Before we engage in a discussion of the finer details of the mathematics behind the early Chinese scales, it would be useful to be familiar with some terminology as well as knowledge of Music Theory. Music Theory is a science in itself. It explores the intrinsic details of music and its scope is far too deep for any single project to cover.
We'll start off with an elemenetary explanation of what are notes.
Notes are actually a sound with a particular frequency (This is briefly explanined in the following page). Over the years, music has evolved to incorporate only a select number of notes. In modern music, a system of 12 notes is in use today.
7 of the fixed notes are termed A, B, C, D, E, F and G. Though you may recognise that the labelling start mostly with a C (ie. C, D, E, F, G, A, B). In addition to these 7 notes, there are 5 more that are represented by adding a '#' (read sharp) or 'b' (read flat) symbol to each note. (ie. A#). These symbols are called 'accidentals'.
Putting these 12 notes together in a progression, we get a chromatic scale.
Simply put, a musical scale is just a sequence of notes. Scales start and end on the same note. This is an important point because a scale spans an octave (2 notes that have 11 notes in between them)
You will observe that this chromatic scale will thus consist of notes in increasing half steps from each other. The half steps in the modern scale are equal in magnitude. The modern scales are thus called equal temperament. These half steps are also known as semi tones.
Combining two semi tones together, we will get a whole tone. ie. C -> C# is a semi tone, whereas C -> D is a whole tone.
7 of the notes are arranged such that the intervals between them are in the
TONE, TONE, SEMITONE, TONE, TONE, TONE, SEMITONE
we get a major scale. (Refer animation below - It shows a major scale starting with C)
The distance between two notes is called an interval (i.e. the difference in pitch between any two notes). Linking to what was mentioned previously, an interval is just the summation of several half steps. The 'size' of any interval is expressed numerically. E.g. from a C to a G, it is a 5th, because the fifth note from C is G (in a C major scale).
Intervals can be understood in scientific terms as the difference in vibrations per second between two pitches. In other words, its is a ratio of the frequencies of two notes.
A list of some of the common ratios of the modern music scale is given below. As an example, click below to here an example of the Perfect Fifth.