Author: Abbatini, Antonio Maria
Title: On the different species of the octave and of the fifth
Source: Bologna, Museo internazionale e biblioteca della musica, MS C.48, ff.43r-48r
[-f.43r-] [Number 6. add. m. sec.] Seventh Lecture On the different species of the octave and of the fifth [-f.44r-] In the previous discourse all the Intervals that can be distinguished which are contained in the octave have been discussed. These are, starting from the smallest, the Comma, the smaller Enharmonic Diesis, the larger enharmonic Diesis, the smaller semitone, the larger semitone, the smaller Tone, the larger Tone, the minor Third, the major Third, the Fourth, the Tritone, the imperfect Fifth, the perfect Fifth, the augmented Fifth, the minor sixth, the major sixth, the minor seventh, the major seventh and, finally, the octave. After explaining all their different names used by the Greeks, it remains for us to consider the species of the aforesaid Intervals, starting from the Minor Third. I am about to illustrate them with as much succinctness and Clarity as possible. Starting from the minor Third, every interval can be classed as compounded or [-f.44v-] uncompounded. It is uncompounded when the interval is considered as being simple, namely not composed of Other Intervals, as, for instance, we shall say of the minor Third, which lays among these notes re mi fà and mi fa sol. If we consider this minor third as a simple interval, namely, as re fà, it is called uncompounded minor third, and considered in this form it is only of one species, but, if it is considered in this other way, namely, re mi fa or mi fa sol, we shall call it compounded, since it is composed of re mi fa or mi fa sol. Starting our discussion from the minor Third, we shal say that when it is considered as compounded it is of Two species. The first one is created when the larger semitone is found in the second interval, as in the case of re mi fa, while the second species is created when the minor semitone is found in the first Interval, as in the case of mi fa sol. The nature of this Interval, when it ascends, as, for instance, in the case of re mi da, is very sweet, while when it descends, as in the case of fa mi re, it is more [second in marg.] intense. The Ditone or major Third, is the other interval which follows immediately after the minor. This interval is contained within the notes ut re mi or fà sol la. This major third is found of Two species, as all the authors agree. The first one is made of the notes ut re mi, while the sacond consists of the notes fa sol la [[although Franchino in the first book, chapter 3 of his practica musica already calls this interval harsh. He says: “in fact, the Ditone of Two Tones is harsh,” and, therefore expert Musicians rule that it should not be placed in the low part, but in the High one, which is a place more suited to its Highness.]] I read in the Musica Aurea by Stefano Vannet, at chapter XXXI of the first book that the Ditone or major third is only of one species, rather than two, because it does not contain the larger semitone which determines the difference among the species, and indeed it is so. Let us hear his own words: “I would not want you to say that the species of the ditone are two, as some have learned wrongly male imbuti sunt. We concede that it is called in two ways or in two different forms. In fact, the species derives from the Semitone rather then from the mutation of the tone.” The Fourth is the next one, as it is the closest interval to the Ditone. This Interval is found of Three species. The first one is created when the larger semitone is placed in the second Interval, as in the case of re mi fa sol. The second species is created when the larger semitone is located in the first interval, as in mi fà sol la. The Third species is created when the larger semitone is placed in the Third Interval, as in ut re mi fà. This interval has something of the intense in Ascending and will be somewhat soft in descending. After the fourth there follows the Tritone, which, as it does not contain the larger semitone and cannot constitute the perfect Octave, is of a single species. The next one is the Diminuished Fifth, which Interval is also of a single species, since the semitone cannot be altered. This Interval cannnot create the perfect diapason either. The interval closest to it is the perfect Diapente or fifth. [--] [third in marg.] This interval is of four species. The first one is created when the larger semitone si found in the second Interval, as in re mi fà sol la. The second species is created when the larger semitone is placed in the first interval, as in the case of mi fa sol re mi. The Third species is created when the larger semitone is located in the fourth interval as in fa sol re mi fa. The fourth and last species is created when the larger semitone is found in the Third interval, as in the case of ut remi fa sol. The Nature of the Fifth in its Ascent up to the semitone has a tense character, whicle from the semitone to