We audiophiles regard specs as being (or should be) related to sonic characteristics. But this is not the primary purpose of specs.
A product is tested and the test results are compared with specs so as to verify that the particular unit does not have defective parts or improper assembly. In other words, "does this unit look like all the others". What it looks like is another issue. The sonic characteristics are determined by the design of the circuitry, and a design that sounds "good" may have some parameters that deviate from the ideal.
That said, there are some parameters of audio equipment which do relate to sonic characteristics, frequency response and distortion are the most obvious. If you intend to make a circuit that processes the audio signal with "Fidelity" distortion is ideally zero and frequency response is broad and flat. If you intend to make a nice sounding circuit, you may want to shape the frequency response and generate some nice harmonics. However, if you do the latter, you are designing a musical instrument, not a high fidelity amplifier.
A product is tested and the test results are compared with specs so as to verify that the particular unit does not have defective parts or improper assembly. In other words, "does this unit look like all the others". What it looks like is another issue. The sonic characteristics are determined by the design of the circuitry, and a design that sounds "good" may have some parameters that deviate from the ideal.
That said, there are some parameters of audio equipment which do relate to sonic characteristics, frequency response and distortion are the most obvious. If you intend to make a circuit that processes the audio signal with "Fidelity" distortion is ideally zero and frequency response is broad and flat. If you intend to make a nice sounding circuit, you may want to shape the frequency response and generate some nice harmonics. However, if you do the latter, you are designing a musical instrument, not a high fidelity amplifier.