"... there are four types of thirds and sixths, which is not true of any other interval ... [though] perhaps someone may still wish to characterize the seventh and the second as major and minor, since it is permissible to make use of them in this light." [II.29.182-4]
"Just as there is only one major key whose signature contains no sharps or flats, there should also be only one minor key with this characteristic." [II.25.172]
"We may only conclude a piece of music by a perfect cadence on the principal note of a mode; otherwise the spirit will not be satisfied. How absurd it is to propose modes which do not submit to these requirements!" [II.21.160]
"... we find included in these two chords [the tonic triad together with the dominant seventh] all the notes of a mode, except the sixth, which, since it has the same nature as the third, is simple to find." [II.21.158]
"Since there are only two thirds, of which one is major and the other minor, we say that there are only two modes, of which one is major and the other minor. It is understood that these words major and minor refer to the third which should accompany the fundamental sound of the mode." [II.21.157]
"A good musician should surrender himself to all the characters he wishes to portray. Like a skillful actor he should take the place of the speaker, believe himself to be at the locations where the different events he wishes to depict occur, and participate in these events as do those most involved in them. He must declaim the text well, at least to himself, and must feel when and to what degree the voice should rise or fall, so that he may shape this melody, harmony, modulation, and movement accordingly." [II.20.156]
"Harmony may unquestionably excite different passions in us depending on the chords that are used. There are chords which are sad, languishing, tender, pleasant, gay, and surprising. There are also certain progressions of chords which expression the same passions." [II.20.154]
"If the composer gives himself the satisfaction of hearing what he has written, his ear will become formed little by little." [II.19.153]
"Certainly a knowledgeable musician can compose a beautiful melodic line suitable to the harmony, but from where does this happy ability come? May nature be responsible? Doubtless. But if, on the contrary, she has refused her gift, how can he succeed? Only by means of the rules. But from where are these rules derived? This is what we must investigate." [II.19.152]
"It is harmony then that guides us, and not melody." [II.19.152]
"Music to which we may add a bass having all the properties just described [that is, of a fundamental bass] will always be good. There may be mistakes in the order of the consonances, in the melody, in the modulation [ie, harmonic progression], in the spacing of the notes which prepare, form, and resolve the dissonance, or even in the beats on which this dissonance should be prepared and heard, but there will be no mistakes in relation to the foundation of the harmony." [II.18.151]
"Further objections could be raised concerning the supernumerary sounds in chords by supposition and in the irregular cadence, and concerning that sound which borrows its fundamental from the fundamental sound itself, for these sounds are not included in our rules, and seem to demand special rules of their own. We need not be overly concerned about this for these sounds should be considered voluntary additions which in no way affect the source." [II.18.147]
"So many chords, so many lively melodies, such boundless variety, such beautiful and fitting expressions, such well-rendered feelings! All this flows from two or three intervals arranged by thirds whose source subsists in a single sound." [II.18.142]
"This reduction of intervals can be related precisely to the reduction of chords: from inverted intervals are formed inverted chords; from doubled intervals, chords by supposition; and from altered intervals, chords by borrowing." [II.18.142]
"The source of harmony does not subsist merely in the perfect chord or in the seventh chord formed from it. More precisely, it subsists in the lowest sound of these two chords, which is, so to speak, the harmonic center to which all the other sounds should be related." [II.18.141]
"Experience offers us a large number of chords susceptible of an infinite diversity, in which we shall always lose our way unless we search of the source elsewhere." [II.18.139]
"It should be noticed that a permanent sound [pedal point] escapes our attention ..." [II.17.136]
"One of the special properties of music, however, is that we may often abuse, even with success, the liberty we have to vary it infinitely. But when reason is in agreement with the ear, we may give music all the variety of which it is susceptible without sinning against its perfection." [II.17.135]
"... we often fear seeing two fifths or two octaves, even when we do not hear them." [II.17.135]
"It is necessary to know how to differentiate a fundamental chord from a derived chord, so as not to confuse their properties." [II.17.131]
"Most musicians take the term license to mean mistake ... [but] licenses are simply evident inversions of our initial perceptions." [II.17.127]
"The meager attention paid until now to the correctness and power of inversion has caused the neglect of the only place in which the secrets of harmony might have been discovered. For if we examine the significance of this inversion as it applies to everything related to harmony ... we shall no longer be able to doubt that inversion is at the center of the great and infinite variety to be found in harmony." [II.17.127]
"This is the nature of the cabal which has risen against all the skillful men of this century. Why trouble inventing entrancing music? They will only judge it worthless." [II.17.125]
"It is some time since anyone has attempted to satisfy reason where music was concerned. Our great masters are content merely to please." [II.17.124]
"... it would be giving too narrow bounds to harmony if we restrained it only to what is most natural; it would be depriving harmony of its right not to submit to all of its [own] properties." [II.17.124]
"... the natural progression of the fundamental bass is to descend a third, a fifth, or even a seventh, so that the dissonance may be prepared and resolved, the inversions of these progressions should be attributed to license, for dissonances are then heard without preparation." [II.17.124]
"From this interval [descending seventh / ascending second] arises license." [II.17.124]
"As soon as the bass descends a seventh of ascends a second, however, we begin to perceive license, even though the dissonance may be prepared and resolved by a consonance." [II.17.124]
"We may observe that when a dissonance is sounded and resolved in the most natural harmony, the fundamental bass is always to be found in the lowest sound, as if this upport were needed to fortify the lowest sound against the harshness of this dissonance." [II.17.12]
"There is still another defect in the [historically received] rules. They do not make the progression of each part clear enough, when they affirm that the sixth should follow the fifth, that the seventh should be resolved by the third, the fifth, or the sixth, etc. Sometimes one of these parts should remain on the same degree, sometimes each of them should move; sometimes one should ascend, sometimes descend, etc. We, instead, clarify this confusion by first of all giving such precise and intelligible rules of modulation, which ought to guide us everywhere, that we cannot be deceived, and by then saying that all minor dissonances should descend diatonically, while all major dissonances should ascend a semitone, no matter how the bass moves, these dissonances being easy to recognize when related to their origin." [II.16.123]
"If we examine an interval in isolation, we shall never be able to define its properties; we must also examine all the different chords in which it may occur. Here one of its sounds should descend, there it should ascend; here its progression is conjunct, there it is disjunct; here it is dissonant, there it is consonant; here it should be syncopated, there it cannot be." [II.16.120]
"What depends upon the eye is less susceptible of illusion than what depends upon the ear. Someone may approve of a chord which displeases someone else. Hence arise conflicting opinions among musicians, with each one stubbornly defending that which his imagination or his limited experience teaches him." [II.16.119]
"All those who have hitherto wished to prescribe rules of harmony have abandoned the source of these rules. As the first sound and the first chord revealed to them was given no sort of prerogative, everything was considered to be equal ... No one said why some dissonances wish to ascend and others to descend. The source was hidden and everyone, according to his own inclination, told us what experience had taught him." [II.16.119]
"... the fourth in the chords of the second [modern dominant seventh in third inversion] and of the small sixth [modern dominant seventh in second inversion] is included within the limits of the octave and all the sounds of chords which are so included may be inverted at will by the composer. We may not invert the lowest sound of the ninth and eleventh chords, however, as this sound should never change its position." [II.16.116]
"In order to convince ourselves that all dissonant chords originate from the seventh chord, we have only to consider whether all chords arising from its inversion contain fewer or more sounds and dissonances, whether they are included within the same limits, and whether they alter the modulation [ie, harmonic progression] in any way." [II.16.115]
"The lowest and fundamental sound of a perfect chord may bear either a major of a minor third." [II.16.114]
"Just as the [interval of the] seventh is the origin of all dissonances, similarly the seventh chord is the origin of all dissonant chords." [II.16.114]
"The true meaning of the rule must be grasped: it does not forbid the minor third ascending nor the major descending. It says only that it is natural and appropriate for the latter to ascend to the octave." [II.14.104]
"(We are speaking here only of the inversion of intervals [that is, upward versus downward articulation] and not of that inversion in which these intervals are related to each other by means of the octave [that is, the relationship that equates the perfect fourth to the perfect fifth, and vice versa]." [II.13.99]
"Zarlino knew no other major dissonance but the tritone, of which he spoke only in passing. Later
authors cite several others, but none have made it clear that they all originate from the major third of the fundamental sound of a seventh chord, just as all minor dissonances originate from the seventh itself. This inattentiveness has hindered these later authors from improving on the rules of Zarlino ..." [II.13.96]
"We must clarify here the difference between the fourth and the eleventh. The latter interval has not hitherto been known by this name, for it has always been confused with the fourth ... the fourth, which can be found only in an inverted chord where it represents the fifth, is consonant, while the eleventh, which determines the first chord of its species since the chord is made up only of sounds contained within this eleventh, is dissonant. Though we figure it with a 4, we do so only to follow common practice." [II.10.91-3]
"A new sound, placed a fifth below the fundamental sound, is substituted for the missing sounds. This new sound consequently forms an eleventh, and not a fourth, with the seventh of the fundamental. We may thus call this chord heteroclite, since it is not divide as are the other chords ..." [II.10.89]
"... the added sound [of a ninth or eleventh positioned beneath a seventh] can never change position. It will always occupy the lowest position, while the other parts may profit from inversion, in which they may mutually participate since they are contained within the prescribed limits of harmony ... the added sound must be regarded as supernumerary, since the fundamental harmony will always subsist without it and the progression of chords is not altered by it." [II.10.89]
"If a fifth sound can be added to the seventh chord at all, it can be added only below and not above." [II.10.88]
"We can derive any melody imaginable and diversify the harmony, by placing in the bass a sound contained in the fundamental chord instead of the fundamental sound itself. This leads directly to an inexhaustible succesion of melodies and chords from which we may shape a piece of music which constantly stirs the listener by the diversity arising from inversion ... The fundamental basses we place below all our examples prove this, and it only remains to make these matters clearer, as we hope to do." [II.8.82]
