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I agree that a sound lacking in mid-freqs may generally end up sounding 'cold', whereas more presence in the mid-range may sound 'warm'
Also I've noticed that sounds containing many high-freqs generally sound 'cold.' This may reinforce the above point, since having lots of high-freqs would generally mean that relatively, the mid range is lower.
I think that bass frequencies would generally sound warm as well, so maybe you can put bass + mids together in terms of 'warmness'.
To summarise, if a sound has relatively more high than mid/bass frequencies then a sound may be heard as 'warm'.
However it's probably more complicated than that. For example, many people in this thread have alluded to the harmonic structure of a sound, specifically talking about analog vs. digital distortion, and saturation. I remember reading somewhere that analog/tube distortion tends to add odd-numbered harmonics whereas digital distortion tends to add even-numbered harmonics? If that is true then perhaps warmth is not just about relative high/mid freqs, but also the makeup of what is in those high freqs.
Finally most people tend to say that analog synths are 'warmer' than digital synths. This may also be related to high-freq content. Take for example the difference between CD and VINYL. CDs could reproduce far more accurately the high-frequencies in a recording that would tend to be lost somewhat (maybe not lost but possible just altered) in a vinyl recording. And people say CDs sound cold. Digital synths probably have a similar effect on high-freqs.
Also this sounds similar to an issue with the Vanguard VSTi, which people said sounded really cold - the original Vanguard had a bug where the high frequencies got all distorted and made more prominent. So that could be what made it sound cold.
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Monsoon - Astrosurf
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