VOLUME

The psychological measure of the magnitude of a SOUND or SOUND OBJECT including its SPECTRUM (frequency and intensity), harmonic content, duration and spatial properties.

  A sine wave with single frequency, and no sense of volume (1 dimensional?)
  A sawtooth wave with a richer spectrum of frequencies, but no time variation (2 dimensional?)
  A complex texture created with sine wave grains, unsynchronized temporal envelopes (3 dimensional?)

 Although volume increases directly with INTENSITY and is colloquially identified with it, it will also be affected by REVERBERATION and RESONANCE, as well as by the presence of OVERTONEs or PARTIALs. An increase or decrease in any of these will affect the total perceived volume of a sound or sound environment. Multiple sources that are similar, such as in a choral ensemble, also enhance the volume of the resultant sound because of their unsynchronized components.

 
Perceived volume increases with spectral richness (y axis), duration (z axis) and density of independent temporal components (x axis)
Reference: B. Truax, "Musical Creativity and Complexity at the Threshold of the 21st Century," Interface, 21(1), 1992, 29-42.
 Two examples of shipbuilding, the first with hammering on a wooden hull in a small room, the second on a steel hull in a large space. Both examples are played with approximately the same sound intensity level but differ considerably in the perceived volume of the sound.
 Synchronized sine wave grains going to unsynchronized grains
 Spectrum of a single 10,000 kg bell, Salvatore Mundi, Salzburg

Pitch synchronous analysis of a trumpet tone. These measurements are for a short tone (0.16 sec.) with a fundamental frequency near 550 Hz (C sharp). Time, measured in units of one pitch period, runs from right to left because the pitch-synchronous programs give more information on the attack (on right of plot) when proceeding backward in time. Seven harmonics are shown here (from M. Mathews and J.C. Risset, "Analysis of Musical-Instrument Tones", Physics Today, 1969, vol. 22, no. 2, p. 26, used by permission of the authors and the American Institute of Physics).

Synchronized envelopes (A) promoting perception of a fused bell-like source; unsynchronized envelopes (B) creating a fluid texture

  Excerpt from Jean-Claude Risset's Inharmonique illustrating the above

Ecological Size - Distance Relationships

What might be called the 'constancy of volume' helps the auditory system resolve any ambiguity in LOUDNESS and distance, such as that between a distant loud sound and a softer nearby one. Acoustic sounds tend to retain their identity and sense of magnitude, regardless of distance or intensity level. In contrast, the parameters of electroacoustic sounds may be varied independently, such as when a FADER changes the loudness of a sound without affecting its overall spectrum.

For instance, in the shipbuilding example above, the apparent size of the metal hulled ship does not change when varying the playback level - it merely sounds more or less distant.

 Synthetic vocal tone with (A) fixed reverberation ratio and decreasing spectral richness (decreased effort) and (B) fixed spectrum but ratio of direct to indirect sound is decreased (increasing distance), from Perry Cook, Music, Cognition and Computerized Sound.
  O Canada horn, Vancouver, nearby and distant