The Complete Works of Gioseffo Zarlino, Vol. 2

the true form of the Diapason octave, placed among the numbers 2 & 1 to give you an example; it holds the first place among them, and among the proportions it is the first; since before these two terms 2 & 1 there is no number that is smaller; thus among the Consonances one finds no other that by origin is before the Diapason; whence the Diapason holds the first place in the low range, and before it one finds no Consonance that is greater or smaller than it. For this reason I have said many times that the Diapason is the First consonance, from which all the others are born, whether they are greater or smaller than it. I add again that it is not only a Principle, but an Element of all the others. Therefore, just as its simple form, contained in its radical terms 2 & 1, does not receive another number or middle term that divides it into two parts; so it does not admit in the first and lowest place of the order of Consonances any middle string, nor even in the lowest part of any Instrument whatsoever, that might divide it into two Intervals; whereby one could hear any effect that is less pleasing than that which one hears when it is sounded simply. In the second place is found the Diapente perfect fifth, whose form is 3 & 2, which among the natural order of numbers also holds the second; for which reason it must be placed without any middle after the Diapason. And just as between 3 & 2 there cannot exist any middle number; so between the extreme strings of the Diapente there cannot fall any middle string that in some part does not offend the sensibility. After this follows in the third place the Diatessaron perfect fourth between 4 & 3, in the natural order of numbers, which does not receive any middle that operates a good effect; whence, all these Consonances being placed one after the other (as I have said elsewhere) upon an Instrument in order, without placing any other string between them, they cause a most pleasing sound and sweet concent to be heard. But if by chance in the low register the Diapason were to be divided, so that in the low part one heard the Diapente, and in the high the Diatessaron, immediately one would hear the concent change form, and a certain something not as pleasing as the first to the Hearing. Inst. lib. 1. cap. 15. And if further between this Diapente a string were interposed, which were to divide it into two parts; that is, into a Ditone major third and a Semiditone minor third, and the latter were placed in the high part and the former in the low part; then one would hear something that would bring great displeasure to the Hearing. This, however, is not the last degree of the little pleasing assembly of Consonances; because there is still something worse; and this happens when the Semiditone comes to hold the place of the Ditone, and the latter the place of the Semiditone, and they are placed between the Diapente in the opposite way to what they were before; that is, that the Ditone held the high place, and the Semiditone the low; because then one would hear that extreme ruin that Consonances gathered together can make; since this order would then be placed in reverse; that is, that the Semiditone would occupy the first place in the low register, the Ditone the second, the Diatessaron the third, the Diapente the fourth, and the Diapason would hold the sixth and last place in the high register. And I believe that all those who have judgment, and have practice with Organs, can know this very well; because when such Instruments are played fully, they reveal such disturbance much more than other instruments that have little spirit. So, Signor Desiderio, it seems to me that now one can understand in what the difference that you asked me about consists, and what it is; which for men of elevated talent is not difficult to learn; but truly so for those who are of little capacity; among whom there are found at present those who do not understand this thing, as if it were a matter of which one could not have any experience; wherefore, not understanding it, they blame it. Having said this, turning to me, Signor Desiderio said: Tell me also this, by your faith, why do these two Intervals that you have lately named cause so much more ruin when placed in the low register than they do when they are situated in the high register? For two reasons, I replied: one, because the place of the Ditone and the Semiditone is not to be placed in the low register, but in the high; the other, because placed in the said way, they are not located in order, according to their degrees and their places, but in reverse: being that those Intervals that are of greater proportion naturally desire the lower place, and those of lesser, the higher place. Nor will you ever find in the Natural Order of Consonances that