Music Theory Basics
Tonal Harmony by Stephen Kotska
Harmony is the sound that results when two or more pitches are performed simultaneously. It is the vertical aspect of music, produced by the combination of the component of the horizontal aspect.
Tonal Harmony refers to music with a tonal center, based on major and/or minor scales, and using tertian chords* that are related to one another and to the tonal center in various ways.
*Tertian means a structure of notes built of thirds.
Chapter one - Elements of the pitch
The Keyboard and Octave Registers
Pitch in music refers to the highness or lowness of a sound. Pitches are named by using the first seven letters of the alphabet: A, B,C, E,F and G.
The C nearest the middle of the keyboard is called middle C, or C4
Notation on the Staff
The staff is the foundation upon which notes are drawn.
The modern staff comprises five lines and four spaces.
Notes on the Staff
Here you can download a pdf in which we show all the notes in the treble and Bass clefs with their pitch names and a way to memorize them easy and fast:
Clefs assign individual notes to certain lines or spaces.
Two clefs are normally used:-The Treble and Bass clefs
A ledger line is a small line that extends the staff when we run out of room. (See previous example with Treble and Bass Clefs)
The Major Scale
A scale is a selection of certain notes within an octave. The major scale is constructed with this formula:
A half step (h) is the distance from a key on the piano to the very next key, white or black.
A whole step (w) skips t very next key and goes instead to the following one.
Key 1 to Key 2 is a half step since they are next to each other:
Key 1 to Key 3 is a whole step:
An accidental is a sign used to raise or lower the pitch of a note.
Let's examine the black key in between C and D. This key could be called C-sharp since it is a half step above C:
And it could also be called D-flat since it is a half step below D:
While flats and sharps alter a note by a half step, the double flat and double sharp alter a note by a whole step.
For example, both D and E-double-flat have the same pitch since you can reach D by going a whole step (or two half steps) down from E
Whenever a certain pitch has multiple names, it is called an enharmonic spelling (C# = Db)
A key signature is a collection of every accidental found in a scale. Keys are used to organize a piece of music. For example, music written in the key of C would center around the tone of C, and would use notes from the C scale (no sharps or flats).
-Tips to memorize the order:• With SHARPS: You can remember this order by using the following saying: “Father Charles Goes Down And Ends Battle”.
• With FLATS: You can remember this order by using the following saying: “Battle Ends And Down Goes Charles' Father”.
Major and Minor Key Signatures
The term Key in music is used to identify the first degree of the scale.
Circle of fifths
A circle of fifths is an arrangement of keys by ascending fifths. It displays how many sharps or flats are in each key. Major keys are noted in capital letters and are found on the outer part of the circle (C,G etc.), and minor keys are in lower case letters on the inner part of the circle (a, e, etc.)
The Minor Scale
The natural minor scale is like a major scale with lowered third, sixth and seventh degree.
To simplify, you can memorize this formula to form a minor scale = whole step - half step - whole step - whole step - half step - whole step - whole step or w - h - w - w - h - w - w
The notes on a major scale sound bright and cheerful while notes on the minor scale sound solemn and sad. There are three types of minor scales.
Types of minor scales
Natural Minor Scale - When you play all the notes in a minor key signature, you are playing the minor scale.
Harmonic Minor Scale - To play a harmonic minor scale, you simply raise the seventh note of the scale by a half-step as you go up and down the scale. For example:
Harmonic A Minor Scale = A - B - C - D - E – F- G# - A
Melodic Minor Scale - When you raise the sixth and seventh notes of a scale by a half step as you go up the scale and then return to the natural minor as you go down the scale. For example:
Melodic A Minor Scale = A - B - C - D - E – F#- G# - A (as you go up the scale)Natural A Minor Scale = A - B - C - D - E – F - G - A (as you go down the scale)
Scale Degree Names
Each note of a scale has a special name, called a scale degree.
The names of the Scale Degrees are:
7. Leading Tone
Example in C major
Example in C minor
An interval measures the distance between two notes.
Melodic and Harmonic Intervals
In a harmonic interval both notes are sounded simultaneously. In a melodic interval notes are played in succession.
