29edo: Difference between revisions

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}}

== Theory ==

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! Cents

! Approx. Ratios of the [[13-limit]]

! colspan="3" | [[Ups and ~~Downs Notation~~]]

! colspan="3" | [[Ups and downs notation]]

([[Enharmonic unisons in ups and downs notation|EUs]]: v3A1 and ^d2)

! colspan="3" |[[SKULO interval names|SKULO interval names and notation]] (K or S = 1)

|-

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| downminor

| zo

| {a, b, 0, 1}

| [a, b, 0, 1>

| 7/6, 7/4

|-

| minor

| fourthward wa

| {a, b}, b < -1

| [a, b>, b < -1

| 32/27, 16/9

|-

| upminor

| gu

| {a, b, -1}

| [a, b, -1>

| 6/5, 9/5

|-

| "

| ilo

| {a, b, 0, 0, 1}

| [a, b, 0, 0, 1>

| 11/9, 11/6

|-

| downmajor

| lu

| {a, b, 0, 0, -1}

| [a, b, 0, 0, -1>

| 12/11, 18/11

|-

| "

| yo

| {a, b, 1}

| [a, b, 1>

| 5/4, 5/3

|-

| major

| fifthward wa

| {a, b}, b > 1

| [a, b>, b > 1

| 9/8, 27/16

|-

| upmajor

| ru

| {a, b, 0, -1}

| [a, b, 0, -1>

| 9/7, 12/7

|}

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| C upmajor or C up

|}

For a more complete list, see [[Ups and ~~Downs Notation~~ #Chords and Chord Progressions]].

For a more complete list, see [[Ups and downs notation #Chords and Chord Progressions]].

== Notation ==

=== Standard notation===

=== Standard notation ===

29edo can be notated three different ways. Using only sharps and flats, the chromatic scale from C is:

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* C𝄪 = F𝄫

=== Ups and downs ===

=== Ups and downs notation ===

Since a sharp raises by three steps, 29edo is a good candidate for [[ups and downs notation]], similar to [[22edo]]. ~~Here~~, ~~sharps and flats with arrows from [[Helmholtz–Ellis notation]]~~ can be ~~used:~~

Since a sharp raises by three steps, 29edo is a good candidate for [[ups and downs notation]], similar to [[22edo]]. Spoken as up, downsharp, sharp, etc. Note that downsharp (v#) can be respelled as dup (^^).

Here, sharps and flats with arrows from [[Helmholtz–Ellis notation]] are used:

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If arrows are taken to have their own layer of enharmonic spellings, then in some cases notes may be best spelled with double arrows.

===Sagittal notation===

=== Sagittal notation ===

This notation uses the same sagittal sequence as EDOs [[15edo#Sagittal notation|15]] and [[22edo#Sagittal notation|22]].

~~====Evo flavor====~~

==== Evo flavor ====

File:29-EDO_Evo_Sagittal.svg

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</imagemap>

====Revo flavor====

==== Revo flavor ====

File:29-EDO_Revo_Sagittal.svg

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== Approximation to JI ==

=== Interval mappings ===

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|-

! [[Harmonic limit|Prime limit]]

! [[Ratio]]<ref>~~Ratios longer than 10 digits are presented by placeholders with informative hints~~</ref>

! [[Ratio]]<ref group="note">{{rd}}</ref>

! [[Monzo]]

! [[Cents]]

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| Minor minthma

|}

~~<references />~~

=== Rank-2 temperaments ===

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Nicetone scale 5435453 and cadence in 29edo

~~=== MisterShafXen's notation ===~~

~~[[MisterShafXen’s 29edo notation]]~~

== Scales ==

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* [[Leapfrog]] diatonic [[5L 2s]] 5552552 (17\29, 1\1)

* [[Leapfrog]] chromatic [[5L 7s]] 3232323223232322 (17\29, 1\1)

* [[Leapfrog]] hyperchromatic [[12L 5s]] 21221221221222122122122 (17\29, 1\1)

* [[Porcupine]] [[1L 6s]] 4444445 (4\29, 1\1)

