Hi KLR,
If I may explain...
Quint system is based on the fundamental principle of the circle of fifths.
The accordions with 120 bass: have 36 notes/3 octaves over three positions:
row 1&2 - C2 to B2
row 3&4 - C3 to B3
row 5&6 - C4 to B4
The accordions with 160 bass: have 48 notes/4 octaves over four positions
rows 1&2 - C1 to B1
rows 3&4 - C2 to B2
rows 5&6 - C3 to B3
rows 7&8 - C4 to B4
As "full size" piano accordions typically have:
41 notes (3 octaves plus a major third)
47 notes (3 octaves plus a major 7th)
this makes for a very balanced instrument range when paired with a 3 or 4 octave quint free bass converter.
It is also worth noting that each position (rows 1&2 etc) contains two rows of fifths, staggered (major third intervals between rows) - the same as fundamental & counter basses on the stradella accordion.
Where quint free bass has less notes compared to other designs, it should also be considered in the context that quint has more repeated notes than other designs. In fact,
every note of the 12 semitone scale (arranged in fifths) is repeated 3 to 4 times (on every octave).
Instruments with 160 bass buttons are usually only played by masters, whereas the 120 bass button instruments are usually played by students or masters who are happy to stay within 3 octaves. Of course, both 120 bass and 160 bass instruments often have two free bass voices or sometimes three voices (160 bass), and therefore the range is extended by additional octaves with register changes.
The traditional heartland of the Quint free bass system is:
United States of America
Italy
New Zealand
However, there are some excellent quint players from other nations including Japan, France (famously R. Galliano), Germany, Austria and Canada (esp. Calgary).
Interestingly, in Canada, under the direction of Sir N. Antonio Peruch the Quint system accordion is studied by several students playing button accordion (treble: C system) with 64 notes and 160 bass in fifths. What are you Canadians like eh!