Perfect, Major and Minor Intevals
A minor second is made up of two half steps
A major second is made up of two half steps
A major third is made up of four half steps
A perfect fourth is made up of five half steps
A perfect fifth is made up of seven half steps
A major sixth is made up of nine half steps
A major seventh is made up of eleven half steps
A perfect eighth (or perfect octave) is made up of twelve half steps
-The terms “major” and “perfect” refer to the interval's quality
-Only seconds, thirds, sixths, and sevenths can have a major quality. Firsts, fourths, fifths, and eighths use “perfect” instead.
A minor interval has one less half step than a major intervalAn augmented interval has one more half step than a perfect intervalA diminished interval has one less half step than a perfect interval
Inversion of Intervals
In music, the verb invert means to move the lowest note in a group an octave higher.
Perfect intervals will always invert to other perfect intervalsMinor intervals and major intervals invert to each otherDiminished and augmented intervals invert to each other
Seconds and sevenths invert to each other
Thirds and sixths invert to each otherFourths and fifths will invert to each other
Consonant and Dissonant Harmonic Intervals
Although the classification of harmonic intervals as consonant (stable) or dissonant (unstable) is dependent on cultural preferences and historical context, Paul Hindemith wrote that the stability of intervals could be rationalized from the location of the interval in the natural harmonic series. Intervals which occur lower in the natural harmonic series are more stable than those that occur farther up the series
Example - The Natural Harmonic Series Above C2
Interval Stability Chart
Chapter two - Elements of the Rhythm
Is a general term used to refer to the time aspect of the music. The term has more than one meaning. it can mean the basic repetitive pulse of the music, or a pattern that is repeated throughout the music, as in "feel the rhythm". It can also refer to a pattern in time of a single small group of notes.
The length of time that a note is played is called its note duration, which is determined by the type of note.
Augmentation dots and tenuto ties are two types of markings used to alter a note's duration
Chart for reference to augmentation dots
A dot increases duration by one half
Beat and Tempo
The beat is the basic pulse of a musical passage. To determine the beat, tap your foot or clap along with music you are listening to.
Tempo is the speed of the Beat, usually expressed in Beats Per Minute (BPM). For example, at 120 BPM there will be 120 beats in one minute. Tempo can also be expressed verbally with such words as Slowly, Fast, Allegro, or Largo.
Here is an example:
Vertical black bars called bar lines divide the staff into bars or measures. Time signatures define the amount and type of notes that each measure contains.
Example:(4/4) contains four quarter notes
The second measure (3/4) contains three quarter notes
6/8 time contains six eighth notes
3/2 time contains three half notes
Simple Time Signatures
Each time signature can be classified into a certain meter. The terms duple, triple, and quadruple refer to the number of beats in a measure. The termsimple means that each of these beats can be broken into two notes. “Duple” refers to the two beats per measure.
For example, 2/4 time is classified as simple duple
“Simple” states that each of these beats can be divided into two notes
2/2 and 2/8 are also simple duple:
3/4 time is classified as simple triple. “Triple” refers to the three beats per measure
Division of the Beat
For durations shorter than the beat, we call them divisions of the beat. Beats generally are divided either into two equal parts, called simple beat, or into three equal parts, called compound beat.
“Simple” states that each of these beats can be divided into two notes:
3/2 and 3/8 are also simple triple
4/4 time is classified as simple quadruple due to its four beats which can be divided into two notes
4/2 and 4/8 are also simple quadruple
Compound Time Signatures
A time signature is a symbol that tells the performer the beat and meter types and what note value will represent the beat.
While beats in simple meter are divided into two notes, beats in compound meter are divided into three. For example, each beat in 6/8 is a dotted quarter note. In fact, all compound meters will have some dotted note as its beat:
9/8 time is classified as compound triple. There are three beats (three dotted quarter notes), thus making the meter triple
Finally, 12/8 time is classified as compound quadruple. There are four beats, thus making the meter quadruple, and since each beat is made up of three notes, the meter is compound
We use the term hypermeter to refer to a regular grouping of measures that is analogous to meter, the expression of a metric pattern at a higher level, as in groups of measures.
More on Durational Symbols
When rhythms are notated, it is customary to use rests, beams, ties and dots in such a way that the metric accent and the individual beats are emphasized rather than obscured.