editing disabled

35-tET or 35-EDO refers to a tuning system which divides the octave into 35 steps of approximately 34.29¢ each.

As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic macrotonal edos: 5edo and 7edo. A single degree of 35edo represents the difference between 7edo's narrow fifth of 685.71¢ and 5edo's wide fifth of 720¢. Because it includes 7edo, 35edo tunes the 29th harmonic with +1 cent of error. 35edo can also represent the 2.3.5.7.11.17 subgroup and 2.9.5.7.11.17 subgroup, because of the accuracy of 9 and the flatness of all other subgroup generators (7/5 and 17/11 stand out, having less than 1 cent error). Therefore among whitewood tunings it is very versatile; you can switch between these different subgroups if you don't mind having to use two different 3/2s to reach the inconsistent 9 (a characteristic of whitewood tunings), and if you ignore 22edo's more in-tune versions of 35edo MOS's and consistent representation of both subgroups. 35edo has the optimal patent val for greenwood and secund temperaments, as well as 11-limit muggles, and the 35f val is an excellent tuning for 13-limit muggles.

A good beginning for start to play 35-EDO is with the Sub-diatonic scale, that is a MOS of 3L2s: 9 4 9 9 4.

Notation


Degrees
Cents
Up/down Notation
0
0
unison
1
D
1
34.29
up unison
^1
D^
2
68.57
double-up unison
^^1
D^^
3
102.86
double-down 2nd
vv2
Evv
4
137.14
down 2nd
v2
Ev
5
171.43
2nd
2
E
6
205.71
up 2nd
^2
E^
7
240
double-up 2nd
^^2
E^^
8
274.29
double-down 3rd
vv3
Fvv
9
308.57
down 3rd
v3
Fv
10
342.86
3rd
3
F
11
377.14
up 3rd
^3
F^
12
411.43
double-up 3rd
^^3
F^^
13
445.71
double-down 4th
vv4
Gvv
14
480
down 4th
v4
Gv
15
514.29
4th
4
G
16
548.57
up 4th
^4
G^
17
582.86
double-up 4th
^^4
G^^
18
617.14
double-downv 5th
vv5
Avv
19
651.43
down 5th
v5
Av
20
685.71
5th
5
A
21
720
up 5th
^5
A^
22
754.29
double-up 5th
^^5
A^^
23
788.57
double-down 6th
vv6
Bvv
24
822.86
down 6th
v6
Bv
25
857.15
6th
6
B
26
891.43
up 6th
^6
B^
27
925.71
double-up 6th
^^6
B^^
28
960
double-down 7th
vv7
Cvv
29
994.29
down 7th
v7
Cv
30
1028.57
7th
7
C
31
1062.86
up 7th
^7
C^
32
1097.14
double-up 7th
^^7
C^^
33
1131.43
double-down 8ve
vv8
Dvv
34
1165.71
down 8ve
v8
Dv
35
1200
8ve
8
D

Ups and downs can be used to name 35edo chords. Because every interval is perfect, the quality can be omitted, and the words major, minor, augmented and diminished are never used.

0-10-20 = C E G = C = C or C perfect
0-9-20 = C Ev G = C(v3) = C down-three
0-11-20 = C E^ G = C(^3) = C up-three
0-10-19 = C E Gv = C(v5) = C down-five
0-11-21 = C E^ G^ = C(^3,^5) = C up-three up-five

0-10-20-30 = C E G B = C7 = C seven
0-10-20-29 = C E G Bv = C(v7) = C down-seven
0-9-20-30 = C Ev G B = C7(v3) = C seven down-three
0-9-20-29 = C Ev G Bv = C.v7 = C dot down seven

For a more complete list, see Ups and Downs Notation - Chord names in other EDOs.

Intervals


(Bolded ratio indicates that the ratio is most accurately tuned by the given 35-edo interval.)
Degrees
Cents value
Ratios in2.5.7.11.17 subgroup
Ratios with flat 3
Ratios with sharp 3
Ratios with patent 9
0
0
1/1
(see comma table)


1
34.29
50/49 , 121/119 , 33/32
36/35
25/24
81/80
2
68.57
128/125
25/24
81/80

3
102.86
17/16
15/14
16/15
18/17
4
137.14

12/11 , 16/15


5
171.43
11/10

12/11
10/9
6
205.71



9/8
7
240
8/7

7/6

8
274.29
20/17
7/6


9
308.57

6/5


10
342.86
17/14

6/5
11/9
11
377.14
5/4



12
411.43
14/11



13
445.71
22/17 , 32/25


9/7
14
480


4/3, 21/16

15
514.29

4/3


16
548.57
11/8



17
582.86
7/5
24/17
17/12

18
617.14
10/7
17/12
24/17

19
651.43
16/11



20
685.71

3/2


21
720


3/2, 32/21

22
754.29
17/11 , 25/16


14/9
23
788.57
11/7



24
822.86
8/5



25
857.14
28/17

5/3
18/11
26
891.43

5/3


27
925.71
17/10
12/7


28
960
7/4



29
994.29



16/9
30
1028.57
20/11


9/5
31
1062.86

11/6 , 15/8


32
1097.14
32/17
28/15
15/8
17/9
33
1131.43




34
1165.71




Rank two temperaments


Periods
per octave
Generator
Temperaments with
flat 3/2 (patent val)
Temperaments with sharp 3/2 (35b val)
1
1\35


1
2\35


1
3\35

Ripple
1
4\35
Secund

1
6\35
Messed-up Baldy
1
8\35

Messed-up Orwell
1
9\35
Myna

1
11\35
Muggles

1
12\35

Roman
1
13\35
Inconsistent 2.9'/7.5/3 Sensi
1
16\35


1
17\35


5
1\35

Blackwood (favoring 7/6)
5
2\35

Blackwood (favoring 6/5 and 20/17)
5
3\35

Blackwood (favoring 5/4 and 17/14)
7
1\35
Whitewood/Redwood

7
2\35
Greenwood

Scales

Commas

35EDO tempers out the following commas. (Note: This assumes the val < 35 55 81 98 121 130|.)
Comma
Monzo
Value (Cents)
Name 1
Name 2
Name 3
2187/2048
| -11 7 >
113.69
Apotome
Whitewood comma

6561/6250
| -1 8 -5 >
84.07
Ripple comma


10077696/9765625
| 9 9 -10 >
54.46
Mynic comma


3125/3072
| -10 -1 5 >
29.61
Small diesis
Magic comma

405/392
| -3 4 1 -2 >
56.48
Greenwoodma


16807/16384
| -14 0 0 5 >
44.13



525/512
| -9 1 2 1 >
43.41
Avicenna


126/125
| 1 2 -3 1 >
13.79
Starling comma
Septimal semicomma

99/98
| -1 2 0 -2 1 >
17.58
Mothwellsma


66/65
| 1 1 -1 0 1 -1 >
26.43




Music

Little Prelude & Fugue, "The Bijingle" by Claudi Meneghin
Self-Destructing Mechanical Forest by Chuckles McGee (in Secund[9])