39edo: Difference between revisions

Line 1:

=~~39 tone equal temperament~~=

==Theory==

'''39-EDO, 39-ED2''' or '''39-tET''' divides the Octave (Ditave 2/1) in 39 equal parts of 30.76923 Cents each one. If we take 22\39 as a fifth, can be used in Mavila Temperament, and from that point of view seems to have attracted the attention of the Armodue school, an Italian group that use the scheme of [[7L 2s|Superdiatonic]] LLLsLLLLs like a basical scale for notation and theory, suited in [[16edo|16-ED2]], and allied systems: [[25edo|25-ED2]] [1/3-tone 3;2]; [[41edo|41-ED2]] [1/5-tone 5;3]; and [[57edo|57]] ED2 [1/7-tone 7;4]. '''Hornbostel Temperaments''' is included too with: [[23edo|23-ED2]] [1/3-tone 3;1]; 39-ED2 [1/5-tone 5;2] & [[62edo|62-ED2]] [1/8-tone 8;3]. [[223edo|223-ED2]], the best accuracy for Hornbostel temperament fits very good with Armodue like 1/29-tone 29;10 version. Note that [[101edo|101]], [[131edo|131]], [[177edo|177]] & [[200edo|200]] ED2s are tempered systems that [http://www.h-pi.com/eop-ogolevets.html Alexei Ogolevets] (Ukraine, 1891 - 1967) was proposing in his List of Temperaments, in which the Armodue system fits very well in all these.

Line 11:

39edo offers not one, but many, possible ways of extending tonality beyond the diatonic scale, even if it doesn't do as good of a job at approximating JI as some other systems do. Because it can also approximate mavila as well as "anti-mavila" (oneirotonic), the latter of which it inherits from [[13edo]], this makes 39edo an extremely versatile temperament usable in a wide range of situations (both harmonic and inharmonic).

==~~'''39-EDO~~ Intervals~~'''~~==

==Intervals==

{| class="wikitable"

Line 22:

{| class="wikitable"

|-

! | '''~~Degrees~~'''

! | '''Degree'''

! | '''Cents ~~size~~'''

! | '''Cents'''

! | '''Armodue note'''

! | '''Armodue'''

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

'''note'''

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

~~[[Ups and Downs Notation|~~notation]]

! | '''[[Nearest just interval|Nearest Just]]'''

'''[[Nearest just interval|I]]nterval'''

! | '''Cents ~~value~~'''

! | '''Cents'''

! | '''Error'''

! | 11-limit Ratio Assuming

Line 52:

Line 51:

| | 1‡ (9#)

| style="text-align:center;" | ^1

| style="text-align:center;" | up unison

| style="text-align:center;" | up unison,

| style="text-align:center;" | D^

downminor 2nd

| style="text-align:center;" | ^D,

vEb

| | 57/56

| | 30.6421

Line 75:

Line 76:

| style="text-align:center;" | ^m2

| style="text-align:center;" | upminor 2nd

| style="text-align:center;" | Eb^

| style="text-align:center;" | ^Eb

| | 39/37

| | 91.1386

Line 86:

Line 87:

| style="text-align:center;" | v~2

| style="text-align:center;" | downmid 2nd

| style="text-align:center;" | Eb^^

| style="text-align:center;" | ^^Eb

| | 44/41

| | 122.2555

Line 97:

Line 98:

| style="text-align:center;" | ^~2

| style="text-align:center;" | upmid 2nd

| style="text-align:center;" | ~~Evv~~

| style="text-align:center;" | vvE

| | 35/32

| | 155.1396

Line 108:

Line 109:

| style="text-align:center;" | vM2

| style="text-align:center;" | downmajor 2nd

| style="text-align:center;" | Ev

| style="text-align:center;" | vE

| | 10/9

| | 182.4037

Line 134:

