If you try to blow a shofar, do not place it inside your mouth, in between your lips, the way you would blow-up a balloon. Place it on your lips. Usually the Shofar is placed in one of the corners of your lips. You should blow air, with your lips tightly closed, emitting the sound of the letter 'P', and vibrating your lips as you release the air. Don't inflate your cheeks and don't force your lungs. Breath as normally as possible. The most difficult part will be to adjust the position of the Shofar on your lips, and avoiding air to escape from any other point of your mouth.
The Shofar, normally, produces one sound. In Rosh haShana we play three different voices, using the same sound. The three voice have theoretically the same length. The first one, Teqi'a is a plain uninterrupted sound. For the sake of illustration of the length, let us imagine that the Teqi'a lasts for nine seconds (in reality, it last less than that). Then we have Shebarim: a sound divided into three smaller unit. Following our example, each unit of the Shebarim will last for3 seconds. And finally, Teru'a : a sound, consisting of nine smaller units, each sound would last for one second.
The typical combination of sounds in Rosh haShana is the following combination:
teqi'a/ shabrim-terua/ tequi'a.
teqi'a/ shebarim/ teqi'a
teqi'a / teru'a/ teqi'a.
This formula repeats itself several times until we reach more that 100 sounds.
Click here to watch a great tutorial on how to blow the Shofar.
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