Bartok - Mikrokosmos Book 1 - 91)* Syncopation(1)
What's the meaning of the notes in between the Grand Staff?
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The star in the middle of the staff actually points us to a footnote given at the end of this first book. In my edition (Boosey & Hawkes), the footnote states:
The rhythmic feeling of the suspensions should be emphasized by some energetic movement such as tapping with the foot in the places marked by rhythmic signatures between the staves.
From a pedagogical standpoint, this helps the performer place the next pitch accurately within the measure. Young musicians often speed through long held notes, so forcing a young player to think about beat 1 of the second measure will help them more successfully play beat 2.