{
  "language": "en",
  "title": "Note against note in three voices",
  "chapter": "Second Exercise · First Lesson",
  "status": "New AI-assisted translation of the retained Latin, prepared for Musicbook; not an independently reviewed scholarly translation.",
  "pages": {
    "81": [
      {
        "type": "heading",
        "level": 1,
        "text": "SECOND EXERCISE. FIRST LESSON. Note against note in three voices."
      },
      {
        "type": "paragraph",
        "text": "That composition in three voices is the most complete of all is evident even from this: in it, a complete harmonic triad can be obtained without the help of another part, whereas the addition of a third part, or of further parts, is virtually nothing but the repetition of a part already present in the harmonic triad. Hence it has almost become a proverb that anyone who can compose correctly in three voices has the broadest possible path open to composition in a greater number of parts."
      },
      {
        "type": "paragraph",
        "text": "Joseph. My mind burns with an extraordinary desire to learn how this kind of composition is to be made. Yet I am considerably afraid that the difficulty of the subject may overwhelm my limited ability and leave my wish unfulfilled."
      },
      {
        "type": "paragraph",
        "text": "Aloys. You have nothing to fear. Since you did not struggle greatly in working out the species in two voices, be confident that, once you have understood what I am about to explain, the task of composing in three voices will not prove so difficult. Begin with the simplest species, note against note, and proceed in the same order that we followed in two voices."
      },
      {
        "type": "paragraph",
        "text": "This simplest species in three voices is therefore a composition",
        "continues": true
      }
    ],
    "82": [
      {
        "type": "paragraph",
        "text": "in equal notes—that is, in three simultaneous semibreves—and consisting entirely of consonances.",
        "continuation": true
      },
      {
        "type": "paragraph",
        "text": "First, observe that the harmonic triad should be used at every harmonic position, or measure, unless some other consideration prevents it."
      },
      {
        "type": "paragraph",
        "text": "Joseph. What is a harmonic triad?"
      },
      {
        "type": "paragraph",
        "text": "Aloys. It is a combination consisting of a third and a fifth. For example:"
      },
      {
        "type": "music",
        "id": "82-a"
      },
      {
        "type": "paragraph",
        "text": "Joseph. But what are the considerations that sometimes prevent us from forming this triad?"
      },
      {
        "type": "paragraph",
        "text": "Aloys. Sometimes a more graceful melodic line calls for another consonance, either a sixth or an octave, in place of the triad. More often, the need to avoid two perfect consonances in immediate succession requires us to depart from the triad and use a sixth instead of the fifth, or an octave, or both. I shall show this in the following example:"
      },
      {
        "type": "music",
        "id": "82-b"
      },
      {
        "type": "paragraph",
        "text": "Joseph. With your permission, Master, I would say that the triad seems to have been omitted without reason in the second measure. In my judgment, the tenor could have been given a fifth, which would have completed the triad; and then, in the third measure, the tenor",
        "continues": true
      }
    ],
    "83": [
      {
        "type": "paragraph",
        "text": "could have been given a third, leaving the other harmonic positions as you set them down. For example:",
        "continuation": true
      },
      {
        "type": "music",
        "id": "83-a"
      },
      {
        "type": "paragraph",
        "text": "These melodic movements seem to interfere neither with the proper progression of the parts nor with the grace of the melody."
      },
      {
        "type": "paragraph",
        "text": "Aloys. I am quite pleased with this observation of yours, and your example cannot be rejected. But who does not see that the first example, mine, accords better with naturalness, order, and variety? With naturalness and order, because the tenor in it moves beautifully downward by step, without a leap, as far as the third measure inclusive. A sixth occurs there, which the note mi in the bass prefers to the other consonances, as has already been said elsewhere. I shall explain the reason for this more fully once again. First, let us set out that arrangement with the sixth:"
      },
      {
        "type": "music",
        "id": "83-b"
      },
      {
        "type": "paragraph",
        "text": "Here the note producing the sixth should be regarded as having been transferred, as it were, from its proper position to another. In its proper position, the arrangement would be as follows:"
      }
    ],
    "84": [
      {
        "type": "music",
        "id": "84-a"
      },
      {
        "type": "paragraph",
        "text": "That C, therefore, forms a harmonic triad when placed in its proper position. When it is moved an octave higher while the other parts remain where they are, it necessarily produces a sixth. This is to be understood only when that mi is followed by fa, as in this example:"
      },
      {
        "type": "music",
        "id": "84-b"
      },
      {
        "type": "paragraph",
        "text": "But if that mi happens to leap elsewhere, it calls for a fifth rather than a sixth, as in the following examples:"
      },
      {
        "type": "music",
        "id": "84-c"
      },
      {
        "type": "paragraph",
        "text": "We must now return to the point from which we have digressed a little: why my example is also better suited to variety. In it, A occurs only once in the tenor, whereas in your example it occurs twice, as you can see:"
      },
      {
        "type": "music",
        "id": "84-d"
      }
    ],
    "85": [
      {
        "type": "paragraph",
        "text": "I tell you now, and for all your future work, that considerable attention must be paid to this variety."
      },
      {
        "type": "paragraph",
        "text": "Joseph. Do not be annoyed if I ask why, in the example you gave a little earlier, you began with the parts so widely separated. It seems to me that it could also have been done differently."
      },
      {
        "type": "paragraph",
        "text": "Aloys. Your hopeful curiosity gives me very little annoyance and a great deal of pleasure. Did you not notice that the bass of that example moves continuously upward by step? The other parts must therefore begin far away from the bass so that they have room to meet it by contrary motion."
      },
      {
        "type": "paragraph",
        "text": "But with what examples will you show that the passage could have been made in another way?"
      },
      {
        "type": "paragraph",
        "text": "Joseph. I shall offer two examples, not to prove my point, but to be taught."
      },
      {
        "type": "music",
        "id": "85-a"
      },
      {
        "type": "paragraph",
        "text": "Aloys. I do not altogether disapprove of these examples of yours. But you see that in the first example, from the first measure to the second, all three parts move upward, some by step and some by leap. This can scarcely happen without some difficulty. Here it occurs between the tenor and the alto, from the first measure to the second, as follows:"
      },
      {
        "type": "music",
        "id": "85-b"
      }
    ],
    "86": [
      {
        "type": "paragraph",
        "text": "From this it is clear that, when the bass is removed, this progression is faulty. Not only does it move, so to speak, from an imperfect to a perfect consonance; worse still, that fifth is not consonant at all, but diminished. The rules must be considered not only in relation to the bass, but also between the other parts themselves wherever possible, although in composition for several voices they need not be observed so rigorously. Thus, even in three voices, weighty reasons may sometimes permit a departure from this strictness in the relation of the parts to the bass. This can be seen in the penultimate measure of the first example: the fifth proceeds to the final octave, a perfect consonance to a perfect consonance, by similar motion, because it cannot be done otherwise. For example:"
      },
      {
        "type": "music",
        "id": "86-a"
      },
      {
        "type": "paragraph",
        "text": "Joseph. Could that difficulty not be avoided by putting a tenth in place of the octave?"
      },
      {
        "type": "paragraph",
        "text": "Aloys. It could, certainly. But that imperfect consonance seems insufficient to establish the completeness and repose required in the final note. The situation is different in four voices: when the fifth is added, those requirements seem to be satisfied despite the presence of the third."
      },
      {
        "type": "paragraph",
        "text": "Joseph. But what do you find worthy of criticism in my second example?"
      },
      {
        "type": "paragraph",
        "text": "Aloys. Nothing, except that sixths approached by ascending motion on the downbeat have a certain harshness. Sixths occurring on the upbeat—which has no place in this species—are more tolerable because they carry less weight. This will be explained more fully elsewhere."
      },
      {
        "type": "paragraph",
        "text": "Let us now proceed to the exercise. To make the construction of this species easier for you by providing a model, I shall compose the first example for you. It will itself have three versions, corresponding to the three parts: first with the cantus firmus in the upper part, second in the middle part, and third in the bass",
        "continues": true
      }
    ],
    "87": [
      {
        "type": "paragraph",
        "text": "part. You must also follow this procedure from now on, using the cantus firmi prescribed earlier in their given order.",
        "continuation": true
      },
      {
        "type": "music",
        "id": "87-a"
      },
      {
        "type": "paragraph",
        "text": "In this example you can see that the harmonic triad has been used in every measure where no other consideration prevented it, with due regard for the principles of progression and motion that have already been repeated so often."
