The following charts show four common pitch and octave numbering systems:
MIDI numbering, Octave Numbering (two common systems), and the Helmholtz Pitch Numbering
(also known as the Helmholtz Pitch Notation System)
The pitch range is the same in each example, but the notation is displayed on different clefs.
Example 1: the notation is shown on a grand staff
Example 2: the same material shown in treble clef
Example 3: the same material shown in bass clef
Example 4: lastly, the material is shown on a staff that changes from bass clef to treble clef.
NOTE: The underlining merely deliniates an octave and is present for no other reason.
Octaves are shown alternately, underlined, and then not underlined.
1: MIDI numbering
2: Octave Numbering (Japanese, Yamaha, Encore)
3: Octave Numbering ("scientific", MusicXML, and others)
4: Helmholtz Pitch Numbering System*
*NOTE: The Helmholtz Pitch Numbering nomenclature shown here is a variation commonly used in the US. It uses apostrophes to indicate the octaves of Middle C and above: ', '', ''', etc. Octaves below C D E ... are indicated with commas, appearing in descending in order: C, D, E, ... C,, D,, E,, ... etc. Superscript lettering, ii, iii, etc. is used (instead of apostrophes) in the original Helmholtz form for upper octaves. Subscripted lettering i, ii, iii ... are used instead of commas to indicate lower octaves.
Helmholtz Pitch Notation may go by different names, including Helmhotlz Pitch Numbering.
It is one of the octave numbering systems widely used in music.
More info about Helmholtz Pitch Notation here ...