8\~~33 ~~third of 291{{c~~}}, which if you like could also be called a flat 19th harmonic, but much more accurately a 13/11 sharp by 1.7{{c}} (if you use the patent val it is an extremely inaccurate 6/5). Another talent it has is that 7/5 is tuned quite accurately by 16\33, and we may put two 8\33 versions of 13/11 together to produce the [[cuthbert triad]]. The 8\33 generator, with MOS of size 5, 9, and 13, gives plenty of scope for these, as well as the 11th, 13th, and 19th harmonics (taking the generator as a 19/16) which are relatively well in tune.

=== Odd harmonics ===

33edo ~~contains an accurate approximation of~~ the ~~Bohlen~~-~~Pierce scale with 4~~\33 ~~near 1\~~[[~~13edt~~]].

33edo is not especially good at representing all rational intervals in the [[7-limit]], but it does very well on the 7-limit [[k*N subgroups|3*33 subgroup]] 2.27.15.21.11.13. On this subgroup it tunes things to the same tuning as [[99edo]], and as a subgroup patent val it tempers out the same commas. The 99 equal temperaments hemififths, amity, parakleismic, hemiwuerschmidt, ennealimmal and hendecatonic can be reduced to this subgroup and give various possibilities for MOS scales, etc. In particular, the [[terrain]] 2.7/5.9/5 subgroup temperament can be tuned via the 5\33 generator. The full system of harmony provides the optimal patent val for [[slurpee]] temperament in the 5-, 7-, 11-, and 13-limits.

~~Other notable 33edo scales are [[diasem]] with {{nowrap|L:m:s {{=}} 5:3:1}}~~ and ~~[[5L 4s]] with {{nowrap|L:s {{=}} 5:2}}~~. ~~This step ratio for 5L&nbsp~~;~~4s is great for its semitone size~~ of ~~72.7¢~~.

While it might not be the most harmonically accurate temperament, it is structurally quite interesting, and it approximates the full 19-limit consort in its own way. You could even say it tunes the 23rd and 29th harmonics ten cents flat if you were so inclined; as well as getting within two cents of the 37th.

=== Miscellany ===

33 is also the number of years in the Iranian calendar's leap cycle, where leap year is inserted once every 4 or 5 years. This corresponds to the [[1L 7s]] with the step ratio of 5:4.

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|-

| 0

| 0¢

| 0

| [[1/1]]

| 0

Line 45:

Line 48:

| [[48/47]]

| 36.448

| ~~−0~~.085

| −0.085

| Augmented Unison

| A1

Line 54:

Line 57:

| [[24/23]]

| 73.681

| ~~−0~~.953

| −0.953

| Double-aug 1sn

| AA1

Line 63:

Line 66:

| [[16/15]]

| 111.731

| ~~−2~~.640

| −2.640

| Diminished 2nd

| d2

Line 72:

Line 75:

| [[12/11]]

| 150.637

| ~~−5~~.183

| −5.183

| Minor 2nd

| m2

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Line 84:

| [[10/9]]

| 182.404

| ~~−0~~.586

| −0.586

| Major 2nd

| M2

Line 171:

Line 174:

| [[11/8]]

| 551.318

| ~~−5~~.863

| −5.863

| Augmented 4th

| A4

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Line 183:

| [[7/5]]

| 582.513

| ~~−0~~.694

| −0.694

| Double-aug 4th

| AA4

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Line 209:

| 690.909

| [[3/2]]

| 701.~~9550~~

| 701.955

| ~~−11~~.046

| −11.046

| Perfect 5th

| P5

Line 224:

Line 227:

| 763.636

| [[14/9]]

| 764.~~9159~~

| 764.916

| ~~−1~~.280

| −1.280

| Double-aug 5th

| AA5

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Line 237:

| [[8/5]]

| 813.686

| ~~−13~~.686

| −13.686

| Double-dim 6th

| d6

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Line 245:

| 836.364

| [[13/8]]

| 840.~~5276~~

| 840.528

| ~~−4~~.164

| −4.164

| Minor 6th

| m6

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| [[5/3]]

| 884.359

| ~~−11~~.631

| −11.631

| Major 6th

| M6

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| 909.091

| [[22/13]]

| 910.~~7903~~

| 910.790

| ~~−1~~.699

| −1.699

| Augmented 6th

| A6

Line 279:

Line 282:

| [[30/17]]

| 983.313

| ~~−1~~.495

| −1.495

| Diminished 7th

| d7

Line 315:

