A review of some basic music theory before the NYU Steinhardt music technology placement exam.

Intervals

Perfect Intervals: 1(perfect unison), 4(perfect 4th), 5(perfect 5th), 8(perfect octave)
Major Intervals: 2(major 2nd), 3(major 3rd), 6(major 6th), 7(major 7th)

Scales

major scale (WWHWWWH)
natural minor scale / aeolian scale (WHWWHWW) = based off the 6th degree that shares the key signature of the major scale
harmonic minor scale(WHWWH1.5H) = natural minor + sharpened 7th degree
melodic minor scale(ASC:WHWWWWH, DESC:WWHWWHW) = the ascending form of the scale has both a raised 6th and 7th degree, and the descending form of the scale reverts back to the natural minor scale form
chromatic scale(H*12) = constructed entirely of half steps or semitones.
wholetone scale(W*6) = constructed entirely of whole-steps or tones.
lydian scale(WWWHWWH) = based off the 4th degree of any major scale (C major scale from its fourth degree (F) -> F lydian scale)
mixolydian scale(WWHWWHW) = based off the 5th degree of any major scale (C major scale from its fifth degree (G), -> G mixolydian scale)

Tonic: the note considered to be the basis of the chord, e.g.: C, D, …
Quality
- major chords = 1,3,5 notes of major scale, major 3rd followed by minor 3rd;
- minor chords = 1,3,5 notes of minor scale, minor 3rd followed by major 3rd, same as a major chord but the third being lowered a semitone
- diminished chords = similar to minor, but the top note (the fifth) is also flattened, minor 3rd followed by minor 3rd.
- augmented chords = similar to major, but the top note (the fifth) is raised by a semitone, major 3rd followed by a major 3rd
- dominat 7th chords = similar to major, with the addition of a flattened seventh above the root note of the chord (C Dominant 7th = C,E,G,bB); within a diatonic context, it’s based from the 5th/dominant of any major key, so in the key of C major, the dominant 7th chord starts on G (GBDF)
Inversion: which note of the chord is placed at the bottom (root, 1st inversion, 2nd inversion)

Relative minor & major keys: the sixth degree of the major key is the relative minor key, both share exactly the same key signature (C major -> A minor); similarly, to find the relative major of a minor key = either count down 6 notes, or count up to the 3rd note.
To add a flat sign, count up four notes from root; to add a sharp, count up five notes.

Simple meters: the top number in the time signature is a 3 or divisible by 2 (e.g., 2/4, 3/4, 4/4, 2/2, 3/2, 4/2).
- 4/4: simple quadruple, can be represented by a ‘C’, known as common time;
- 2/2 can be represented by ‘C’ with a vertical line through it, known as cut common time
- 2/4: simple duple meter. A bar consists of 2 crotchet beats
- 2/3: simple triple meter. A bar consists of 3 crotchet beats
Compound meters: top number in the time signature is divisible by 3, by a number greater than 1 (e.g., 6/8, 9/8, 12/8). The rhythmic value that is defined in the bottom number of the time signature, is grouped in 3s, which gives them distinct feel
Beams: lines that connect shorter note values and help to clearly display the main beats of a meter.
Grouping: as a general rule, the main beats of the meter must be clearly visible within the displayed rhythm at all times