From the time of Pythagoras the octave has been the fundamental reference point for defining and ordering differences in pitch and our Western music scales have been selected from the plethora of different ways of filling in that octave gap. The most influential has been the group of “modes” ascribed to the Greeks which became the musical language of the Christian church and out of this collection came the powerful major/minor system which catalysed the incredible development of Western music in the 2nd millennium. These modes were based on steps of tones and semitones and their particular character was related to the position of the semitones in the sequence of eight notes. In the manuscript of each mode and scale, the semitone steps are asterisked. This section also gives examples of octave spanning scales which contain less than eight notes with the corollary that some of these patterns include steps of a tone and a half or three semitones.

In addition to the selection of our major/minor system there was a second profoundly important decision which resulted in the establishment of the equal temperament tuning system for keyboards which meant that the instrument could modulate though all possible keys without the need for retuning. The significant marker for this development was the publication of J S Bach’s ‘The Well-Tempered Klavier’. While these exercises are of necessity presented using the equal-temperament system the techniques do allow the singing voice to adjust the tuning of leading and ‘accidental’ notes to obtain the subtle nuances of modulations which have been compromised by the rigidity of the keyboard tuning. Eg the ability, denied to the piano, of making a difference between Eb and D#.

The television series ‘Howard Goodall’s Big Bangs’ is an excellent introduction to this important part of music history.