Note: This post is meant for players already familiar with overtones, and who have already expanded their range to 3 octaves or more. For a more comprehensive approach to working on overtones try this post.
Ever tried slurring up the overtone series? You can pretty easily jump from the fundamental pitch (low note) to the first octave or from the fundamental to some higher pitch in the series, but most players find starting on anything higher in the series and trying to slur up from there to be impossible. However, once you get high enough (altissimo Bb) it becomes fairly easy to slur up, that is if you can play up there already.
Slurring altissimo Bb to C (first slur below) using the Bb series is fairly easy and a great starting point for this exercise. With a little experimentation and determination you will find you can slur up and down some of the partials right below the altissimo Bb mark as well, so on the Bb series that would be altissimo Ab to Bb, the second slur below. The slurs can be a lot easier if you start with the higher note slurring down and then come back up. With daily practice you can work all the way down to octave key Bb or even further down the series, which is no small feat. It is possible to go further down than notated in this exercise, however they will come much easier after you have can consistently execute the higher slurs . If you get stuck on a certain set of overtones, use a higher series such as the ones based off low B, C or Db to transition from a higher slur down to the more challenging slur.
The Why
This kind of practice works the muscles of the vocal tract in a more intense way than the run of the mill overtone playing. It's another level of overtone practice for those who have extended their range to 4 octaves or more and need an exercise to help them continue developing their muscles without the threat of embouchure tightening that can easily result from practicing prolonged periods in the extreme upper register.
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