Conn 4M-Transitional Curved Soprano
Date: 1930, Owner unknown
This is a curved soprano saxophone in Bb (and not an alto saxophone). Strictly speaking there is no "transitional" model. At the time Conn tended to gradually change and (usually, depending on your point of view) improve their instruments. The "transitional" is a modern term for instruments from a period that may have features of both the New Wonder models and the later "Standard" models (a.k.a. "M-series"). For the soprano saxophones things are more complicated because apparently Conn never produced a true "Standard series" soprano but continued to use New Wonder tooling. However, it is suggested by various sources that around 1929 Conn lengthened their soprano by ¾", requiring a different mouthpiece.
From what I have been able to infer from various sources on the internet, including this review by Thomas Zinnen of an 18M New Wonder II straight soprano, the sound of Conn's soprano saxophones was "awesome", however at the price of being finicky with mouthpieces. Thomas says that while the New Wonder II requires a vintage mouthpiece to be in tune with itself, the later series (which would have been the "standard" series) was built longer requiring specifically a Conn mouthpiece. Considering the date of 1929 for this to have happened, the "transitional" soprano probably requires a Conn "short" soprano mouthpiece.
What Conn said in 1929:
Our new model has the finest playing scale, richest tone, and most pleasing response in the history of the Bb curved soprano.