Line 318:

| [[23/12]]

| 1126.319

| ~~−0~~.953

| −0.953

| Double-dim 8ve

| dd8

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default [[File:33-EDO_Sagittal.svg]]

</imagemap>

== Approximation to JI ==

{{Q-odd-limit intervals|32.87|apx=val|header=none|tag=none|title=15-odd-limit intervals by 33cd val mapping}}

== Nearby equal temperaments ==

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| 2.3.5

| 81/80, 1171875/1048576

| {{mapping| 33 52 76 }} (~~33cd~~)

| {{mapping| 33 52 76 }} (33c)

| +5.59

| 4.13

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Brightest mode is listed except where noted.

* Deeptone[7], 5 5 5 4 5 5 4 (diatonic)

** Fun 5-tone subset of Deeptone[7] 9 5 5 4 10

* Deeptone[12], 4 4 1 4 1 4 4 1 4 1 4 1 (chromatic)

* Deeptone[19], 3 1 3 1 1 3 1 1 3 1 3 1 1 3 1 1 3 1 1 (enharmonic)

Line 1,396:

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=== Modern renderings ===

; {{W|Johann Sebastian Bach}}

* [https://www.youtube.com/watch?v=IhR9oFt5zx4 "Contrapunctus 4" from ''The Art of Fugue'', BWV 1080] (~~1742–1749~~) ~~–~~ rendered by Claudi Meneghin (2024)

* [https://www.youtube.com/watch?v=IhR9oFt5zx4 "Contrapunctus 4" from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)

* [https://www.youtube.com/watch?v=ynPQPm_ekos "Contrapunctus 11" from ''The Art of Fugue'', BWV 1080] (~~1742–1749~~) ~~–~~ rendered by Claudi Meneghin (2024)

* [https://www.youtube.com/watch?v=ynPQPm_ekos "Contrapunctus 11" from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)

=== 21st century ===

; [[Bryan Deister]]

* [https://www.youtube.com/watch?v=swyP6tB78k0 ''groove 33edo''] (2023)

* [https://www.youtube.com/watch?v=GypR6x_Ih1I ''33edo jam''] (2025)

* [https://www.youtube.com/shorts/mkaaAJEyGFU ''33edo riff''] (2025)

; [[Peter Kosmorsky]]

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; [[Budjarn Lambeth]]

* [https://youtu.be/scCuGXnj5IY ''Music in 33EDO (33-Tone Equal Temperament) ~~–~~ Feb 2024''] (2024)

* [https://youtu.be/scCuGXnj5IY ''Music in 33EDO (33-Tone Equal Temperament) – Feb 2024''] (2024)

; [[Claudi Meneghin]]

* [https://www.youtube.com/watch?v=REkrbdesbLo ''Rising Canon on a Ground'', for Baroque Oboe, Bassoon, Violone] (2024) ~~–~~ ([https://www.youtube.com/watch?v=4fhcNPjFv14 for Organ])

* [https://www.youtube.com/watch?v=REkrbdesbLo ''Rising Canon on a Ground'', for Baroque Oboe, Bassoon, Violone] (2024) – ([https://www.youtube.com/watch?v=4fhcNPjFv14 for Organ])

* [https://www.youtube.com/watch?v=pkYN8SX6luY ''Lytel Twyelyghte Musicke (Little Twilight Music)'', for Brass and Timpani] (2024)

