Regardless if you are an improviser or a ligit (classical) player it´s very important to be able to hear the music you play. And that is actually hearing it before you play it (if you can´t hear it while playing you should consider plumbing or mountain climbing instead of playing music). Knowing what the next note is going to sound like makes it much easier to play in tune and with rich sound. I would actually say that the audience can hear the difference if you know the music by heart or not, even if you play it correct and in tune.
And hearing the music beforehand is closely connected to ear training and being familiar with your instrument. This exercise focuses on the sound of the different inversions of a major and minor third. By playing a F-triad, Bb-triad and Db-triad starting on the note F, you get to learn the feel of the functions in the triad. How does the tonic feel? The third? The fifth? And how do i adjust tuning to compensate for the different roles of the note?
You should always be able to sing a major third from any given note in all inversions. That´s actually quite hard! Try this exercise on the instrument. When you get familiar with the sound of it, try it on the mouthpiece sitting by the piano, checking that you play it right. Then try singing it!
Believe me, this is good stuff!
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