The Complete Works of Gioseffo Zarlino, Vol. 2

the Ditone follows the Semiditone immediately towards the high register; but you will find the contrary; that the Ditone holding the lower place, the Semiditone immediately follows it towards the high register; so that such disorder arises from these causes, even though one and the other are consonant. Therefore, Signor Desiderio added, from what I see, the poor agreement that the parts of a composition sometimes make proceeds not only from the mixing of Dissonances that is sometimes made inside it; but from placing the Consonances in them in bad order. That is in fact the case, replied Master Claudio. It was not then beside the point, said Master Adriano, that in my compositions I have avoided, as much as I could, placing such Consonances in the low part in the way you have declared; because it seemed to me all too true that they did not sound well; although I did not know how to give any reason for it, but I heard that they did not fully satisfy my sense. There are also other observations, Master, I replied to him, in your Compositions, which you have learned by means of the sense, as that which is the principle of our knowledge, which are not of little importance; of which, even if you do not know how to tell the reason, there are not lacking those who tell it for you. But to return to our purpose, I say that the reason that moved the Pythagoreans, and Pythagoras first, to say that all the Intervals that were smaller than the Diatessaron were dissonant is this, in my judgment, and as I have declared to you: because they did not have knowledge of the Degrees and proper places of the Consonances, and in what manner they had to be disposed and placed in order. Wherefore, having known, if indeed they knew it, that those consonances that are smaller than the Diatessaron, as are the Ditone and the Semiditone, so pleasing to us, when placed in the low part generated dissonance rather than consonance; for not having been known by them such difference, that is, that placed in their proper and natural places, they generate a pleasing sound to the hearing; and on the contrary an unpleasing one when they are placed outside their natural places; therefore they judged that they were by any means dissonant. Therefore, from not knowing the degrees, and the order, and the proper places of the consonances, it was born that the Ancients denied that those Intervals that are smaller than the Diatessaron were consonant. Was it not enough at least to know, said Signor Desiderio, that placed in the high register, and in their proper places, they were and are consonant? I have already said, I added, that they did not consider this, rather they never knew it; being that if they had known it, there is no doubt that they would have put it into use, or at least would have left some memory of it, as some of our Moderns have done; who, even if they have not demonstrated that the Ditone contained by the sesquiquarta 4:3 proportion, and the Semiditone contained by the sesquiquinta 5:4 proportion, were consonant, have at least with great doubt affirmed that the Ditone composed of two sesquioctave 9:8 Tones, and the Semiditone, which contains one sesquioctave Tone and a minor Semitone, considered from the side of their proportions, were dissonant; leaning on this opinion: that other than the Multiple and Superparticular, Consonances could not have their forms, and that considered in act in Sounds, or in Voices, they were consonant; because See chap. 12. lib. 4. suppl. when they wanted, they heard them as such. But they were mistaken; because when they heard them as consonant, they were contained by Superparticular proportions, and not by Superpartient, as they believed; and the error of these men could arise from not having had sufficient principles in their demonstrations, and little experience of the things of Music; because it was not sufficient to say only that the Consonances were those that had their form from the Multiple or Superparticular genus, contained between the parts of the Quaternary number; but it was necessary rather to say that they were those that had their forms from those proportions that are found in act between the parts of the Senario the number 6. Therefore, said Master Francesco, they could not demonstrate the things of Music perfectly, not having such principles; being that from them one has the knowledge (as I have heard said many times) of all the things that are treated in any science whatsoever. You speak the truth, I replied; wherefore one must know that to want to demonstrate the things of Music perfectly, one must add to those Principles, by means of which others have demonstrated, those things that lead us to the end of that,