* [[Porcupine]] [[7L 1s]] 44444441 (4\29, 1\1)

* [[Porcupine]] [[7L 8s]] 313131313131311 (4\29, 1\1)

* [[Porcupine]] [[7L 15s]] 2112112112112112112111 (4\29, 1\1)

* [[Negri]] [[1L 8s]] 333333335 (3\29, 1\1)

* [[Negri]] [[9L 1s]] 3333333332 (3\29, 1\1)

* [[Negri]] [[10L 9s]] 2212121212121212121 (3\29 1\1)

* [[Semaphore]] [[4L 1s]] 56666 (6\29, 1\1)

* [[Semaphore]] [[5L 4s]] 551515151 (6\29, 1\1)

* [[Semaphore]] [[5L 9s]] 41411411411411 (6\29, 1\1)

* [[Semaphore]] [[5L 14s]] 3113111311131113111 (6\29, 1\1)

* Pathological [[semaphore]] [[5L 19s]] 211121111211112111121111 (6\29, 1\1)

* [[Nautilus]] [[1L 13s]] 22222222222223 (2\29, 1\1)

* [[Nautilus]] [[14L 1s]] 222222222222221 (2\29, 1\1)

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: Furthermore, since external images can break, we recommend that you replace the above with a local copy of the image.

</div>

* [[Lumatone mapping for 29edo]]

== Music ==

=== Modern renderings ===

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* [https://www.youtube.com/watch?v=uGOK7WtVtlM "Contrapunctus 4" from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)

* [https://www.youtube.com/watch?v=jcZaU5PrhvU "Contrapunctus 11" from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)

* [https://www.youtube.com/watch?v=-Sa8IhljHM0 ''BACH - RICERCAR a 6 from the Musical Offering, tuned into 29-EDO'', BWV 1079] (1742-1749) - rendered by Claudi Meneghin (2025)

* [https://www.youtube.com/watch?v=856A7vTqIW8 ''Bach, Art of Fugue: Contrapunctus 11, tuned into 29-edo (harpischord)''] (1740-1746) - rendered by Claudi Meneghin (2025)

; {{W|Nicolaus Bruhns}}

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* [https://www.youtube.com/watch?v=HGQ2b6v0TWE ''Glass Animals - Life Itself''] (2023)

* [https://www.youtube.com/watch?v=ktk0VWbUbDg ''microtonal improvisation in 29edo''] (2023)

* [https://www.youtube.com/shorts/fyPaaW9AyMA ''Homestuck: Pipeorgankind (microtonal cover in 29edo)''] (2024)

* [https://www.youtube.com/shorts/SH5IQOi33Oo ''29edo groove''] (2025)

; [[duckapus]]

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* "Chill Bells" from ''Melancholie'' (2023) [https://open.spotify.com/track/30Ik57efXmIae1YSgTgdIE Spotify] | [https://francium223.bandcamp.com/track/chill-bells Bandcamp] | [https://www.youtube.com/watch?v=Qbz2a4PMnjY YouTube]

* from ''XenRhythms'' (2024)

** "All 29" – [https://francium223.bandcamp.com/track/all-29 Bandcamp] | [https://www.youtube.com/watch?v=C-FFLXHSO_k YouTube]

** "All 29" – [https://open.spotify.com/track/7I0fLgRPKdqCK51PUnt4Oe Spotify] | [https://francium223.bandcamp.com/track/all-29 Bandcamp] | [https://www.youtube.com/watch?v=C-FFLXHSO_k YouTube]

** "Do Not Immerse Yourself In Fire Or Water" – [https://francium223.bandcamp.com/track/do-not-immerse-yourself-in-fire-or-water Bandcamp] | [https://www.youtube.com/watch?v=NHDvNQbBHV0 YouTube] – ~~immunity~~[14] in 29edo tuning

** "Do Not Immerse Yourself In Fire Or Water" – [https://open.spotify.com/track/5FUmlRP1JjLsH99vXbJhXH Spotify] | [https://francium223.bandcamp.com/track/do-not-immerse-yourself-in-fire-or-water Bandcamp] | [https://www.youtube.com/watch?v=NHDvNQbBHV0 YouTube] – in Immunity[14], 29edo tuning

