39edo: Difference between revisions

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A particular anecdote with this system was made in the ''Teliochordon'', in 1788 by {{w|Charles Clagget}} (Ireland, 1740?–1820), a little extract [http://ml.oxfordjournals.org/content/76/2/291.extract.jpg here].

As a [[superpyth]] system, 39edo is intermediate between [[17edo]] and [[22edo]] {{nowrap|(39 {{=}} 17 + 22)}}. The specific 7-limit variant supported by 39et is [[quasisuper]]. While 17edo is superb for melody (as documented by [[George Secor]]), it does not approximate the 5th harmonic at all and only poorly approximates the 7th. 22edo is much better for 5-limit and 7-limit harmony but is less effective for melody because the [[diatonic semitone]] is [[quartertone]]-sized, which results in a very strange-sounding [[5L 2s|diatonic scale]]. 39edo offers a compromise, since it still supports good 5- and 7-limit harmonies (though less close than 22edo), while at the same time having a diatonic semitone of 61.5 cents, as the ideal diatonic semitone for melody is somewhere in between 60 and 80 cents, i.e. a third tone, by Secor's estimates.

As a [[superpyth]] system, 39edo is intermediate between [[17edo]] and [[22edo]] {{nowrap|(39 {{=}} 17 + 22)}}; its fifth thus falls in the "shrub region" where the diatonic thirds are between standard neogothic thirds and septimal thirds. The specific 7-limit variant supported by 39et is [[quasisuper]]. While 17edo is superb for melody (as documented by [[George Secor]]), it does not approximate the 5th harmonic at all and only poorly approximates the 7th. 22edo is much better for 5-limit and 7-limit harmony but is less effective for melody because the [[diatonic semitone]] is [[quartertone]]-sized, which results in a very strange-sounding [[5L 2s|diatonic scale]]. 39edo offers a compromise, since it still supports good 5- and 7-limit harmonies (though less close than 22edo), while at the same time having a diatonic semitone of 61.5 cents, as the ideal diatonic semitone for melody is somewhere in between 60 and 80 cents, i.e. a third tone, by Secor's estimates.

Alternatively, if we take 22\39 as a fifth, 39edo can be used as a tuning of [[mavila]], and from that point of view it seems to have attracted the attention of the [[Armodue]] school, an Italian group that use the scheme of [[7L 2s|superdiatonic]] LLLsLLLLs like a base scale for notation and theory, suited in [[16edo]], and allied systems: [[25edo]] [1/3-tone 3;2]; [[41edo]] [1/5-tone 5;3]; and [[57edo]] [1/7-tone 7;4]. The [[hornbostel]] temperament is included too with: [[23edo]] [1/3-tone 3;1]; 39edo [1/5-tone 5;2] & [[62edo]] [1/8-tone 8;3]. The mavila fifth in 39edo like all mavila fifths is very, very flat, in this case, 25{{c}} flat.

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=== Subsets and supersets ===

Since 39 factors into {{nowrap| 3 × 13 }}, 39edo contains [[3edo]] and [[13edo]] as subsets.

Since 39 factors into {{nowrap| 3 × 13 }}, 39edo contains [[3edo]] and [[13edo]] as subsets. Multiplying 39edo by 2 yields [[78edo]], which corrects several harmonics.

== Intervals ==

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| 2/1

|}

~~== Approximation to JI ==~~

~~=== Zeta peak index ===~~

~~{{ZPI~~

~~| zpi = 173~~

~~| steps = 39.1237487937926~~

~~| step size = 30.6719073963176~~

~~| tempered height = 5.593908~~

~~| pure height = 0.227566~~

~~| integral = 0.926356~~

~~| gap = 14.714802~~

~~| edo = 39edo~~

~~| octave = 1196.20438845639~~

~~| consistent = 7~~

~~| distinct = 7~~

}}

== Regular temperament properties ==

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=== Other ===

39edo offers approximations of [[pelog]] and [[mavila]] using the flat fifth as a generator.

39edo offers approximations of [[pelog]] and [[mavila]] using the flat fifth as a generator. Pelog can also be approximated as 4 5 13 4 13.

It also offers ''many'' possible [[pentatonic]] scales, including the [[2L~~ ~~3s]] mos (which is 9 7 7 9 7). [[Slendro]] can be approximated using ~~this~~ scale or using something like the [[quasi-equal]] 8 8 8 8 7. ~~A more~~ expressive [[pentatonic]] scale is the oneirotonic subset 9 6 9 9 6. Many Asian{{clarify|which ones specifically}} and [[African music|African]] {{clarify|which ones specifically}} musical styles can thus be accommodated.

