From the earliest times Music was potent magic - altering the minds and emotions and thus altering reality thru its effects on the behavior of listeners.

Vibrational Basics

A note is a single tone, pitch or frequency.
A doubling of the frequency of any note produces a higher note with the same pitch, as in middle C and high C on a piano. this is known as an Octave.

Octaves go on forever above and below our musical scale, they are simply halving's or doublings of frequency. One drum beat per second is what middle C sounds like 8 Octaves down. By some strange coincidence, there are 50 octaves from a beat of one per second (the lowest range of the human heartbeat) to the frequency of visible light. A beat or Rhythm is a couple octaves below what we hear as music and light and color are a few dozen octaves above music.

A chord is any two notes or pitches played simultaneously.
All chords produce certain sounds which are unique because whenever two notes are played together, a third note or beat is also heard. this third note is not inherent in either note but only as a synergetic consequence of their unity, constructed in the brain.
Two notes played together produce a third, three notes played together produce three other notes from the various combinations of two notes, four notes produces six new tones, five produces eleven, and so on. The notes may not always sound like musical pitches because their frequencies may be below 16 cycles per second, the minimum frequency that sounds like a note to our ears.

The secondary notes (children, or 2nd level 'iteration' (repeating sequence) of the first notes) interact with one another and create tertiary notes (grandchildren or 3rd level iterations) and so on, to infinity, so that the combinations become rather astounding.

Standing Waves - sound and form
When a vibration or wave reflects off of something, such as another wave, it can interfere with its own reflection. The interference is alternately constructive or destructive as the two waves move past each other. This creates a standing wave . Only waves with certain frequencies can create standing waves. This is because the distance from one node to the next must always be some fraction of the total length (one half, one third, etc.).

all objects have a frequency or set of frequencies with which they naturally resonate when struck, plucked, strummed or somehow disturbed. Each of the natural frequencies at which an object vibrates is associated with a standing wave pattern. When an object is forced into resonance vibrations at one of its natural frequencies, it vibrates in a manner such that a standing wave is formed within the object. So the natural frequencies of an object are merely the harmonic frequencies at which standing wave patterns are established within the object.

These standing wave patterns represent the lowest energy vibrational modes of the object or complex system. While there are countless way by which an object can vibrate (each associated with a specific frequency), objects favor only a few specific modes or patterns of vibrating.
The favored modes (patterns) of vibration are those which result in the highest amplitude vibrations with the least input of energy.

Test this: Step into your bathroom and close the door. If it's a bathroom with lots of tile it should be quite resonant.
Hum a melody or a variety of different notes .... you will notice one note seems to "Echo" considerably longer and sound louder than the others. This note is the resonant pitch of your bathroom. The room wants to vibrate along with that note - and the note travels thru the surfaces with less loss of energy and therefore echoes louder. This can be used for psycho-acoustical effects by testing and then playing a song in the Root-Note of a room, so that the room itself acts as an amplifier for the vibrational structure of the song.

the Musical Scale

The musical scale is not an accident. It is a natural consequence of pure mathematics and nature. It's more proper to say it was discovered - not invented. This is one reason why music can be seen as the true universal language. Music is vibrational physics and math that is sensed almost as a language be the ear/brain combination. Many musicians tend to overlook or forget this fact.

The scale we use divides the octave based on the harmonic series into 12 notes, the 12th being the same note an octave higher than the first. Many other harmonic subdivisions of the octave are possible yielding scales of 42, 60 even 360 notes (ancient chinese scale) per octave. Music has existed in written form as far back as the ancient Sumerians It is an interesting 'coincidence' that the old frequency for middle C seems to have been about 256, which is a doubling of 128, which is 64 doubled, which is 32 and so on, neatly landing back at the number 1.

Spheres of Sound:
Illustrated sequence of wave vibrations on the harmonic diagonal
(from http://www.lambdoma.com/ )
The tone C is the whole, a ratio of 1:1, therefore C encloses the total space.
The tone G*, a ratio of 2:3 or 12 in inverse, falls next in the sequence, so becomes 2 of C. Subsequent tones of F, 3:4; A, 3:8; E, 5:6; B, 9:16; D, 8:9, all become 2 of the previous tone and form comma-like wave motions when drawn, so that an extended line does not twist when it meets the diagonal. It is thus easy to see an expansion or contraction.

An expansion goes away from the diagonal, while a contraction moves toward a diagonal. By reducing the scale , the whole takes on the familiar form of the PROGRESSION BY SQUARES, and is likened to a falling body.
* Note: For the drawings the ratios are in wavelengths. Some of the wavelengths are in inverse relationship to the frequencies of the notes. Therefore 2:3 in frequencies in music is an F, while 2:3 is a G in wavelength.

41 Octaves above Sound - notes have color

We hear about ten octaves of sound and see about one octave of light with our eyes.
Because going up an octave is doubling, each octave has a bandwidth (range of frequencies) that is as large as the sum of all bandwidths of the preceding octaves (similar to each time a population doubles). This means that visible light, 41 octaves up from from the middle of our hearing range, is an octave with a bandwidth many times greater than that of all 10 octaves of the hearing range. So the human eye has a very wide range even though it sees in only one octave.