* [https://www.youtube.com/watch?v=di4qn2VFYbs ''Plane Sonatina No. 1''] (2025)

* [https://www.youtube.com/watch?v=ifvvww20XAU ''Strank Running''] (2025)

; [[Igliashon Jones]]

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== See also ==

* [[~~Arto and Tendo~~ Theory]]

* [[User:Unque/29edo Composition Theory|Unque's approach]]

* [[~~Lumatone mapping for 29edo~~]]

* [[Extraclassical tonality]]

* [[67ed5]] - octave-stretched 29edo, improves harmonics 5.7.11.13.17 but damages 2.3

* [[67ed5]] – octave-stretched 29edo, improves harmonics 5.7.11.13.17 but damages 2.3

== Notes ==

== References ==

[[Category:IMPORTDEBUG - Change External Images]]

[[Category:3-limit record edos|##]]

[[Category:3-limit]]

[[Category:Subgroup temperaments]]

[[Category:~~Listen~~]]

[[Category:Twentuning]]

[[Category:Negri]]

[[Category:Petrmic]]

[[Category:Porcupine]]

[[Category:~~Subgroup temperaments]]~~

[[Category:Listen]]

~~[[Category:Twentuning~~]]

@@ Line 6: / Line 6: @@
 }}
 {{Infobox ET}}
-{{EDO intro|29}}
+{{ED intro}}
 == Theory ==
@@ Line 44: / Line 44: @@
 ! Cents
 ! Approx. Ratios of the [[13-limit]]
-! colspan="3" | [[Ups and Downs Notation]]
+! colspan="3" | [[Ups and downs notation]]
+([[Enharmonic unisons in ups and downs notation|EUs]]: v<sup>3</sup>A1 and ^d2)
 ! colspan="3" |[[SKULO interval names|SKULO interval names and notation]] (K or S = 1)
 |-
@@ Line 359: / Line 360: @@
 | downminor
 | zo
-| {a, b, 0, 1}
+| [a, b, 0, 1>
 | 7/6, 7/4
 |-
 | minor
 | fourthward wa
-| {a, b}, b &lt; -1
+| [a, b>, b &lt; -1
 | 32/27, 16/9
 |-
 | upminor
 | gu
-| {a, b, -1}
+| [a, b, -1>
 | 6/5, 9/5
 |-
 | "
 | ilo
-| {a, b, 0, 0, 1}
+| [a, b, 0, 0, 1>
 | 11/9, 11/6
 |-
 | downmajor
 | lu
-| {a, b, 0, 0, -1}
+| [a, b, 0, 0, -1>
 | 12/11, 18/11
 |-
 | "
 | yo
-| {a, b, 1}
+| [a, b, 1>
 | 5/4, 5/3
 |-
 | major
 | fifthward wa
-| {a, b}, b &gt; 1
+| [a, b>, b &gt; 1
 | 9/8, 27/16
 |-
 | upmajor
 | ru
-| {a, b, 0, -1}
+| [a, b, 0, -1>
 | 9/7, 12/7
 |}
@@ Line 436: / Line 437: @@
 | C upmajor or C up
 |}
-For a more complete list, see [[Ups and Downs Notation #Chords and Chord Progressions]].
+For a more complete list, see [[Ups and downs notation #Chords and Chord Progressions]].
 == Notation ==
-=== Standard notation===
+=== Standard notation ===
 edo can be notated three different ways. Using only sharps and flats, the chromatic scale from C is:
@@ Line 452: / Line 453: @@
 * C𝄪 = F𝄫
-=== Ups and downs ===
+=== Ups and downs notation ===
-Since a sharp raises by three steps, 29edo is a good candidate for [[ups and downs notation]], similar to [[22edo]]. Here, sharps and flats with arrows from [[Helmholtz–Ellis notation]] can be used:
+Since a sharp raises by three steps, 29edo is a good candidate for [[ups and downs notation]], similar to [[22edo]]. Spoken as up, downsharp, sharp, etc. Note that downsharp (v#) can be respelled as dup (^^).
