Let’s start the concept of sonic imagery with examining a steady-state signal-generator tone in an anechoic chamber. You would readily notice that the perceived size of the sonic image is proportional to wavelength. IE: High-frequencies (HFs), as in treble, seem tiny & easily to pin-point due to their short wavelengths ( ½" - 6½"; 17mm - 170mm ); low-frequencies (LFs), as in bass, seem huge & harder to track back to the source due to their long wavelengths ( 5'6" - 55'0"; 1.7m - 17m ). It should be noted that these values are estimates as the speed of sound is depenent on temperature & humidity, which is why it also reduces with altitude.

Compression & rarefaction waves. While compression is self-explanatory, rarefaction isn’t. Rarefaction waves are the opposite of compression waves. You might want to say expansion waves, but no one does. This is important because humans hear predominantly compression waves, whose magnitude is perceived logarithmically.

Harmonics. Harmonics are multiples of the original signal frequency which usually have proportional envelopes. Thus, the terms “even harmonics” & “odd harmonics” you may heard before in regard to tube amplifier total harmonic distortion (THD) for even & odd multiples, respectively; good tube ampfliers produce more even order THD than solid-state but less odd order THD. The 1st harmonic is a multiple of 2, which means it’s an even harmonic. This span also happens to correspond with a musical octave, as in one octave above the original signal. Then there’s a subharmonic, which is one octave below the original signal. Below is an example tabulated from a 1kHz original signal.

frequency	multiple	harmonic	octave
500Hz	½	(sub)	-1
1,000Hz	1	...	0
2,000Hz	2	1st (even)	1
3,000Hz	3	2nd (odd)	1.585
4,000Hz	4	3rd (even)	2
5,000Hz	5	4th (odd)	2.322
6,000Hz	6	5th (even)	2.585
7,000Hz	7	6th (odd)	2.807
8,000Hz	8	7th (even)	3
9,000Hz	9	8th (odd)	3.170

Fourier series. This is a set of harmonic simple sinusoidal functions that comprise a complex waveform. Say for a simplified academic exercise your instrument produces square waves. This characteristic waveform determines the majority of an instrument’s unique voice. Below, we show the construction of a square wave by consecutively adding increasing odd harmonics of ever reducing loudness. Consequently, whereas a simple sinusoid images at it's own single Fourier frequency, a square-wave of the same frequency has more pin-point image due to its associated Fourier harmonics (much higher frequencies; much shorter wavelengths).

We can also show the analysis of these components via a plot of the magnitude vs frequency. This is often referred to as a Fast-Fourier Transform (FFT). However, those of you with equalizers may be more familiar with a similar plot called Real-Time Analysis (RTA).

f(t) = sin(ω•t) + sin(3•ω•t)/3 + sin(5•ω•t)/5 + sin(7•ω•t)/7 + sin(9•ω•t)/9 + …

f(t) = sin(ω•t) + sin(2•ω•t)/2 + sin(3•ω•t)/3 + sin(4•ω•t)/4 + sin(5•ω•t)/5 + …

f(t) = 1 + cos(ω•t) + cos(2•ω•t) + cos(3•ω•t) + cos(4•ω•t) + cos(5•ω•t) + …

Envelope. Envelopes bound the magnitude of a carrier signal. There can be periodic envelopes like beating, but here we're interested in an exponential decay envelope of a transient signal. We can examine the following crude approximation.

We can approximate a step function by indexing a biased extremely long period square wave by simply adding unity & halving the sum. Multiplying the steady-state signal by this step function models the semi-infinite initiation.
f(t) = ½•[ 1 + sin(ω•t) + sin(3•ω•t)/3 + sin(5•ω•t)/5 + sin(7•ω•t)/7 + … ]
Furthermore, we can superimpose an approximate exponential decay by indexing a reverse-sawtooth wave.
f(t) = ⅔•[ sin(ω•t) + sin(2•ω•t)/2 + sin(3•ω•t)/3 + sin(4•ω•t)/4 + … ]
Take note of all the harmonic components & how every one is at maximum positive slope. This means they are all compression waves. We hear every single harmonic component. It’s these HF cues that are directly coupled to the signature waveform that help really focus the sonic image. It’s this aspect that is inaudible when phase is inverted from absolute phase as the compression waves become rarefaction waves, thereby making lifesize sonic holographic images sculpted in vivid depth of detail become magnified, panaramic & shallow.

Other cues help too like valving on horns, fretting on guitars, the strike on a cymbal. However, we are ignoring the relationship because they have their own transient envelopes & sonic images that already happen to coincide with the principle signal. So, for our purposes we’re treating them separately.

Also, since the signal is decaying, the peak compression wave of the inverted signal is a tad quieter than the original signal. This also gives one the impression that inverted signals are about 2dB quieter. Of course this perceived discrepancy depends on the rate of decay of each signal, whose damping is unique to each & every instrument.

Phasing, or rate of phase is also important. Take a 1khz sinuous tone & a smaller 2nd harmonic of 3kHz. I can coalesce the two with a shifted phase & make a square-wave resemble a triangular-wave.

Remember this completely changes the voice of the instrument. However, this case (@ 120º/octave) is an extreme example. In my experience, phasing of 30º/octave is virtually undetectable. However, the absolute phase can accumulate at that phasing rate over several octaves & eventually invert the signal. “That” is audible as discussed.