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
 {{ED intro}}
 == Theory ==
-=== Harmonics ===
+=== Structural properties ===
-edo is not especially good at representing all rational intervals in the [[7-limit]], but it does very well on the 7-limit [[k*N subgroups|3*33 subgroup]] 2.27.15.21.11.13. On this subgroup it tunes things to the same tuning as [[99edo]], and as a subgroup patent val it tempers out the same commas. The 99 equal temperaments hemififths, amity, parakleismic, hemiwuerschmidt, ennealimmal and hendecatonic can be reduced to this subgroup and give various possibilities for MOS scales, etc. In particular, the [[Subgroup temperaments#Terrain|terrain]] 2.7/5.9/5 subgroup temperament can be tuned via the 5\33 generator. The full system of harmony provides the optimal patent val for [[Mint_temperaments#Slurpee|slurpee temperament]] in the 5-, 7-, 11-, and 13-limits.
+While relatively uncommon, 33edo is actually quite an interesting system. As a multiple of [[11edo]], it approximates the 7th and 11th harmonics via [[orgone]] temperament (see [[26edo]]). 33edo also tunes the 13th harmonic slightly flat, allowing it to approximate the 21st and 17th harmonics as well, having a [[3L&nbsp;7s]] with {{nowrap|L {{=}} 4|s {{=}} 3}}. The 33c ({{val| 33 52 76 93 }}) and 33cd ({{val| 33 52 76 92 }}) mappings temper out [[81/80]] and can be used to represent [[1/2-comma meantone]], a [[Meantone family#Flattertone|"flattertone"]] tuning where the whole tone is [[10/9]] in size. Indeed, the perfect fifth is tuned about 11{{c}} flat, and two stacked fifths fall only 0.6{{c}} flat of 10/9. Leaving the scale be would result in the standard diatonic scale ([[5L&nbsp;2s]]) having minor seconds of four steps and whole tones of five steps. This also results in common practice minor and major chords becoming more supraminor and submajor in character, making everything sound almost neutral in quality.
+Instead of the flat 19-step fifth you may use the 20-step sharp fifth, over 25{{c}} sharp. Two of these lead to a 9/8 of 7\33, which is about 22/19 in size and may be counted as a small third. Between the flat 5\33 version of 9/8 and the sharp 7\33 version there is, of course, a {{nowrap|6\33 {{=}} 2\[[11edo|11]]}} interval of 218{{c}}. Together, these add up to {{nowrap|6\33 + 5\33 {{=}} 11\33 {{=}} 1\3}}, or 400{{c}}, the same major third as 12edo. We also have both a 327{{c}} minor third ({{nowrap|9\33 {{=}} 6\22 {{=}} 3\11}}), the same as that of [[22edo]], and a flatter 8\33 third of 291{{c}}, which if you like could also be called a flat 19th harmonic, but much more accurately a 13/11 sharp by 1.7{{c}} (if you use the patent val it is an extremely inaccurate 6/5). Another talent it has is that 7/5 is tuned quite accurately by 16\33, and we may put two 8\33 versions of 13/11 together to produce the [[cuthbert triad]]. The 8\33 generator, with MOS of size 5, 9, and 13, gives plenty of scope for these, as well as the 11th, 13th, and 19th harmonics (taking the generator as a 19/16) which are relatively well in tune.
-While it might not be the most harmonically accurate temperament, it is structurally quite interesting, and it approximates the full 19-limit consort in its own way. You could even say it tunes the 23rd and 29th harmonics ten cents flat if you were so inclined; as well as getting within two cents of the 37th.
+edo contains an accurate approximation of the [[Bohlen–Pierce]] scale with 4\33 near [[13edt|1\13edt]].
-{{Harmonics in equal|33}}
-=== Structural properties ===
+Other notable 33edo scales are [[diasem]] with {{nowrap|L:m:s {{=}} 5:3:1}} and [[5L&nbsp;4s]] with {{nowrap|L:s {{=}} 5:2}}. This step ratio for 5L&nbsp;4s is great for its semitone size of 72.7{{c}}.
