N or M?

The naming of octaves

Music is an activity in which the gifted are so far beyond the masses that many of the enshrined techniques seem to possess almost mystical significance. Music is said to be, and most probably correctly, a highly mathematical discipline, but just as mathematicians have to put up with irrational numbers, so musicians have to accept the fact that the universal diatonic scale appears to be based on an interval, the whole tone, for which there is no satisfactory unifying mathematical basis. However there are aspects of music where the processes of historical development may have introduced avoidable complexity’

One area where musical terminology could be improved, and which might not be highly contentious, is in the naming of octaves. The octave interval is a frequency doubling which can be continued up or down with no beginning or end. In music only about eight octaves are important, with most of the activity in the middle four. A central nomenclature is required, but one that is clear and simple and solves the problem of where to start. Whatever the current system is, there is a very strong case to be made that an alphabetical one would be better and the proposal is to use the central letters m and n in lower case for the octaves above and below middle C. The idea is taken from the Church of England marriage ceremony where the man m is joined to the woman n and so hints at the lower voice m and the higher voice n.

The important octaves would then be:-

j  k  l  m  n  o  p  q

Fine as this might be, there is a serious problem. Although the defining interval in music is the octave, musical notation is not, apparently based on octave repeats, though it could be, and until it is, the question of where octave notation starts remains unresolved.

If each 5-stave-line repeat spanned exactly one octave the trivia of presentation could be put on one side, allowing musicians get on with the real work. This can be done and many others have shown exactly how to achieve it. Current nomenclature attempts to fit a seven-note repeat to binary (line/space) notation. The result is that at each repeat, higher or lower, the phase changes so any given note moves line-to-space or space-to-line.  Where most people, who, lets face it, are not going to have careers in music, find this most difficult is at the ledger lines, especially where they are also trying to master both the base and treble clef. So, without stopping to ask, ‘why do we have these different clefs?’ It is worth going straight to the alternative.

The seven-note diatonic scale has twelve semitones and based on these twelve notes, it repeats perfectly on line/space notation. However it takes longer to do so than in the current system, requiring 6 lines and 6 spaces. Starting with middle C on the ledger line below the treble clef, it arrives at C’ on the ledger line above the treble clef and all the octaves stack, up or down, with just one ledger line between them. In mathematical parlance we might say, ‘What could be more beautiful than that?’ but the big question is, ‘What would be lost from music if this nomenclature were to be adopted?

It would undoubtedly draw a line  between what was and what is, and the number of people able to read the hand-written scores of the old-masters would fall dramatically. The next, and most obvious thing is that accidentals would largely disappear, except in key signatures, thereby changing the visual flavour of music, because key changes would no longer signal themselves. There are several ways in which this might be redressed. One would be to print out-of-key notes bold, or faint, until a new key signature appeared.

Why not D?

An alien, seeing the piano keyboard for the first time and concluding that there was something special about the note D, would be both right and wrong.  The pattern of white and black notes, which is symmetrical about D, (and about G-sharp/A-flat) has its origin in the fact that the white notes are dedicated to the key of C major. The pattern may have little further significance. Nevertheless it is not without significance that, in classical music, D major is the most used major key and D minor the most used minor key, probably making D the most popular of the 12 notes. The only other significance to the pattern is the effect it could have on reading keyboard music in chromatic notation.

With  D as the ledger note, the four ‘white’ notes F, G, A, B lie in the white spaces between the five stave lines. C occupies the top stave line and E the bottom stave line. The very significant notes F-sharp and B-flat would occupy the second and fourth stave lines.  No other ledger note gives such a beautiful and memorable order.

Novices often find learning to read music to be difficult, and success may not necessarily correlate with intelligence, or even perhaps with musicality.  Many quite competent amateur musicians claim to be unable to read music. Others only read the treble clef and some, perhaps a majority, are not confident with extreme ledger lines. In fact there are some very real problems, because what appears to be a geometrical representation is, in reality anything but. The number of semitones between successive lines or successive spaces is either 3 or 4, and of course the pattern varies from key to key. Nevertheless despite the challenge, or perhaps because of it, many established musicians would consider the learning task to be a rite-of-passage, performing the invaluable service of sorting the wheat from the chaff.

The present Author had very little trouble in learning base and treble clefs, in fact this is his only musical skill, but did notice a remarkable fact. That whilst it is quite easy to play a note from the score, actually naming the note is not so easy and may underlie problems in actually learning scores, even when they are very familiar.

The benefits and transparency of semitone notation are well-known to a few. Its most distinguished protagonist was, perhaps unfortunately, Schoenberg. Unfortunate because this tends to cause confusion of semitone notation with twelve tone composition and brings the immediate feeling that it will be both abstruse and difficult. So despite Schoenberg’s eloquence and eminence, it has not ‘caught on’.

One reason for raising the issue at this time is that the digital revolution makes it a simple matter to experiment with printing techniques and to transpose music from one notation to another. The challenge would be to find ways to overcome the vertical expansion of one octave to a stave-set rather than about 1.5 octaves and undoubtedly the absence of clutter that semitone notation brings would help a great deal.

See also  ‘Lenny learns his scales’.

Notes and notation