The Prime Octave

When talking or writing a lot about tuning, descriptive shortcuts are inevitable.  Referring to the A3/A4 octave as the “Prime” octave came about as one of those shortcuts.
Soon after that, the term ‘Sub-Prime’ was used to describe or identify the octave below the prime octave.  The A2-A3 octave.

The Prime octave is the A3-A4 octave.
When a “-” is placed between two musical notes, it denotes a range. A3-A4 represents the range from A3 up to and including A4.

The term ‘Prime’ applies not only to the A3/A4 and A2/A3 octaves, but also to the intervals that fall within those ranges.
When a “/” is placed between two notes, it signifies an interval. A3/A4 represents the interval of an octave, also known as the Prime octave.

The ‘Prime’ octave is both the A3/A4 interval and is also the ‘range’ of notes (A3-A4) between and including A3 & A4.

 

The ‘Subprime’ refers to the interval A2/A3, and the range of notes (A2-A3) between and including A2 & A3.

 

There are a pair of ‘Prime 5ths’ in the prime octave.
There is a lower prime 5th (A3/E4) and the upper prime 5th (D4/A4).

And, there are a pair of ‘Subprime 5ths in the Subprime octave.
The lower Sub-prime 5ths is A2/E3 (lower) and the upper subprime 5th is D3/A3.