name

ratio

nat.

temp.

semi-tones

unison

$\frac{d}{d}$

$\frac{1}{1}$

1.0000

1

octave

$\frac{2d}{d}$

$\frac{2}{1}$

2.0000

12

perfect 5th

$\frac{s}{d}=\frac{l}{r}=\cdots =\frac{2m}{l}=\text{q}$

$\frac{3}{2}$

1.4983

7

perfect 4th

$\frac{f}{d}=\frac{s}{r}=\cdots =\frac{2m}{t}=\text{q}$

$\frac{4}{3}$

1.3348

5

major 3rd

$\frac{m}{d}=\frac{l}{f}=\frac{t}{s}=\frac{{\text{q}}^{\text{4}}}{4}$

$\frac{5}{4}$

1.2599

4

minor 3rd

$\frac{f}{r}=\frac{s}{m}=\frac{2d}{l}=\frac{2r}{t}=\frac{4}{{\text{q}}^3}$

$\frac{6}{5}$

1.1892

3

major 6th

$\frac{l}{d}=\frac{t}{r}=\frac{2r}{f}=\frac{2m}{s}=\frac{{\text{q}}^3}{2}$

$\frac{5}{3}$

1.6818

9

minor 6th

$\frac{m}{d}=\frac{l}{f}=\frac{t}{s}=\frac{8}{{\text{q}}^4}$

$\frac{8}{5}$

1.5874

8

major 2nd

$\frac{r}{d}=\frac{m}{r}=\frac{s}{f}=\frac{l}{s}=\frac{t}{l}=\frac{{\text{q}}^2}{2}$

$\frac{9}{8}$

1.1225

2

minor 7th

$\frac{r}{d}=\frac{m}{r}=\frac{s}{f}=\frac{l}{s}=\frac{t}{l}=\frac{4}{{\text{q}}^2}$

$\frac{16}{9}$

1.7818

10

minor 2nd

$\frac{f}{m}=\frac{2d}{t}=\frac{8}{{\text{q}}^5}$

$\frac{16}{15}$

1.05946

1

major 7th

$\frac{2m}{f}=\frac{2d}{t}=\frac{{\text{q}}^5}{4}$

$\frac{15}{8}$

1.8877

11

chromatic

$\frac{2m}{f}=\frac{2d}{t}=\frac{{\text{q}}^5}{4}$

$\frac{25}{24}$

1.05946

1

aug. 4th

$\frac{t}{f}=\frac{{\text{q}}^6}{8}$

$\frac{45}{32}$

1.4142

6

dim. 5th

$\frac{2f}{t}=\frac{16}{{\text{q}}^6}$

$\frac{64}{45}$

1.4142

6

dim. 7th

$\frac{64}{{\text{q}}^9}$

$\frac{128}{75}$

1.6818

9