> How many notes are there?” Boulanger would ask. 12? 88? As many as could be imagined? The answer Boulanger sought was seven, the diatonic scale, to which everything else was an inflection or embellishment.
That's a strange view I have never encountered before. In nature there's an infinite number of frequencies, and in the Western system of equal temperament, surely there are the 12 notes of the chromatic scale?
To think that sharps or flats are not really notes, but simply modulations of actual notes is... unusual? I wonder what she based this on, and who shared the same ideas... Is there a tradition that has historically taught this as well?
Not unusual, historical. The primality of the diatonic scale in Western music goes way back, and even now we use the language of the diatonic scale when trying to describe each of the twelve notes in our system. But it's more than just names: it's ingrained in the structure of our music as well, as to what notes and harmony are chosen.
In the early 20th c. a more expansive, what we call "atonal," form of music arose that used the chromatic scale without any particular referent to a diatonic system. Some music analysts and teachers even started to replace note names with note indices to avoid diatonic confusion. Atonal composition became popular among avant-garde and film composers in the mid-20th century, and is still with us. The diatonic system, though, has proved quite tough to kill off.
That is actually the way I think of notes in tonal music: You've got a root, a second, a third, … , a sixth and a seventh. But there are different kinds of each degree of the scale (apart from the root): the second could be minor or major or augmented (`sharp 9' is jazz lingo); the third could be major or minor etc.
But you don't have to choose just one type of third or fifth etc. in a given piece of music (or part thereof). You can have a single melodic phrase that uses both the major and the minor third, but I think of these as two different `inflections' of the same degree of the scale, the third.
Likewise, you can have a chord that contains more than one version of the same degree of the scale. In the chord E7#9 (E, G#, B, D, F##) the G on the top is being described as F##, but what I hear is two different versions of the third (major and minor) simultaneously.
Blues music certainly thinks in this way. When a blues musician bends around on the third or fourth, it's all the one note, but `inflecting' or `embelishing' that note.
Ah yes, it makes sense when put that way. (Yet most of the time in a melody, a note that is outside the scale doesn't much sound as an inflection but as "wrong". Whereas a small vibrato (oscillating around the proper pitch without going too far away) feels more like a true modulation. And a portamento can make use of frequencies that aren't even in the chromatic scale at all.)
In a scale that can compose into chords, anything too adjacent is dissonant, so doe ray mi fa so la ti or some of the other keys or modes could be considered a base.
Not really. White keys are only "proper notes" in the scale of C major (or Am); in other scales, notes can fall on black keys, modulated by white keys; and also, the modulation is sometimes above and sometimes below the note, depending on the scale, something that the keyboard doesn't emphasize or make visible in any way.
That's a strange view I have never encountered before. In nature there's an infinite number of frequencies, and in the Western system of equal temperament, surely there are the 12 notes of the chromatic scale?
To think that sharps or flats are not really notes, but simply modulations of actual notes is... unusual? I wonder what she based this on, and who shared the same ideas... Is there a tradition that has historically taught this as well?