The frequency ratio between the perfect fourth and perfect fifth is what is originally termed a tone or whole tone.
We can continue to divide the monochord by selecting nice mathematical ratios, and arriving at a set of notes that we use to create music with a particular character or flavour.... And that is exactly what various ancient greek tribes and other cultures did, arriving at their own particular musical cultures.
In the West, over the last, say, 400 years there has been a move towards equal temperament.
The real advantage of equal temperament is that there are a set of notes that can be used to approximate all kinds of tunings derived by just intonation with only small compromises in the frequency. The various Modes of the ancient Greeks were originally just intonations but in our Equal Temperament tuning on the guitar, they now form various scales in the 12-TET system.
The 12 tone equal temperament is based on increments of half the whole tone derived above, spread out evenly (logarithmically) across the octave. These half tones - or semitones - correspond to the frets along the fingerboard of the guitar.
We will soon be examining scales, so rather than draw the monochord as we have been, we will now present the monochord in a form more like the string on a guitar. The string below is a representation of the guitar string from the open string to the 12th fret.
Also, while we are at it we should get used to a new way to graphically represent the guitar fretboard.
The circles represent a fingertip being placed on the fretboard to form a new note. The number shows the number of the fret nearest to the right. The strings are from the top-E string (the thin one) down to the bottom-E 6th string (the thick one).
So in the example above we show a series of notes. Namely, in ascending pitch : Open E-string (6th string), C at the 3rd fret of the A (5th) string, F at the 3rd fret of the D (4th) string, and C on the first fret of the B (2nd) string.
You can build a scale out of all the half-steps along the string. This is called a chromatic scale, but doesn't really lend itself to melodious composition and is useful mostly for practice. Normally, a diatonic scale is built from 7 notes along the string plus an 8th note - the octave - to bring the scale full circle. A penatatonic scale selects 5 notes plus the octave, and there are also hexatonic scales using 6 notes, and so on.
The most common scales - and therefore the first you should endeavour to learn - are the Major scale, the Minor scale and the Minor Pentatonic (or Blues) scale. These are all detailed in the coming sections.