Durational values are indicated using a system of symbols that show the relationships of notes to each other: each note value is equal to one half of the next larger value and twice the next smallest value. As note values get smaller, the system continues indefinitely, with each successively smaller note value adding one flag (or beam). In practice, one rarely sees note values shorter than the sixty-fourth note.

A scale is a collection of pitches from which a composition is constructed. In tonal music, each note in a scale, or scale degree, has a unique sound that differentiates it from the other scale degrees. This unique sound is defined by the strength of its desire to resolve and the path it takes to return to the first scale degree, which is also called the tonic pitch.

Improvisation is the act of creating music in the moment. While we tend to think of improvisation as “making up” music as we perform it, most skilled improvisers employ well-defined guidelines and a toolbox of techniques that allow them to express themselves musically and creatively. Effective improvisation requires a thorough knowledge of the musical style as well as the ability to recreate what one hears in the musical ear into one’s voice or instrument. Improvisation happens frequently in some styles of music (jazz and popular), but can be needed at any time, such as when an instrument malfunctions, the wind blows a page of music off the stand, or your memory leaves you under the stress of live performance. The value of improvisation cannot be overlooked; it is a means of employing your musical imagination and, perhaps most importantly, allows you confidently express yourself and demonstrate your command and fluency of the musical language.

Meters are defined both by the number of beats in a measure and the number of divisions in each beat. In compound meter, the beat is divided into three parts, and the beat-note value can be a dotted quarter, dotted eighth, or dotted half note. The divisions are always beamed in groups of three, and compound meters can be duple, triple, or quadruple. The multiple of the beat is twice the value of the beat note.

An interval is the space between two pitches. Intervals have three characteristics:

1. Size: the number of letter names or scale degrees that separate the two pitches
2. Quality: the specific distance between the two pitches
3. Direction: ascending, descending, or harmonic

Learning to sing and identify intervals without first having an established a tonal center are important skills for musicians to master and will increase your ability to deal with increasingly complex music in your future.

Triads are three-note chords that contain the following characteristics:

1. Root: the lowest pitch of the triad when spelled in its most compact position
2. Quality: the specific sound of the triad (major, minor, diminished, or augmented)
3. Inversion: an expression of which member of the triad (root, third, or fifth) is the lowest in the texture
4. Ordering and Voicing: the specific way that the triad is presented.

Triads are one of the foundational building blocks of tonal music. You will most likely be required to learn the unique sound of each triad quality to be able to sing and recognize them individually and in the music that you hear.

In tonal music, a seventh can be added to any chord without changing its function, although the chord’s resonant sound and desire towards resolution will change.

When we listen to music, we tend to organize the notes, rhythms, and chords into larger structures called phrases, or statements that form a complete musical idea. Skilled musicians use various types of phrases to create a musical narrative, or story that draws a listener into and through a piece of music.

A triplet is a group of three even notes performed in the same time as two notes of equal value. Triplets are indicated with the number “3” and often have a slur or bracket above or below the notes.

Chromatic tones are pitches that are not a part of the major or minor scale of the prevailing key. Chromaticism “fills in” the spaces between diatonic scale degrees, adds musical color and direction to melodies, and serves as the foundation for altered chords, tonicization, and modulation. The chromatic scale consists of twelve pitches, each roughly the same distance from the pitches around them. Note that chromatic pitches are labeled based on their resolution. A chromatic pitch resolving up to a G would be an F-sharp, and the “same” pitch resolving down to F would be a G-flat.

Modulation is the change of tonal centers within a composition. Modulation can occur between any two keys, and consists of using chromaticism to transform the pitch content of the original key into that of the destination key. This chromaticism causes the locations of the half steps, which define one’s sense of tonal center, to point toward a different pitch as the tonic. The fewer pitches that are altered, the more closely related the keys are. The more pitches that are altered, the more distantly related the keys are. If these changes are temporary or fleeting and the listener retains the sense of the original tonal center, then a tonicization rather than a modulation has occurred. If, however, these changes persist or are confirmed with a convincing cadence, then a modulation has occurred.

Changing meter refers to meter changes that occur between measures with the same beat-note value, such as 3/4 to 4/4 or 6/8 to 9/8. The African American folk song “The Swallow” is an example of simple changing meter.

Pentatonic scales contain five notes separated by major seconds and minor thirds. The arrangement of these intervals is what differentiates the various forms of the pentatonic scale.

Authors’ Note: The traditional solfège syllables that you have used in the rest of this text fundamentally show relationships between tonal structures. All of the elements in this module deal with post-tonal music, where a sense of tonal centricity is often blurred at best or, more commonly, avoided altogether. As a result, this module will shift to using numbers that indicate the quantity of semitones away from a starting pitch, except where the student is instructed to hear a structure using tonality.