This posts is part of a series about the octave as a way of understanding the world.
The previous post was about The Pythagorean Octave.
The philosopher and spiritual teacher G I Gurdjieff came across the law of seven in his travels in Asia around the beginning of the 20th century. Like the law of three, Gurdjieff saw the law of seven as a fundamental law of the universe, governing the progression of the vibrations which underlie all reality. The key insight is that whilst we might think that these vibrations change uniformly, in fact there are discontinuities, places where the change speeds up or slows down. These discontinuities mean that processes never go straightforwardly: impulses stall, or unintentionally change direction.
This is not just of theoretical interest, but is vital to our own well-being and self-development. To take a simple example, I might sit down with the best of intentions to write another paragraph of this article, but instead after a little while I find myself browsing images of cats. This can be seen as an operation of the law of the seven: intentions go astray.
Once we understand the law of seven, and more importantly observe it operating within ourselves, we can begin to think about how to work with the law of seven to achieve our intentions.
Gurdjieff learnt about the law of seven in the mysterious Sarmoung Monastery, built into the system of movements that he learnt there. His visit is portrayed in the film “Meetings with Remarkable Men” by Peter Brook:
What is the Law of Seven?
A description of the law of seven is given in Ouspensky’s book In Search of the Miraculous. He quotes Gurdjieff explaining that the law was known to ancient science, and was expressed in a formula which was handed down from teacher to pupil, from one school to another:
“In very remote times one of these schools found that it was possible to apply this formula to music. In this way was obtained the seven-tone musical scale which was known in the most distant antiquity, then forgotten, and then discovered or ‘found’ again. The seven-tone scale is the formula of a cosmic law which was worked out by ancient schools and applied to music” 
Ouspensky goes on to define the law in similar terms to the Pythagorean octave, but with slightly different ratios between the notes.  The structure of the octave is the same, with seven notes and two semi-tone intervals (mi=fa and si=do):
do – re – mi = fa – sol – la – si = do
Ouspensky explains that these semi-tone intervals are where a ‘retardation of vibration’ takes place, causing a deviation from the original direction, so that instead of going in a straight line, any process veers off:
Why we can’t do things
Gurdjieff said that the law of seven “shows why straight lines never occur in our activities; why, having begun to do one thing, we in fact constantly do something entirely different, often the opposite of the first, although we do not notice this and continue to think that we are doing the same thing that we began to do.
“All this and many other things can be explained only with the help of the law of octaves together with an understanding of the role and significance of the ‘hiccups’ which cause the line of development of force continually to change, to go in a broken line, to become its ‘own opposite’, and so on.
“Such a course of things, that is, a change of direction, we can observe in everything. After a certain period of energetic activity or strong emotion or a right understanding, a reaction comes: work becomes tedious and tiring; moments of fatigue and indifference enter into feeling; instead of right thinking, a search for compromises begins and results in suppression or evasion of difficult problems.
“But the line continues to develop — though now not in the same direction as at the beginning. Work becomes mechanical; feeling becomes weaker and descends to the level of the common events of the day; thought becomes dogmatic, literal. Everything proceeds in this way for a certain time; then again there is a reaction, again a stop, again a deviation. The development of the force may continue — but the work which was begun with great zeal and enthusiasm has become an obligatory and useless formality. A number of entirely foreign elements have entered into feeling — considering, vexation, irritation, hostility. Thought goes round in a circle, repeating what was known before, and the way out which had been found becomes more and more lost.
Why civilisations and religions fail
“The same thing happens in all spheres of human activity. In literature, science, art, philosophy, religion; in individual and, above all, in social and political life, we can observe how the line of the development of forces deviates from its original direction and goes, after a certain time, in a diametrically opposite direction, still preserving its former name. A study of history from this point of view shows the most astonishing facts which mechanical humanity is far from desiring to notice.”
“Perhaps the most interesting examples of such change of direction in the line of development of forces can be found in the history of religion, particularly in the history of Christianity if it is studied dispassionately. Think how many turns the line of development of forces must have taken to come from the Gospel preaching of love to the Inquisition; or to go from the ascetics of the early centuries studying esoteric Christianity to the scholastics who calculated how many angels could be placed on the point of a needle.” 
How can we work with the Law of Seven?
Ouspensky goes on to explain that it is possible for processes to develop in a constant direction if the two intervals in the octave are filled with an additional shock of the right force and character. This can happen by accident, but can also be arranged intentionally:
“[A man] can learn to recognise the moments of the ‘intervals’ in all lines of his activity and learn to create the ‘additional shocks,’ in other words, learn to apply to his own activities the method which cosmic forces make use of in creating ‘additional shocks’ at the moments necessary.”
“The possibility of artificial, that is, specially created, ‘additional shocks’ gives a practical meaning to the study of the law of octaves and makes this study obligatory and necessary if a man desires to step out of the role of passive spectator of that which is happening to him and around him.”
The law of seven and its study is at the centre of Gurdjieff’s method. Through it we can develop an understanding of the cosmos and of ourselves, and learn to begin the Work of self development.
The octave as previously described has two intervals where deflections take place, one between mi and fa, and the other between si and do, but Gurdjieff also mentions a third interval which has a different character, and that is the interval between the notes sol and la. In Beelzebub’s Tales , Gurdjieff calls this interval Harnel-Aoot, and says that it is ‘disharmonised’ by the effect of the other two intervals. (He does describe the nature of this disharmonisation, but we won’t explore that further here). So the full structure of the octave can be read as:
do – re – mi = fa – sol ≈ la – si = do
 In Search of the Miraculous, P D Ouspensky, Chapter 7. Available online at http://www.ardue.org.uk/university/intro/octave.html
 Ouspensky uses 10/9 instead of 9/8 for the tones re-mi and sol-la, and 16/15 instead of 256/243 for the semitones mi-fa and si-do.
 Chapter 39 of “Beelzebub’s Tales To His Grandson”. This book, though fantastic, requires hard study! An electronic version of Chapter 39 is here.