Just Intonation versus Equal Temperment
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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

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

tonic

I

1 : 1

0

1

0