4/4 vs 3/4

[hgrind]

I have a 4/4 bass with a 110 cm/43,3 string length. Will I have much to gain in terms of playability to get a 3/4 bass with shorter (say 5 cm/2 inches) string length? I really like the bass, it has a great sound, but it is big and I really have to stretch my fingers to hit right.

[Silversorcerer]

I figured it out in inches once:


String length and comfort / playability:

String length; longest whole step (half position)*; whole step at heel (D harmonic)*

41.5 inches: 39.1708 - 34.8972 = 4.2735; 27.6667 - 24.6481 = 3.01 inches

42 inches: 39.6427 - 35.3176 = 4.3251; 28 - 24.9452 = 3.05 inches

43 inches: 40.5866 - 36.1585 = 4.428; 28.6667 - 25.5391 = 3.1276 inches

44.25 inches: 41.7664 - 37.2097 = 4.5568; 29.5 - 26.2815 = 3.2185 inches

*Calculations of actual experienced stretches to reach across whole steps based on the twelfth root of 2 as the factor between half steps. The calculations show that the hand only must stretch slightly more than a quarter of an inch farther at the most between the shortest string given and the longest. The difference is dramatically reduced as one moves up the fingerboard. The difference looks daunting when considering the total difference or 2.75 inches. But that is a difference the hand experiences only in small fractions.