Does a paper exist on this subject.
Engineering octave (2xfrequancy) and ear brain octave are not the same thing. Our brain needs more than x2f, x4f, x8f otherwise it sounds cheap and small, flat.
This is an excellent publication on the subject. Octave equivalence - Terhardt:
http://www.mmk.ei.tum.de/fileadmin/w00bqn/www/Personen/Terhardt/ter/top/octequiv.html
At very high notes the difference what our brain wants and what simple intenger multiplication of frequency gives is magnified.
So, how far up is Dave Gilmour's intonation on the highest note of Comfortably Numb - Pink Floyd on the electric guitar solo towards the end of the song from "equal" temperament calculations?
Is it close to half semitone up (from "equal" temperament calculatiins) so that it sounds perfect and breathtaking to those millions of satisfied Pink Floyd listeners.
How about the high note intonation of the great St Martin in the Fields Orchestra conducted by Sir Neville Marriner. For example on Corcierto d' Aranjuez part 2.
How about the very high notes from the electronic Solina String Ensemble organ on those brilliant French band Air songs possibly inspired by the high note night forest sounds of Versailles? Is the recording studio near the forest? How much was the master tuning control of the Solina increased so that those very high electronic string notes reminds us that we are humans?
Other fabulous sounding high notes that would be of interest to be measured are on the song I've Had the Time of my Life from the movie Dirty Dancing.
See also the Pleiades tuning.
Is inputing numbers on an online tone generator while the music is being played at very low acoustic volume a way to do these comparisons? Low volume is needed, as pitch depends on acoustic intensity, so that meaningful comparisons can be made. Here is a brilliant online sinewave generator
http://onlinetonegenerator.com
Reference:
Engineering vs ear brain octave - euroelectron
Bibliography:
Sound and Hearing - S. S. Stevens, Warshofsky - Life science series - from page 77, The Mind's Influence
(Engineering) Octave Strech - Terhardt
http://www.mmk.ei.tum.de/fileadmin/w00bqn/www/Personen/Terhardt/ter/top/octstretch.html
Octave Equivalence - Terhardt
http://www.mmk.ei.tum.de/fileadmin/w00bqn/www/Personen/Terhardt/ter/top/octequiv.html
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