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