the end is somewhat soft and Sweet, while, when it descends to the dirst tone it has something of the intense and in any other case it is soft. As to the augmented fifth, since the semitone cannot be changed, is of a single species and it cannot constitute a perfect Diapason. The minor sixth is of Three species. The first one occurs when the larger semitone is found in the second and in the fifth Interval, as in the case of re mi fa sol la fa from A la mi re to Ffaut. The secon species occurs when it has the larger semitone in the first and in the fourth Interval, [- -] as in the case of mi fa re re ut fa sol da Be mi to g sol re ut. The third species has the larger semitone as its first and last Interval, as in the case of mi fa sol re mi fa between Elami and C sol fa ut. The nature of this interval is the same as the one described in the case of the third and the fourth. The major sixth is of Three species, as in the case of the minor sixth. The first species occurs when the larger semitone is found in the Third interva, as in ut re mi fa sol la from C sol fa ut to High A la mi re. The second species occurs when the larger semitone is found in the second Interval as in re mi fa sol re mi from D sol re to High B mi. The Third species is created when the larger semitone is found in the fourth interval as in fa sol re mi fa sol From F fa ut to High D sol re. The Nature of this interval is similar to the one of the Fifth, taking into account the different steps. The minor seventh is found of five varieties. The first one has the larger semitone in the third and in the Last Interval, as from G sol re to High F faut. The second one has the larger semitone in the second and in the Fifth interval as in the case of re mi fa re mi fa sol from A la mire to High Be mi. The Third species has the semitone in the second Interval and in the last one as in re mi fa re sol re mi [-f.47r-] fa from D sol re to High C sol fa ut. The fourth species has the larger semitone in the first and in the fifth interval as in mi fa sol re mi fa sol From E la mi to High D sol re. The fifth species has the largest semitone in the first and in the Fourth Interval, as in mi fa sol re mi fa sol la From B mi to High A la mi re. Its nature is the same as the one of the Fifth and of the minor Third, since is composed of them. The major seventh is found of just Two species. The first one has the larger semitone in the third Interval as in the case of ut re mi fa sol re mi From C sol fa ut to High B mi. The second species has the larger semitone in the fourth Interval as in fa sol re mi fa sol la from F fa ut to High E la Mi. Its nature is similar to the one of the Fifth and of the major third, since it progresses through the same steps. It is left to us only to see which ones are the species of the octave of this Queen of all the Consonances and how many they are. This most perfect interval is of seven species. The first one has the larger semitone in the second and Fifth interval, as in re mi fa re mi fa sol la from A la mi re to High A la mi re. The secons species of the octave has the larger semitone in the first and fourth Interval, as in [-f.47v-] mi fa re mi fa sol re mi From B mi to High B mi. The Third species has the larger semitone in the third and in the Last Interval, as in Ut re mi fà sol re mi fà from C sol fa ut to High C sol fa ut. The Fourth species has the semitone in the second, third and sixth Interval, as in re mi fa sol re mi fa sol From D sol re to High D sol re. The Fifth species has the larger semitone in the Fifth interval as in mi fa sol re mi fa sol la From E la mi to High E la mi. The sixth species has the larger semitone in the Fourth and Last Interval, as in fa sol re mi fa re mi fa from F fa ut to High Ef fa ut. The seventh and last species of the octave has the semitone in the Third and sixth interval, as in ut re mi fa re mi fa sol From G sol re ut to High G sol re ut. This interval, both in ascending and in descending, is grave, resonant, Harmonious and Sweet. In short, it satisfies the Ear which has nothing more to desire, since it is utterly perfect. With the help of God, the species of all the Intervals, which are contained within the Octave, have been illustrated, [-f.48r-] starting from the minor Third. It is a topic which requires Study and memory, and that is so necessary to the Composer of Music in order to construct his Composition according to the rules that nothing is more necessary. In fact, it teaches us the composition of the Tones, which is a necessary subject for the Composer to study, as I said already, so that he may acquire knowledge of this or that Other Tone or mode, as we want to call them. In fact the Composer must think first of all to the mode or Tone on which he wants to Compose its Composition before he does anything else. But, since I promised to Demostrate Some Consonances, so that one might experience in practice what I said about the proportions which represent them, do let us come to their practical application.
