Building Scales

The Whole Tone

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.

Just Intonation - In music, just intonation is any musical tuning in which the frequencies of notes are related by ratios of whole numbers. Any interval tuned in this way is called a just interval; in other words, the two notes are members of the same harmonic series.
Equal temperament - A system of tuning in which every pair of adjacent notes has an identical frequency ratio. In modern Western music the octave is divided into a series of 12 (logarithmically) equal steps. This tuning, or twelve-tone equal temperament, is often abbreviated as 12-TET.

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.

12-TET

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.

Notation

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.

Chromatic Scale - In equal temperament the chromatic scale is made up of all 12 semi-tones and the octave. Originally, it was a Pythagorean scale made of a series of eleven 3:2 perfect fifths - but that is all a bit academic now. The chromatic scale is a term you can understand these days to mean all the notes on the fretboard.
Diatonic Scale - The diatonic scale is a seven note scale (aka heptatonic scale is Greek for '7 notes') across the 12 semitone steps spanning octaves. However in a diatonic scale there are 5 whole-tone steps and 2 half-tone steps to make the numbers of notes equal seven. To make the scale sound smooth the half-tone steps are spread out as far apart from each other in the sequence as possible, resulting in several possible variations of diatonic scales, called modes.
Pentatonic Scale - A pentatonic scale is made up of five notes per octave. Pentatonic scales are common in folk-inspired and ethnic musical traditions, including American Blues and Rock.
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