Comprehensive Music Theory: Scales, Intervals, and Triads Study Guide

Pitch Recognition: One method of practice involves identifying pitches that spell out words (e.g., "Quarter").
Enharmonic Notes: Enharmonic notes are pitches that sound the same but have different names. For example, an enharmonic equivalent for $C\#$ must be identified using a keyboard layout.
Tooling: A keyboard sheet is a critical reference for identifying specific notes and their enharmonic equivalents, such as $B\flat$ and $F\flat$ .
Visualizing Notation: When requested to create an enharmonic note for $C\#$ , it is necessary to actually draw/write the note rather than just naming it.

Simple Meter Definition: In simple meter, notes are beamed together by the beat.
Eighth Note Subdivision: A single quarter note is equivalent to $2$ eighth notes ( $2 \times \text{1/8}$ ).
Sixteenth Note Subdivision: A single quarter note is equivalent to $4$ sixteenth notes ( $4 \times \text{1/16}$ ).
Beaming Rules: * In simple meter, $4$ sixteenth notes constitute one full beat and should be beamed together. * A specific rhythmic figure involves an eighth note flanked by sixteenth notes. In this case, the sixteenth flags point back toward the central eighth note. Visually, the long note is in the middle, and the outer notes have two flags (beams).
Counting Syllables for Simple Meter: * Quarter note: " $1$ ". * Eighth notes: " $1, te$ " (or " $1, 2$ "). * Subdivided groupings: " $1, te, ta$ ". * Sixteenth notes: " $1, ta, te, ta$ ".

Compound Meter Definition: In compound meter, one beat is represented by a dotted quarter note.
Subdivisions of the Beat: * One beat equals $3$ eighth notes. * One beat equals $6$ sixteenth notes.
Beaming Rules: * All $6$ sixteenth notes in a single beat are placed on a single beam. * These groupings indicate double flags for the sixteenth values.
Counting Syllables for Compound Meter: * The syllables used are: " $1, la, li, 2, la, li$ ".

General Rule for Relative Keys: The major key is always higher than its relative minor. * To find the relative minor from a major key: Move down $3$ half steps ( $1, 2, 3$ ). * To find the relative major from a minor key: Move up $3$ half steps.
Specific Key Relationships: * Relative Major of $A$ minor: $C$ Major. * Relative Minor of $A$ Major: $F\#$ minor (The instructor notes $A$ Major has $3$ sharps). * Relative Minor of $F\#$ Major ( $6$ sharps): $D\#$ minor.

D Major Scale: Written in whole notes as $D, E, F\#, G, A, B, C\#, D$ . * Key Signature of D Major: Contains $2$ sharps: $F\#$ and $C\#$ . * Half Steps: In a major scale, the half steps occur between the $3\text{rd}$ and $4\text{th}$ degrees, and the $7\text{th}$ and $8\text{th}$ (octave) degrees.
Interval Analysis: * To identify an interval, determine if the top note is within the major scale of the bottom note. * Example: An interval from $A$ to $C\#$ is a Major Third ( $M3$ ) because $C\#$ is in the key of $A$ Major.
Interval Inversions: * The Rule of 9: The number of the original interval plus the number of its inversion must equal $9$ . * A Third ( $3$ ) inverts to a Sixth ( $6$ ). * A Seventh ( $7$ ) inverts to a Second ( $2$ ). * A Fifth ( $5$ ) inverts to a Fourth ( $4$ ). * Quality Inversion Rules: * Major ( $M$ ) inverts to Minor ( $m$ ). * Minor ( $m$ ) inverts to Major ( $M$ ). * Perfect ( $P$ ) inverts to Perfect ( $P$ ). * Augmented ( $A$ ) inverts to Diminished ( $d$ ). * Diminished ( $d$ ) inverts to Augmented ( $A$ ).

Example 1: Major to Minor Inversion * Original: Major Third ( $M3$ ). * Inversion: Minor Sixth ( $m6$ ). * Logic: If the top note is lowered, the interval becomes minor.
Example 2: Perfect Fifth ( $P5$ ) * Inverts to a Perfect Fourth ( $P4$ ). * Logic: $5 + 4 = 9$ ; Perfect stays Perfect.
Example 3: Augmented Fourth ( $A4$ ) * The key of $C$ has no sharps. If the note is raised (e.g., $C$ to $F\#$ ), a Perfect Fourth becomes an Augmented Fourth. * Inversion: Diminished Fifth ( $d5$ ).
Example 4: Diminished Sixth ( $d6$ ) * In the key of $B$ , which has $5$ sharps ( $F\#, C\#, G\#, D\#, A\#$ ), a $G$ natural would make a minor interval. A $G$ flat (lowered further) makes it diminished. * Inversion: Augmented Third ( $A3$ ).

Pure (Natural) Minor Scale: * To write a pure minor scale (e.g., $D$ pure minor), plug in the key signature of its relative major. * Example: For $D$ natural minor, use the key signature of $F$ Major ( $1$ flat: $B\flat$ ).
Harmonic Minor Scale: * First, find the relative major to determine the base key signature (e.g., for $B\flat$ minor, the relative major is $D\flat$ Major). * $D\flat$ Major has $5$ flats: $B\flat, E\flat, A\flat, D\flat, G\flat$ . * Rule: To make it harmonic minor, raise the $7\text{th}$ scale degree by a half step.

Triad Structure: Visualized on staff paper as either "space, space, space" or "line, line, line."
Determining Quality from a Major Triad: * Major Triad: Uses the notes found in the major key of the root note. * Minor Triad: Lower the third degree by one half step ( $\downarrow 3\text{rd}$ ). * Augmented Triad: Raise the fifth degree by one half step ( $\uparrow 5\text{th}$ ). * Diminished Triad: Lower both the third and the fifth degrees by one half step ( $\downarrow 3\text{rd}, \downarrow 5\text{th}$ ).
Specific Triad Applications: * $B$ Major Triad: Roots in keys of $F\#, C\#, G\#, D\#, A\#$ . Lowering the third makes it $B$ minor. * $D$ Augmented Triad: Start with $D, F\#, A$ (D Major). Raise the fifth to $A\#$ to get $D, F\#, A\#$ . * $B\flat$ Minor Triad: Start with $B\flat, D, F$ ( $B\flat$ Major). Lower the third to $D\flat$ to get $B\flat, D\flat, F$ . * $F$ Diminished Triad: Start with $F, A, C$ ( $F$ Major). Lower the third to $A\flat$ and the fifth to $C\flat$ . * $G$ Major Triad: Contains an $F\#$ in the key, but the triad itself is $G, B, D$ .

Final Exam Materials: Students are permitted to use three specific cheat sheets (the three sheets discussed in class). No other materials, such as the textbook or mobile phones, are allowed.
Correction/Clarification: White-out (liquid paper) is permitted for use on the exam.
Schedule: The final exam will be held on Tuesday at the same time and location as the current session.