Title: On the different species of the octave and of the fifth
Source: Bologna, Museo internazionale e biblioteca della musica, MS C.48, ff.43r-48r
[-f.43r-] [Number 6. add. m. sec.] Seventh Lecture On the different species of the octave and of the fifth [-f.44r-] In the previous discourse all the Intervals that can be distinguished which are contained in the octave have been discussed. These are, starting from the smallest, the Comma, the smaller Enharmonic Diesis, the larger enharmonic Diesis, the smaller semitone, the larger semitone, the smaller Tone, the larger Tone, the minor Third, the major Third, the Fourth, the Tritone, the imperfect Fifth, the perfect Fifth, the augmented Fifth, the minor sixth, the major sixth, the minor seventh, the major seventh and, finally, the octave. After explaining all their different names used by the Greeks, it remains for us to consider the species of the aforesaid Intervals, starting from the Minor Third. I am about to illustrate them with as much succinctness and Clarity as possible. Starting from the minor Third, every interval can be classed as compounded or [-f.44v-] uncompounded. It is uncompounded when the interval is considered as being simple, namely not composed of Other Intervals, as, for instance, we shall say of the minor Third, which lays among these notes re mi fà and mi fa sol. If we consider this minor third as a simple interval, namely, as re fà, it is called uncompounded minor third, and considered in this form it is only of one species, but, if it is considered in this other way, namely, re mi fa or mi fa sol, we shall call it compounded, since it is composed of re mi fa or mi fa sol. Starting our discussion from the minor Third, we shal say that when it is considered as compounded it is of Two species. The first one is created when the larger semitone is found in the second interval, as in the case of re mi fa, while the second species is created when the minor semitone is found in the first Interval, as in the case of mi fa sol. The nature of this Interval, when it ascends, as, for instance, in the case of re mi da, is very sweet, while when it descends, as in the case of fa mi re, it is more [second in marg.] intense. The Ditone or major Third, is the other interval which follows immediately after the minor. This interval is contained within the notes ut re mi or fà sol la. This major third is found of Two species, as all the authors agree. The first one is made of the notes ut re mi, while the sacond consists of the notes fa sol la [[although Franchino in the first book, chapter 3 of his practica musica already calls this interval harsh. He says: “in fact, the Ditone of Two Tones is harsh,” and, therefore expert Musicians rule that it should not be placed in the low part, but in the High one, which is a place more suited to its Highness.]] I read in the Musica Aurea by Stefano Vannet, at chapter XXXI of the first book that the Ditone or major third is only of one species, rather than two, because it does not contain the larger semitone which determines the difference among the species, and indeed it is so. Let us hear his own words: “I would not want you to say that the species of the ditone are two, as some have learned wrongly male imbuti sunt. We concede that it is called in two ways or in two different forms. In fact, the species derives from the Semitone rather then from the mutation of the tone.” The Fourth is the next one, as it is the closest interval to the Ditone. This Interval is found of Three species. The first one is created when the larger semitone is placed in the second Interval, as in the case of re mi fa sol. The second species is created when the larger semitone is located in the first interval, as in mi fà sol la. The Third species is created when the larger semitone is placed in the Third Interval, as in ut re mi fà. This interval has something of the intense in Ascending and will be somewhat soft in descending. After the fourth there follows the Tritone, which, as it does not contain the larger semitone and cannot constitute the perfect Octave, is of a single species. The next one is the Diminuished Fifth, which Interval is also of a single species, since the semitone cannot be altered. This Interval cannnot create the perfect diapason either. The interval closest to it is the perfect Diapente or fifth. [--] [third in marg.] This interval is of four species. The first one is created when the larger semitone si found in the second Interval, as in re mi fà sol la. The second species is created when the larger semitone is placed in the first interval, as in the case of mi fa sol re mi. The Third species is created when the larger semitone is located in the fourth interval as in fa sol re mi fa. The fourth and last species is created when the larger semitone is found in the Third interval, as in the case of ut remi fa sol. The Nature of the Fifth in its Ascent up to the semitone has a tense character, whicle from the semitone to the end is somewhat soft and Sweet, while, when