Music is a universal art that exists in all cultures and civilizations. It can be traced back as a ceremonial art thousands of years ago. However, music in the form that we know it today — Western art music — evolved no less than about 1000 years ago. The foundations of Western art music, beginning with the traditions of people like Saint Hildegard Von Bingen, Palestrina, and Johann Sebastian Bach, evolved into what we know today as one of the most intricate and interesting art forms in existence. In fact, even the modern popular music owes more to the traditions of Western art music than any other. Therefore, for our purposes, we will be concerned with the study of Western art music.
One of the things that makes music so interesting is that fact that it must be thought of in two primary ways: vertically and horizontally. The horizontal aspect of music is synonymous with that of melody. Of course, consequentially, the vertical study music must be concerned with the doctrine of harmony. The fundamental question that theorists ask themselves is how these two aspects of music correlate with one another. And indeed... of what is music composed? In this sense, the basic definition of music theory can be the study of the language and notation in music. The first step in understanding the materials of music - what makes up music - is to know with what the various branches of music theory deal.
The development of harmony is quite an interesting study, beginning with foundations set in place by the great compositional masters, eventually evolving into the 20th century eccentricities of Stockhausen and Xenakis. The word harmony comes from the Greek word harmonia, which means "join, or concord". In this sense alone, it can be inferred that harmony deals with the conjunction of various tones. The first book written on the doctrine of harmony was the Treatise on Harmony, by Jean-Philippe Rameau, written in the year 1722. He (and most other music theorists) define the most basic unit of harmony as the interval.
The definition of an interval is the distance between two notes of pitches. Note that there is in fact a difference between the terms note and pitch. A note refers to the notation on staff paper, whereas a pitch is the sound produced. An interval must be only two pitches, or it is called a chord. There are two ways intervals can be broadly classified:
a). Harmony (vertical)
b). Melodic (horizontal)
A harmonic interval is the interval produced when two notes are simultaneously played. But knowing that it is an interval is not enough. We must ask ourselves what kind of interval it is. What is the classification? The general classifications are:
When an interval is referred to as a "third" (or "fourth", etc), it is called a general classification. In order for the classification to be specific, the certain quality must be named. It is advisable to understand the following table:
| Number of
|Diatonic interval||Short||Chromatic interval||Short|| Latin
|0||Perfect Unison||P1||Diminished second||d2|
|1||Minor second||m2||Augmented unison||A1||Semitone||S|
|2||Major second||M2||Diminished third||d3||Whole tone||T|
|3||Minor third||m3||Augmented second||A2|
|4||Major third||M3||Diminished fourth||d4|
|5||Perfect fourth||P4||Augmented third||A3|
|7||Perfect fifth||P5||Diminished sixth||d6|
|8||Minor sixth||m6||Augmented fifth||A5|
|9||Major sixth||M6||Diminished seventh||d7|
|10||Minor seventh||m7||Augmented sixth||A6|
|11||Major seventh||M7||Diminished octave||d8|
|12||Perfect octave||P8||Augmented seventh||A7|
What must also be defined in an interval is the difference between consonance and dissonance. According to Pythagoras, consonance occurs when "ratios of lower simple numbers are more consonant than those that are higher". The consonant intervals in the common practice period of Western art music are:
According to Roger Kamien (2008) a dissonance is an "unstable tone combination is a dissonance; its tension demands an onward motion to a stable chord. Thus dissonant chords are 'active'; traditionally they have been considered harsh and have expressed pain, grief, and conflict." There are several kinds of dissonant intervals according to the famous music theorist, Johannes de Garlandia:
When speaking in regards to the structure of an interval, it must be understood what a simple interval is. Likewise, the concept of the compound interval must be understood. A simple interval is an interval that spans no more than an octave. When an interval spans more than an octave (making it a "stack" of simple intervals) it is called a compound interval. One example of this is the major 10th, where it spans one octave plus one major third. Therefore, the interval is simply called a "compound major third". A major seventeenth (two staff positions above two octaves) is another example of compound major third, and can be built either by adding up two octaves and one major third, or four perfect fifths.
