The elements of music (rhythm & pitch)
Division of pitch into melody and harmony
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
Distinguishing between rhythm and meter
Determining the meter without a time signature
Natural division of rhythms
Assigning numerical values to rests
Numerical values of dotted notes
The 3:1 ratio in dotted rhythms
Advantages and disadvantages of notating with ties vs. dots
Re-designation of the unit
New numerical values of notes
Understand relative durations with regard to a new unit of measurement
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
Simple meter and compound meter
Duple, triple, and quadruple meter
Artificial divisions of the beat or beats
Artificial division of parts of the beat
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
Indefinite vs. definite pitch
Modern vs. ancient definition of pitch
Introduction to the staff
Movement on the staff (step, skip, repeat)
Letter names on the staff
Direction of note stems (and rationale)
Introduction to the keyboard
Correlation of staff to the keyboard
Half steps and whole steps
Sharps and flats on the keyboard
Enharmonic keyboard notes
Reading sharps and flats on the staff
Sharps and flats within measures
The definition of interval
Melodic vs. harmonic intervals
Identifying intervals on the keyboard
Identifying intervals on the staff
Pythagoras and the monochord
Consonance and dissonance
Definition and history of the modern scale
Intervals and the major scale
Greek semi tone and whole tone
Constructing scales on the keyboard
Constructing scales on the staff
How to determine the key from the sharps/flats
How to determine how many and which sharps/flats are in a given key
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
Why the double sharp is necessary
Why the double flat is necessary
Abbreviations for interval qualities
Which qualities, when inverted, become which qualities
Reducing compound intervals
How to determine the quality of compound intervals
The difference between intervals and chords
Deriving the ratio of the major and minor 3rds using the monochord
The Pythagoras experiment and the major chord
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
Constructing natural minor scales on the keyboard & staff
Ascending vs. descending melodic minor scale
Constructing harmonic minor scales on the keyboard & staff
Constructing melodic minor scales on the keyboard & staff
Determining the relative minor
Determining the relative major
Determining the key of music with shared key signatures
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
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
Root position, 1st inversion and 2nd inversion
Intervals in chord inversions
How to identify chord inversions by name, quality and inversion
Inversions and the primary chords
Use of inversions to improve transition between chords
Function names of the scale degrees
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
Finding the root in a dominant seventh chord
How to identify a dominant seventh chord
Dominant seventh chords with missing notes
Perfect authentic cadence
Imperfect authentic cadence
History of the church modes
Complex vibration of a string
What the numbers of the harmonic series express
Hearing overtones (and experiment)
Nature’s hierarchy of harmonic sound
Objective measurement of consonance and dissonance
History of consonance and dissonance
Brief history of tuning systems
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