Examples of the laws of three and seven in the music of Gurdjieff / de Hartmann

by Wim van Dullemen ©2002

Although music can never be reduced to rationality, even a superficial form-analysis of Gurdjieff's music cannot fall to show examples in which he represented these laws in a musical format. After some brief remarks about the music of Gurdjieff and De Hartmann, two examples will be played and discussed step-by-step: 'Hymn from a great Temple nr.1' and 'Prayer and Despair'.

Music is a world in itself. Each child, man and woman has his/her own experience, of irreplaceable value, in this God-given realm. Trying to improve your understanding of music however, demands discipline. In this discipline, we have first to define the context of a musical specimen and then we have to analyse it to the limit of where the intellectual insight can bring us. Having reached that frontier, we try to open ourselves completely to the possible emotional meaning and the reason, in real music always sacred, why this music exists.

'The intellectual approach is only a small part of the total exercise and should never have an aggressive impact. It should be like studying a flower, so carefully that it is not damaged.' [1] The interpretations of the two hymns of Gurdjieff and De Hartmann given here serve only as an example to encourage others to explore the music their own way. They indicate a possible way of being open to the music, that is all. No Interpretation whatsoever can replace music, they present only passing visions that continually have to be changed and renewed through new efforts in listening, analysing and playing.

In trying to find examples of Gurdjieff's Laws of Three and Seven, the danger is of course that we are looking for something we have already found; the most unscientific approach possible! This is what the Germans call: 'hineininterpretieren'. It resembles the procedure of the poor devil who started calculating all night long until his calculations showed him that he actually was a rich man! I shall try to avoid that danger as much as possible by splitting up the observations in 'facts and fantasies'; that means basic textual analysis and subjective interpretation.

Hymn from a great Temple I

This composition is 'antiphonal' in the extreme. That means it is in a pure call-response format. This musical practice is widely used in classical music, but only in a disguised way. In its plain form it is practised only in folk and religious music, f.i. it is still alive in New Guinean and African musical traditions. The last influence can still be detected in spiritual and chain-gang work songs in the U.S.A. Another variety can be heard in Liturgical chanting; where the priest chants a short phrase - f.i. Kyrie Eleison - and the community answers with the same phrase, with a slight melodic modification. The reason for the extreme antiphonal character of this piece must be that we are dealing here with a representation on the keyboard of a Liturgy Ceremony.

I have no doubts whatsoever - based on textual evidence, f.i. the length, limited range and absence of large intervals - that in this composition the 'calls' - 6 in total - were sung by a community. Neither do I have any doubts, although I cannot prove it, that this music was the result of an impressive effort by Gurdjieff to pass on all the sounds of a particular liturgy exactly as he remembered them; including non-musical sounds, like mumbling of prayers, sacred gestures and the sounding of heavy objects. [3]

The 'response' part is highly characteristic of this hymn. It is a seven-note pattern in the low bass region that is repeated in the same form throughout the piece seven times. De Hartmann has emphasised that each note should be struck with force. Therefore the response was not chanted. It could be a staccato low growl by one or a few elderly men, but more likely it is the sound of an unusual heavy and large stringed instrument. Further in 3 places notes in the lowest keyboard-region are hit, without any melodic or rhythmic function. These echo the liturgical sounding of three (!) different large objects; bells or massive gongs.

To illustrate the musical pattern of this composition I refer to my graphic representation (illustration 1). I am indebted for this particular musical notation-system to the inventors of it; Georg Balan and the directors of the 'Musicosophia' Institute in Germany, who were so kind to instruct me in its use.

It shows that the ceremony opens and closes with the same musical statement. In between are the six calls and seven responses. The seven responses are divided by two highly irregular rhythmic interventions that each time push the calls higher up in the melodic scale. Much could be added about this piece, where each note does have a function, but I have to limit myself in this written account. Obviously it will be hard to

deny a total analogy between the Law of Seven and the musical structure of this piece, that in all likelihood represents a ceremony performed to anchor the specific characteristics of this law into the life of the community.

Prayer and Despair(second hymn from the album 'Sacred Hymns)

Basic Textual Facts:

'Prayer and Despair' consists of one small melodic formula that is repeated throughout (hereafter referred to as: 'the formula'). This form of music is called 'iterative' and is usually associated with primitive or simple traditional folk music. The formula of this hymn, however, is not only of an astonishing beauty, but is a mathematical pattern in which the numbers 3 and 7 are interwoven. It has 3 units, divided over 7 counts, the first unit being in its turn also divided in 7 smaller sub-counts. ( see overhead 2)

The composition starts with the statement of the formula in its pure form, played in the middle region of the instrument. Then it is repeated a number of times in the bass region, adding more and more embellishments. [4] This process is repeated 3 times, until an entirely new melodic influence intervenes, after which the piece ends with the last Statement of the formula.

Formula + left hand repeats give respectively the numbers 14, 7 and 8, suggesting strongly that the formula itself is part of a greater cycle of 7.The 7 subcounts of the first unit of the formula are enlarged in 7 counts of the formula and again enlarged in the 7 (with the one 8 as exception) repeats of the formula. 3 cycles of 7 embedded within each other.

The formula - in either pure or embellished formal - is repeated 32 times. This chain of repetition is broken up in 3 well-defined places, where the formula falls apart in a bass line to sustain the melody. These deviations are melody driven and are indicated below. The most striking of these is the 32-component [5], where a new melody is coming in.