When speaking of inversions (as they relate to intervals) there are two kinds with which to be concerned:
a). Harmonic inversion (the process of inverting an interval)
b). Melodic Inversion (also called "mirror" writing)
We will first be concerned with the process of inverting the interval. The process by which one inverts a given interval is quite simple in concept: one will raise or lower a note by one octave (making sure it is a simple interval). The interval produced and the original interval should be equal to nine. For example, if a major third is inverted by moving the bottom interval upwards one octave it becomes a minor sixth. But in this example, something else happens. Not only the does the name of the interval change, but so does the quality of the interval. In fact, the major third becomes opposite of what it was, making it a minor sixth. When inverting an interval, the harmonic quality always reverses (with the exception of perfect intervals, which remain perfect). The following are two tables to illustrate the concept of harmonic inversion:
|Interval quality under inversion|
|Interval name under inversion|
When this concept is applied to melodies, the inversion is essentially the reverse melody. For instance, if the original melody has a rising major third, the inverted melody has a falling major third (or perhaps more likely, in tonal music, a falling minor third). In the 20th century doctrine of twelve-tone technique, the inversion of the tone row is the called prime series.
An Enharmonic Equivalent is a note (enharmonic tone), interval (enharmonic interval), or key signature which is equivalent to some other note, interval, or key signature, but "spelled" differently. For example, in twelve-tone equal temperament, which is the modern system of musical tuning, the notes B and C♭ are enharmonically equivalent. They are the same key on a keyboard (and thus are identical in pitch), although they have different names and diatonic functions.
Let us use the opening of Mozart's sonata in C major, K.545. The first question we must ask ourselves is why is this called C major? It contains several notes besides "C". A key is when all tones in a given piece of music relate to one central tone. In the case of Mozart's sonata in C major, all other tones relate around the note C. This definition of key is perfectly adequate, but it fails to tell one the relationship between keys. What kind of relationship exists between the central tone and the related?
The tonic is the central tone of a key. Notes, in the common practice period, relate to a given tonic. In the Mozart example, both hands strike the tonic (C) at the beginning. The left hand predominately stays at C for the first 4 measures, before moving downwards to end on C. The right hand does not return to C after the opening measures, however it's subsequent course of action points to C. But the interesting thing about the piece is that the melody does not complete it's circle to end on C, but rather ends on D. As a matter of fact, the melodic goal of reaching C is not fulfilled until the end of the piece.
From this description, we can gather than the tonic forms a general point of departure from which all other tones move to reach the melodic goal. Compositionally, a composer can enhance the feeling of finality at the end of a piece by not always reaching the goal at the moment we expect.
Now that an understanding of intervals is established, the theoretical basis for the western scale can be explored. A scale is a series of intervals (ascending or descending) that provides the material for a musical composition. Scales can be defined in two ways: based on the intervals, or based on the number of pitches. Based on the intervals a scale contains, they can be broken into two main categories:
A major scale (also known as Ionian mode) is composed of seven distinct notes (also called scale degrees). The structure of the major scale is that there are 2 semitones between the first note and second note. Likewise between the second and third note. There is, however, only one semitone between the 3rd and 4th notes. Every other subsequent note has 2 semitones, with the exception of the last (7th note) leading into the octave. The semitone structure is 2 2 1 2 2 2 1.
The minor scale includes at least three essential scale degrees: The tonic, a minor third above the tonic, and a perfect fifth above the tonic, together composing the tonic minor triad. There exists 3 kinds of minor scales: natural minor, harmonic minor, and melodic minor. The natural minor scale (also known as aeolian mode). In a harmonic minor scale, the seventh degree is chromatically altered 1 semitone upwards. A characteristic of the harmonic minor scale is the inclusion of two sets of chords whose inversions are structurally identical. This gives a sense of ambiguous tonality. One is the diminished seventh chord (found on the 2nd, 4th, 6th and 7th degrees). The other is the augmented chord (found on the 3rd, 5th and 7th degrees). On occasion, the harmonic minor scale is referred to as the Mohammedan scale (for it's root in Arabic tonality). A melodic minor scale was used apropos the awkward leap in choral music between the 6th and 7th degrees of the harmonic minor scale. Composers (especially Mozart) felt it would be easier to have a whole step between these two tones, as it would induce better melodic writing. This invention is sometimes known as the heptatonia seconda.
There are, of course, other scales with will be discussed in detail in later chapters. Examples include the chromatic scale (using all 13 tones of Western tonality) and the pentatonic scale.
The circle of fifths is an easy way to illustrate the relationship between all the major and minor keys.
Each degree of the diatonic scale is given a name. It is advisable for one to memorize the names: