What is a Spectrogram?
In order to give insight into the spectral differences of the different instruments, I will use a spectrogram, which is a graph that shows the evolution of the spectrum (the frequency contents) of a signal over time. Often, the frequency is on the vertical axis and time is on the horizontal axis. A spectrogram is computed by “chopping up” the signal into chunks and computing a spectrum for each of those. These different spectra are then put next to each other (as vertical lines) to form a 2D image. The figure below is an example.1
1 “What is a spectrogram?,” TomRoelandts.com, last modified November 20, 2013, https://tomroelandts.com/articles/what-is-a-spectrogram.
It is no surprise that in this day and age there is clear footage about Hammond organ and piano spectrograms. In the upper right clip you can see how the timbre of the Hammond organ changes while pulling out the drawbars. The clip underneath I made myself with Musiclab Chrome Experiments online. Have a close look at how the piano tones are very different in the low, middle and high register (the lows in the high register come from the hammer hitting the strings).
What do these examples tell us?
1) Piano waveforms die out, Hammond organ waveforms can go on forever due to the ungoing alternating current while you hold one or more keys.
2) The waveforms made on a piano are very broad in the low and very compact in the high register. The higher you play on the piano, the less overtones sit in the audible register, consequently making the sound more defined.
3) Hammond organ frequencies are much more concentrated then piano frequencies. As a result, the Hammond organ sounds more dense than a piano, especially in the low register.