      },
      {
        "type": "paragraph",
        "text": "Joseph. Yet from the seventh measure to the eighth, in the alto in relation to the bass, you seem not to have observed the rule that says: from an imperfect consonance to a perfect consonance by contrary motion. You have proceeded by similar motion instead."
      },
      {
        "type": "paragraph",
        "text": "Aloys. Your observation is correct. But you must remember what I said a little earlier: in three voices, when there is no other way to avoid a greater difficulty, we may sometimes depart from that strictness."
      },
      {
        "type": "paragraph",
        "text": "Joseph. I do remember. But it seems to me that it could have been done correctly while still observing the rule, if the bass had proceeded by contrary motion from F to the higher C, in this way:"
      },
      {
        "type": "music",
        "id": "87-b"
      }
    ],
    "88": [
      {
        "type": "paragraph",
        "text": "Aloys. That difficulty would indeed have been met by contrary motion. But do you not see that two similar violations would immediately follow—from the ninth note to the tenth, and from the tenth to the last? Moreover, in the ninth measure the tenor and bass would form a unison, as you see. That contributes less to the harmony than an octave. Besides, in this kind of composition we should not go beyond the limits of the five staff lines without a serious need."
      },
      {
        "type": "paragraph",
        "text": "Joseph. The reasons you have given convince me completely. But perhaps it could be done this way?"
      },
      {
        "type": "music",
        "id": "88-a"
      },
      {
        "type": "paragraph",
        "text": "Aloys. Still less so. Do you not remember that a leap of a major sixth is forbidden? What, then, should we think of a leap of a seventh? We must take account of the natural ease of singing. I shall now make an example with the cantus firmus in the middle part."
      },
      {
        "type": "music",
        "id": "88-b"
      },
      {
        "type": "paragraph",
        "text": "Joseph. Why did you use an octave in the ninth measure? It seems to me that there was room there for a fifth, and thus for the harmonic triad, without any obstacle."
      }
    ],
    "89": [
      {
        "type": "paragraph",
        "text": "Aloys. That is so; it could have been used. But if you look a little more closely, you will find that the octave serves the melodic line better. As I have often said, and shall have to say still more often, great weight must be given to the melody. One example remains to be completed, with the cantus firmus in the bass."
      },
      {
        "type": "music",
        "id": "89-a"
      },
      {
        "type": "paragraph",
        "text": "Joseph. I find nothing doubtful in this example except the final measure. It seems that placing a third there instead of the fifth would have added more harmony to that position."
      },
      {
        "type": "paragraph",
        "text": "Aloys. Your judgment is sound. But what kind of third do you think should have been placed there: major or minor? If minor, do you not feel that it is ineffective for bringing the piece to a close? If major, that is equally beside the point. This mode is established with a minor third, namely F without a sharp. Since the ears have become accustomed to that course of melody throughout the cantus firmus, hearing the sharp at the end would cause a certain offence. It will therefore be wiser to omit the third altogether."
      },
      {
        "type": "paragraph",
        "text": "Now proceed to compose examples in the other five remaining modes, placing the cantus firmus in each of the three parts, as I have said and done, and observing everything explained so far."
      },
      {
        "type": "music",
        "id": "89-b"
      }
    ],
    "90": [
      {
        "type": "paragraph",
        "text": "Joseph. I had considerable difficulty constructing the final cadence. In the penultimate measure there is no place for the standard cadential formula illustrated here:"
      },
      {
        "type": "music",
        "id": "90-a"
      },
      {
        "type": "paragraph",
        "text": "The mode does not naturally provide a perfect fifth in that position, nor does it admit the sharp by means of which the standard cadential formula could be formed. I therefore thought that the ending could be concluded only in the way I have done it. Yet I remain somewhat doubtful about the major third placed in the final note. I remember your saying above that in modes of this kind the third should be omitted altogether and a fifth put in its place."
