Kaaba’s Numerical Picture of Harmonic Origins

A recent plan of the Kaaba[1] indicates that its walls, by their odd-number proportionality, symbolised the numerical origins of musical harmony through the first six numbers, 1, 2, 3, 4, 5 & 6, sometimes called the Senarius meaning “existence out of six”.

According to Plato, the world was created using the rules of musical harmony in a scheme involving perfect fifths of 3/2, fourths of 4/3 and tones of 9/8, leaving “leftover” semitones of 256/243: a rudimentary musical scale. This only used prime numbers 2 and 3 and multiplications with themselves and each other; a system called Pythagorean tuning. The Kaaba incorporates another prime number 5, called the human number, this enabling two more large intervals called thirds, the major third of 5/4 and minor third of 6/5. Using 5 enables more and better scales to be formed and fills in the gap between 4 and 6 to show all the large intervals in the first six numbers, 1:2:3:4:5:6. This fuller tuning system has been found in the ancient Near East as long ago as the Sumerians, in their tuning texts on cuneiform (c. 3000 BC onwards).

Ernest G McClain wrote on the proportions of the Kaaba[2]:

“What follows is an adventure in imagination which aims at grounding the Kaaba’s proportions in the sacred sciences of earlier civilizations. Since Islam already claims a very great antiquity for the Kaaba, any explanation which appears plausible will merely have the effect of supporting the Islamic claim. My argument is based on the very interesting coincidence between the Kaaba’s proportions—not its absolute measures—and those of the Temple of Poseidon in Plato’s myth of Atlantis, a myth which has proved capable of very detailed explanation by the methods and metaphors of the Pythagoreans. The temple of Poseidon is described as involving the ratios “6:3 plethra (full)” meaning 6:5:4:3. The Kaaba’s proportions are precisely these:


Meditations through the Quran. Ernest G McClain. Maine: Nicolas-Hays 1981. 78-79. 
  Width Length Height
Measures (in meters) 10 12 16
Proportions (in smallest integers) 5       : 6  
    3       : 4

We can say that the Kaaba” embodies” the ratios 3:4:5:6, the numbers 3 and 6 being an “octave identity” in Pythagorean harmonic theory. We are investigating notthe visible geometry of the Kaaba but the proportions which have their meaningin the invisible sonar implications of a number theory which the whole ancientworld shared in common for several millennia before Muhammad.”

My own measures for the monument (derived from the previously mentioned plan) seem different in giving a width of 11 yards rather than 10 metres but 11 yards are 10.0584 metres and McClain’s figures (after Titus Burckhardt) were only approximate. My length is 39 feet which is 11.89 metres, that is, nearly 12. My geometrical proposal is illustrated below in figure 1.


Figure 1 The Emergence of proportionality within the Kaaba’s grid of 143 square yards.

The walls of the Kaaba can be considered as blocks one-yard square. The inside floor area would then be 9 x 11 = 99 square yards, the number symbolic of the ninety-nine names of Allah. When seen as a set of nested rectangles, the sequence 13:11:9:7:5:3:1 arises, in which 7 is the middle term and the sum is 49 or 7 squared, seven being the number that terminates the senarius. The walls of the Kaaba also seem to have a meaning in inches since the outer perimeter is 123 = 1728 inches, symbolic in numbers given for near-eastern arks, whilst the inner perimeter is 1440 inches, symbolic of Adam when his letter numbers of 1.4.40 are placed in decimal position notation [McClain, The Myth of Invariance, p126].

Figure 2 Inner and outer perimeter lengths in inches

Sacred buildings are obviously related to arks and salvation whilst the Biblical figure of Adam was further developed in the Prophet’s new narrative; that the Kaaba was a building created by God when Adam was made, whilst Abraham and Ishmael, his first son, built the earliest version made by human hands. Mohammad himself participated in a major rebuilding of the Kaaba after flood damage, which could have been designed to the present Kaaba’s proportionality and later works all based on that footprint.

It is the perimeter lengths of the Kaaba’s nested rectangles (figure 1) which tell the story of the senarius.

half perimeter perimeter senarius interval
3 + 1 = 4 4 × 2 = 8  8/8 = 1 Unison (1:1)
5 + 3 = 8 8 × 2 = 16 16/8 = 2 Octave (1:2)
7 + 5 = 12 12 × 2 = 24 24/8 = 3 Fifth (2:3)
9 + 7 = 16 16 × 2 = 32 32/8 = 4 Fourth (3:4)
11 + 9 = 20 20 × 2 = 40 40/8 = 5 Major Third (4:5)
13 + 11 = 24 24 × 2 = 48 48/8 = 6 Minor Third (5:6)

Table 1 Outer perimeters of nested rectangles indicating the Senarius

Conclusions

McClain’s intuition has continued to be valid, that the Kaaba enshrined the senarius or “creation out of six” of musical harmony. It seems likely that the building employed ordinary feet and yards to embody successive perimeters, with inches providing additional meanings congruent with McClain’s published work on ancient near-eastern harmonic code numbers and the Bible. This innovative and previously unknown way of using nested rectangles and adjacent odd number-pairs, to symbolise the senarius, should give weight to the idea that this focal monument for Islam symbolised a harmonic basis for the creation of the world on which it sits.


[1] https://en.wikipedia.org/wiki/Kaaba#/media/File:Kaaba-plan.svg


[2] A uniform spelling of the Kaaba has been imposed. Continuing, he wrote: Muhammad, as an ” unlearned” man, has no share in this ancient science; he is merely the agent—as he conceived himself to be—by which ancient knowledge came to new life in Arabia. Before embarking on our new study of the Kaaba, let us first notice the role which number plays in the Quran. My whole study would be invalidated— at least for a Muslim—if the Quran itself did not virtually ignore geometry and laud, instead, number and proportion.

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