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• The definition of music
• The elements of music (rhythm & pitch)
• Division of pitch into melody and harmony
• Rhythmic notation
• Understanding relative durations of sound
• The whole, half, quarter, 8th and 16th notes
• Why notes are named the way they are
• Relative durations vs. assigning numerical values
• The unit of measurement
• Beat
• Tempo
• Meter
• Distinguishing between rhythm and meter
• Bar lines and measures
• Time signatures
• 2/4, 3/4 and 4/4 meters
• Determining the meter without a time signature
• Natural division of rhythms
• Strong and weak pulses
• Rests
• Assigning numerical values to rests
• The whole rest and meter
• Dotted notes
• Numerical values of dotted notes
• History of dotted notes
• Dotted rhythms
• The 3:1 ratio in dotted rhythms
• The tie
• Ties vs. dotted notes
• Advantages and disadvantages of notating with ties vs. dots
• Re-designation of the unit
• 3/8 and 6/8 meters
• New numerical values of notes
• Understand relative durations with regard to a new unit of measurement
• Strength of pulses
• Designating the half note as the unit
• Notating 2/2 meter or “cut” time
• Numerical values of note durations in 2/2 meter
• Comparison of 4/4 meter and 2/2 meter
• Reasons for 2/2 meter
• Classifying meters
• Simple meter and compound meter
• Duple, triple, and quadruple meter
• Complex meter
• Artificial divisions of the beat or beats
• Artificial division of parts of the beat
• Common types of tuplets
• Definition of triplets & duplets
• Identifying triplets & duplets
• Ratio of triplets & duplets
• Numerical value of triplets & duplets
• Artificial divisions in relation to simple and compound meters
• Sound waves
• Frequency
• Indefinite vs. definite pitch
• Modern vs. ancient definition of pitch
• Pitch experiments
• Introduction to the staff
• How the mind sees number
• Ledger lines
• Clefs
• Movement on the staff (step, skip, repeat)
• The musical alphabet
• Letter names on the staff
• The grand staff
• Direction of note stems (and rationale)
• Introduction to the keyboard
• Groups of black keys
• Letter names of keys
• Correlation of staff to the keyboard
• Half steps and whole steps
• Sharps and flats on the keyboard
• Enharmonic equivalents
• Enharmonic keyboard notes
• Reading sharps and flats on the staff
• Sharps and flats within measures
• The natural sign
• The definition of interval
• Melodic vs. harmonic intervals
• Identifying intervals on the keyboard
• Identifying intervals on the staff
• Ratios and intervals
• Pythagoras and the monochord
• Consonance and dissonance
• Definition and history of the modern scale
• The major scale
• Intervals and the major scale
• Basis of the scale
• Basis of the whole tone
• Greek tetrachords
• Greek semi tone and whole tone
• Constructing scales on the keyboard
• Constructing scales on the staff
• Definition of "key"
• The key signature
• The circle of 5ths
• The order of sharps
• The order of flats
• How to determine the key from the sharps/flats
• How to determine how many and which sharps/flats are in a given key
• Enharmonic keys
• Interval number vs. interval quality
• Major, minor and perfect interval qualities
• Determining an intervals’ number and quality
• Connection of interval qualities to the major scale
• Identifying intervals on the staff
• Augmented and diminished interval qualities
• How augmented and diminished intervals are formed
• The double sharp
• Why the double sharp is necessary
• The double flat
• Why the double flat is necessary
• The tritone
• Abbreviations for interval qualities
• Enharmonic intervals
• Complementary intervals
• Which qualities, when inverted, become which qualities
• Simple intervals
• Compound intervals
• Reducing compound intervals
• How to determine the quality of compound intervals
• Open and close harmony
• The difference between intervals and chords
• Major and minor chords
• Deriving the ratio of the major and minor 3rds using the monochord
• The Pythagoras experiment and the major chord
• Block and broken chords
• Augmented and diminished chords
• Music’s move from the horizontal to the vertical
• Mathematical proportions of the major, minor, augmented and diminished triads
• Understanding the harmonic mean
• The harmonic mean and the major chord
• Understanding the arithmetic mean
• The arithmetic mean and the minor chord
• The geometric mean and the augmented and diminished chords
• Relation of chords to the major scale
• The number of possible triads constructed from the pitches of the major scale
• Order and quantity of triad qualities formed from the major scale
• Roots of chords, scales, and keys
• Comparison of the major and minor scales
• Tetrachords in minor scales
• The natural minor scale
• Constructing natural minor scales on the keyboard & staff
• The harmonic minor scale
• The melodic minor scale
• Ascending vs. descending melodic minor scale
• Constructing harmonic minor scales on the keyboard & staff
• Constructing melodic minor scales on the keyboard & staff
• Relative keys
• Determining the relative minor
• Determining the relative major
• Determining the key of music with shared key signatures
• Parallel keys
• Difference between parallel and relative keys
• Relation of chords to the natural minor scale
• Order and quantity of triad qualities formed from the natural minor scale
• Relation of chords to the harmonic minor scale
• Order and quantity of triad qualities formed from the harmonic minor scale
• The major scale degrees
• Naming the scale degree using Roman numerals
• Naming triads using Roman numerals
• Benefit to using degree vs. letter name
• Primary chords and their importance
• Relationship between chords
• Chord inversions
• Root position, 1st inversion and 2nd inversion
• Intervals in chord inversions
• The root rule
• How to identify chord inversions by name, quality and inversion
• Voices of a chord
• Voice leading
• Inversions and the primary chords
• Chord progressions
• Use of inversions to improve transition between chords
• Introduction to function
• Function names of the scale degrees
• Extending the triad
• Dominant seventh chords
• Other names and notation of the dominant seventh chord
• Why the dominant seventh chord is named the way it is
• Inversion of the dominant seventh chord
• 3rd inversion
• Finding the root in a dominant seventh chord
• How to identify a dominant seventh chord
• Dominant seventh chords with missing notes
• Major 7th chords
• Minor 7th chords
• Diminished 7th chords
• Musical punctuation
• Perfect authentic cadence
• Imperfect authentic cadence
• Half cadence
• Plagal cadence
• Deceptive cadence
• Hexatonic scale
• Whole tone scale
• Chromatic scale
• Pentatonic scale
• Tonal music
• Tonal centers
• Polytonal music
• Atonal music
• Free atonal
• Strict atonal
• Twelve-tone technique
• Tone rows
• The ancient Greek modes
• History of the church modes
• Modern modes
• The harmonic series
• Overtones
• Fundamental of a pitch
• Complex vibration of a string
• What the numbers of the harmonic series express
• Hearing overtones (and experiment)
• Timbre
• Nature’s hierarchy of harmonic sound
• Objective measurement of consonance and dissonance
• History of consonance and dissonance
• Tuning pitches
• Brief history of tuning systems
• Pythagorean tuning
• Just intonation
• Equal temperament
• Definition of cents
• Tuning of the modern piano
• Benefits and shortcomings of the different tuning systems
• Apps that demonstrate and compare some of the tuning systems
• Overview of the four main periods of western art music