-While relatively uncommon, 33edo is actually quite an interesting system. As a multiple of [[11edo]], it approximates the 7th and 11th harmonics via [[orgone]] temperament (see [[26edo]]). 33edo also tunes the 13th harmonic slightly flat, allowing it to approximate the 21st and 17th harmonics as well, having a [[3L&nbsp;7s]] with {{nowrap|L {{=}} 4|s {{=}} 3}}. The 33c ({{val| 33 52 76 93 }}) and 33cd ({{val| 33 52 76 92 }}) mappings temper out [[81/80]] and can be used to represent [[1/2-comma meantone]], a [[Meantone family#Flattertone|"flattertone"]] tuning where the whole tone is [[10/9]] in size. Indeed, the perfect fifth is tuned about 11{{c}} flat, and two stacked fifths fall only 0.6{{c}} flat of 10/9. Leaving the scale be would result in the standard diatonic scale ([[5L&nbsp;2s]]) having minor seconds of four steps and whole tones of five steps. This also results in common practice minor and major chords becoming more supraminor and submajor in character, making everything sound almost neutral in quality.
-Instead of the flat 19-step fifth you may use the 20-step sharp fifth, over 25{{c}} sharp. Two of these lead to a 9/8 of 7\33, which is about 22/19 in size and may be counted as a small third. Between the flat 5\33 version of 9/8 and the sharp 7\33 version there is, of course, a {{nowrap|6\33 {{=}} 2\[[11edo|11]]}} interval of 218{{c}}. Together, these add up to {{nowrap|6\33 + 5\33 {{=}} 11\33 {{=}} 1\3}}, or 400{{c}}, the same major third as 12edo. We also have both a 327¢ minor third ({{nowrap|9\33 {{=}} 6\22 {{=}} 3\11}}), the same as that of [[22edo]], and a flatter 8\33 third of 291{{c}}, which if you like could also be called a flat 19th harmonic, but much more accurately a 13/11 sharp by 1.7{{c}} (if you use the patent val it is an extremely inaccurate 6/5). Another talent it has is that 7/5 is tuned quite accurately by 16\33, and we may put two 8\33 versions of 13/11 together to produce the [[cuthbert triad]]. The 8\33 generator, with MOS of size 5, 9, and 13, gives plenty of scope for these, as well as the 11th, 13th, and 19th harmonics (taking the generator as a 19/16) which are relatively well in tune.
+=== Odd harmonics ===
+{{Harmonics in equal|33}}
-edo contains an accurate approximation of the Bohlen-Pierce scale with 4\33 near 1\[[13edt]].
+edo is not especially good at representing all rational intervals in the [[7-limit]], but it does very well on the 7-limit [[k*N subgroups|3*33 subgroup]] 2.27.15.21.11.13. On this subgroup it tunes things to the same tuning as [[99edo]], and as a subgroup patent val it tempers out the same commas. The 99 equal temperaments hemififths, amity, parakleismic, hemiwuerschmidt, ennealimmal and hendecatonic can be reduced to this subgroup and give various possibilities for MOS scales, etc. In particular, the [[terrain]] 2.7/5.9/5 subgroup temperament can be tuned via the 5\33 generator. The full system of harmony provides the optimal patent val for [[slurpee]] temperament in the 5-, 7-, 11-, and 13-limits.
-Other notable 33edo scales are [[diasem]] with {{nowrap|L:m:s {{=}} 5:3:1}} and [[5L&nbsp;4s]] with {{nowrap|L:s {{=}} 5:2}}. This step ratio for 5L&nbsp;4s is great for its semitone size of 72.7¢.
+While it might not be the most harmonically accurate temperament, it is structurally quite interesting, and it approximates the full 19-limit consort in its own way. You could even say it tunes the 23rd and 29th harmonics ten cents flat if you were so inclined; as well as getting within two cents of the 37th.
+=== Miscellany ===
 is also the number of years in the Iranian calendar's leap cycle, where leap year is inserted once every 4 or 5 years. This corresponds to the [[1L&nbsp;7s]] with the step ratio of 5:4.
@@ Line 33: / Line 36: @@
 |-
 | 0
-| 0¢
+| 0
 | [[1/1]]
 | 0
@@ Line 45: / Line 48: @@
 | [[48/47]]
 | 36.448
-| &minus;0.085
+| −0.085
 | Augmented Unison
 | A1
@@ Line 54: / Line 57: @@
 | [[24/23]]
 | 73.681
-| &minus;0.953