It also offers ''many'' possible [[pentatonic]] scales, including the [[2L 3s]] mos (which is 9 7 7 9 7). [[Slendro]] can be approximated using that scale or using something like the [[quasi-equal]] 8 8 8 8 7 or 8 8 7 8 8.

One expressive [[pentatonic]] scale is the oneirotonic subset 9 6 9 9 6.

Many Asian{{clarify|which ones specifically}} and [[African music|African]] {{clarify|which ones specifically}} musical styles can thus be accommodated.

== Instruments ==

=== Lumatone mapping ===

See [[Lumatone mapping for 39edo]]

=== Skip fretting ===

'''Skip fretting system 39 2 5''' is a [[skip-fretting]] system for [[39edo]]. All examples on this page are for 7-string [[Guitar|guitar.]]

; Prime harmonics

1/1: string 2 open

2/1: string 5 fret 12 and string 7 fret 7

3/2: string 3 fret 9 and string 5 fret 4

5/4: string 1 fret 9 and string 3 fret 4

7/4: string 5 fret 8 and string 7 fret 3

11/8: string 2 fret 9 and string 4 fret 4

=== Prototypes ===

[[File:TECLADO_39-EDD.PNG|alt=TECLADO 39-EDD.PNG|800x467px|TECLADO 39-EDD.PNG]]

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''39edo fretboard visualization''

==~~= Lumatone mapping =~~==

== Music ==

~~See~~ [[~~Lumatone mapping for~~ 39edo]]

; [[Bryan Deister]]

* [https://www.youtube.com/shorts/oeFI957W-xg ''39edo''] (2023)

* [https://www.youtube.com/watch?v=XLRaG_pBN7k ''39edo jam''] (2025)

* [https://www.youtube.com/shorts/4y11CWLIHNA ''Sinner's Finale - Genshin Impact (microtonal cover in 39edo)''] (2025)

~~== Music ==~~

; [[Randy Wells]]

* [https://www.youtube.com/watch?v=Q9wQV1J5eLE ''Romance On Other Planets''] (2021)

[[Category:Listen]]

