A TUNING FOR SATIE'S VEXATIONS
Here is a a:link to Kraig Grady's Scale
Here is a a:link to Warren Burt's scale
An excerpt from the Microfest Performance
Alternative tuning for Erik Satie’s Vexations Terumi Narushima
Scale Degree 
Letter Name 
Interval Size 
0 
C 
0.000 unison 
1 
B# 
188.253 cents 
2 
Db 
206.133 cents 
3 
C# 
224.012 cents 
4 
Ebb 
241.892 cents 
5 
D 
259.771 cents 
6 
Eb 
295.530 cents 
7 
D# 
483.783 cents 
8 
E 
519.542 cents 
9 
F 
555.301 cents 
10 
Gb 
591.060 cents 
11 
F# 
779.313 cents 
12 
G 
815.072 cents 
13 
Ab 
850.831 cents 
14 
G# 
868.711 cents 
15 
Bbb 
886.590 cents 
16 
A 
1074.843 cents 
17 
Bb 
1110.602 cents 
18 
A# 
1128.482 cents 
19 
Cb 
1146.361 cents 
20 
B 
1164.241 cents 
21 
C 
1200.000 octave 
In an article titled “Understanding Satie’s Vexations”, Satie scholar Robert Orledge suggests that the structure of Vexations is based on numbers from the Lucas series (1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843…). To accommodate the 21 different spellings of notes in Satie’s score, I decided to use a 21tone subset of a 29tone scale (29 being the closest Lucas number larger than 21). The fact that nearly all of the chords in Vexations are diminished triads gave me the idea of arranging the notes of the scale as three chains of minor thirds as shown below. The chains are a:linked by notes of the augmented triad (FAC#) found in the 2nd and 19th chords of the score.


aug 





G# 
– 
B 
– 
D 
– 
F 
– 
Ab 
– 
Cb 
– 
Ebb 






































B# 
– 
D# 
– 
F# 
– 
A 
– 
C 
– 
Eb 
– 
Gb 
– 
Bbb 






















































A# 
– 
C# 
– 
E 
– 
G 
– 
Bb 
– 
Db 











Three chains of minor thirds with brackets showing diminished triads found in Satie’s Vexations. Chains are a:linked by augmented triad FAC#.