: A pentatonic scale has 5 notes per octave; a western scale has 12. You might think
: that there is not much chance that the pentatonic scale is a subset of the western
: scale, maybe just another set of 5 chosen frequencies. But as you pointed out, the 5
: black keys are a pentatonic scale and that is definitely a subset.
: How does it happen that the scales are not completely unrelated? I would say “Ask a
: musicologist”; I am an electrical engineer with a background in math and physics.
: But you were already talking to a musicologist, so I'll take a try at an
: explanation, but don't believe all that you hear here.
: … and note that it ignores Scott Gleeson’s question about picking American folk
: As things vibrate in nature, wind through the trees, air through a pipe, a plucked
: string, a piece of metal hit by a rock, they vibrate in natural frequencies
: depending on physical dimensions, material properties, and a host of other factors.
: They also create harmonics at the same time. If you multiply a frequency by an
: integer (whole number) and keep dividing by 2 until you get a number that is less
: than twice the base frequency (that is, less than an octave away), you will get a
: note from a natural scale. Repeat this with enough integers and you’ll get the whole
: natural scale.
: These, unfortunately, are not geometrically spaced, so physicists even them out by
: using a constant multiplying factor between notes (twelfth root of 2). A nice thing
: about doing it this way, is that scales based on any note from the “physics” scale
: are a subset of the previous scale. This is not true of the natural scale. By the
: way, notes from the natural and physics scale are so close that most people can’t
: distinguish one entire scale from the other, although they can distinguish a note
: from a scale, from the same note on the other scale.
: That’s my take on it. Anyone else want to take a try?
: --Previous Message--
: We were talking with a musicologist friend a few weeks ago, my burning question was
: what do people believe these days is the biological basis of music, is there a
: universal basis for music across human cultures? She said that there is
: surprisingly little that is universal, and the biological basis is still a mystery.
: The main universal seems to be the octave, and beyond that probably the pentatonic
: scale (12356, the black notes on the piano). She said this seems to be found in
: almost all folk music.
: She asked for an example American folk song (she is Israeli). Without thinking I
: said “Tom Dooley”. We sang it and sure enough, entirely from the pentatonic scale
: (the only exception is the high part sung with the chorus, which includes a 4, but
: this was probably added later by the Weavers, sounds like classic Pete Seeger
: counterpoint). Another notable feature about Tom Dooley is that the chorus has the
: same melody as the verse, which adds to the monotonous quality. So maybe, rather
: than looking for other songs with two chords about murder, they should have been
: looking for other pentatonic tunes. One that struck me today is “Paradise”, a John
: Prine tune I love that also has the verse and chorus sharing the same melody, and
: sure enough, all pentatonic all the time. Also two chords, maybe also about a
: murder of sorts (“Mr. Peabody’s coal train has hauled it away”).