Prime? What do you mean by that?
The Prime Octave
When we were working on all this, we kept needing to talk about the A3/A4 octave. In order for us to be specific, we needed to make sure we were clear as to exactly which notes and which octave we were discussing. Over time, it just became easier to use the words ‘Prime octave’ instead of saying the A3/A4 octave.
And since we were always starting with A4, and then finding A3 to establish the width of the A3/A4 octave, and since establishing the width of the A3/A4 octave is a very important first step and of ‘prime’ importance for the tuning, we began referring to it as the Prime octave, instead of the “A3/A4” octave.
The Prime 5ths
Since the widths of the A3/E4 5th and the D4/A4 5th were critical for us in finding a really good width for the prime octave, we began referring to them as the Prime 5ths, with the A3/E4 being the lower prime 5th, and the D4/A4 being the upper prime 5th.
The Prime 4ths
Same way with the prime 4ths: A3/D4 and E4/A4.
It is just easier to refer to them as the lower and upper prime 4th than to have to say A3/D4 or E4/A4.
We can just talk or write about the upper 5th or the lower 4th, and we knew instantly specifically the interval we were describing.
The Sub Prime Octave, 5ths, and 4ths.
Eventually we began using the word ‘Sub prime’ to refer to the A2/A3 octave – the octave ‘below’ the prime.
And, it was then a simple conversion to also begin referring to the 4ths and 5ths within that subprime octave as the subprime 4ths and 5ths. It’s just much easier to refer to them as a subprime 4th or 5th, either upper or lower. Rather than describing the A2/E3 and the D3/A3 5th, or the A2/D3 4th or the E3/A3 4th.