Part I: Rudiments, Units 1-7
Study Guide 1: Pitch Names, Intervals, Scales, Key Signatures, Triads; Rhythm and Meter
Musical pitches are named using the first seven letters of the alphabet. On the white notes of the piano keyboard, the note C is always located immediately to the left of a “two-group” of black keys. The note F is located just to the left of a “three-group” of black keys.
It is often helpful to indicate the specific octave placement when naming pitches. A system widely used today assigns a number to the notes from C up to B within each octave. Middle C equals C4. The lowest C on the piano is C1.
A more traditional method labels each octave with names (such as contra and great) in combination with letters and numbers. The great staff and the full piano keyboard are shown below, with numerical and traditional names across the full range of the keyboard. (Click to enlarge.)
See the video: Introduction to Intervals
An interval is the distance between two pitches. The distance from one note on the keyboard to the next closest note up or down is a half step. Two half steps combine to form a whole step.
Intervals are classified as major (M), minor (m), perfect (P), diminished (d), and augmented (A).
Seconds, thirds, sixths, and sevenths may be major, minor, diminished, or augmented.
The unison, fourth, fifth, and octave may be only perfect, augmented, or diminished.
A minor second equals one half step. A major second equals one step.
A minor third spans a step and a half step. The major third spans two steps.
A perfect fourth spans two steps and a half step. The augmented fourth spans three steps.
Smaller intervals can combine to form larger intervals, as follows:
A diminished fifth spans a perfect fourth and a minor second. A perfect fifth spans a major third and a minor third.
A minor sixth spans a perfect fifth and a minor second. A major sixth spans a perfect fifth and a major second.
A minor seventh spans a perfect fifth and a minor third. A major seventh spans a perfect fifth and a major third.
Inversion of Intervals
An interval is inverted by transferring its lower note into the higher octave or by transferring its higher note into the lower octave. Major intervals invert to minor intervals; minor intervals invert to major intervals.
Seconds and sevenths are classified as dissonances.
Thirds and sixths are classified as imperfect consonances
Perfect intervals invert to perfect intervals. The P4, P5, P1, and P8 are perfect consonances.
Augmented intervals invert to diminished intervals; diminished intervals invert to augmented intervals. All augmented and diminished intervals are dissonances.
The Major Scale
The major scale is comprised of a fixed pattern of whole steps and half steps:
You can build a major scale starting on any note if you follow the pattern of whole steps (major seconds) and half steps (minor seconds).
The three forms of the minor scale allow for the variable sixth and seventh scale degrees. Those scale degrees are not altered in the natural minor scale:
The harmonic minor scale employs the raised seventh scale degree to form the leading tone. An augmented second results between the sixth and seventh scale degree:
The melodic minor scale raises both the sixth and seventh scale degrees ascending. The descending form is equivalent to the natural minor.
For each major key, there is a relative minor key that shares the same key signature. The tonic note of the relative minor key is a minor third below the major key tonic note.
Realtive keys share the same key signature:
Parallel keys share the same tonic:
A major triad has a major third between the root and third, a minor third between the third and the fifth, and a perfect fifth between the root and the fifth.
A minor triad has a minor third between the root and third, a major third between the third and the fifth, and a perfect fifth between the root and the fifth.
An augmented triad has a major third between the root and third, a major third between the third and the fifth, and an augmented fifth between the root and the fifth.
A diminished triad has a minor third between the root and third, a minor third between the third and the fifth, and a diminished fifth between the root and the fifth.
Putting it All Together: Intervals, Triads, and Scales
It is important to understand how notes in a scale may combine to form intervals and triads. Here below is a major scale ascending through intervals of a second:
A major scale ascending in thirds:
Here are the intervals, expanding from the perfect unison to the perfect octave, ascending from the tonic note in the major scale:
The intervals descending from the tonic note in the major scale:
The triads in the major scale are shown below. Note that the triad built on the 7th scale degree, the leading tone, is a diminished triad.
Rhythm and Meter
Meter is the organization of musical time into recurring patterns of accent. Each complete unit constitutes a measure. The first beat of every measure is called the downbeat. The beat unit divides to form smaller note values. Simple division of the beat is binary, dividing the beat value into two equal parts. As shown below, 2/4 meter provides an example. Every beat can divide to form a pair of eighth notes. The beat unit is the quarter note. The background unit is the largest possible division of the beat. In this case, it is the eighth note.
In simple meters the upper number of the time signature indicates the number of beats, and the lower number indicates the note value of the beat. The meter signature of 2/4, with two quarter-note beats per measure, is a simple duple meter. Meters having two beats per measure are duple; three beats per measure, triple; four beats per measure, quadruple.
“Cut time” or 2/2 meter is another example of simple duple meter. Theqre are two half-note beats per measure; the background unit is the quarter note.
Compound meters have triple division, with three background units per beat. Consequently, the beat unit in compound meter is always a dotted note. In compound meters, the upper number indicates the number of background units, and the lower number, the value of the background unit. To find the number of beats per measure, divide the upper number in the meter signature by three. In this example of compound duple meter, the dotted quarter receives the beat; the background unit is the eighth note:
This minuet provides an example of simple triple meter, with three beats per measure and duple division of the beat.
In this example of compound triple meter, the dotted quarter receives the beat; the background unit is the eighth note:
“Common time” or 4/4 meter is a simple quadruple meter. There are four quarter-note beats per measure, with duple division:
In this example of compound quadruple meter, the dotted eighth receives the beat. Triple division of the beat is characteristic of the gigue: