Just Intonation versus Equal Temperment
Interval |
Frequency Ratio |
Deviation of Equal from Just (%) |
||||
|
|
Just Intonation |
N |
Equ. Temp. (2N/12) |
|
|
octave |
I |
2 : 1 |
12 |
2 |
0 |
|
Maj. 7th |
VII |
15 : 8 |
11 |
1.8877 |
+0.68 |
|
min. 7th |
minor 7th |
vii |
9 : 5 |
10 |
1.7818 |
-1.00 |
grave minor 7th |
16 : 9 |
+0.23 |
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harmonic minor 7th |
7 : 4 |
+1.80 |
||||
dim. 7th / Maj. 6th |
vii° / VI |
5 : 3 |
9 |
1.6818 |
+0.91 |
|
min. 6th / Aug. 5th |
vi / V+ |
8 : 5 |
8 |
1.5874 |
-0.79 |
|
perfect 5th |
V |
3 : 2 |
7 |
1.4983 |
-0.11 |
|
dim. 5th |
V° |
64 : 45 |
6 |
1.4142 |
-0.56 |
|
Aug. 4th |
IV+ |
45 : 32 |
+0.57 |
|||
perfect 4th |
IV |
4 : 3 |
5 |
1.3348 |
+0.11 |
|
Maj. 3rd |
III |
5 : 4 |
4 |
1.2599 |
+0.79 |
|
Min. 3rd |
iii |
6 : 5 |
3 |
1.1892 |
-0.90 |
|
Maj. 2nd |
II |
9 : 8 |
2 |
1.1225 |
-0.23 |
|
min. 2nd |
minor tone |
ii |
10 : 9 |
1 |
1.0595 |
-4.60 |
semitone |
16 : 15 |
-0.68 |
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tonic |
I |
1 : 1 |
0 |
1 |
0 |