+{{Sharpness-sharp3a}}
+Here, sharps and flats with arrows from [[Helmholtz–Ellis notation]] are used:
 {{Sharpness-sharp3}}
@@ Line 461: / Line 464: @@
 If arrows are taken to have their own layer of enharmonic spellings, then in some cases notes may be best spelled with double arrows.
-===Sagittal notation===
+=== Sagittal notation ===
 This notation uses the same sagittal sequence as EDOs [[15edo#Sagittal notation|15]] and [[22edo#Sagittal notation|22]].
-====Evo flavor====
+==== Evo flavor ====
 <imagemap>
 File:29-EDO_Evo_Sagittal.svg
@@ Line 474: / Line 477: @@
 </imagemap>
-====Revo flavor====
+==== Revo flavor ====
 <imagemap>
 File:29-EDO_Revo_Sagittal.svg
@@ Line 487: / Line 489: @@
 == Approximation to JI ==
 [[File:29ed2.svg|250px|thumb|right|alt=alt : Your browser has no SVG support.|15-odd-limit intervals approximated in 29edo]]
 === Interval mappings ===
 {{Q-odd-limit intervals|29}}
@@ Line 560: / Line 563: @@
 |-
 ! [[Harmonic limit|Prime<br>limit]]
-! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
+! [[Ratio]]<ref group="note">{{rd}}</ref>
 ! [[Monzo]]
 ! [[Cents]]
@@ Line 755: / Line 758: @@
 | Minor minthma
 |}
-<references />
 === Rank-2 temperaments ===
@@ Line 872: / Line 874: @@
 Nicetone scale 5435453 and cadence in 29edo
-=== MisterShafXen's notation ===
-[[MisterShafXen’s 29edo notation]]
 == Scales ==
@@ Line 882: / Line 881: @@
 * [[Leapfrog]] diatonic [[5L 2s]] 5552552 (17\29, 1\1)
 * [[Leapfrog]] chromatic [[5L 7s]] 3232323223232322 (17\29, 1\1)
-* [[Leapfrog]] hyperchromatic [[12L 5s]] 21221221221222122122122 (17\29, 1\1)
 * [[Porcupine]] [[1L 6s]] 4444445 (4\29, 1\1)
 * [[Porcupine]] [[7L 1s]] 44444441 (4\29, 1\1)
-* [[Porcupine]] [[7L 8s]] 313131313131311 (4\29, 1\1)
-* [[Porcupine]] [[7L 15s]] 2112112112112112112111 (4\29, 1\1)
 * [[Negri]] [[1L 8s]] 333333335 (3\29, 1\1)
 * [[Negri]] [[9L 1s]] 3333333332 (3\29, 1\1)
-* [[Negri]] [[10L 9s]] 2212121212121212121 (3\29 1\1)
 * [[Semaphore]] [[4L 1s]] 56666 (6\29, 1\1)
 * [[Semaphore]] [[5L 4s]] 551515151 (6\29, 1\1)
 * [[Semaphore]] [[5L 9s]] 41411411411411 (6\29, 1\1)
-* [[Semaphore]] [[5L 14s]] 3113111311131113111 (6\29, 1\1)
-* Pathological [[semaphore]] [[5L 19s]] 211121111211112111121111 (6\29, 1\1)
 * [[Nautilus]] [[1L 13s]] 22222222222223 (2\29, 1\1)
 * [[Nautilus]] [[14L 1s]] 222222222222221 (2\29, 1\1)
@@ Line 965: / Line 958: @@
 : <small>Furthermore, since external images can break, we recommend that you replace the above with a local copy of the image.</small>
 </div>
+* [[Lumatone mapping for 29edo]]
 == Music ==
 === Modern renderings ===
@@ Line 971: / Line 964: @@
 * [https://www.youtube.com/watch?v=uGOK7WtVtlM "Contrapunctus 4" from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)
 * [https://www.youtube.com/watch?v=jcZaU5PrhvU "Contrapunctus 11" from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)
