In some levels I've got problem with choppy music. It sounds like stuttering, repeating short fragments.
I think "Buffer underrun" problem has something in common with that. Does anyone have a similar problem?

Here is excerpt from Debug Log.txt:

(23:18:53.479) [OpenAL] Buffer underrun on Cycle ^ Aeolian_Consequent_3Bars with source 274
(23:18:53.490) [OpenAL] Buffer underrun on Cycle ^ Locrian_Triplets_9bars with source 271
(23:18:53.501) [OpenAL] Buffer underrun on Cycle ^ Aeolian_Triplets_9Bars with source 290
(23:18:53.511) [OpenAL] Buffer underrun on Cycle ^ Aeolian_Antecedent_3Bars with source 307
(23:18:53.521) [OpenAL] Buffer underrun on Ambience ^ night_01 with source 276
(23:27:09.867) [OpenAL] Buffer underrun on Ambience ^ water_base with source 314
(23:27:10.155) [OpenAL] Buffer underrun on Ambience ^ wind_01 with source 313
(23:27:11.272) [OpenAL] Buffer underrun on Ambience ^ water_waves with source 316
(23:27:11.376) [OpenAL] Buffer underrun on Ambience ^ water_base with source 314
(23:27:11.638) [OpenAL] Buffer underrun on Ambience ^ night_01 with source 276
(23:27:11.650) [OpenAL] Buffer underrun on Spire ^ twinkle with source 405

I'm having the exact same sound issue, though checking the Debug Log after quitting the program doesn't show any of the OpenAL messages you got.

Edit: Wow. That is a big huge drag in the Sync rooms. One thing I've noticed is that gameplay seems to be choppier when the music falls apart. A room that plays smoothly with the music playing normally gets glitchy along with the soundtrack. I know they may both be symptoms of the same problem, but since it sounds like there are multiple soudtracks playing at once when it falls apart I've got to wonder if the engine is trying to play multiple instances of the same sound file, and is bogging down as a result.

(My computer is probably around the minimum that could run this game. Core i3, 4Gb, Intel 4000 series gfx.)

According to minimum requirements Intel Core 2 Duo 2.8Ghz or equivalent processor should be good enough. I've got old DELL with Pentium IV 3.06Ghz, 2GB RAM, Radeon HD3650 gfx, but overall game works more then good, except mentioned music problems in some levels. And I don't know if my soundcard is OpenAL-compatible.