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What is music?
Map of the fretboard
The Major Scale
The C Major scale
Notes "or pitches" are the most absorbing of the elements that make up music. The time elements, like tempo and rhythm, are more of a 'feel' thing. Notes, however, are a more exacting science. The way they blend together, and, more importantly, don't blend together is a never ending source of wonder to me, even after playing for 50 years.
Melody is the 'linear', or horizontal, way of using notes, where they come one at a time with time; Harmony is the vertical way, where notes ring out together as chords.
Scientifically speaking, sound is really molecules of air, moving in waves, that reach our eardrums and translate into all that we hear. The waves are measured in hertz, or 'how many waves hit your eardrum per second'. We can hear tones from about 20Hz (very low) to 17,000 Hz (very high). The note A, second fret of the 4th string, rings out at 440 Hz; the open A string, an octave lower, rings out at 220 Hz; the A note on the thin string, 5th fret rings out at 880 Hz. So, take any note, double its frequency and you have that same note an octave higher; half it, and you have the same note an octave lower.
It's all mathematics. Here's another example: The formula for determining how far apart the frets on a guitar should be is f2 = 21/12 x f1 ... if that's not mathematics, I don't what is. But it's the art of making music that I love, not the science. I find it endlessly fascinating that we can manipulate sound in the ways that we do through musical instruments, that these sounds can affect us so deeply.
If you're at all familiar with the piano, you'll know that those '#/b" notes -- sharp/flat -- are the black keys on the keyboard. Guitars make no distinction between natural notes and the #/b notes, they're all mixed in together and look the same on the fretboard.
Because of browser incompatibility, I'll just use the hash sign (#) and a lowercase B (b) for those symbols throughout the site.