There are 12 tones in our Western musical system. There could be more, there could be less, but in Western music, the use of 12 tones is the given. We are given 12 tones to create music with. A tone can also be called a pitch. Pitch is the relative highness or lowness of a tone.
This 12 tone system is called Equal Temperament (equally spaced half steps). Just Intonation is another system of tuning based on the pure vibrations of nature (where the harmonics of a given tone are the basis of the tuning - only that key is in 'perfect' tune).
The 12 tones lie one-half step to the next or previous. On the guitar, one half-step is one fret. Every next tone (fret) is one half-step away. Half-steps can also be called semitones (where a tone is a whole step, which equals 2 semitones). We will be using the term half-step in every instance.
For whatever tone we put at one, we cycle through the 12, then back to the original (whatever we put at one). Any of the 12 tones can be placed at 1. After 12, we go back to 1.
So, the first piece of our music theory system: there are 12 tones [for teachers: "same number as months in a year" aids as a statement], and they lie ½ step apart.
One possible relationship between colors & music tones:
The 12 consist of:
The chromatic scale is a summary of 12 half steps, starting from any tone (our musical ruler for measurement):
A note that is 2 half steps away from a given tone is called a whole step (w or 2; on guitar a whole step is 2 frets). Example: C to D. The whole step should not be confused with the whole note () in musical notation (rhythmic duration).
There are two more naturals than sharps/flats; therefore, there must be two places where naturals touch. These naturally occurring half steps exist between B/C & E/F (no sharp or flat between). B goes directly to C, and E goes directly to F. [B# is C, Cb is B, E# is F, Fb is E].
The two pairs of naturally occuring half-steps are in the above. There isn't a sharp/flat between those tones (the two places on the piano with no black note between = B/C & E/F).
A key is a tonal center. The key is the central tone that a piece of music finally rests (tonality) in our ear.
Chords are a combination of '3' or more tones played together (harmony). 2 tones work just fine too. Ultimately, a single ringing tone is a chord [Harmonics].
Scales are a series of individual tones played one after another - alphabetically (whether naturals or sharped/flatted tones) ascending & descending. They are tone groups.
Arpeggios are chords played one note at a time (ringing or not ringing together). An arpeggio is a 'broken chord.'
A root is a tone that names a key, chord, or scale. It is the starting point for building something. It is the number 1 [or zero with Numera] in our traditional music theory system for building anything. It can also be denoted R or 1 (or 0 in numberical chromatics).
We are running against music dictionarys with our definition of the word root. Dictionaries call the base tone of a chord, a root, while calling the base tone of a scale, a tonic. This is a semantic point, yet important. Our basic point is that if a tone of a scale can be a root of a chord, it can also be a root to a scale. We can build anything from a given root. Scale tones are often called degrees (& have their own corresponding names).
When we play an instrument that can sound all the tones of a scale at the same time, is that not a chord?
The naming of a scale degree as a root doesn't inflict any theoretical damage, rather, it creates one less boundary. You can call it Frank if musicianers you work with also call it Frank. The purpose of theory is to create a language that is capable of communicating musical ideas. The only worthwhile theory for us, is applied theory. In musicianer's applications, root is used as we are defining it. Usage dictates meaning, not musicologists defining boundaries.
With our definition, there is more intellectual freedom & the understanding that chords & scales are ultimately the same thing.