+* [https://www.youtube.com/watch?v=-Sa8IhljHM0 ''BACH - RICERCAR a 6 from the Musical Offering, tuned into 29-EDO'', BWV 1079] (1742-1749) - rendered by Claudi Meneghin (2025)
+* [https://www.youtube.com/watch?v=856A7vTqIW8 ''Bach, Art of Fugue: Contrapunctus 11, tuned into 29-edo (harpischord)''] (1740-1746) - rendered by Claudi Meneghin (2025)
 ; {{W|Nicolaus Bruhns}}
@@ Line 990: / Line 985: @@
 * [https://www.youtube.com/watch?v=HGQ2b6v0TWE ''Glass Animals - Life Itself''] (2023)
 * [https://www.youtube.com/watch?v=ktk0VWbUbDg ''microtonal improvisation in 29edo''] (2023)
+* [https://www.youtube.com/shorts/fyPaaW9AyMA ''Homestuck: Pipeorgankind (microtonal cover in 29edo)''] (2024)
+* [https://www.youtube.com/shorts/SH5IQOi33Oo ''29edo groove''] (2025)
 ; [[duckapus]]
@@ Line 1,003: / Line 1,000: @@
 * "Chill Bells" from ''Melancholie'' (2023) [https://open.spotify.com/track/30Ik57efXmIae1YSgTgdIE Spotify] | [https://francium223.bandcamp.com/track/chill-bells Bandcamp] | [https://www.youtube.com/watch?v=Qbz2a4PMnjY YouTube]
 * from ''XenRhythms'' (2024)
-** "All 29" – [https://francium223.bandcamp.com/track/all-29 Bandcamp] | [https://www.youtube.com/watch?v=C-FFLXHSO_k YouTube]
+** "All 29" – [https://open.spotify.com/track/7I0fLgRPKdqCK51PUnt4Oe Spotify] | [https://francium223.bandcamp.com/track/all-29 Bandcamp] | [https://www.youtube.com/watch?v=C-FFLXHSO_k YouTube]
-** "Do Not Immerse Yourself In Fire Or Water" – [https://francium223.bandcamp.com/track/do-not-immerse-yourself-in-fire-or-water Bandcamp] | [https://www.youtube.com/watch?v=NHDvNQbBHV0 YouTube] – immunity[14] in 29edo tuning
+** "Do Not Immerse Yourself In Fire Or Water" – [https://open.spotify.com/track/5FUmlRP1JjLsH99vXbJhXH Spotify] | [https://francium223.bandcamp.com/track/do-not-immerse-yourself-in-fire-or-water Bandcamp] | [https://www.youtube.com/watch?v=NHDvNQbBHV0 YouTube] – in Immunity[14], 29edo tuning
+* [https://www.youtube.com/watch?v=di4qn2VFYbs ''Plane Sonatina No. 1''] (2025)
+* [https://www.youtube.com/watch?v=ifvvww20XAU ''Strank Running''] (2025)
 ; [[Igliashon Jones]]
@@ Line 1,034: / Line 1,033: @@
 == See also ==
-* [[Arto and Tendo Theory]]
+* [[User:Unque/29edo Composition Theory|Unque's approach]]
-* [[Lumatone mapping for 29edo]]
+* [[Extraclassical tonality]]
-* [[67ed5]] - octave-stretched 29edo, improves harmonics 5.7.11.13.17 but damages 2.3
+* [[67ed5]] – octave-stretched 29edo, improves harmonics 5.7.11.13.17 but damages 2.3
+== Notes ==
+<references group="note" />
+== References ==
+<references />
 [[Category:IMPORTDEBUG - Change External Images]]
+[[Category:3-limit record edos|##]] <!-- 2-digit number -->
-[[Category:3-limit]]
+[[Category:Subgroup temperaments]]
-[[Category:Listen]]
+[[Category:Twentuning]]
 [[Category:Negri]]
 [[Category:Petrmic]]
 [[Category:Porcupine]]
-[[Category:Subgroup temperaments]]
+[[Category:Listen]]
-[[Category:Twentuning]]