Quote:
Originally Posted by RockManDan By the time the mid-20th century had rolled around, people had pretty much exhausted the melodies of basic diatonic scales. |
That's pretty much a ludicrous claim.
Even if we define "melody" as just enough notes to set one line of iambic pentameter to song [that'd be ten notes] and confine ourselves to one octave alone, the number of possible diatonic melodies is 8 ^ 10, which is well over a
billion distinct melodies.
And that's ignoring the fact that we can use a great variety of accidentals, note durations, added octaves, multi-section phrases, etc. Even if we were to grant that a melody shouldn't skip around randomly through the diatonic scale, the number of pleasing-sounding melodies generateable with the simple tools of diatonic scales [we'll leave out chromaticism entirely], rhythmic variation [heck, let's even leave out dotted notes and allow ourselves only the breve, semi-breve, minim, and crotchet], and larger forms [say, a 4-line stanza of iambic pentameter], we'd end up with millions upon millions of possibilities.
Start on the tonic, then progress by step or skip of a third [allowing ourselves only one melodic "leap" for interest] for four lines of ten notes, then return to the tonic, allowing for notes to vary rhythmically among four possible durations:
Something like: 1 * ( 5 ^ 9 [9 notes in a row of one step or skip up or down] * 7 [our one melodic leap] ) * 4 [we can have four such melodic lines] * 4 [each note can have four rhythmic values] = ~219 million melodies.
[actually, I just completely botched that math... much of the multiplication would actually be exponentiation, giving an astronomically large number, in the order of magnitude of billions
of billions]
Let's presume that there are roughly 100 million songs that were written during the second millennium [roughly the frame of time the diatonic scale ruled alone]. Now, let's imagine what kind of musical material we'd need to have, at the the turn of the 20th century [near the end of that second millennium] to have truly "exhausted" the possibilities [assuming, of course, that every song had a different melody].
Let's say a "melody" could contain only 4 notes [any of which with equal probability], and each note could only take 4 rhythmic values. That gives us 16 possible options at each point in our melody.
How many notes would we need to have 100 million possible melodies? That is, how many notes long would a "melody" be? Would we need to be composing symphonies or folk songs before exhausting our possibilities?
Turns out we'd need somewhere between 6 or 7 notes to a melody [remember, each of which can only contain 4 different notes and 4 different rhythmic values] to generate 100 million melodies.
Even the simplest of musical systems [pitch + timing] turns out to be virtually infinitely combinatorial.
Even a morse code binary system of either "short" or "long" notes, that could take either pitch "a" or pitch "b" would give us over a million distinct melodies after just 10 notes [only four possible "notes"]!