Line 135:

downminor 3rd

| style="text-align:center;" | E^,

| style="text-align:center;" | ^E,

vF

Fv

| | 15/13

| | 247.7411

Line 158:

| style="text-align:center;" | ^m3

| style="text-align:center;" | upminor 3rd

| style="text-align:center;" | F^

| style="text-align:center;" | ^F

| | 43/36

| | 307.6077

Line 169:

| style="text-align:center;" | v~3

| style="text-align:center;" | downmid 3rd

| style="text-align:center;" | F^^

| style="text-align:center;" | ^^F

| | 17/14

| | 336.1295

Line 180:

| style="text-align:center;" | ^~3

| style="text-align:center;" | upmid 3rd

| style="text-align:center;" | F#vv

| style="text-align:center;" | vvF#

| | 26/21

| | 369.7468

Line 191:

| style="text-align:center;" | vM3

| style="text-align:center;" | downmajor 3rd

| style="text-align:center;" | F#v

| style="text-align:center;" | vF#

| | 34/27

| | 399.0904

Line 213:

| style="text-align:center;" | v4

| style="text-align:center;" | down 4th

| style="text-align:center;" | Gv

| style="text-align:center;" | vG

| | 30/23

| | 459.9944

Line 235:

| style="text-align:center;" | ^4

| style="text-align:center;" | up 4th

| style="text-align:center;" | G^

| style="text-align:center;" | ^G

| | 23/17

| | 523.3189

Line 244:

| | 553.8462

| | 5‡ (4#)

| style="text-align:center;" | ^^4

| style="text-align:center;" | v~4

| style="text-align:center;" | ~~double-up~~ 4th

| style="text-align:center;" | downmid 4th

| style="text-align:center;" | G^^

| style="text-align:center;" | ^^G

| | 11/8

| | 551.3179

Line 255:

| | 584.6154

| | 6b

| style="text-align:center;" | ~~vvA4~~,

| style="text-align:center;" | ^~4,

^d5

| style="text-align:center;" | ~~double-down aug~~ 4th,

| style="text-align:center;" | upmid 4th,

updim 5th

| style="text-align:center;" | G#vv,

| style="text-align:center;" | vvG#,

Ab^

^Ab

| | 7/5

| | 582.5122

Line 273:

| style="text-align:center;" | vA4,

~~^^d5~~

v~5

| style="text-align:center;" | downaug 4th,

~~double-up dim~~ 5th

downmid 5th

| style="text-align:center;" | G#v,

| style="text-align:center;" | vG#,

Ab^^

^^Ab

| | 10/7

| | 617.4878

Line 288:

| | 646.1538

| | 6v

| style="text-align:center;" | ~~vv5~~

| style="text-align:center;" | ^~5

| style="text-align:center;" | ~~double-down~~ 5th

| style="text-align:center;" | upmid 5th

| style="text-align:center;" | ~~Avv~~

| style="text-align:center;" | vvA

| | 16/11

| | 648.6821

Line 301:

| style="text-align:center;" | v5

| style="text-align:center;" | down 5th

| style="text-align:center;" | Av

| style="text-align:center;" | vA

| | 34/23

| | 676.6811

Line 345:

| style="text-align:center;" | ^m6

| style="text-align:center;" | upminor 6th

| style="text-align:center;" | Bb^

| style="text-align:center;" | ^Bb

| | 27/17

| | 800.9096

Line 356:

| style="text-align:center;" | v~6

| style="text-align:center;" | downmid 6th

| style="text-align:center;" | Bb^^

| style="text-align:center;" | ^^Bb

| | 21/13

| | 830.2532

Line 367:

| style="text-align:center;" | ^~6

| style="text-align:center;" | upmid 6th

| style="text-align:center;" | ~~Bvv~~

| style="text-align:center;" | vvB

| | 28/17

| | 863.8705

Line 378:

| style="text-align:center;" | vM6

| style="text-align:center;" | downmajor 6th

| style="text-align:center;" | Bv

| style="text-align:center;" | vB

| | 72/43

| | 892.3923

Line 404:

downminor 7th

| style="text-align:center;" | B^,

| style="text-align:center;" | ^B,

Cv

vC

| | 26/15

| | 952.2589

Line 428:

| style="text-align:center;" | ^m7

| style="text-align:center;" | upminor 7th

| style="text-align:center;" | C^

| style="text-align:center;" | ^C

| | 9/5

| | 1017.5963

Line 439:

| style="text-align:center;" | v~7

| style="text-align:center;" | downmid 7th

| style="text-align:center;" | C^^

| style="text-align:center;" | ^^C

| | 64/35

| | 1044.8604

Line 450:

| style="text-align:center;" | ^~7

| style="text-align:center;" | upmid 7th

| style="text-align:center;" | C#vv

| style="text-align:center;" | vvC#

| | 41/22

| | 1077.7445

Line 461:

| style="text-align:center;" | vM7

| style="text-align:center;" | downmajor 7th

| style="text-align:center;" | C#v

| style="text-align:center;" | vC#

| | 74/39

| | 1108.8614

Line 483:

| style="text-align:center;" | v8

| style="text-align:center;" | down-8ve

| style="text-align:center;" | Dv

| style="text-align:center;" | vD

| | 112/57

| | 1169.3579

Line 489:

| |

|-

| | 39'''··'''~~(or 0)~~

| | 39'''··'''

| | 1200

| | 1

Line 500:

| |

|}

Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and Downs Notation#Chord ~~names in other EDOs~~|Ups and Downs Notation - Chord ~~names in other EDOs]].~~

Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and Downs Notation#Chords and Chord Progressions|Ups and Downs Notation - Chords and Chord Progressions]].

~~==Instruments (prototypes):==~~

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

~~''An illustrative image of a 39-ED2 keyboard''~~

~~{| class="wikitable"~~

|-

|-

~~| | 39-EDD fretboard visualization~~

|}

==~~~~39 tone equal [[modes~~]]~~==

==39 tone equal modes==

14 14 11 - [[MOSScales|MOS]] of type [[2L 1s]]

Line 583:

Line 570:

2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 - [[MOSScales|MOS]] of type [[8L 23s]]

==~~~~39edo and world music~~:~~==

==39edo and world music==

39edo is a good candidate for a "universal tuning" in that it offers reasonable approximations of many different world music traditions; it is one of the simplest edos that can make this claim. Because of this, composers wishing to combine multiple world music traditions (for example, gamelan with maqam singing) within one unified framework would find 39edo an interesting possibility.

Line 631:

Line 618:

[[Category:Todo:add definition]]

[[Category:Todo:unify precision]]

==Instruments (prototypes)==

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

''An illustrative image of a 39-ED2 keyboard''

{| class="wikitable"