+| −0.953
 | Double-aug 1sn
 | AA1
@@ Line 63: / Line 66: @@
 | [[16/15]]
 | 111.731
-| &minus;2.640
+| −2.640
 | Diminished 2nd
 | d2
@@ Line 72: / Line 75: @@
 | [[12/11]]
 | 150.637
-| &minus;5.183
+| −5.183
 | Minor 2nd
 | m2
@@ Line 81: / Line 84: @@
 | [[10/9]]
 | 182.404
-| &minus;0.586
+| −0.586
 | Major 2nd
 | M2
@@ Line 171: / Line 174: @@
 | [[11/8]]
 | 551.318
-| &minus;5.863
+| −5.863
 | Augmented 4th
 | A4
@@ Line 180: / Line 183: @@
 | [[7/5]]
 | 582.513
-| &minus;0.694
+| −0.694
 | Double-aug 4th
 | AA4
@@ Line 206: / Line 209: @@
 | 690.909
 | [[3/2]]
-| 701.9550
+| 701.955
-| &minus;11.046
+| −11.046
 | Perfect 5th
 | P5
@@ Line 224: / Line 227: @@
 | 763.636
 | [[14/9]]
-| 764.9159
+| 764.916
-| &minus;1.280
+| −1.280
 | Double-aug 5th
 | AA5
@@ Line 234: / Line 237: @@
 | [[8/5]]
 | 813.686
-| &minus;13.686
+| −13.686
 | Double-dim 6th
 | d6
@@ Line 242: / Line 245: @@
 | 836.364
 | [[13/8]]
-| 840.5276
+| 840.528
-| &minus;4.164
+| −4.164
 | Minor 6th
 | m6
@@ Line 252: / Line 255: @@
 | [[5/3]]
 | 884.359
-| &minus;11.631
+| −11.631
 | Major 6th
 | M6
@@ Line 260: / Line 263: @@
 | 909.091
 | [[22/13]]
-| 910.7903
+| 910.790
-| &minus;1.699
+| −1.699
 | Augmented 6th
 | A6
@@ Line 279: / Line 282: @@
 | [[30/17]]
 | 983.313
-| &minus;1.495
+| −1.495
 | Diminished 7th
 | d7
@@ Line 315: / Line 318: @@
 | [[23/12]]
 | 1126.319
-| &minus;0.953
+| −0.953
 | Double-dim 8ve
 | dd8
@@ Line 356: / Line 359: @@
 default [[File:33-EDO_Sagittal.svg]]
 </imagemap>
+== Approximation to JI ==
+{{Q-odd-limit intervals}}
+{{Q-odd-limit intervals|32.87|apx=val|header=none|tag=none|title=15-odd-limit intervals by 33cd val mapping}}
 == Nearby equal temperaments ==
@@ Line 381: / Line 388: @@
 | 2.3.5
 | 81/80, 1171875/1048576
-| {{mapping| 33 52 76 }} (33cd)
+| {{mapping| 33 52 76 }} (33c)
 | +5.59
 | 4.13
@@ Line 484: / Line 491: @@
 Brightest mode is listed except where noted.
 * Deeptone[7], 5 5 5 4 5 5 4 (diatonic)
+** Fun 5-tone subset of Deeptone[7] 9 5 5 4 10
 * Deeptone[12], 4 4 1 4 1 4 4 1 4 1 4 1 (chromatic)
 * Deeptone[19], 3 1 3 1 1 3 1 1 3 1 3 1 1 3 1 1 3 1 1 (enharmonic)
@@ Line 1,396: / Line 1,404: @@
 === Modern renderings ===
 ; {{W|Johann Sebastian Bach}}
-* [https://www.youtube.com/watch?v=IhR9oFt5zx4 "Contrapunctus 4" from ''The Art of Fugue'', BWV 1080] (1742&ndash;1749) &ndash; rendered by Claudi Meneghin (2024)
+* [https://www.youtube.com/watch?v=IhR9oFt5zx4 "Contrapunctus 4" from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)
-* [https://www.youtube.com/watch?v=ynPQPm_ekos "Contrapunctus 11" from ''The Art of Fugue'', BWV 1080] (1742&ndash;1749) &ndash; rendered by Claudi Meneghin (2024)
+* [https://www.youtube.com/watch?v=ynPQPm_ekos "Contrapunctus 11" from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)
 === 21st century ===
 ; [[Bryan Deister]]
 * [https://www.youtube.com/watch?v=swyP6tB78k0 ''groove 33edo''] (2023)
+* [https://www.youtube.com/watch?v=GypR6x_Ih1I ''33edo jam''] (2025)
+* [https://www.youtube.com/shorts/mkaaAJEyGFU ''33edo riff''] (2025)
 ; [[Peter Kosmorsky]]
@@ Line 1,407: / Line 1,417: @@
 ; [[Budjarn Lambeth]]
-* [https://youtu.be/scCuGXnj5IY ''Music in 33EDO (33-Tone Equal Temperament) &ndash; Feb 2024''] (2024)
+* [https://youtu.be/scCuGXnj5IY ''Music in 33EDO (33-Tone Equal Temperament) – Feb 2024''] (2024)
 ; [[Claudi Meneghin]]
-* [https://www.youtube.com/watch?v=REkrbdesbLo ''Rising Canon on a Ground'', for Baroque Oboe, Bassoon, Violone] (2024) &ndash; ([https://www.youtube.com/watch?v=4fhcNPjFv14 for Organ])
+* [https://www.youtube.com/watch?v=REkrbdesbLo ''Rising Canon on a Ground'', for Baroque Oboe, Bassoon, Violone] (2024) – ([https://www.youtube.com/watch?v=4fhcNPjFv14 for Organ])
 * [https://www.youtube.com/watch?v=pkYN8SX6luY ''Lytel Twyelyghte Musicke (Little Twilight Music)'', for Brass and Timpani] (2024)