29edo: Difference between revisions

Line 41:

! Degree

! 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]]

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

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

|-

| 0

Line 59:

| [[25/24]], [[33/32]], [[56/55]], [[81/80]]

| ^1, vm2

| up unison, downminor 2nd

| up unison, downminor 2nd

| ^D, vEb

| S1, sm2

Line 109:

| [[8/7]], [[7/6]], [[15/13]]

| ^M2, vm3

| upmajor 2nd, downminor 3rd

| upmajor 2nd, downminor 3rd

| ^E, vF

| SM2, sm3

Line 159:

| [[9/7]], [[13/10]]

| ^M3, v4

| upmajor 3rd down 4th

| upmajor 3rd down 4th

| ^F#, vG

| SM3, s4

Line 189:

| [[7/5]], [[18/13]]

| vA4, d5

| downaug 4th, dim 5th

| downaug 4th, dim 5th

| vG#, Ab

| kA4, d5

Line 199:

| [[10/7]], [[13/9]]

| A4, ^d5

| aug 4th, updim 5th

| aug 4th, updim 5th

| G#, ^Ab

| A4, Kd5

Line 229:

| [[14/9]], [[20/13]]

| ^5, vm6

| up 5th, downminor 6th

| up 5th, downminor 6th

| ^A, vBb

| S5, sm6

Line 279:

| [[7/4]], [[12/7]], [[26/15]]

| ^M6, vm7

| upmajor 6th, downminor 7th

| upmajor 6th, downminor 7th

| ^B, vC

| SM6, sm7

Line 329:

| [[48/25]], [[64/33]], [[55/28]], [[160/81]]

| ^M7, v8

| upmajor 7th, down 8ve

| upmajor 7th, down 8ve

| ^C#, vD

| SM7, s8

Line 350:

{| class="wikitable center-all"

|-

! ~~Quality~~

! quality

! [[~~Color~~ name]]

! [[color name]]

! ~~Monzo~~ format

! monzo format

! ~~Examples~~

! examples

|-

| downminor

Line 395:

| 9/7, 12/7

|}

All 29edo chords can be named using ups and downs. Alterations are always enclosed in parentheses, additions never are. An up or down immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13). Here are the zo, gu, yo and ru triads:

Line 402:

Line 401:

! [[Kite's color notation|color of the 3rd]]

! JI chord

! ~~Notes~~ as edosteps

! notes as edosteps

! ~~Notes~~ of C chord

! notes of C chord

! ~~Written~~ name

! written name

! ~~Spoken~~ name

! spoken name

|-

| zo

Line 476:

Line 475:

== Regular temperament properties ==

{~~{comma basis begin}}~~

{| class="wikitable center-4 center-5 center-6"

! rowspan="2" | [[Subgroup]]

! rowspan="2" | [[Comma list]]

! rowspan="2" | [[Mapping]]

! rowspan="2" | Optimal 8ve stretch (¢)

! colspan="2" | Tuning error

|-

! [[TE error|Absolute]] (¢)

! [[TE simple badness|Relative]] (%)

|-

| 2.3

Line 526:

Line 533:

| 2.42

| 5.85

~~{{comma basis end}~~}

|}

* 29et (29g val) has a lower relative error than any previous equal temperament in the [[23-limit]]. The next equal temperament doing better in this subgroup is [[46edo|46]].

* 29et does well in the no-17 [[19-limit]] and no-17 23-limit, being consistent to the no-17 [[23-odd-limit]]. However, [[15edo]] is lower in relative error in both these subgroups than 29.

Line 535:

Line 542:

{| class="commatable wikitable center-all left-3 right-4 left-6"

|-

! [[Harmonic limit|Prime limit]]

! [[Harmonic limit|Prime limit]]

! [[Ratio]]<ref>~~{{rd}}~~</ref>

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

! [[Monzo]]

! [[Cents]]

Line 736:

Line 743:

* [[List of 29et rank two temperaments by badness]]

{{rank-2 ~~begin}}~~

{| class="wikitable center-all left-5"

|+ Table of rank-2 temperaments by generator

|-

! Periods per 8ve

! Generator*

! Cents*

! Associated Ratio*

! Temperament

|-

| 1

Line 766:

Line 780:

| 248.3

| 15/13

| [[Immunity]] / [[immune]] [[Hemigari]]

| [[Immunity]] / [[immune]] [[Hemigari]]

|-

| 1

Line 802:

Line 816:

| 496.6

| 4/3

| [[Garibaldi]] / [[andromeda]] [[Leapday]]

| [[Garibaldi]] / [[andromeda]] [[Leapday]]

|-

| 1

Line 821:

Line 835:

| 3/2

| [[Edson]]

~~{{rank-2 end}~~}

|}

~~{{orf}}~~

<nowiki/>* [[Normal lists|octave-reduced form]], reduced to the first half-octave

=== The Tetradecatonic System ===

Line 933:

Line 947:

External image: https://fbcdn-sphotos-c-a.akamaihd.net/hphotos-ak-prn1/r90/550502_538613626155939_2005925977_n.jpg

External image: https://fbcdn-sphotos-c-a.akamaihd.net/hphotos-ak-prn1/r90/550502_538613626155939_2005925977_n.jpg

: WARNING: MediaWiki doesn't have very good support for external images.