|-

|-

| | 39-EDD fretboard visualization

|}

@@ Line 1: / Line 1: @@
-=<span style="color: #9900ab; font-family: 'Times New Roman',Times,serif; font-size: 113%;">39 tone equal temperament</span>=
+==Theory==
 '''39-EDO, 39-ED2''' or '''39-tET''' divides the Octave (Ditave 2/1) in 39 equal parts of 30.76923 Cents each one. If we take 22\39 as a fifth, can be used in Mavila Temperament, and from that point of view seems to have attracted the attention of the Armodue school, an Italian group that use the scheme of [[7L 2s|Superdiatonic]] LLLsLLLLs like a basical scale for notation and theory, suited in [[16edo|16-ED2]], and allied systems: [[25edo|25-ED2]] [1/3-tone 3;2]; [[41edo|41-ED2]] [1/5-tone 5;3]; and [[57edo|57]] ED2 [1/7-tone 7;4]. '''Hornbostel Temperaments''' is included too with: [[23edo|23-ED2]] [1/3-tone 3;1]; 39-ED2 [1/5-tone 5;2] &amp; [[62edo|62-ED2]] [1/8-tone 8;3]. [[223edo|223-ED2]], the best accuracy for Hornbostel temperament fits very good with Armodue like 1/29-tone 29;10 version. Note that [[101edo|101]], [[131edo|131]], [[177edo|177]] &amp; [[200edo|200]] ED2s are tempered systems that [http://www.h-pi.com/eop-ogolevets.html Alexei Ogolevets] (Ukraine, 1891 - 1967) was proposing in his List of Temperaments, in which the Armodue system fits very well in all these.
@@ Line 11: / Line 11: @@
 edo offers not one, but many, possible ways of extending tonality beyond the diatonic scale, even if it doesn't do as good of a job at approximating JI as some other systems do. Because it can also approximate mavila as well as "anti-mavila" (oneirotonic), the latter of which it inherits from [[13edo]], this makes 39edo an extremely versatile temperament usable in a wide range of situations (both harmonic and inharmonic).
-==<u>'''39-EDO Intervals'''</u>==
+==Intervals==
 {| class="wikitable"
@@ Line 22: / Line 22: @@
 {| class="wikitable"
 |-
-! | '''Degrees'''
+! | '''Degree'''
-! | '''Cents size'''
+! | '''Cents'''
-! | '''Armodue note'''
+! | '''Armodue'''
-! colspan="3" | [[Ups and Downs Notation|ups and]] [[Ups and Downs Notation|downs]]
+'''note'''
+! colspan="3" | [[Ups and Downs Notation|ups and downs notation]]
-[[Ups and Downs Notation|notation]]
 ! | '''[[Nearest just interval|Nearest Just]]'''
 '''[[Nearest just interval|I]]nterval'''
-! | '''Cents value'''
+! | '''Cents'''
 ! | '''Error'''
 ! | 11-limit Ratio Assuming
@@ Line 52: / Line 51: @@
 | | 1‡ (9#)
 | style="text-align:center;" | ^1
-| style="text-align:center;" | up unison
+| style="text-align:center;" | up unison,
-| style="text-align:center;" | D^
+downminor 2nd
+| style="text-align:center;" | ^D,
+vEb
 | | 57/56
 | | 30.6421
@@ Line 75: / Line 76: @@
 | style="text-align:center;" | ^m2
 | style="text-align:center;" | upminor 2nd
-| style="text-align:center;" | Eb^
+| style="text-align:center;" | ^Eb
 | | 39/37
 | | 91.1386
@@ Line 86: / Line 87: @@
 | style="text-align:center;" | v~2
 | style="text-align:center;" | downmid 2nd
-| style="text-align:center;" | Eb^^
+| style="text-align:center;" | ^^Eb
 | | 44/41
 | | 122.2555
@@ Line 97: / Line 98: @@
 | style="text-align:center;" | ^~2
 | style="text-align:center;" | upmid 2nd
-| style="text-align:center;" | Evv
+| style="text-align:center;" | vvE
 | | 35/32
 | | 155.1396
@@ Line 108: / Line 109: @@
 | style="text-align:center;" | vM2
 | style="text-align:center;" | downmajor 2nd
-| style="text-align:center;" | Ev
