f*1=/sjust (sumn n*abs(?n))2?/122?/172?/192?/222?/312?/412?/53
unison
1/1=1.000cost()=0
minor 2nd
16/15≈1.067cost(4,-1,-1)=3
1↦1.059-7.2e-3
2↦1.085+1.8e-2
2↦1.076+9.0e-3
2↦1.065-1.6e-3
3↦1.069+2.7e-3
4↦1.070+3.3e-3
5↦1.068+9.1e-4
neutral 2nd
11/10=1.100cost(-1,0,-1,0,1)=6
2↦1.122+2.2e-2
2↦1.085-1.5e-2
3↦1.116+1.6e-2
3↦1.099-8.7e-4
4↦1.094-6.4e-3
6↦1.107+6.8e-3
7↦1.096-4.1e-3
major 2nd
9/8=1.125cost(-3,2)=2
2↦1.122-2.5e-3
3↦1.130+5.1e-3
3↦1.116-9.3e-3
4↦1.134+9.3e-3
5↦1.118-6.7e-3
7↦1.126+6.3e-4
9↦1.125-8.9e-5
supermajor 2nd
8/7≈1.143cost(3,0,0,-1)=3
2↦1.122-2.0e-2
3↦1.130-1.3e-2
4↦1.157+1.4e-2
4↦1.134-8.5e-3
6↦1.144+7.2e-4
8↦1.145+2.0e-3
10↦1.140-3.1e-3
subminor 3rd
7/6≈1.167cost(-1,-1,0,1)=4
3↦1.189+2.3e-2
4↦1.177+1.0e-2
4↦1.157-9.6e-3
5↦1.171+4.0e-3
7↦1.169+2.8e-3
9↦1.164-2.3e-3
12↦1.170+3.3e-3
minor 3rd
6/5=1.200cost(1,1,-1)=3
3↦1.189-1.1e-2
4↦1.177-2.3e-2
5↦1.200+1.0e-4
6↦1.208+8.1e-3
8↦1.196-4.1e-3
11↦1.204+4.4e-3
14↦1.201+9.3e-4
neutral 3rd
11/9≈1.222cost(0,-2,0,0,1)=6
3↦1.189-3.3e-2
5↦1.226+3.9e-3
5↦1.200-2.2e-2
6↦1.208-1.4e-2
9↦1.223+6.9e-4
12↦1.225+2.7e-3
15↦1.217-5.5e-3
major 3rd
5/4=1.250cost(-2,0,1)=2
4↦1.260+9.9e-3
5↦1.226-2.4e-2
6↦1.245-5.3e-3
7↦1.247-3.2e-3
10↦1.251+5.7e-4
13↦1.246-4.2e-3
17↦1.249-1.0e-3
supermajor 3rd
9/7≈1.286cost(0,2,0,-1)=5
4↦1.260-2.6e-2
6↦1.277-8.6e-3
7↦1.291+5.2e-3
8↦1.287+9.5e-4
11↦1.279-6.9e-3
15↦1.289+2.9e-3
19↦1.282-3.6e-3
perfect 4th
4/3≈1.333cost(2,-1)=1
5↦1.335+1.5e-3
7↦1.330-3.0e-3
8↦1.339+5.6e-3
9↦1.328-5.5e-3
13↦1.337+4.0e-3
17↦1.333-3.7e-4
22↦1.333+5.3e-5
diminished 5th
7/5=1.400cost(0,0,-1,1)=5
6↦1.414+1.4e-2
8↦1.386-1.4e-2
9↦1.389-1.1e-2
11↦1.414+1.4e-2
15↦1.398-1.5e-3
20↦1.402+2.3e-3
26↦1.405+5.0e-3
augmented 4th
10/7≈1.429cost(1,0,1,-1)=5
6↦1.414-1.4e-2
9↦1.443+1.5e-2
10↦1.440+1.2e-2
11↦1.414-1.4e-2
16↦1.430+1.5e-3
21↦1.426-2.4e-3
27↦1.423-5.1e-3
perfect 5th
3/2=1.500cost(-1,1)=1
7↦1.498-1.7e-3
10↦1.503+3.4e-3
11↦1.494-6.2e-3
13↦1.506+6.2e-3
18↦1.496-4.5e-3
24↦1.500+4.2e-4
31↦1.500-5.9e-5
subminor 6th
14/9≈1.556cost(1,-2,0,1)=5
8↦1.587+3.2e-2
11↦1.566+1.0e-2
12↦1.549-6.3e-3
14↦1.554-1.1e-3
20↦1.564+8.4e-3
26↦1.552-3.5e-3
34↦1.560+4.4e-3
minor 6th
8/5=1.600cost(3,0,-1)=2
8↦1.587-1.3e-2
12↦1.631+3.1e-2
13↦1.607+6.8e-3
15↦1.604+4.2e-3
21↦1.599-7.2e-4
28↦1.605+5.4e-3
36↦1.601+1.3e-3
neutral 6th
18/11≈1.636cost(1,2,0,0,-1)=6
9↦1.682+4.5e-2
12↦1.631-5.2e-3
13↦1.607-3.0e-2
16↦1.656+1.9e-2
22↦1.635-9.3e-4
29↦1.633-3.6e-3
38↦1.644+7.4e-3
major 6th
5/3≈1.667cost(0,-1,1)=3
9↦1.682+1.5e-2
13↦1.699+3.2e-2
14↦1.667-1.4e-4
16↦1.656-1.1e-2
23↦1.672+5.8e-3
30↦1.661-6.1e-3
39↦1.665-1.3e-3
supermajor 6th
12/7≈1.714cost(2,1,0,-1)=4
9↦1.682-3.2e-2
13↦1.699-1.5e-2
15↦1.728+1.4e-2
17↦1.708-5.8e-3
24↦1.710-4.1e-3
32↦1.718+3.4e-3
41↦1.710-4.8e-3
minor 7th
7/4=1.750cost(-2,0,0,1)=3
10↦1.782+3.2e-2
14↦1.770+2.0e-2
15↦1.728-2.2e-2
18↦1.763+1.3e-2
25↦1.749-1.1e-3
33↦1.747-3.0e-3
43↦1.755+4.8e-3
neutral 7th
11/6≈1.833cost(-1,-1,0,0,1)=5
10↦1.782-5.2e-2
15↦1.843+1.0e-2
17↦1.859+2.6e-2
19↦1.820-1.4e-2
27↦1.829-4.4e-3
36↦1.838+4.6e-3
46↦1.825-8.3e-3
major 7th
15/8=1.875cost(-3,1,1)=3
11↦1.888+1.3e-2
15↦1.843-3.2e-2
17↦1.859-1.6e-2
20↦1.878+2.9e-3
28↦1.870-4.8e-3
37↦1.869-5.8e-3
48↦1.873-1.6e-3
octave
2/1=2.000cost(1)=0