Piano Music Theory & Notation Syllabus

What does a dot after a note do to its duration? Give the formula.

It adds half the note's value: dotted value $= 1.5 \times$ original, i.e., value $\times \frac{3}{2}$. Example: a dotted half note $= 2 + 1 = 3$ beats.

How many beats is a dotted quarter note in $\frac{4}{4}$ time?

$1 + \frac{1}{2} = 1\frac{1}{2}$ beats (a quarter plus an eighth).

What is a tie, and how does it differ from a slur?

A tie is a curved line connecting two notes of the same pitch, combining their durations into one unbroken sound. A slur connects notes of different pitches and means play them smoothly (legato).

What is syncopation?

Rhythmic emphasis placed on normally weak beats or on off-beats (between beats), disrupting the expected pattern of strong and weak beats.

What is a triplet, and how is its duration calculated?

A tuplet of 3 notes played in the time normally taken by 2 of the same value. Example: an eighth-note triplet fills one quarter-note beat, so each note lasts $\frac{1}{3}$ of a beat.

What is a tuplet in general, and what is a duplet?

A tuplet is any grouping that fits an irregular number of notes into a beat (triplets, quintuplets, etc.). A duplet fits 2 notes in the time of 3 — used in compound meter (the opposite of a triplet).

How do you determine an interval's number (size)?

Count the letter names from the lower note to the upper note, counting both endpoints. Example: C up to G spans C-D-E-F-G = a 5th.

What are a unison and an octave in interval terms?

A unison (prime, 1st) is two notes of the same pitch; an octave (8th) spans eight letter names to the same letter name higher, e.g., $C_4$ to $C_5$.

Which interval numbers can be "perfect," and which can be "major" or "minor"?

Perfect: unison, 4th, 5th, octave (1, 4, 5, 8). Major/minor: 2nd, 3rd, 6th, 7th. An interval is never both perfect and major/minor.

How many half steps are in a major 3rd and in a minor 3rd?

Major 3rd = 4 half steps (e.g., C-E); minor 3rd = 3 half steps (e.g., C-E$\flat$).

How many half steps are in a perfect 4th, a perfect 5th, and a perfect octave?

Perfect 4th = 5 half steps, perfect 5th = 7 half steps, perfect octave = 12 half steps.

What happens to an interval's quality when a perfect or major interval is made a half step larger, or a perfect or minor interval a half step smaller?

A half step larger than perfect or major = augmented. A half step smaller than perfect or minor = diminished.

What is the tritone, and what are its two common spellings from C?

The interval of 6 half steps, dividing the octave exactly in half. From C: augmented 4th (C-F$\sharp$) or diminished 5th (C-G$\flat$).

State the two rules for inverting an interval (number and quality).

Numbers: original + inversion = 9 (a 3rd inverts to a 6th, a 2nd to a 7th). Quality: major $\leftrightarrow$ minor, augmented $\leftrightarrow$ diminished, perfect stays perfect.

What is the inversion of a major 3rd? Verify with an example.

A minor 6th, since $3 + 6 = 9$ and major inverts to minor. Example: C up to E (major 3rd) inverts to E up to C (minor 6th).

What is the order of sharps in a key signature, and a mnemonic for it?

F, C, G, D, A, E, B — "Father Charles Goes Down And Ends Battle." The order of flats is the reverse: B, E, A, D, G, C, F.

How do you identify a major key from a sharp key signature?

Go up a half step from the last (rightmost) sharp. Example: last sharp $C\sharp$ $\to$ key of D major.

How do you identify a major key from a flat key signature?

The second-to-last flat names the key (e.g., three flats B$\flat$, E$\flat$, A$\flat$ $\to$ E$\flat$ major). Exception: one flat = F major (memorize).

What is the pattern of whole (W) and half (H) steps in a major scale?

W-W-H-W-W-W-H. Example: C major = C-D-E-F-G-A-B-C with half steps between E-F and B-C.

What is the pattern of whole and half steps in a natural minor scale?

W-H-W-W-H-W-W. Example: A natural minor = A-B-C-D-E-F-G-A.

How do harmonic and melodic minor differ from natural minor?

Harmonic minor raises the 7th degree by a half step. Melodic minor raises the 6th and 7th ascending and reverts to natural minor descending.

What are relative keys, and how do you find the relative minor of a major key?

Relative keys share the same key signature but have different tonics. The relative minor's tonic is a minor 3rd below (the 6th degree of) the major tonic — e.g., C major and A minor.

What are parallel keys? Give an example and state how they differ from relative keys.

Parallel keys share the same tonic but different key signatures, e.g., C major and C minor. Relative keys share the signature but not the tonic; parallel keys share the tonic but not the signature.

What is a triad, and how is it built?

A three-note chord built by stacking two 3rds above a root: root, 3rd, and 5th.

Define the four triad qualities by their stacked 3rds (bottom to top).

Major = major 3rd + minor 3rd (C-E-G). Minor = minor 3rd + major 3rd (C-E$\flat$-G). Diminished = minor 3rd + minor 3rd (C-E$\flat$-G$\flat$). Augmented = major 3rd + major 3rd (C-E-G$\sharp$).

What are the qualities of the triads built on each degree of a major scale, in Roman numerals?

I (major), ii (minor), iii (minor), IV (major), V (major), vi (minor), vii$^{\circ}$ (diminished).

In Roman numeral analysis, what do uppercase, lowercase, $^{\circ}$, and $+$ indicate?

Uppercase = major triad, lowercase = minor triad, $^{\circ}$ = diminished, $+$ = augmented. The numeral itself shows the scale degree of the chord's root.

What are the names of scale degrees 1, 4, 5, and 7?

1 = tonic, 4 = subdominant, 5 = dominant, 7 = leading tone (in major and harmonic minor). Also: 2 = supertonic, 3 = mediant, 6 = submediant.

Define the authentic cadence and the plagal cadence.

Authentic: V $\to$ I (dominant to tonic), the strongest ending; it is "perfect" (PAC) when both chords are in root position and the tonic is in the soprano. Plagal: IV $\to$ I, the "Amen" cadence.

Define the half cadence and the deceptive cadence.

Half cadence: any phrase ending on V — sounds unfinished. Deceptive cadence: V resolves to a chord other than I, most often vi, evading the expected resolution.