I found another academic study online, this time a doctoral work by Thomas Zinninger in 2013 entitled
An Analysis of Concert Saxophone Vibrato Through the Examination of Recordings by Eight Prominent Soloists. These soloists were top names from the classical saxophone world over many years (Abato, Bornkamp, Delangle, Londeix, Mule, Murphy, Rascher and Rousseau).
The work contains a section on Variance Above and Below Pitch which seems most relevant and here are some brief extracts.
- On pre-existing recordings, far too many variables such as intonation of the soloist, intonation of the accompaniment, or playback speed of the recording exist to simply measure a note against its “correct” pitch. Furthermore, the “correct” pitch within the software will always be with respect to equal temperament tuning, a system the saxophone is not constrained by. The only way to measure the amount of vibrato extent above and below the intended pitch on pre-existing recordings was to find notes that contained both straight tone and vibrato.
- Thirty-four notes (an average of 4.25 per soloist) across all recordings were found that contained both straight tone and vibrato. The majority of these had straight tone at the beginning of the note with vibrato added later, but the opposite was found in a few. The extent from the straight tone to the highest pitch and lowest pitch within the vibrato cycle was measured and then compared to the overall vibrato extent of the note. The mean extent across all soloists was 28.7% above the pitch, and 71.3% below the pitch. This finding agrees with the pedagogical belief that saxophone vibrato exists mostly below the intended pitch, but conflicts with those who believe it is only below the pitch. Of all notes measured, only two (one by Bornkamp, and one by Londeix) had zero extent above the static pitch.
- Each soloist followed the general trend of playing vibrato with a greater extent below than above pitch, although Delangle’s variance was close to even. Rascher was the only soloist to use vibrato that neared 100% below the pitch. It is clear that the notion of saxophone vibrato being “under” the pitch is quite universal. Of every note measured, only three (one each by Bornkamp, Delangle, and Rousseau) had a greater variance above the pitch than below.
Again, this is for classical saxophonists only, but the methodology is interesting and the conclusions well supported by actual data from musical (rather than laboratory) recordings rather than subjective impressions or intentions.
Rhys