+| style="text-align:center;" | vE
 | | 10/9
 | | 182.4037
@@ Line 134: / Line 135: @@
 downminor 3rd
-| style="text-align:center;" | E^,
+| style="text-align:center;" | ^E,
+vF
-Fv
 | | 15/13
 | | 247.7411
@@ Line 158: / Line 158: @@
 | style="text-align:center;" | ^m3
 | style="text-align:center;" | upminor 3rd
-| style="text-align:center;" | F^
+| style="text-align:center;" | ^F
 | | 43/36
 | | 307.6077
@@ Line 169: / Line 169: @@
 | style="text-align:center;" | v~3
 | style="text-align:center;" | downmid 3rd
-| style="text-align:center;" | F^^
+| style="text-align:center;" | ^^F
 | | 17/14
 | | 336.1295
@@ Line 180: / Line 180: @@
 | style="text-align:center;" | ^~3
 | style="text-align:center;" | upmid 3rd
-| style="text-align:center;" | F#vv
+| style="text-align:center;" | vvF#
 | | 26/21
 | | 369.7468
@@ Line 191: / Line 191: @@
 | style="text-align:center;" | vM3
 | style="text-align:center;" | downmajor 3rd
-| style="text-align:center;" | F#v
+| style="text-align:center;" | vF#
 | | 34/27
 | | 399.0904
@@ Line 213: / Line 213: @@
 | style="text-align:center;" | v4
 | style="text-align:center;" | down 4th
-| style="text-align:center;" | Gv
+| style="text-align:center;" | vG
 | | 30/23
 | | 459.9944
@@ Line 235: / Line 235: @@
 | style="text-align:center;" | ^4
 | style="text-align:center;" | up 4th
-| style="text-align:center;" | G^
+| style="text-align:center;" | ^G
 | | 23/17
 | | 523.3189
@@ Line 244: / Line 244: @@
 | | 553.8462
 | | 5‡ (4#)
-| style="text-align:center;" | ^^4
+| style="text-align:center;" | v~4
-| style="text-align:center;" | double-up 4th
+| style="text-align:center;" | downmid 4th
-| style="text-align:center;" | G^^
+| style="text-align:center;" | ^^G
 | | 11/8
 | | 551.3179
@@ Line 255: / Line 255: @@
 | | 584.6154
 | | 6b
-| style="text-align:center;" | vvA4,
+| style="text-align:center;" | ^~4,
 ^d5
-| style="text-align:center;" | double-down aug 4th,
+| style="text-align:center;" | upmid 4th,
 updim 5th
-| style="text-align:center;" | G#vv,
+| style="text-align:center;" | vvG#,
-Ab^
+^Ab
 | | 7/5
 | | 582.5122
@@ Line 273: / Line 273: @@
 | style="text-align:center;" | vA4,
-^^d5
+v~5
 | style="text-align:center;" | downaug 4th,
-double-up dim 5th
+downmid 5th
-| style="text-align:center;" | G#v,
+| style="text-align:center;" | vG#,
-Ab^^
+^^Ab
 | | 10/7
 | | 617.4878
@@ Line 288: / Line 288: @@
 | | 646.1538
 | | 6v
-| style="text-align:center;" | vv5
+| style="text-align:center;" | ^~5
-| style="text-align:center;" | double-down 5th
+| style="text-align:center;" | upmid 5th
-| style="text-align:center;" | Avv
+| style="text-align:center;" | vvA
 | | 16/11
 | | 648.6821
@@ Line 301: / Line 301: @@
 | style="text-align:center;" | v5
 | style="text-align:center;" | down 5th
-| style="text-align:center;" | Av
+| style="text-align:center;" | vA
 | | 34/23
 | | 676.6811
@@ Line 345: / Line 345: @@
 | style="text-align:center;" | ^m6
 | style="text-align:center;" | upminor 6th
-| style="text-align:center;" | Bb^
+| style="text-align:center;" | ^Bb
 | | 27/17
 | | 800.9096
@@ Line 356: / Line 356: @@
 | style="text-align:center;" | v~6
 | style="text-align:center;" | downmid 6th
-| style="text-align:center;" | Bb^^
+| style="text-align:center;" | ^^Bb
 | | 21/13
 | | 830.2532
@@ Line 367: / Line 367: @@
 | style="text-align:center;" | ^~6
 | style="text-align:center;" | upmid 6th
-| style="text-align:center;" | Bvv
+| style="text-align:center;" | vvB
