One of these popped up on e Bay in January, I never saw one before. The picture was very clear. I just searched for it but it is gone. I should have saved it. The description of the sound was a cross between the clarinet and the oboe.
Yes bass tarogatok do exist and in increasing numbers in Hungary as they are being manufactured by Gregus Pal over there. The resemble a large wooden straignt tenor saxophone, and when I have heard them played they produce a sound very similar to as tenor sax but much more mellow. They are quite expensive, but in a tárogató quartet they really do make a difference. They should really be called a tenor tárogató. Gregus is also producing an alto tárogató now and I believe in the Hungarian National Museum there is an example of a contrabass tárogató - unfortunately I have never been able to get to the museum when in Budapest, but I am going over there again soon and will endeavour to get in there.
Stowasser listed seven sizes, down to contrabass in Eb. As to the sound of the tárogató--it was quite beloved of Arthur Benade, the acoustician, who said that the tárogató has generally more stable regimes of oscillation than the saxophone. I am now playing my Stowasser Bb instrument with a rather hard reed on an original mouthpiece with the tip opened way up, and it has a beautiful dark sound, much less brash than a soprano sax. The usual tárogató sound is not the only possibility, just as today's in-your-face sax growl on a high-baffle mpc is a far cry from the sweet tone of a classical sax player.
There is also variation between tárogatók. Schunda types have a wider top and narrower cone angle, giving them a bit honkier sound, but also more stuffy. They also tend to "oversteer" on pitch, and one needs to stay more on top of intonation, even when the native intonation is good. Stowassers feel more modern to me, with a broader sound, slightly more diffuse. The notes "slot" more--meaning the tube has stronger impedances. Of course this is hard to appreciate when the instrument is played like a kazoo with #1 reeds and near-zero lip damping, as is typical of much of the traditional playing. BTW listen to the same folks playing the same tunes on sax and you will immediately recognize that this is not due to the instrument. It is a choice, though not one that I would make...
Now that I have good instruments in both Bb and C, I must say that I am surprised at the difference in tone color one step makes. The C instrument is significantly brighter, though not in a shrill way. I should do done recordings and post, though I won't be able to think about that until after I return from China in October.