A single tone can be dissonant with its own high harmonics

Evidence

The critical bandwidth concept explains the self-dissonance, or autodissonance, of a tone with many harmonics. The association of dissonance with narrow musical intervals (a minor third or less) rather than an absolute number of beats has an interesting consequence—namely, that periodic tones can be dissonant with themselves. Consider a 100 Hz periodic tone with many partials extending up above 5000 or 10,000 Hz. This tone will of course typically have 100, 200, … Hz partials; these low partials cause no trouble and are well out of each other’s way, so to speak. The ratio 200:300, for example, is a perfect fifth, and 300:400 a perfect fourth. But things soon start to deteriorate. If the 15th and 16th partials are healthy, we get the interval 15:16, a minor second: still on the list of named intervals, but normally considered dissonant. If a 100 Hz tone rich in harmonics is played, this interval is there, buzzing away. What about the ratio 26:27, or 25:27? If there are many high partials, these intervals are present, and indeed many others just as irritating. The tone may be classified as harsh, or raspy; this is the single-tone version of dissonance, in Helmholtz’s view. For a 500 Hz tone, autodissonance begins around the 7th partial—3500 Hz—if those partials are prominent. If the partials remain strong much above that, the tone becomes less pleasant, and raspy perhaps. The critical band overlap of the higher partials is shown schematically in figure 26.4. — Eric J. Heller, Why You Hear What You Hear- An…, 2331

Categorization

• XREF: Connects to the ‘can’t be described by a single melody’ synthesis-of-a-tone problem — a single tone is internally a chord of partials, so autodissonance is a crucial corrective to the naive ‘tone = one note’ model.