 | | 28/17
 | | 863.8705
@@ Line 378: / Line 378: @@
 | style="text-align:center;" | vM6
 | style="text-align:center;" | downmajor 6th
-| style="text-align:center;" | Bv
+| style="text-align:center;" | vB
 | | 72/43
 | | 892.3923
@@ Line 404: / Line 404: @@
 downminor 7th
-| style="text-align:center;" | B^,
+| style="text-align:center;" | ^B,
-Cv
+vC
 | | 26/15
 | | 952.2589
@@ Line 428: / Line 428: @@
 | style="text-align:center;" | ^m7
 | style="text-align:center;" | upminor 7th
-| style="text-align:center;" | C^
+| style="text-align:center;" | ^C
 | | 9/5
 | | 1017.5963
@@ Line 439: / Line 439: @@
 | style="text-align:center;" | v~7
 | style="text-align:center;" | downmid 7th
-| style="text-align:center;" | C^^
+| style="text-align:center;" | ^^C
 | | 64/35
 | | 1044.8604
@@ Line 450: / Line 450: @@
 | style="text-align:center;" | ^~7
 | style="text-align:center;" | upmid 7th
-| style="text-align:center;" | C#vv
+| style="text-align:center;" | vvC#
 | | 41/22
 | | 1077.7445
@@ Line 461: / Line 461: @@
 | style="text-align:center;" | vM7
 | style="text-align:center;" | downmajor 7th
-| style="text-align:center;" | C#v
+| style="text-align:center;" | vC#
 | | 74/39
 | | 1108.8614
@@ Line 483: / Line 483: @@
 | style="text-align:center;" | v8
 | style="text-align:center;" | down-8ve
-| style="text-align:center;" | Dv
+| style="text-align:center;" | vD
 | | 112/57
 | | 1169.3579
@@ Line 489: / Line 489: @@
 | |
 |-
-| | 39'''··'''(or 0)
+| | 39'''··'''
 | | 1200
 | | 1
@@ Line 500: / Line 500: @@
 | |
 |}
-Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and Downs Notation#Chord names in other EDOs|Ups and Downs Notation - Chord names in other EDOs]].
+Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and Downs Notation#Chords and Chord Progressions|Ups and Downs Notation - Chords and Chord Progressions]].
-==<u>Instruments (prototypes):</u>==
-[[File:TECLADO_39-EDD.PNG|alt=TECLADO 39-EDD.PNG|800x467px|TECLADO 39-EDD.PNG]]
-''An illustrative image of a 39-ED2 keyboard''
-{| class="wikitable"
-|-
-| | [[File:Custom_700mm_5-str_Tricesanonaphonic_Guitar.png|alt=Custom_700mm_5-str_Tricesanonaphonic_Guitar.png|826x203px|Custom_700mm_5-str_Tricesanonaphonic_Guitar.png]]
-|-
-| | 39-EDD fretboard visualization
-|}
-==<u>39 tone equal [[modes]]</u>==
+==39 tone equal modes==
 14 11 - [[MOSScales|MOS]] of type [[2L 1s]]
@@ Line 583: / Line 570: @@
 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 - [[MOSScales|MOS]] of type [[8L 23s]]
-==<u>39edo and world music:</u>==
+==39edo and world music==
 edo is a good candidate for a "universal tuning" in that it offers reasonable approximations of many different world music traditions; it is one of the simplest edos that can make this claim. Because of this, composers wishing to combine multiple world music traditions (for example, gamelan with maqam singing) within one unified framework would find 39edo an interesting possibility.
@@ Line 631: / Line 618: @@
 [[Category:Todo:add definition]]
 [[Category:Todo:unify precision]]
+==Instruments (prototypes)==
+[[File:TECLADO_39-EDD.PNG|alt=TECLADO 39-EDD.PNG|800x467px|TECLADO 39-EDD.PNG]]
+''An illustrative image of a 39-ED2 keyboard''
+{| class="wikitable"
+|-
+| | [[File:Custom_700mm_5-str_Tricesanonaphonic_Guitar.png|alt=Custom_700mm_5-str_Tricesanonaphonic_Guitar.png|826x203px|Custom_700mm_5-str_Tricesanonaphonic_Guitar.png]]
+|-
+| | 39-EDD fretboard visualization
+|}