1. In musical set theory, a set of three different chromas (octavegeneralized pitches) is a trichord (Rahn, 1980). The term triad tends to be reserved for major, minor, diminished, and augmented triads; that is, for musically familiar or basic trichords. If some tones in a trichord are doubled (played in more than one octave register), the chord comprises three chromas but more than three tones. A tetrachord is a set of four chromas. By polyphony we mean music comprising several partly independent voices (rather than voices that move in parallel).
2. A pitch at an MF is always a virtual pitch, but not all virtual pitches are at MFs. The pitch at or near the fundamental of a HCT, in which the fundamental is present and audible, is usually virtual. But if the spectral pitch of the lowest partial is more salient than the coinciding virtual pitch, as in some high-pitched musical sounds, the main pitch is spectral.
3. A spectral pitch is the pitch of a pure tone—whether heard in isolation or as part of a complex sound, as a partial. Like any other pitch, spectral pitch is fundamentally subjective and experiential in nature, because empirical pitch judgments are always mediated by the listener's consciousness (Terhardt, 1998). In a common procedure for pitch judgment, a listener hears a complex sound and a pure tone in alternation and adjusts the frequency of the pure tone until the two sounds have the same pitch. The physiological correlates of spectral pitch in the peripheral auditory system are complex; both spectral and virtual pitch depend in general on a mixture of temporal and spectral information and processes (Moore, 2003). If we ignore physiology and consider only the relationship between spectral pitches and partial frequencies, the relationship is still complex: spectral pitches and corresponding spectral frequencies differ from each other depending on the sound levels of the partials and the degree to which they mask each other (pitch shifts). If a partial is completely masked, its spectral pitch ceases to exist.
4. In music theory, a “chord” is often a familiar triad or seventh chord, or a sonority constructed according to the principle of stacked thirds. But the word “chord” may also refer to any simultaneity of any tones from the chromatic scale, which is how we use the word in this paper. Our definition is consistent with polyphonic musical practice since the Middle Ages, in which almost all possible pitch-class sets were used (Parncutt et al., 2018). It is also consistent with the idea of additive harmony in early modernism (Blӓttler, 2017) and the jazz-theory concept of bitonal chords that combine lower and upper structures (Pease & Pullig, 2001). Alternative terms for “chord” in this sense include “simultaneity” or “sonority.” An OCT is a complex tone whose partials are spaced at octave intervals across the audible spectrum. Shepard tones are OCTs whose amplitude envelope is bell-shaped. In this study, the amplitude envelope of OCTs was flat before amplification; low and high frequencies were instead attenuated by a mixture of acoustical phenomena (frequency response of sound card and headphones) and psychoacoustical phenomena (auditory threshold, curves of equal loudness, and masking).
5. We distinguish between pitch and chroma. Pitch is the perceived height of a tone on a one-dimensional scale from low to high. Chroma is octave-generalized, musically categorized pitch. There are 12 chromas: C, C≯/D♭, D, etc. Each chroma can be realized in different octave registers. A chroma is also a psychological category: in a musical context based on the chromatic scale, pitches lying within roughly a quartertone of a chroma's centre pitch are perceived as belonging to that chroma (cf. Burns & Ward, 1978). A “chord chroma” is a chroma corresponding to one of the chord's notes; other chromas are “non-chord tones.”