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Updated: May 3, 2025
In general, when two tones are related, as 2n:3, 5, 7, 9, 15 in which 2n denotes every power of two, including 2o=1, with the progression from the first to the second, there is bound up a tendency to return to the first. Thus the fundamental fact of melodic sequence may be said to be the primacy of 2 in vibration rates. But 2n, in a scale containing 3, 5, etc., is always what we know as the tonic.
In this case reduction of the chromosomes does not occur at all, the eggs develop with 2N chromosomes and all develop into females. Under unfavourable conditions reduction or meiosis occurs, and two kinds of eggs larger and smaller are formed, both with N chromosomes. The larger only develops when fertilised and give rise to females with 2N chromosomes.
There is also evidence that in some cases, e.g. the sea-urchin, the female is heterozygous, forming gametes, some with N and some with N+ chromosomes, while the male gametes are all N. Fertilisation then produces male-producing eggs with 2N chromosomes, female-producing with 2N+.
We may call this reduced number N and the full number 2N. The ova developing by parthenogenesis and giving rise to males segment in the usual way, and all the cells both of soma and gametocytes contain only N chromosomes.
Thus denoting any tone by 1, it is always to 1 or 2, or 2n that we wish to return, from any other possible tone; while 3 and 5, 5 and 7, leave us indifferent as to their succession.
On fertilisation two kinds of zygotes are formed, female-producing eggs with 2N chromosomes, and male-producing eggs with 2N-1 or 2N-2 chromosomes.
Must we, then, say that the finality of the tonic is a unique, inexplicable phenomenon? giving up the nature of melody as a problem if not insoluble, at least unsolved? The feeling of finality in the return to 2n is explained by Lipps and his followers, from the fact that the two-division is most natural, and so tones of 2n vibrations would have the character of rest and equilibrium.
Here again parthenogenesis continues for generation after generation so long as conditions are favourable, i.e. in summer, and the eggs are in the same condition as in Daphnia, etc., that is to say, reduction does not occur, and the number of chromosomes is 2N. Under unfavourable conditions males are developed as well as females by parthenogenesis, but the males arise from eggs which undergo partial reduction of chromosomes, only one or two being separated instead of half the whole number.
In the maturation divisions reduction does not occur, N chromosomes passing to one gamete, none to the other, and the latter perishes so that the sperms all contain N chromosomes. When fertilisation occurs the zygote therefore contains 2N chromosomes and becomes female. Here then we have no segregation of Fxf in the ova.
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