      },
      {
        "type": "paragraph",
        "text": "Aloys. You have exercised very prudent judgment about the final cadence. Because of the particular position of the semitone, the standard cadential formula is not possible there, and a particular form of cadence therefore had to be made. Nor should the major third in the final note trouble you. What I said about omitting the third must be understood to apply wherever that is possible. You therefore judged correctly that a fifth could not be put in the final note of that example without two fifths in immediate succession. A major third had consequently to be used in its place, since the minor third, owing to its greater imperfection, is less suited to concluding the ending. Continue."
      },
      {
        "type": "music",
        "id": "90-b"
      }
    ],
    "91": [
      {
        "type": "music",
        "id": "91-a"
      },
      {
        "type": "music",
        "id": "91-b"
      },
      {
        "type": "music",
        "id": "91-c"
      },
      {
        "type": "music",
        "id": "91-d"
      }
    ],
    "92": [
      {
        "type": "music",
        "id": "92-a"
      },
      {
        "type": "music",
        "id": "92-b"
      },
      {
        "type": "music",
        "id": "92-c"
      }
    ],
    "93": [
      {
        "type": "music",
        "id": "93-a"
      },
      {
        "type": "music",
        "id": "93-b"
      },
      {
        "type": "music",
        "id": "93-c"
      }
    ],
    "94": [
      {
        "type": "music",
        "id": "94-a"
      },
      {
        "type": "paragraph",
        "text": "Joseph. Here are the remaining examples in the modes. In my judgment, they are well made insofar as the restrictions of the cantus firmus allow. But if the necessity of following the cantus firmus had not limited my freedom to compose, I think the composition could have been enriched with the harmonic triad in many places."
      },
      {
        "type": "paragraph",
        "text": "Aloys. You are right. In due course, you will be set to work on free composition, without being bound to a cantus firmus. Yet it is incredible how much benefit this exercise—building above a cantus firmus—brings to the student of this discipline. Through this practice alone, equipped both with experience and with understanding, the student can be led to a true knowledge of the art. I therefore urge this exercise upon you again and again; it cannot be impressed on you too often."
      },
      {
        "type": "paragraph",
        "text": "Having completed the examples of the first species, we must now proceed to the second."
      }
    ]
  },
  "notes": [
    {
      "id": "source-third",
      "block": "p81-1",
      "title": "“Third part” in the opening paragraph",
      "text": "The printed Latin reads tertiæ (“third”), with a handwritten correction above it. The argument appears to call for “fourth,” since three voices already form the triad. This translation retains the printed reading rather than silently correcting it."
    },
    {
      "id": "sixth-arrangement",
      "block": "p83-3",
      "title": "An arrangement containing a sixth",
      "text": "The phrase sexta Hypothesis is interpreted here as the harmonic arrangement containing a sixth, following the surrounding discussion and the illustrated chord; it is not rendered as a reference to the sixth measure."
    },
    {
      "id": "tactus",
      "title": "Tactus and hypothesis",
      "text": "In these numbered first-species examples, tactus is translated as “measure” and hypothesis as “harmonic position” or “arrangement.” These choices describe the units being discussed; they do not equate the historical tactus with a modern quarter-note beat."
    },
    {
      "id": "species",
      "title": "Species, voices, and the given melody",
      "text": "Species retains its technical counterpoint meaning. Bicinium, tricinium, and quadricinium are rendered as composition in two, three, and four voices. Cantus firmus is retained as the standard term for the given melody."
    },
    {
      "id": "thesis-arsis",
      "block": "p86-5",
      "title": "Downbeat and upbeat",
      "text": "Thesis and arsis are rendered as downbeat and upbeat in this rhythmic context. The Latin transcription retains the printed spelling Arhsi. These terms have varied meanings in other historical contexts."
    },
    {
      "id": "cadence",
      "title": "Clausula formalis and mode",
      "text": "Clausula formalis is rendered as “standard cadential formula,” rather than treated as a generic modern chord progression. Tonus is rendered as “mode” in the discussion of the remaining modal exercises."
    }
  ]
}