Melody

Interval - The distance between two notes (See: Intervals)
  Step - A 2nd, or two notes adjacent on the staff
    Half Step - A step whose two notes are as close together as possible (ex. G and Ab)
    Whole Step - A step whose two notes have one other note between them (ex. G and A)
  Skip - a 3rd
  Leap - A 4th or larger

Tritone - An augmented 4th or diminished 5th (ex. C and F#)

Scale degrees (Notated with carets: 1̂2̂3̂4̂5̂6̂7̂)
  1̂ - Tonic
  2̂ - Supertonic
  3̂ - Mediant
  4̂ - Subdominant
  5̂ - Dominant
  6̂ - Submediant
  7̂ - Leading tone/subtonic
These scale degree names can also be used to refer to the chord built on them, i.e. "the tonic chord" being the I chord.

Chord Tones - Notes contained in the underlying chord

Non-chord Tones - Notes not contained in the underlying chord. Typically, when they appear in a melody, they fall into one of the following use cases:
  Passing tone - A note that connects two different chord tones by step
  Neighbor tone - A note a step above or below a chord tone that then returns to the same tone.
  Appoggiatura - A note on a strong beat that resolves by step, typically approached by leap in the opposite direction.
  Escape tone - A note on a weak beat that resolves by skip or leap, approached by step in the opposite direction
  Suspension - A note from a previous chord that "hangs over" into the next and resolves by step, typically downward.
  Anticipation - A note from the coming chord that "jumps the gun" by sounding before the current chord changes to include it.

Phrase - A musical "sentence", typically 4 or 8 measures long, ending with a cadence.

Motive - A short musical idea, typically 2-8 notes, often repeated or sequenced within a phrase

Sequence - Repetition of an idea but shifted one or more notes up or down

Contour - The overall shape of a melody in terms of intervals

Resolve - To move from a state of tension to relief, dissonance to consonance, or instability to stability

Chromatic - Using accidentals to move by half steps


Harmony

Root - Note on which a chord is named and built.
  Root position - A spelling of a chord where the root is the lowest note
  Inversion - A spelling of a chord where the root is not the lowest note

Chord types
  Triads - 3 distinct notes: the root, the 3rd, and the 5th
     Major, minor, diminished, augmented
  7th chords - 4 distinct notes: the root, the 3rd, the 5th, and the 7th.
Dominant, Major, minor, minor-major, diminished, half-diminished (Link)

Roman Numerals - Indicate a chord built on a certain scale degree. Capital for major, lowercase for minor, b or # indicate the root is lowered or raised. Inversions are notated with intervals above the bass: I6 for 3rd on bottom (1st inversion) and I64 for 5th on bottom (2nd inversion)

Example in the key of C:

Cadence - A specific chord sequence at the end of a phrase
  Authentic cadence - V -> I or i
    Perfect Authentic Cadence - Both the V and I chord are in root position, and the melody moves by step to 1̂
    Imperfect Authentic Cadence - Either of the conditions for a PAC are not met.
  Half Cadence - Anything -> V
Phrygian Half Cadence - iv6 -> V specifically
  Plagal Cadence - IV or iv -> I or iv

Secondary Dominant - A V chord borrowed from another key.
Examples in the key of C:

The D major chord isn't found natively in the key of C, but it is the V chord of the key of G. Here it's borrowed to intensify the movement to G before finally resolving back to C. Notated I, V/V, V, I, because D is acting as the V chord of the V chord, hence secondary dominant.




 Another example would be C, A, Dm, G, where A is the V chord of the ii chord, Dm.

I, V/ii, ii, V



Modulation - Transitioning from one key to another, often mid-phrase

Parallel keys - Major and minor keys starting on the same note

Relative keys - Major and minor keys sharing the same key signature

Mode Mixture - The use of chords from another mode starting on the same note. (Mainly, using chords from a parallel key, such as using chords from Cm in C or vice versa)

Picardy 3rd - Occurs when a passage or piece otherwise in a minor key ends with a Major I chord.

Diatonic - using the notes provided by a key signature (as in, not chromatic—no accidentals)

Tonal/tonality - Refers to a system of music defined by the relationships between scale degrees and chords to a primary note (the tonic or I/i chord), set in a major or minor key with all its implications. Almost all Western music is tonal.

Modal/modality - Refers to a system of music using a primary note but not necessarily including defined chord/scale degree relationships. Typically diatonic, but not limited to Major/minor keys.


Rhythm

Meter - The number and grouping of beats per measure (defined by the top number of the time signature)
  Duple meter - 2 beats
  Triple meter - 3 beats
  Quadruple meter - 4 beats
  Compound meter - each beat is divided into 3 smaller beats (6, 9, 12)
  Simple meter - division of beats not specified (2, 3, 4)

Downbeat - the first beat of a measure

Upbeat - Context dependent. Can mean
  1.) Beats 2 and 4 in quadruple meter, or 2 and 3 in triple meter
  2.) Offbeats (ex. halfway between beats 1 and 2)
  3.) A pickup, or the beat before a downbeat/beginning of melody
  4.) Uplifting and energetic

Subdivision - The division of a beat into smaller note values (ex. a quarter note can be subdivided into 8ths, 16th, or triplets.)

Strong and weak beats - Beats that are more or less emphasized depending on meter. Downbeats are always strong (and beat 3 in quadruple meter), upbeats are weaker and offbeats are weaker still.

Syncopation - Rhythmic emphasis of a weak beat that "covers up" the following stronger beat.

Hemiola - A rhythmic effect caused by grouping 6 beats into 3 groups of 2, when they previously have been 2 groups of 3.


Form and Style

Form - the structure of a piece of music in terms of larger sections
  Binary Form - AB, where A and B represent distinct sections with contrasting characteristics
  Ternary Form - ABA or ABA'
  A' (or any letter ') - Pronounced "A Prime", where a section is clearly the same as a previous A section but altered in some way, especially the ending.
  Rondo - A form with a key theme that returns between successive new material (ex. ABACADA)

Style directives - indicate tempo and/or aesthetic characteristics by which a piece or section is to be played.
Tempo, from fastest to slowest, all ranges are relative:
  Presto - Rapid (168-200 bpm - beats per minute)
  Vivace - Lively, fast (138-168)
  Allegro - Cheerful, fast (116-144)
  Moderato - Moderately (100-120)
  Andante - "Walking", casual (70-100)
  Lento - Slow (54-90)
  Adagio - Very slow, expressive (48-76)
  Largo - Broad, slow (40-60)
  Grave - "Grah-vey" Serious, slow, still (<44)

Suffixes can be attached to some of these to modify their meaning
  -etto - A little, or somewhat. (ex. Larghetto—a little slow, not as slow as Largo. Allegretto—a little fast, not as fast as Allegro.)
 - issimo - Very (ex. Prestissimo—extremely rapid.)

Modifiers:
  Non - Not
   Con - With 
   Senza - Without 
  Più - More
  Meno - Less
  Molto - Very
  Poco - A little
  Ma - But
  Tanto - So much
  Troppo - Too much
  Sempre - Always
  Simile - In the same way
  Subito - Suddenly
  Quasi - As if, partially, almost 

Mood/aesthetic:
  Agitato - Agitated
  Animato - Animated, with spirit 
   Appasionato - Passionately 
  Cantabile - In a singing style
  Giocoso - Merrily
  Grazioso - Gracefully
  Dolce - Sweetly
  Espressivo - Expressively
  Leggiero - Lightly, swiftly 
 Maestoso - Majestically