Although this commentator is certainly no cantor by any stretch of the imagination there have been requests by more than a few individuals looking to gain access to some of the "traditional messianic prayer chants" in Hhebrew. Apparently a good portion of these chants can be found on the internet but often times they are not readily downloadable!
Now ... if you can tolerate the poor voice one should at least be able get a feel for the basic rhythm and cadence of some of the well known Hebraic prayer chants.
When you launch one ot these "mp3" files you may have to direct your browser with which application to open up the chant with ... ie ... windows media player, etc. Otherwise you can simply choose download the file to your computer. Note: these files are clean and contain nothing but the audio)
Shema Yisrael (Hear O'Israel)
Avot (Amidah #1 - G_D of our fathers);
Gibbor ADONAI (Amidah #2 - Mighty G_D);
V'Shamru (The Children of Israel shall keep the Shabbat);
Kedusha (Sanctification prayer);
Kaddish (Prayer of remembrance, mourning and praise);
Ma Tovu (How lovely are your tents oh Jacob);
Mi Kamocha (Who is like YOU O'LORD);
Ho Doo L' ADONAI (Give thanks to ADONAI for HE is good);
Shalom Aleychem (Peace be unto you ministering angels of G_D);
ADON Olam (G_D of Eternity);
Ayn KALOHEYNU (there is none like our G_D);
Ayn Kamocha (there is none like You O'G_D);
Mizmor L'David (a psalm of David #23 - Compliments of Rabbi Mark Shulman);
YESHUA's Prayer (a.k.a. the disciples prayer);
Vayahee Beenso haAhron (when the ark would travel);
Aaronic Benediction (the priestly blessing)
Shalom Aleichem ... P.R. Otokletos
ps ... if you can't tolerate the poor voice ... don't say that you were not warned! But in the end we can only try!