The Shulchan Aruch states that the pitch of a shofar can be high or low (586, 6). This ruling is derived from the Gemara (Rosh Hashana 27b), which states as follows:
היה קולו דק או עבה או צרור כשר שכל הקולות כשירין בשופר
Here we see that not only high- and low-pitched shofars can be used to fulfill the mitzvah, but even a “hoarse” tone, which Rashi describes as a “dry” tone.
Sometimes the pitch of a shofar will change midway. A tekiah starts high and then in the middle suddenly changes to a lower note. Or it may start as a clear tone and then suddenly shift to raspy. The custom is that the tekiah is acceptable, and does not have to be repeated.
There are two notable cases where the tekiah may have to be repeated:
- If there is a break that can be detected by the listeners
- If it trills
Note that if a shofar shound is not produced and air can be heard passing through the shofar, this is not considered קול שופר and therefore does not affect the order of the required shofar notes.
When looking at shofars for sale, keep in mind that you will find it easier to play it well if the sound is clear, not raspy, and the notes are easy to hit, without skipping up or down.
Yemenite shofars are typically able to produce a wider range of notes than rams horn shofars. Long kudu shofars may have an especially wide range.