For whatever scale (the specified set of musical notes ordered by pitch) you’re in, the first note of the scale is the root. I will be focusing on major scales, which are one of our most commonly used types of scales. If you’re interested in other scales, check out the patterns for minor, augmented, and diminished, to name a few.
A major scale is built using five whole steps and two half steps. You can think of a whole step as going from one note to the next, for example C to D, and a half step as going from one note to its sharp or flat, for example C to C#. Major scales contain seven different notes, with the eighth note being the octave of the root.
Each scale has seven modes: Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian (a trick for remembering this is I Don’t Punch Like Muhammad A Li). The mode that the scale is in tells where the whole and half steps are placed. A very commonly used mode is the first mode (Ionian), which starts with the root note and follows the pattern WWHWWWH, where W = whole and H = half. In the C major scale this would be CDEFGABC. The second mode starts and ends on the second note of the scale, but stays within the scale’s key, causing the pattern to change. In C, the Dorian mode scale is DEFGABCD (with no sharps or flats since C major has no sharps or flats).
The chromatic scale contains all twelve tones (aka each different note that can be played on a piano). Music theory has a visual representation of relationships among these twelve tones, called the Circle of Fifths. If you follow the circle clockwise, each note is the fifth of the preceding note, meaning that if you think of each note in turn as the root of a major scale, the note following would be fifth of that scale. Going counterclockwise gives you a circle of fourths.
Notes that are placed very close together on the scale have pitches that are close together, meaning that their frequencies are very similar. Playing two of these notes at the same time, for example C and C# or C and D, creates an interference pattern that alternates in volume between loud, when the waves have constructive interference, and soft, when they have destructive interference. This produces a beating sound. When tuning an instrument, hearing a beat frequency means your note is slightly off pitch from the note you’re trying to match. You can hear this frequency by playing two notes side-by-side on a piano.