: WARNING: MediaWiki doesn't have very good support for external images.

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

</div>

Line 941:

Line 955:

=== Modern renderings ===

; {{W|Johann Sebastian Bach}}

* [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)

; {{W|Nicolaus Bruhns}}

* [https://www.youtube.com/watch?v=me7dHmo3cVs ''Prelude in E Minor "The Great"''] ~~–~~ rendered by Claudi Meneghin (2023)

* [https://www.youtube.com/watch?v=me7dHmo3cVs ''Prelude in E Minor "The Great"''] – rendered by Claudi Meneghin (2023)

* [https://www.youtube.com/watch?v=-E-2mszlgWM ''Prelude in E Minor "The Little"''] ~~–~~ rendered by Claudi Meneghin (2024)

* [https://www.youtube.com/watch?v=-E-2mszlgWM ''Prelude in E Minor "The Little"''] – rendered by Claudi Meneghin (2024)

=== 21st century ===

Line 966:

Line 980:

; [[E8 Heterotic]]

* [https://youtu.be/_1snAPXErOQ?si=p2Pucp9aQDW6DMZE ''Glaukos Circuit''] (2019) ~~–~~ chiptune

* [https://youtu.be/_1snAPXErOQ?si=p2Pucp9aQDW6DMZE ''Glaukos Circuit''] (2019) – chiptune

; [[Pedro Laranjeira Finisterra]]

Line 974:

Line 988:

* "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://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://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

; [[Igliashon Jones]]

Line 1,001:

Line 1,015:

; [[Xotla]]

* "Nodal Plane" from ''Micro Biological'' (2019) ~~–~~ [https://open.spotify.com/track/1fuvjoPm5IP9MH8SrSMa7C Spotify] | [https://xotla.bandcamp.com/track/nodal-plane-22edo-29edo Bandcamp] | [https://youtu.be/3CPbU-W-sgg?si=cZGe_HhACJ24CzE2 YouTube] ~~–~~ in part, the other part being in [[22edo]]

* "Nodal Plane" from ''Micro Biological'' (2019) – [https://open.spotify.com/track/1fuvjoPm5IP9MH8SrSMa7C Spotify] | [https://xotla.bandcamp.com/track/nodal-plane-22edo-29edo Bandcamp] | [https://youtu.be/3CPbU-W-sgg?si=cZGe_HhACJ24CzE2 YouTube] – in part, the other part being in [[22edo]]

* "Microclusters" from ''Microtonal Allsorts'' (2023) ~~–~~ [https://open.spotify.com/track/1fhxkBvlA2VrqEV0n3KteT Spotify] | [https://xotla.bandcamp.com/track/microclusters-29edo Bandcamp] | [https://www.youtube.com/watch?v=F1SFjxVwLlg YouTube]

* "Microclusters" from ''Microtonal Allsorts'' (2023) – [https://open.spotify.com/track/1fhxkBvlA2VrqEV0n3KteT Spotify] | [https://xotla.bandcamp.com/track/microclusters-29edo Bandcamp] | [https://www.youtube.com/watch?v=F1SFjxVwLlg YouTube]

== See also ==

@@ Line 41: / Line 41: @@
 ! Degree
 ! 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]]
-! colspan="3" | [[SKULO interval names|SKULO interval names and notation]] {{nowrap|(K or S {{=}} 1)}}
+! colspan="3" |[[SKULO interval names|SKULO interval names and notation]] (K or S = 1)
 |-
 | 0
@@ Line 59: / Line 59: @@
 | [[25/24]], [[33/32]], [[56/55]], [[81/80]]
 | ^1, vm2
-| up unison,<br />downminor 2nd
+| up unison,<br>downminor 2nd
 | ^D, vEb
 | S1, sm2
@@ Line 109: / Line 109: @@
 | [[8/7]], [[7/6]], [[15/13]]
 | ^M2, vm3
-| upmajor 2nd,<br />downminor 3rd
+| upmajor 2nd,<br>downminor 3rd
 | ^E, vF
 | SM2, sm3
@@ Line 159: / Line 159: @@
 | [[9/7]], [[13/10]]
 | ^M3, v4
-| upmajor 3rd<br />down 4th
+| upmajor 3rd<br>down 4th
 | ^F#, vG
 | SM3, s4
@@ Line 189: / Line 189: @@
 | [[7/5]], [[18/13]]
 | vA4, d5
-| downaug 4th,<br />dim 5th
+| downaug 4th,<br>dim 5th
 | vG#, Ab
 | kA4, d5
@@ Line 199: / Line 199: @@
 | [[10/7]], [[13/9]]
 | A4, ^d5
-| aug 4th,<br />updim 5th
+| aug 4th,<br>updim 5th
 | G#, ^Ab
 | A4, Kd5
@@ Line 229: / Line 229: @@
 | [[14/9]], [[20/13]]
 | ^5, vm6
-| up 5th,<br />downminor 6th
+| up 5th,<br>downminor 6th
 | ^A, vBb
 | S5, sm6
@@ Line 279: / Line 279: @@
 | [[7/4]], [[12/7]], [[26/15]]
 | ^M6, vm7
-| upmajor 6th,<br />downminor 7th
+| upmajor 6th,<br>downminor 7th
 | ^B, vC
 | SM6, sm7
@@ Line 329: / Line 329: @@
 | [[48/25]], [[64/33]], [[55/28]], [[160/81]]
 | ^M7, v8
-| upmajor 7th,<br />down 8ve
+| upmajor 7th,<br>down 8ve
 | ^C#, vD
 | SM7, s8
@@ Line 350: / Line 350: @@
 {| class="wikitable center-all"
 |-
-! Quality
+! quality
-! [[Color name]]
+! [[color name]]
-! Monzo format
+! monzo format
-! Examples
+! examples
 |-
 | downminor
@@ Line 395: / Line 395: @@
 | 9/7, 12/7
 |}
 All 29edo chords can be named using ups and downs. Alterations are always enclosed in parentheses, additions never are. An up or down immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13). Here are the zo, gu, yo and ru triads:
@@ Line 402: / Line 401: @@
 ! [[Kite's color notation|color of the 3rd]]
 ! JI chord
-! Notes as edosteps
+! notes as edosteps
-! Notes of C chord
+! notes of C chord
-! Written name
+! written name
-! Spoken name
+! spoken name
 |-
 | zo
@@ Line 476: / Line 475: @@
 == Regular temperament properties ==
-{{comma basis begin}}
+{| class="wikitable center-4 center-5 center-6"
+! rowspan="2" | [[Subgroup]]
+! rowspan="2" | [[Comma list]]
+! rowspan="2" | [[Mapping]]
+! rowspan="2" | Optimal<br>8ve stretch (¢)
+! colspan="2" | Tuning error
+|-
+! [[TE error|Absolute]] (¢)
+! [[TE simple badness|Relative]] (%)
 |-
 | 2.3
@@ Line 526: / Line 533: @@
 | 2.42
 | 5.85
-{{comma basis end}}
+|}
 * 29et (29g val) has a lower relative error than any previous equal temperament in the [[23-limit]]. The next equal temperament doing better in this subgroup is [[46edo|46]].
 * 29et does well in the no-17 [[19-limit]] and no-17 23-limit, being consistent to the no-17 [[23-odd-limit]]. However, [[15edo]] is lower in relative error in both these subgroups than 29.
@@ Line 535: / Line 542: @@
 {| class="commatable wikitable center-all left-3 right-4 left-6"
 |-
-! [[Harmonic limit|Prime<br />limit]]
+! [[Harmonic limit|Prime<br>limit]]
-! [[Ratio]]<ref>{{rd}}</ref>
+! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
 ! [[Monzo]]
 ! [[Cents]]
@@ Line 736: / Line 743: @@
 * [[List of 29et rank two temperaments by badness]]
-{{rank-2 begin}}
+{| class="wikitable center-all left-5"
+|+ Table of rank-2 temperaments by generator
+|-
+! Periods<br>per 8ve
+! Generator*
+! Cents*
+! Associated Ratio*
+! Temperament
 |-
 | 1
@@ Line 766: / Line 780: @@
 | 248.3
 | 15/13
-| [[Immunity]] / [[immune]]<br />[[Hemigari]]
+| [[Immunity]] / [[immune]]<br>[[Hemigari]]
 |-
 | 1
@@ Line 802: / Line 816: @@
 | 496.6
 | 4/3
-| [[Garibaldi]] / [[andromeda]]<br />[[Leapday]]
+| [[Garibaldi]] / [[andromeda]]<br>[[Leapday]]
 |-
 | 1
@@ Line 821: / Line 835: @@
 | 3/2
 | [[Edson]]
-{{rank-2 end}}
+|}
-{{orf}}
+<nowiki/>* [[Normal lists|octave-reduced form]], reduced to the first half-octave
 === The Tetradecatonic System ===
@@ Line 933: / Line 947: @@
 <div class="external-image-warning" style="background-color:#f8f9fa; border: 1px solid #eaecf0; padding-left: 0.5em; padding-right:0.5em; display:inline-block">
-External image: https://fbcdn-sphotos-c-a.akamaihd.net/hphotos-ak-prn1/r90/550502_538613626155939_2005925977_n.jpg<br />
+External image: https://fbcdn-sphotos-c-a.akamaihd.net/hphotos-ak-prn1/r90/550502_538613626155939_2005925977_n.jpg<br>
-: <small><b>WARNING</b>: MediaWiki doesn't have very good support for external images.</small><br />
+: <small><b>WARNING</b>: MediaWiki doesn't have very good support for external images.</small><br>
 : <small>Furthermore, since external images can break, we recommend that you replace the above with a local copy of the image.</small>
 </div>
@@ Line 941: / Line 955: @@
 === Modern renderings ===
 ; {{W|Johann Sebastian Bach}}
-* [https://www.youtube.com/watch?v=uGOK7WtVtlM "Contrapunctus 4" from ''The Art of Fugue'', BWV 1080] (1742–1749) &ndash; 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) &ndash; 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)
 ; {{W|Nicolaus Bruhns}}
-* [https://www.youtube.com/watch?v=me7dHmo3cVs ''Prelude in E Minor "The Great"''] &ndash; rendered by Claudi Meneghin (2023)
+* [https://www.youtube.com/watch?v=me7dHmo3cVs ''Prelude in E Minor "The Great"''] – rendered by Claudi Meneghin (2023)
-* [https://www.youtube.com/watch?v=-E-2mszlgWM ''Prelude in E Minor "The Little"''] &ndash; rendered by Claudi Meneghin (2024)
+* [https://www.youtube.com/watch?v=-E-2mszlgWM ''Prelude in E Minor "The Little"''] – rendered by Claudi Meneghin (2024)
 === 21st century ===
@@ Line 966: / Line 980: @@
 ; [[E8 Heterotic]]
-* [https://youtu.be/_1snAPXErOQ?si=p2Pucp9aQDW6DMZE ''Glaukos Circuit''] (2019) &ndash; chiptune
+* [https://youtu.be/_1snAPXErOQ?si=p2Pucp9aQDW6DMZE ''Glaukos Circuit''] (2019) – chiptune
 ; [[Pedro Laranjeira Finisterra]]
@@ Line 974: / Line 988: @@
 * "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" &ndash; [https://francium223.bandcamp.com/track/all-29 Bandcamp] | [https://www.youtube.com/watch?v=C-FFLXHSO_k YouTube]
+** "All 29" – [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" &ndash; [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://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
 ; [[Igliashon Jones]]
@@ Line 1,001: / Line 1,015: @@
 ; [[Xotla]]
-* "Nodal Plane" from ''Micro Biological'' (2019) &ndash; [https://open.spotify.com/track/1fuvjoPm5IP9MH8SrSMa7C Spotify] | [https://xotla.bandcamp.com/track/nodal-plane-22edo-29edo Bandcamp] | [https://youtu.be/3CPbU-W-sgg?si=cZGe_HhACJ24CzE2 YouTube] &ndash; in part, the other part being in [[22edo]]
+* "Nodal Plane" from ''Micro Biological'' (2019) – [https://open.spotify.com/track/1fuvjoPm5IP9MH8SrSMa7C Spotify] | [https://xotla.bandcamp.com/track/nodal-plane-22edo-29edo Bandcamp] | [https://youtu.be/3CPbU-W-sgg?si=cZGe_HhACJ24CzE2 YouTube] – in part, the other part being in [[22edo]]
-* "Microclusters" from ''Microtonal Allsorts'' (2023) &ndash; [https://open.spotify.com/track/1fhxkBvlA2VrqEV0n3KteT Spotify] | [https://xotla.bandcamp.com/track/microclusters-29edo Bandcamp] | [https://www.youtube.com/watch?v=F1SFjxVwLlg YouTube]
+* "Microclusters" from ''Microtonal Allsorts'' (2023) – [https://open.spotify.com/track/1fhxkBvlA2VrqEV0n3KteT Spotify] | [https://xotla.bandcamp.com/track/microclusters-29edo Bandcamp] | [https://www.youtube.com/watch?v=F1SFjxVwLlg YouTube]
 == See also ==