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== Harmony ==
''Harmony '' is the pattern of how frequencies interact. Most natural sounds are relatively noisy - they contain a random selection of frequencies. The true definition of noise is sound with equal distribution of all audible frequencies. Consider an untuned radio or TV, which produces white noise - you cannot "zero-in" on any particular frequency, although your brain may try. Noise is chaos, and all true noise is undifferentiatable from other true noise, regardless of its source. Conversely, a pure frequency is represented by a sine wave. Again, this is more easily understood by our minds - we can recognize it easily and even recreate it vocally. But of course it is boring. Popular instruments do not create a pure, single frequency, but a multitude of frequencies (and noise). This is discussed further in timbre below. But most instruments are designed to create notes, which are based around a fundamental frequency. This frequency is the most prominent and recognizable. Harmony is concerned mostly with the interaction of these fundamental frequencies.
When different notes are combined, they produce different waveforms. 2 different notes played simultaneously is known as an ''interval''. 3 or more is known as a ''chord''. Some intervals and chords are perceived as being more harmonic than others. This is driven by the ratio of the fundamental frequencies involved. We have already mentioned that a 4th is 4/3 higher than the base frequency. A 5th is 3/2 the base frequency. Basically, the simpler the ratio between the frequencies can be represented, the more harmonic the two notes are. The simplest ratio is an octave - which is simply 2 x contains 2x the original pitch.
'''Rather than deal with everything in absolute frequencies, note names are used to keep things from becoming complicated. ''' Because the octave is so harmonic, it is treated harmonically equivalent. Once the octave is reached, the note names repeat, and for harmonic purposes they are treated identically. For instance you have an A at 110 HZ and another A at 220 HZ. Also, you have E at 165 HZ, and an E at 330 HZ. The 110-165 HZ A-E fifth interval is harmonically equivalent to the 220-330 HZ A-E fifth interval(both contain intervals with 3:2 ratios). Thus, '''for purely harmonic reasons, absolute frequency is not important'''. Only the relative the frequency of one note to others is important. Between 110 HZ and 220 HZ, you have the notes A, B, C, D, E, F, and G. Between 220 HZ and 440 HZ, you have A, B, C, D, E, F, and G again. Obviously, even if the note names are the same, they will sound differently since they relate to different fundamental frequencies. However, harmonically, A is A, B is B, regardless of which octave it actually belongs to.
While the frequency spectrum is infinite, for harmonic reasons, it is dividied into octaves (n - frequency to 2nfrequency). There are only 12 possible notes in one octave (A, A#, B, C, C#, D, D#, E, F, F#, G, G#). And the most common scales only use 7 of those notes (C Major: C, D, E, F, G, A, B). This does not mean the composer/performer is strictly limited to those fundamental frequencies. It is simply used to provide a simplifying framework to build upon, like tempo. Later we will explore why Western music uses the 12 tones per octave and discuss common intervals, chords, and progressions.
Another topic for the composer is ''arrangement''. Arrangement describes applying some musical idea into a selection of instruments. For example, if you were arranging a piece for flute, piano, and bass, you would likely have the flute play the melody, the piano playing chords, and the bass usually playing the root note of the chords. Naturally, melody is usually given a higher-pitch than the other instruments, and the root note of chords is usually played in the lowest-frequencies. We could come up with different arrangements that are harmonically equivalent; however, they would likely be less enjoyable to listen to.
== Melody ==