Music Theory Background
Figure 1: C major (top) and F major (bottom) keys and their constituent chords [2].
In order to determine what makes a good playlist, it is important to first understand the quantifiable aspects of music theory. Tempo refers to how fast or slow a piece of music is perceived, and is typically measured in beats per minute (BPM). Pulses are organized into groups of strong and weak beats, which determines a piece’s meter. In Western popular music, triple and quadruple meters are common. A musical key is a collection of pitches and chords related to a central tone. In Western 12-tone music theory, there are 12 major and 12 minor keys, each with seven primary pitches and chords. Keys that share common chords are called “closely related”, and modulation, or switching keys, typically flows between keys that are related. In a major key, the closely related keys are the subdominant (moving down a fifth), the dominant (moving up a fifth), and the submediant (switching to the relative minor) [1]. For example, the keys of C and F, shown in Fig. 1, share four chords (C, Dm, F, and Am). F is the dominant in the key of C, and transitioning between these keys typically sounds pleasing because there is little dissonance between the chords in each key.
In a popular music setting, harmonic mixing refers to transitioning between songs in closely related keys. The Camelot Wheel, shown in Fig. 2, is a convenient visual aid used by DJs to represent the relationships between keys [3]. Each key is assigned a number and a letter, based on its tonic pitch and classification as major or minor, respectively. In the Camelot system, there are three options for creating a harmonic transition. The first is to simply remain in the same box, as two songs in the same key won’t have clashing tones. Next, incrementing or decrementing one hour by moving clockwise or counterclockwise by one space while remaining in the same wheel represents moving up or down a fifth, which ensures a transition to a closely related key. Finally, it is possible to switch from the outer wheel to the inner wheel or vice-versa to transition between a major key and its relative minor.
While these rules for harmonic mixing are a good starting place for ordering a playlist, it is important to note that music is subjective, and that modern music theory is largely rooted in a specific style of 3 Western European instrumental music that may not apply to all songs. Therefore, harmonic analysis will be considered alongside other quantifiable measures, such as tempo and meter, in order to generate optimal song orders.
Figure 2: The Camelot Wheel, a visual system for understanding key relationships
Playlist Analysis
Existing playlists with contrasting styles were analyzed for tempo, meter, and key to look for patterns in what subjectively sounds “good”. The first playlist features mid-tempo pop rock songs and was intentionally harmonically mixed before the conception of this project. A subset of the playlist is shown in Tab. 1. All four songs are in major keys and the transition between each song modulates by a fifth to ensure that they keys are closely related. The songs have varying tempos but share the same meter. Qualitatively, the songs are driven by strong piano and percussion sounds with a heavy downbeat emphasis.
Table 1: Playlist section featuring harmonically mixed up-tempo pop-rock songs.
The second playlist contains more stripped-back songs with minimal production featuring prominent vocals and strings. A subset of four songs is shown in Tab. 2. No special attention was given to key or meter when creating this playlist, but all four songs happen to be in triple meter and three of the four are in the same key. Three of the songs (Art Exhibit, Last Words of a Shooting Star, and Sprained Ankle) are up-tempo and have a clear guitar/ukulele-driven pulse that is easy to detect. This is in contrast with Historians, where the tempo is more difficult to detect as the pulse is derived from syllable timing in the vocals. It will be important to consider that a song’s rhythm section (or lack thereof) may impact our ability to accurately implement pulse detection.
Table 2: Playlist section featuring stripped-back acoustic songs with prominent vocals.