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}}
}}
{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|29}}
{{ED intro}}


== Theory ==
== Theory ==
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! Cents
! Cents
! Approx. Ratios of the [[13-limit]]
! 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)
! colspan="3" |[[SKULO interval names|SKULO interval names and notation]] (K or S = 1)
|-
|-
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| downminor
| downminor
| zo
| zo
| {a, b, 0, 1}
| [a, b, 0, 1>
| 7/6, 7/4
| 7/6, 7/4
|-
|-
| minor
| minor
| fourthward wa
| fourthward wa
| {a, b}, b &lt; -1
| [a, b>, b &lt; -1
| 32/27, 16/9
| 32/27, 16/9
|-
|-
| upminor
| upminor
| gu
| gu
| {a, b, -1}
| [a, b, -1>
| 6/5, 9/5
| 6/5, 9/5
|-
|-
| "
| "
| ilo
| ilo
| {a, b, 0, 0, 1}
| [a, b, 0, 0, 1>
| 11/9, 11/6
| 11/9, 11/6
|-
|-
| downmajor
| downmajor
| lu
| lu
| {a, b, 0, 0, -1}
| [a, b, 0, 0, -1>
| 12/11, 18/11
| 12/11, 18/11
|-
|-
| "
| "
| yo
| yo
| {a, b, 1}
| [a, b, 1>
| 5/4, 5/3
| 5/4, 5/3
|-
|-
| major
| major
| fifthward wa
| fifthward wa
| {a, b}, b &gt; 1
| [a, b>, b &gt; 1
| 9/8, 27/16
| 9/8, 27/16
|-
|-
| upmajor
| upmajor
| ru
| ru
| {a, b, 0, -1}
| [a, b, 0, -1>
| 9/7, 12/7
| 9/7, 12/7
|}
|}
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| C upmajor or C up
| 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 ==
== Notation ==
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* C𝄪 = F𝄫
* 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}}
{{Sharpness-sharp3}}


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default [[File:29-EDO_Revo_Sagittal.svg]]
default [[File:29-EDO_Revo_Sagittal.svg]]
</imagemap>
</imagemap>
=== MisterShafXen's notation ===
[[MisterShafXen’s 29edo notation]]


== Approximation to JI ==
== Approximation to JI ==
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=== Interval mappings ===
=== Interval mappings ===
{{Q-odd-limit intervals|29}}
{{Q-odd-limit intervals|29}}
=== Zeta peak index ===
{| class="wikitable center-all"
! colspan="3" | Tuning
! colspan="3" | Strength
! colspan="2" | Closest edo
! colspan="2" | Integer limit
|-
! ZPI
! Steps per octave
! Step size (cents)
! Height
! Integral
! Gap
! Edo
! Octave (cents)
! Consistent
! Distinct
|-
| [[116zpi]]
| 28.9399661541990
| 41.4651487014917
| 5.566209
| 1.000619
| 14.904418
| 29edo
| 1202.48931234326
| 8
| 7
|}


== Regular temperament properties ==
== Regular temperament properties ==
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| Minor minthma
| Minor minthma
|}
|}
<references />


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
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* [[Leapfrog]] diatonic [[5L 2s]] 5552552 (17\29, 1\1)
* [[Leapfrog]] diatonic [[5L 2s]] 5552552 (17\29, 1\1)
* [[Leapfrog]] chromatic [[5L 7s]] 3232323223232322 (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]] [[1L 6s]] 4444445 (4\29, 1\1)
* [[Porcupine]] [[7L 1s]] 44444441 (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]] [[1L 8s]] 333333335 (3\29, 1\1)
* [[Negri]] [[9L 1s]] 3333333332 (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]] [[4L 1s]] 56666 (6\29, 1\1)
* [[Semaphore]] [[5L 4s]] 551515151 (6\29, 1\1)  
* [[Semaphore]] [[5L 4s]] 551515151 (6\29, 1\1)  
* [[Semaphore]] [[5L 9s]] 41411411411411 (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]] [[1L 13s]] 22222222222223 (2\29, 1\1)
* [[Nautilus]] [[14L 1s]] 222222222222221 (2\29, 1\1)
* [[Nautilus]] [[14L 1s]] 222222222222221 (2\29, 1\1)
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: <small>Furthermore, since external images can break, we recommend that you replace the above with a local copy of the image.</small>
: <small>Furthermore, since external images can break, we recommend that you replace the above with a local copy of the image.</small>
</div>
</div>
 
* [[Lumatone mapping for 29edo]]
== Music ==
== Music ==
=== Modern renderings ===
=== 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=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=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}}
; {{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=HGQ2b6v0TWE ''Glass Animals - Life Itself''] (2023)
* [https://www.youtube.com/watch?v=ktk0VWbUbDg ''microtonal improvisation in 29edo''] (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]]
; [[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]
* "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)  
* 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]]
; [[Igliashon Jones]]
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== See also ==
== 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: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:Negri]]
[[Category:Petrmic]]
[[Category:Petrmic]]
[[Category:Porcupine]]
[[Category:Porcupine]]
[[Category:Subgroup temperaments]]
[[Category:Listen]]
[[Category:Twentuning]]
Retrieved from "https://en.xen.wiki/w/29edo"