The medieval situation

We can now consider how western music developed by using notes of the seven-pitch scale as simultaneous intervals, and the problems into which it ran when extending it to a twelve-pitch scale, bearing in mind that if the deductions we made in Chapter 4 about harmonics are correct, we have to seek alternative explanations for the selection of intervals.

The period between 1100 and 1500 was remarkable for musical experiments. Polyphonic music was developed; it was virtually dependent on the evolution of a viable notation system. As the reader may know (perhaps in rather greater detail than the author), notation started with signs associated with words as a reminder of where pitch should go up or down without indicating how much, then pitch changes were indicated by signs on horizontal lines, eventually standardised on five spaced lines representing the heptatonic scale of pitches CDEFGABC, the set of ratios selected by hearing on monophonic instruments. The staff system is irregular in that some steps from line to space and space to line are one semitone and some are two. But it is logical to hearing, because the scale can be positioned anywhere in relation to the staff lines by clefs. In other words, it is implicit that intervals are ratios. When further pitches were added, they were indicated by accidentals (see also Appendix 1). The duration of pitches was first shown by a heterogeneous collection of signs attached to the pitch indicators, but the chaotic state it got into was revolutionised by the invention of the bar and barline; its implications are considered in Chapter 11. Once the notation system did correspond with the way hearing perceived the pitch relationships, and with the time patterns in which composers’ cortices used the pitches, the rate at which music developed from around 1500 was little short of explosive.

The organ

The organ is of great antiquity but it was a long time before it could make its special contribution. If the description by Vitorius of the hydraulus is to be believed, it had a keyboard in the first century AD with levers not dissimilar to a modern keyboard but about twice the size.