That's not how I understand the musical scale, if I even understood you correctly.
By relative interval I understand the interval within an octave, so C-D is a second regardless of the octave. The frequencies (notwithstanding fine tuning), double each octave. Of course the absolute difference is proportional to the power of two, depending on the octave.
The picture is different when counting the proportion relative a fundamental frequency of your choice. That's how dezibell is generally defined, arbitrarily over some reference point. This has two interesting consequences. When counting keys not modulo 8 but continuously, the ratio D5 over C5 is much lower than D4 over C4. Second, if you want integer multiples of the fundamental's wave length, the first multiple spans an octave, and only the fourth or fifth octave has a full scale--this chromatic scale worked reasonably well tested on AVR with a buzzer, except that F needed adjustment taken from a frequency table.
This means there can be no second in the lowest register unless you invert the programm and scale the higher octaves down linearly. In that case, the interference from the second (ca. 9/8'th of the fundamental's wave length) sounds extremely grating when played as a chord; the attenuation where the maxima of both waves meet forms the actual fundamental and your notes lie 9 to 8 above it, canceling each other out half the time; this is easier illustrated with a sixth that would be 1.5 of the base key. It is not a good illustration of music theory though, more like information theory while the signal chain is computationally intractable.
Jazz musicians, huh