it descends to the dirst tone it has something of the intense and in any other case it is soft. As to the augmented fifth, since the semitone cannot be changed, is of a single species and it cannot constitute a perfect Diapason. The minor sixth is of Three species. The first one occurs when the larger semitone is found in the second and in the fifth Interval, as in the case of re mi fa sol la fa from A la mi re to Ffaut. The secon species occurs when it has the larger semitone in the first and in the fourth Interval, [- -] as in the case of mi fa re re ut fa sol da Be mi to g sol re ut. The third species has the larger semitone as its first and last Interval, as in the case of mi fa sol re mi fa between Elami and C sol fa ut. The nature of this interval is the same as the one described in the case of the third and the fourth. The major sixth is of Three species, as in the case of the minor sixth. The first species occurs when the larger semitone is found in the Third interva, as in ut re mi fa sol la from C sol fa ut to High A la mi re. The second species occurs when the larger semitone is found in the second Interval as in re mi fa sol re mi from D sol re to High B mi. The Third species is created when the larger semitone is found in the fourth interval as in fa sol re mi fa sol From F fa ut to High D sol re. The Nature of this interval is similar to the one of the Fifth, taking into account the different steps. The minor seventh is found of five varieties. The first one has the larger semitone in the third and in the Last Interval, as from G sol re to High F faut. The second one has the larger semitone in the second and in the Fifth interval as in the case of re mi fa re mi fa sol from A la mire to High Be mi. The Third species has the semitone in the second Interval and in the last one as in re mi fa re sol re mi [-f.47r-] fa from D sol re to High C sol fa ut. The fourth species has the larger semitone in the first and in the fifth interval as in mi fa sol re mi fa sol From E la mi to High D sol re. The fifth species has the largest semitone in the first and in the Fourth Interval, as in mi fa sol re mi fa sol la From B mi to High A la mi re. Its nature is the same as the one of the Fifth and of the minor Third, since is composed of them. The major seventh is found of just Two species. The first one has the larger semitone in the third Interval as in the case of ut re mi fa sol re mi From C sol fa ut to High B mi. The second species has the larger semitone in the fourth Interval as in fa sol re mi fa sol la from F fa ut to High E la Mi. Its nature is similar to the one of the Fifth and of the major third, since it progresses through the same steps. It is left to us only to see which ones are the species of the octave of this Queen of all the Consonances and how many they are. This most perfect interval is of seven species. The first one has the larger semitone in the second and Fifth interval, as in re mi fa re mi fa sol la from A la mi re to High A la mi re. The secons species of the octave has the larger semitone in the first and fourth Interval, as in [-f.47v-] mi fa re mi fa sol re mi From B mi to High B mi. The Third species has the larger semitone in the third and in the Last Interval, as in Ut re mi fà sol re mi fà from C sol fa ut to High C sol fa ut. The Fourth species has the semitone in the second, third and sixth Interval, as in re mi fa sol re mi fa sol From D sol re to High D sol re. The Fifth species has the larger semitone in the Fifth interval as in mi fa sol re mi fa sol la From E la mi to High E la mi. The sixth species has the larger semitone in the Fourth and Last Interval, as in fa sol re mi fa re mi fa from F fa ut to High Ef fa ut. The seventh and last species of the octave has the semitone in the Third and sixth interval, as in ut re mi fa re mi fa sol From G sol re ut to High G sol re ut. This interval, both in ascending and in descending, is grave, resonant, Harmonious and Sweet. In short, it satisfies the Ear which has nothing more to desire, since it is utterly perfect. With the help of God, the species of all the Intervals, which are contained within the Octave, have been illustrated, [-f.48r-] starting from the minor Third. It is a topic which requires Study and memory, and that is so necessary to the Composer of Music in order to construct his Composition according to the rules that nothing is more necessary. In fact, it teaches us the composition of the Tones, which is a necessary subject for the Composer to study, as I said already, so that he may acquire knowledge of this or that Other Tone or mode, as we want to call them. In fact the Composer must think first of all to the mode or Tone on which he wants to Compose its Composition before he does anything else. But, since I promised to Demostrate Some Consonances, so that one might experience in practice what I said about the proportions which represent them, do let us come to their practical application.
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