Triads are the fundamental building blocks in diatonic harmony. (Read The Essences of Harmony.) You probably are familiar with triad arpeggios, but players always practice arpeggios as a melody.

Try this:

  1. Sing a note. 
  2. From that note, sing a major triad arpeggio – three notes only.

Did sing the arpeggios starting on the root go up the triad (IE: F, A, C)?

Nine of ten saxophonists sing from the root position, starting on the root going up. That is how method books teach arpeggios. It is a melodic approach to learning arpeggios, which mainly develops basic finger technique.

Now try this:

  1. Sing a different note. 
  2. Sing a major triad going down from the root (Root, 5th, 3rd).  
  3. Sing three notes, only.

How easy was singing the arpeggio down compared to singing up the arpeggio? For most players, it is easier to sing the arpeggio up even though they both started on the root of the chord. Also, the second arpeggio was in the second inversion (pop up).

In addition to developing finger technique, singing in different directions with different inversions develops harmonic imagination. To sing the arpeggio down, you must hear the bottom note.