I believe what you are referring to as “attack” is actually “overtone”. An overtone is any frequency of a note higher than the target fundamental pitch. In the electric piano world, these frequencies are often described as “attack”, “bell”, “metallic”, “glassy”, “crystalline”, etc.
Meanwhile, a “harmonic” is a specific type of overtone… one that is a multiple integer of the fundamental pitch. In our piano, as well as a vintage Rhodes, the most apparent overtone presents as an octave above the target fundamental pitch.
There is an interesting separation of overtone and harmonic control within the nature of this type of electric piano. Overtone content can be controlled by adjusting high frequency eq (usually within the 2k-4k range), whereas harmonics are accentuated by sliding the Voice Control lever to the right, or if your piano does not have Voice Control, adjusting the free ends of the tines towards the center of the pickup pole pieces.
Another interesting nature of these instruments is that overtone (and to a lesser extent, harmonic) content does become less apparent as we play further up the scale. This is because the target fundamental pitches of the upper notes are quite similar in frequency to the overtones heard in the midrange of the piano, as well as physicality of the tone generators in the upper registers either naturally not producing such pitches, or perhaps producing overtones out of our range of hearing and/or our ability to amplify such pitches. An interesting analogy is the Hammond Organ – the upper drawbars “fold back” in pitch, dropping down by an octave at certain points in order to maintain some sort of harmonic presence in the upper ranges, as opposed to drifting off into obscurity as the pitches become too high for our ears to identify.
What I hear in these recordings are the phenomena as described, which is to say, the overtone drop off at around the usual F5 – G5 range. There is however, definite compensation within the playing (some passages including note excursions lower than the overtone drop off point, as well as some simultaneous playing of the midrange section with the treble section) and within the eq and processing of the instrument, being in a professional studio environment.
Boosting specific high frequency response in your amplification will have an effect. I would suggest running through a multi-band equalizer – either outboard, or one within a recording program. This will help with experimentation and analysis of how accentuating and reducing certain frequencies affect your overall tone.
Another useful tool may be found in various types of compression, which may also serve to help arrive at your desired sound. Compression not only serves to even out volume within a performance, as it can also be used to balance the many frequencies present within the sound of an instrument.
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