(Today we celebrate the Sun-Jupiter conjunction in the Sign of Virgo. Along with this heavenly direction sacred to the Love of Nature which nourishes and grows all Forms, let us try to orient our thought to this 2nd Ray polarity, presenting the twofold factors of Growth for the science of Harmonics)*
Infinity I § 200 – The vibration of the heart draws the spirit to its destiny and moves the levers which guide it to what is due to it. Therefore, when the creative power is on the way to completion, the heart resounds. Any vibratory commitment evokes a reply there, and the ray emits a corresponding vibration: the sensitive heart assimilates the rays received. The concordant vibrations generate harmony.
INDEX AND GENERATOR
We have come to one of the most important phenomena for all researches into harmonic series and groups: limitation…
In Harmonics there is a distinction between the internal and the external limit: the first is called the “generator” and the second the “index”.
The INDEX is the limit of the external development fixed for the series or for the group.
However, it is not a question simply of an external device. In reality, every index has its own “face”, not only because of the numbers contained, but also and especially because of the tonal values.
Index 1 remains in the peace of Unity; 2 contains it developed in the trinity; 3 sees the great interval of the fifth appear, etc. Thus in the whole of every index something new occurs which did not exist before. Every index has its own characteristic aspect, its own shape, and it is not a simple accumulation which is already foreseeable. It should be noted, inter alia, that only the odd indices produce new values. Nevertheless, the aspect of Index 3 is quite different from that of Index 4, even if only new octaves come in here, and this difference is important for the interior arrangement.
‘GENERATOR’ is the term chosen to indicate a principle, a directive, an inner law which presides over the construction of form.
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For Harmonics, the most important generator is the “Senary”, that is the finite series of numbers from 1 to 6 and their reciprocal numbers. We have already said what is meant by “emmelic” and “ekmelic”.** All the emmelic numbers are contained in the Senary, while the ekmelic numbers are excluded.
The Generator works as the principle of selection from the inside and constructs any configuration in the ambit of a certain Index. The reader is asked to train himself in this sense and he will be convinced of the peculiar tendency of the Generator to define a shape.
Index is therefore to limit outwardly; Generator for building from within. Since no limitless figures exist, the Generators are always limited by a certain index, and at this “edge” they meet. The Index can never be greater than the development of the Generator, and the latter (if the figure must have a sense, and since in theory neither Index nor Generator can be ∞) must have an Index, that is a limit.
EMERGING CONSIDERATIONS
These two concepts, of the Index and Generator, have an immense significance in Harmony, so that to represent all the fields of possible application is not possible in a book, but only to give a very few examples regarding creation in nature. The aspect generator can be described as the principle of universal selection; if we add the concept of index, the main way we can speak of it is as a “limit of the group”, which is the Form of all values, from within and without…. In any case where the construction of a form is considered, we encounter always two basic principles: the process from inside to outside and the limit imposed from outside. These two principles can be isolated only in a theoretical sense, but this is impossible in practice. They are, however, not linked by a rigid relationship, but in a living interchange, and perhaps only in this dialectic is the solution of the riddle of the general construction of form.
It is interesting to note that sciences consider especially the generative aspect, while that of the index is taken as a simple statement of fact.
Each atom consists of a generative selection of quantum orbits, and of the “Number” of its nucleus; the dependence of the index from the inner selection should be unquestionable; precisely therein the difference of the various atomic structures lies. Each crystal is formed according to the Generator of its class; it could conceivably grow unlimited, but actually crystals – like trees – do not grow till the sky: they must therefore conform also to an Index.
An artist not only chooses the material for his/her work, but imposes strict limits, which result from an interior choice. So the work of art is limited not only in an external sense, but also inwardly, and these limitations depend on each other. It can be said that the value of this work depends on the balance between the two principles. A monument originates always and only by a choice of materials and projects, and the Index of its architecture must consist of the harmony of its parts, otherwise it would not have lasted.
The Senarius.
If we equate Index and generator, that is, if we limit the Senarius to the finite series 1, 2, 3, 4, 5, 6, we obtain the corresponding crossed harmonic series. On the other hand, if we set the index for example to 16, and connect with vertical and horizontal lines the values contained in the senarius , we get the following figure, where there are also marked, and only, the equitonals with value C. We see that the Senarius comprises a closed world, which nonetheless tends to ∞ in two directions.
Other brief remarks follow on the Senarius, which appears almost everywhere, in crystallography as well as in chemistry, plants, etc. To be remembered are the subdivision of the round angle in 360°, the 12 months, the 24 hours, the zodiac, the examples of Greek architecture, etc. Everything demonstrates the great, creative impulse of the inner senarius.