@@ Line 7: / Line 7: @@
 A particular anecdote with this system was made in the ''Teliochordon'', in 1788 by {{w|Charles Clagget}} (Ireland, 1740?–1820), a little extract [http://ml.oxfordjournals.org/content/76/2/291.extract.jpg here].
-As a [[superpyth]] system, 39edo is intermediate between [[17edo]] and [[22edo]] {{nowrap|(39 {{=}} 17 + 22)}}. The specific 7-limit variant supported by 39et is [[quasisuper]]. While 17edo is superb for melody (as documented by [[George Secor]]), it does not approximate the 5th harmonic at all and only poorly approximates the 7th. 22edo is much better for 5-limit and 7-limit harmony but is less effective for melody because the [[diatonic semitone]] is [[quartertone]]-sized, which results in a very strange-sounding [[5L 2s|diatonic scale]]. 39edo offers a compromise, since it still supports good 5- and 7-limit harmonies (though less close than 22edo), while at the same time having a diatonic semitone of 61.5 cents, as the ideal diatonic semitone for melody is somewhere in between 60 and 80 cents, i.e. a third tone, by Secor's estimates.
+As a [[superpyth]] system, 39edo is intermediate between [[17edo]] and [[22edo]] {{nowrap|(39 {{=}} 17 + 22)}}; its fifth thus falls in the "shrub region" where the diatonic thirds are between standard neogothic thirds and septimal thirds. The specific 7-limit variant supported by 39et is [[quasisuper]]. While 17edo is superb for melody (as documented by [[George Secor]]), it does not approximate the 5th harmonic at all and only poorly approximates the 7th. 22edo is much better for 5-limit and 7-limit harmony but is less effective for melody because the [[diatonic semitone]] is [[quartertone]]-sized, which results in a very strange-sounding [[5L 2s|diatonic scale]]. 39edo offers a compromise, since it still supports good 5- and 7-limit harmonies (though less close than 22edo), while at the same time having a diatonic semitone of 61.5 cents, as the ideal diatonic semitone for melody is somewhere in between 60 and 80 cents, i.e. a third tone, by Secor's estimates.
 Alternatively, if we take 22\39 as a fifth, 39edo can be used as a tuning of [[mavila]], and from that point of view it seems to have attracted the attention of the [[Armodue]] school, an Italian group that use the scheme of [[7L 2s|superdiatonic]] LLLsLLLLs like a base scale for notation and theory, suited in [[16edo]], and allied systems: [[25edo]] [1/3-tone 3;2]; [[41edo]] [1/5-tone 5;3]; and [[57edo]] [1/7-tone 7;4]. The [[hornbostel]] temperament is included too with: [[23edo]] [1/3-tone 3;1]; 39edo [1/5-tone 5;2] &amp; [[62edo]] [1/8-tone 8;3]. The mavila fifth in 39edo like all mavila fifths is very, very flat, in this case, 25{{c}} flat.
@@ Line 22: / Line 22: @@
 === Subsets and supersets ===
-Since 39 factors into {{nowrap| 3 × 13 }}, 39edo contains [[3edo]] and [[13edo]] as subsets.
+Since 39 factors into {{nowrap| 3 × 13 }}, 39edo contains [[3edo]] and [[13edo]] as subsets. Multiplying 39edo by 2 yields [[78edo]], which corrects several harmonics.
 == Intervals ==
@@ Line 722: / Line 722: @@
 | 2/1
 |}
-== Approximation to JI ==
-=== Zeta peak index ===
-{{ZPI
-| zpi = 173
-| steps = 39.1237487937926
-| step size = 30.6719073963176
-| tempered height = 5.593908
-| pure height = 0.227566
-| integral = 0.926356
-| gap = 14.714802
-| edo = 39edo
-| octave = 1196.20438845639
-| consistent = 7
-| distinct = 7
-}}
 == Regular temperament properties ==
@@ Line 939: / Line 923: @@
 === Other ===
-edo offers approximations of [[pelog]] and [[mavila]] using the flat fifth as a generator.
+edo offers approximations of [[pelog]] and [[mavila]] using the flat fifth as a generator. Pelog can also be approximated as 4 5 13 4 13.
-It also offers ''many'' possible [[pentatonic]] scales, including the [[2L&nbsp;3s]] mos (which is 9 7 7 9 7). [[Slendro]] can be approximated using this scale or using something like the [[quasi-equal]] 8 8 8 8 7. A more expressive [[pentatonic]] scale is the oneirotonic subset 9 6 9 9 6. Many Asian{{clarify|which ones specifically}} and [[African music|African]] {{clarify|which ones specifically}} musical styles can thus be accommodated.
+It also offers ''many'' possible [[pentatonic]] scales, including the [[2L 3s]] mos (which is 9 7 7 9 7). [[Slendro]] can be approximated using that scale or using something like the [[quasi-equal]] 8 8 8 8 7 or 8 8 7 8 8.
+One expressive [[pentatonic]] scale is the oneirotonic subset 9 6 9 9 6.
+Many Asian{{clarify|which ones specifically}} and [[African music|African]] {{clarify|which ones specifically}} musical styles can thus be accommodated.
 == Instruments ==
+=== Lumatone mapping ===
+See [[Lumatone mapping for 39edo]]
+=== Skip fretting ===
+'''Skip fretting system 39 2 5''' is a [[skip-fretting]] system for [[39edo]]. All examples on this page are for 7-string [[Guitar|guitar.]]
+; Prime harmonics
+/1: string 2 open
+/1: string 5 fret 12 and string 7 fret 7
+/2: string 3 fret 9 and string 5 fret 4
+/4: string 1 fret 9 and string 3 fret 4
+/4: string 5 fret 8 and string 7 fret 3
+/8: string 2 fret 9 and string 4 fret 4
 === Prototypes ===
 [[File:TECLADO_39-EDD.PNG|alt=TECLADO 39-EDD.PNG|800x467px|TECLADO 39-EDD.PNG]]
@@ Line 953: / Line 961: @@
 ''39edo fretboard visualization''
-=== Lumatone mapping ===
+== Music ==
-See [[Lumatone mapping for 39edo]]
+; [[Bryan Deister]]
+* [https://www.youtube.com/shorts/oeFI957W-xg ''39edo''] (2023)
+* [https://www.youtube.com/watch?v=XLRaG_pBN7k ''39edo jam''] (2025)
+* [https://www.youtube.com/shorts/4y11CWLIHNA ''Sinner's Finale - Genshin Impact (microtonal cover in 39edo)''] (2025)
-== Music ==
 ; [[Randy Wells]]
 * [https://www.youtube.com/watch?v=Q9wQV1J5eLE ''Romance On Other Planets''] (2021)
 [[Category:Listen]]