This 14-32 cog cluster is rather good!
sprkts exact
14
16.07
18.44
21.17
24.29
27.88
32
sprkts integer
14
16
18
21
24
28
32
delta squared
0.0%
0.5%
19.5%
2.8%
8.6%
1.4%
0.0%
error =
0.57
The only real trouble spot with the 14-32 cluster is the "ideal"
18.44 sprocket; both 18 and 19 will give large errors.
Let's look at some of the alternatives!
Changing the bottom to 13 only makes matters worse:
sprkts ideal
13
15.11
17.55
20.40
23.70
27.54
32
sprkts integer
13
15
18
20
24
28
32
delta squared
0.0%
1.1%
20.0%
15.7%
9.0%
21.3%
0.0%
error =
0.82
With a 7-speed cluster, the 13-31 grouping that worked out so well
with 5 gears is no longer so good:
sprkts ideal
13
15.03
17.37
20.07
23.20
26.82
31.00
sprkts integer
13
15
18
20
23
27
31
delta squared
0.0%
0.1%
39.9%
0.6%
4.1%
3.2%
0.0%
error =
0.69
So this is a rather nice choice. Thank you Shimano.