theory

[Tom Cole]

Thanks, Dave, for your definitive explanation of interval nomenclature.
Having been blessed/burdened with musical training myself, I am equally
concerned with the proper spelling of both musical intervals and words.
The convention of the use of the word "sharp", I believe, only applies
to the physical key and to dogmatically call the black notes of
intervals "sharps", irrespective of their relationships to other notes,
is to ignore musical convention and I don't think we want to knowingly
do that.

I don't expect that everyone on this list has a music education and this
mistake will be made, of course. But I'm not sure that this point has
been made before and I'm glad that you did.

Tom Cole


Dave Nereson wrote:
> 
>     To my mind, "piano tuning theory", music theory, and historical temperaments are all the same theory, that is, the mathematical relationships in the Western, or European diatonic scale (as opposed to 5-tone scales, 1/4-steps, etc. used in other parts of the world).  Yes, F to G# is an augmented second and F to Aflat is a minor third, because Fanything to G anything has to be some kind of second,  and F anything to A anything has to be some kind of third.  Regardless how those intervals are tuned, whether pure ("just") or tempered, they should still have the same names, the accidentals (sharps & flats) determining whether they're 'perfect', 'Major', 'minor', 'diminished', or 'augmented'.  They can even be doubly augmented or doubly diminished, depending how they're spelled.  But somewhere along the line, piano tuners decided to call the black keys "sharps".  We re-lacquer or refinish the sharps, not the flats, even though they're the same.  The reason was probably so they!
 c!
> ould call the black notes by one name, rather than two,  when writing down, teaching, or notating different temperaments.  After all, some of the white keys also have two names:  C is also B#; B is also C flat, and the same with E & F.  And in some pieces of music, double sharps and double flats occur.  C## is D;  C double flat is B flat, etc.   But this would get sticky when writing, teaching, or learning temperaments, so "let's call them all sharps" must have been the consensus, or convention.
>     In equal temperament, an attempt is made to make all like-kind intervals expanded or contracted by the same amount so that one can play in all keys with no overly offensive intervals.  In the historical temperaments, some intervals of the same type are expanded or contracted more than others.  This makes some keys sweet and harmonious, others grating and dissonant, depending which chords are used.  But they're still spelled the same on the sheet music.
>     String players will (unconsciously sometimes) play F# sharper than G flat, if the F# is in a dissonant chord that's resolving to a consonant one, that is, if the F# is a seventh resolving to an octave or an augmented 4th resolving to a "perfect" fifth ("perfect" meaning that it's not diminished or augmented, even though on the piano, it may be contracted from a perfect 3:2 beatless fifth).  F# and G flat, in equal temperament, may be the same frequency, but to make sense musically in terms of key signature and chords, they're not interchangeable.
>                                                                                         --Dave Nereson, RPT & former music major