This is a nice theory the OP has there, but it's basically wrong.
What he's describing is technically correct, but it's not the reason why Pioneer Mixers sound different from A&H Mixers.
First to the EQs. There are two main reasons why there are EQs on a DJ Mixer:
1. To avoid crashing frequencies when mixing, by removing the respective band on one channel if necessary
2. To adjust frequencies on single tracks to match them to the overall sound, e.g. if you're playing an old disco record that has less bass than a modern production, or you're playing a worn out record that lacks highs.
For everything else, you should trust the producer to have balanced the individual frequencies in his track so that the tracks sounds as good as possible and the sound guy in the venue you're playing at to have the settings of the system so it delivers the optimal sound (with the EQs on the mixer centred!). There is absolutely no reason to adjust the channel EQ (apart from the two mentioned above) and you shouldn't do it, as you actually woul probably make the sound worse.
If the OP's theory was true, Pioneer and A&H mixers would sound identical when the EQs are in the center position, which they don't. And here's why:
1. Pioneer mixers (the new ones post 500/600) are digital, whereas A&H mixers are analogue. Now what does that mean. As someone mentioned above, every component a signal passes can color the sound. Every ANALOGUE component, that is. A digital signal does not get affected by the various components it passes through, as it is merely a stream of 1s and 0s. So apart from the manipulation that is deliberatly applied to the signal through use of EQs and EFX, the signal stays completely unaffected inside a Pioneer mixer, while in an A&H mixer the actual audio signal runs through a number of electric components, each of them slightly affecting the signal. Manufacturers actually chose the components they use at least partly by the way they affect the sound...
Another difference between analogue and digital sets in once you get into clipping. Digital mixers can either clip or not clip. Once you reach 0 dBFS you clip, below that you're fine. With analogue mixers it's more of a slight progression, once you come to the end of the headroom. And while digital clipping is harsh/diharmonic, analogue clipping actually adds harmonic overtones to the signal, which are often perceived as "warmth". (By no means do I want to encourage anybody to clip his mixer to get a warm sound. Clipping is just bad and will eventually kill your speakers. Period!)
2. While Pioneer mixers have a rather flat frequency response, A&H mixers deliberatly colour the sound, on top of what I said above. A friend of mine did a test and found out that the Xone's slightly boost the signal at about 50Hz, which is where kick drum and/or bass are sitting in many modern dance tracks, which adds to the warm sound as well.
If you think an A&H mixer sounds warm, you should try listen to an old Bozak mixer. Those things really emphasized the low end, partly to make up for the thin bass frequencies in disco records back in the days.
OT: @Citizen_Insane: Actually he ended them with "Ceterum censeo carthaginem esse delendam"
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