39edo: Difference between revisions

39edo, with its 400{{c}} major third, [[tempering out|tempers out]] the [[128/125|diesis]] (128/125), and using the 39d val, the septimal comma, [[64/63]], as well as [[126/125]] are added to the comma list. In the 11-limit we find that the equal temperament tempers out [[99/98]] and [[121/120]]. Tempering out both 128/125 and 64/63 makes 39et, in some few ways, allied to [[12edo|12et]] in [[support]]ing [[augene]], and is in fact, an excellent choice for a 7-limit augene tuning. It also tempers out the [[amity comma]] (1600000/1594323), and supports the variant of amity known as [[accord]].  

If we take 22\39 as a fifth, 39edo can be used as a tuning of [[mavila]] through the 39bc val, 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.  

== Intervals ==

|-

! rowspan="2" | #

! rowspan="2" | Cents

|-

! 39d val

|-

| 0

| 0.0

|-

| 1

| 30.8

|-

| 2

| 61.5

| ''[[21/20]]'', [[36/35]]

|-

| 3

| 92.3

|-

| 4

| 123.1

| [[15/14]]

|-

| 5

| 153.8

|-

| 6

| 184.6

| [[10/9]]

|-

| 7

| 215.4

| [[9/8]]

| ''[[8/7]]''

|-

| 8

| 246.2

| [[81/70]]

|-

| 9

| 276.9

| [[7/6]]

|-

| 10

| 307.7

| [[6/5]]

|-

| 11

| 338.5

| [[11/9]]

|-

| 12

| 369.2

| [[27/22]]

|-

| 13

| 400.0

| [[5/4]]

|-

| 14

| 430.8

| ''[[35/27]]''

| [[9/7]], [[14/11]]

| 15

| 461.5

| [[35/27]]

|-

| 492.3

| [[4/3]]

|-

| 17

| 523.1

| [[27/20]]

|-

| 18

| 553.8

| [[11/8]]

|-

| 19

| 584.6

| [[7/5]]

|-

| 20

| 615.4

| [[10/7]]

|-

| 646.2

| [[16/11]]

|-

| 22

| 676.9

| [[40/27]]

|-

| 23

| 707.7

| [[3/2]]

|-

| 24

| 738.5

| [[54/35]]

|-

| 25

| 769.2

| ''[[54/35]]''

| [[11/7]], [[14/9]]

| 26

| 800.0

| [[8/5]]

|-

| 27

| 830.8

| [[44/27]]

|-

| 28

| 861.5

| [[18/11]]

|-

| 29

| 892.3

| [[5/3]]

|-

| 30

| 923.1

| [[12/7]]

|-

| 31

| 953.8

| [[7/4]], ''[[12/7]]''

| [[140/81]]

| 984.6

| [[16/9]]

| ''[[7/4]]''

|-

| 33

| 1015.4

| [[9/5]]

|-

| 34

| 1046.2

|-

| 35

| 1076.9

| [[28/15]]

|-

| 36

| 1107.7

|-

| 37

| 1138.5

| [[35/18]], ''[[40/21]]''

| [[27/14]], ''[[96/49]]''

| 38

| 1169.2

|-

| 39

| 1200.0

|}

|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator

|-

! Generator*

! Cents*

| 5\39

| 153.8

| [[1L 6s]], [[7L 1s]], [[8L 7s]], [[8L 15s]], [[8L 23s]]

|-

| 10\39

| 307.7

| [[3L 1s]], [[4L 3s]], [[4L 7s]], [[4L 11s]], [[4L 15s]], [[4L 19s]], [[4L 23s]], [[4L 27s]], [[4L 31s]]

|-

|-

| 3

|-

| 3

| [[Triforce]] (39)

| [[3L 3s]], [[6L 3s]], [[9L 6s]], [[15L 9s]]

|-

| 3

|-

| 13

| [[Tridecatonic]]

| [[13L 13s]]

|}

== Octave stretch or compression ==

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.  

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

== Scales ==

* Extended quasisuper: 4 3 6 3 4 3 6 4 3 3

* ''The scales listed in: [[User:BudjarnLambeth/Quasipelog theory]]''

[[Category:Listen]]