rabeach
The Scientific Pitch Notation is the American Standard Pitch Notation. The USA has not even adopted the International System of Units (SI) so I wonder by what authority is the American Standard Pitch Notation being referred to as the Scientific Pitch Notation.:-)
Scientific Pitch Notation is not a part of the midi specification. Midi specifies frequency by addressing five octaves below and above middle C and assigning midi note 60 to middle C. Nowhere is C4 specified as the pitch notation for midi note 60 or is the Scientific Pitch Notation adopted in the standard.
Sorry if my point was ambiguous. The MIDI spec is, as you note, mute about the use of octave notation. It does define a middle C note number, from which one can logically derive the octave location of the other MIDI note numbers. The confusion suffered by the OP and others comes from the fact that the notation of the correct octave by various designers of MIDI devices is not standardized to a common notation. To find such a standard, they, and the musicians of the world, would need to look outside of the MIDI spec to a widely accepted standard. There are historically a bunch of ways that octaves have been referenced including by name, location on various instruments, use of alphabetical abbreviations etc. American Standard Pitch Notation was put forth by the Acoustical Society of America in the 1930's as a simple standard using a note name followed by a number to indicate the octave, which can be easily recognized and converted to a frequency by someone who does not read music (scientists and the like). Whether this system is more scientific than say the Helmholtz system is arguable, but it is actually more widely recognized by that name than by the American Standard appellation, and is the only way you are likely to find octave notation in scientific articles. In any event, using the style of the scientific notation system but moving the middle C to C3 or C5 can only cause unnecessary confusion.
There is also some confusion introduced by the use of the term
scientific pitch to define an even tempered scale based on C4=256 which is favored in physics textbooks and articles because it allows all the C's to be whole numbers in the binary system. The standard accepted by most musicians is the International Standards Organization Acoustics -- Standard tuning frequency (Standard musical pitch) iso16:1975 which sets A in the treble clef to 440 Hz +or - 0.5 Hz, putting C4 at a mathmatically less attractive 261.62 Hz.
Système International d’Unités (SI, International System of Units) does not include a musical pitch designation at all but uses a derived unit of frequency, the Hertz