Changing a component’s phase by 180 degrees is equivalent to subtracting that partial

Evidence

The phase, which expresses the starting value of the individual sine wave components, also affects the waveshape. Figure 1.52 shows what happens to a square wave if alternate partials are subtracted rather than added, and this is equivalent to changing the phase of these components by 180°; that is, alternate frequency components start from halfway around the circle compared with the other components, as shown by the dotted line in Figure 1.52. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 454

Categorization

• DEFINE: A crisp conceptual equivalence — phase inversion equals sign flip in the time domain — clarifying how phase relates to waveshape.
• XREF: connects to: Phase shifting shared partials inadvertently alters amplitude through interference — Eric J. Heller, Why You Hear What You Hear- An…, 2210; A 180-degree phase shift occurs crossing any isolated resonance — Eric J. Heller, Why You Hear What You Hear- An…, 1013; Driven resonator phase shifts 180 degrees across its resonance

Broader Connections

• Driven resonator phase shifts 180 degrees across its resonance #corroborates (0.80)
• Phase shifting shared partials inadvertently alters amplitude through interference #complicates (0.75) — Eric J. Heller, Why You Hear What You Hear- An…, 2210
• A 180-degree phase shift occurs crossing any isolated resonance #qualifies (0.72) — Eric J. Heller, Why You Hear What You Hear- An…, 1013