Start:right hand formula; 7-countsleft hand formulas in counts: 8-7-7-7-8-8-7-7-7-8-7-7-4right hand formula renewedleft hand formulas in counts: 7-7-7-8-7-7right hand formula renewedleft hand formulas in counts: 7-7-9-6-11-8-7right hand formula renewed twicenew melodic Intervention in counts: 4-4-32right hand formula renewed for the last timeend.

In the context of the 'Laws' of Gurdjieff it is of course difficult to avoid the association between the two break-ups (see above 8 and 9) and the two intervals in the 'Law of Seven' and not to interpret the 32-component at the end of the piece as a breakthrough of a new octave. The more so because this whole composition is an extremely complex labyrinth of musical units of three and seven.

Each time the left hand takes over the formula, a higher placed melody starts; a long line without any rest or pause; it never breaks or stops: an 'unending'-melody. It becomes temporarily silent each time the formula is renewed.

So the composition consists of three basic components: the formula itself, the variations of the formula in the bass and the melody line. These are placed in three defined and limited regions of the keyboard and do not intermingle. These three components suggest to me totally different atmospheres that, although they do not touch each other, maintain a balance together, like three planets circling around each other in a blue sky.

In the middle of the piece the whole delicately balanced construction is threatened by a flood of left-hand arpeggios. This flood, representing no doubt the 'despair' component, is brought about by a harmonic shift in the formula as played in the bass. Instead of the fifth note of the scale (a) the formula stops, again and again until the end of the entire composition only at the fourth note (g), creating tension because the unfinished 'sub-tonic' is denied the harmonic solution of the 'tonic'.

It is noteworthy that whereas the bass cannot resolve the tension of the sub-tonic 'g', the formula in the right hand goes on unaltered - and keeps sounding the resolution-note 'a'. Further it should not be missed that even after the new melodic Intervention, that sounds like grace

from heaven, the bass cannot raise the 'g' to the 'a' level and diminish the tension. That leaves the piece with an open end: the bass is unresolved, the prayer, the 'formula', is in harmony with itself, but neither 'formula' nor the new melody that sheds its light and consolation can reach or influence the unfinished state-of-affairs within the bass-formula.

Interpretation:With reference to the limitations of any interpretation given earlier in this article I will quite simply give my vision as stimulated by the basic facts.

This piece has at least a title - thank God - and therefore we know that it is about prayer and despair.

The 'formula' represents the inner praying of man. Its sounds resigned, quietly and withdrawn, in between all the turmoils. It has to be renewed all the time, has to be continuous.

The unending melody line sounds far off, another world, where creation is expanding all the time.

The bass line stands for the earth. The first interval occurs; how remarkable that listeners are not mentally aware that something is happening, but their feeling and sensation notice a difference. The bass line continues in a seemingly harmonious state but then......it reaches the first long held note ('fermate'). This note sounds like a sombre warning, something is going to happen, tension accumulates, but we do not know what is going to come. This note is the 'g'. Would it be accidental that the last 'warning-gong' of the First Temple Hymn was a 'g' also?Would it be accidental that g-minor is the tonality that Mozart exclusively employs for his most desperate moments? [6]

No. This note is a symbol for the unfinished state of the earth and the suffering caused by that. The despair comes in like roiling waves that shake the house. But the prayer inside man is renewed, again and again. Then, after the prayer has been repeated twice, a heavenly melody breaks through like a ray of sunlight. This tenderness pervades everything, but the bass sounds again soft, like a sombre echo, the 'g' as a remembrance that the state of the earth is not and cannot be altered.

What strikes the most is the inner relation of the three components: earth - inner prayer - heaven. Only the inner prayer is able to reach the harmony note 'a', provided this prayer is according to the intricate pattern of three and seven. This suggest that without the inner prayer, not only the whole construction would fall apart but the earth note would have to fall down the scale from 'g' back to 'd', which means here 'Holy The Firm' below the low end of the octave. This musical piece becomes unforgettable the moment one realises that it tells us that only the inner prayer of mankind keeps this creation in balance.

If one can visualise the mathematical construction while remaining open towards the emotional impact of this composition, one is overcome by such awe that all further words stop.

Wim van Dullemen

[1]...Quotation from Uwe Fricke, Director of the Int. School for Education in Conscious Music Listening, Germany, from a private conversation '97[3]...A transcription of sounds in another medium is called 'onomatopoeia', and I do have reason to believe that they occur in the musical work of Gurdjieff.[4]...De Hartmann did not 'bar' this manuscript, which is an unusual practice.[5]...Remember that the total repeat of formula is also 32! I doubt if the slightest note in this piece is accidental and the recurrence of the number 32 is reminiscent of Bach's famous number trick in the first prelude of 'Das Wohltemperierte Klavier' .[6]...Misha Donat 'Mozart's Piano Concertos' 1993, included in the Philips-cassette of the piano performances by Mitsuko Uchida.

Hymn from a great Temple I

The Formula:

consits of: 3 units and 7 countsfirst unit consists of: 7 counts

Architecture of the 'magnified' formula: 3 concentric circles:

first seven counts form one unit in seven counts; these seven counts form one count in a greater cycle of seven counts.

Architecture of whole composition: