1986The Journal of the Acoustical Society of AmericaRequires access

Residue pitch and beats as heard in a musical context

John R. Pierce

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Abstract

Published residue pitch measurements give the pitch of the missing fundamental for tones consisting of three, and even two, successive harmonics over a wide range of harmonic numbers and frequencies. Presentations closer to a musical context give other results. Scales spanning an octave played with two and three sinusoidal components of constant frequency difference sound like steadily ascending scales. The last tone (frequency ratio 3:2 or 4:3:2) sounds higher in pitch than the first (frequency ratio 2:1 or 3:2:1) when played immediately after it. Other examples contrast the first 6 equal-amplitude harmonic partials with tones consisting of the upper 2, 3, 4, and 5 harmonics. These latter tones do not match the pitch of the 6-partial tone when the literature says they should. Tunes and scales were played with tones with two sinusoidal components spaced by the pitch frequency. The tune or scale is heard only at high levels, and “in the ear,” not coming from the speakers. Can there be pitch without place? Reported residue pitches do not correspond to pitches heard in a musical context.

About this research paper

What this paper is about

Published residue pitch measurements give the pitch of the missing fundamental for tones consisting of three, and even two, successive harmonics over a wide range of harmonic numbers and frequencies. Presentations closer to a musical context give other results. Scales spanning an octave played with two and three sinusoidal components of constant frequency difference sound like steadily ascending scales. The last tone (frequency ratio 3:2 or 4:3:2) sounds higher in pitch than the first (frequency ratio 2:1 or 3:2:1) when played immediately after it. Other examples contrast the first 6 equal-amplitude harmonic partials with tones consisting of the upper 2, 3, 4, and 5 harmonics. These latter tones do not match the pitch of the 6-partial tone when the literature says they should. Tunes and scales were played with tones with two sinusoidal components spaced by the pitch frequency. The tune or scale is heard only at high levels, and “in the ear,” not coming from the speakers. Can there be pitch without place? Reported residue pitches do not correspond to pitches heard in a musical context.

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Available abstract

Published residue pitch measurements give the pitch of the missing fundamental for tones consisting of three, and even two, successive harmonics over a wide range of harmonic numbers and frequencies. Presentations closer to a musical context give other results. Scales spanning an octave played with two and three sinusoidal components of constant frequency difference sound like steadily ascending scales. The last tone (frequency ratio 3:2 or 4:3:2) sounds higher in pitch than the first (frequency ratio 2:1 or 3:2:1) when played immediately after it. Other examples contrast the first 6 equal-amplitude harmonic partials with tones consisting of the upper 2, 3, 4, and 5 harmonics. These latter tones do not match the pitch of the 6-partial tone when the literature says they should. Tunes and scales were played with tones with two sinusoidal components spaced by the pitch frequency. The tune or scale is heard only at high levels, and “in the ear,” not coming from the speakers. Can there be pitch without place? Reported residue pitches do not correspond to pitches heard in a musical context.

Key concepts: Pitch (Music), Acoustics, Octave (electronics), Harmonics, Musical tone, Relative pitch, Fundamental frequency, Tone (literature)

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