"... the progression of the dissonances depends on the consonances closest to them." [II.7.79]
"We customarily say that dissonance disturbs the ear in the same way that badly assorted colors disturb the eye, thus attributing to the senses the effect that the objects which act on them have on one another. For further proof that this idea of the collision of sounds is not simply our invention, we need only look up the literal meaning of the term syncopation, which is principally applied to the use of dissonance. This term is composed of two Greek words: syn and copto. The first signifies together and the other I hit or I collide." [II.7.78]
"The different situations in which dissonances occur oblige us to name them differently in order to facilitate their use, but there is basically only one dissonance, from which all the others are derived either directly or indirectly, as we shall see later. This dissonance, which we have already designated as the seventh, is more easily recognized as the interval of a second; this comes to the same thing, since the second is the inversion of the seventh." [II.7.78]
"A skillful man should always figure his bass, especially when his examples are in only two parts, so that these examples can be judged fairly. Otherwise, false conclusions may be drawn from them." [II.5.69]
"The major third is thus the origin of all the major dissonances and the seventh is the origina of all the minor dissonances, without exception." [II.5.65]
"The first of the two notes forming the perfect cadence in the bass is called the dominant, because it must always preceded the final note and therefore dominate it." [II.5.65]
"'The major seeks to become major, ie, to ris, and the minor to fall.' ... we should accept as a general rule that everything which is major or augmented should rise, while everything which is minor or diminished should fall." [II.5.64 quoting Zarlino]
"Though we have regarded the fifth as the primary element of all chords, this quality should also be attributed to the thirds of which the fifth is made up." [II.5.64]
"... the progression of all intervals in the perfect cadence is determined by the progression of the thirds which are predominant in the chords." [II.5.63]
"The fifth is the primary element of all chords; ie, a chord cannot subsist without either it or the fourth which represents it." [II.4.63]
"Once we are aware of the progressions appropriate for each part, we are certainly free to give one part the progression suitable for another." [II.2.62]
"Those whose voices are deep enough naturally descend a fifth at endings, while those cannot do so ascend a fourth. This is clear proof of the power of the octave, which is always present in either of the sounds forming it, and of the relationship between the fourth and the fifth arising from the division of the octave." [II.1.60]
"... intervals can not be consonant unless they are separated." [II.1.60]
"... when we give a progression to the part representing this undivided string, we can only make it proceed by those consonant intervals obtained from the first divisions of this string. Each sound will consequently harmonize with the sound preceding it." [II.1.60]
"... all derivatives of the first dissonant chord [modern dominant seventh] are distinguished by individual names ['chord of the small / large sixth', 'chord of the second'], while the derivatives of the other seventh chords have a common name, since they determine nothing but are themselves determined by the modulation [ie, harmonic progression]." [I.9.53]
"... the differences among the perfect chords and seventh chords are due only to the different positions of the thirds, or to an inversion in the order of these thirds." [I.9.52]
"If we take the seventh chord of Article iii [modern dominant seventh] and transpose its lowest and fundamental sound a semitone higher, we form the chord in question [modern diminished seventh] ... We may accept the diminished seventh chord as long as the fundamental is not destroyed by the transposition of the lowest sound. We must therefore consider this lowest and fundamental sound to be implied in the sound substituted for it, so that the source continues to exist ... in order to distinguish this last chord [modern diminished seventh] and its derivatives from the chord from which they originate, we shall call them borrowed, since they borrow their perfection from a sound which does not actually appear." [I.8.50]
"... we cannot derive one chord from another which is neither perfect nor complete ..." [I.8.48]
"This chord [modern dominant seventh] seems to exist in order to make the perfection of consonant chords more wonderful, for it always precedes them, or rather should always be followed by the perfect chord or its derivatives. This property also applies to the derivatives of this chord." [I.8.42]
"The minor perfect chord can be discussed in the same way as the major, since it is similarly constructed and gives, by its inversion, the same chords as the major." [I.8.42]
"... the perfect chords, made up of only three different sounds, can therefore produce ... only three different chords, of which it is the first and fundamental." [I.8.40]
"Notice that dissonant chords formed by adding a minor third to one of the two perfect chords are much more tolerable than those formed by adding a major third." [I.7.39]
"To make matters simpler, we could consider thirds for the time being as the sole elements of all chords. To form the perfect chord, we must add one third to the other; to form all dissonant chords, we must add three or four thirds to one another." [I.7.39]
"... though experience proves that there are some chords which exceed the octave, reason tells us that the fundamental may subsist only within this octave; thus, so as not to destroy the fundamental, it must be supposed by a new sound added a fifth or a third below it. This sound should be regarded as supernumerary, even though the interval it forms with the fundamental sounds is always one which this last sound chose for the construction of chords." [I.7.38]
"Observe that there can be no complete chord without the fifth, nor consequently without the union of the two thirds which form the fifth; for all chords should be based on the perfect chord formed from this union. As a result, if the fifth is not heard in a chord, the fundamental is either inverted, supposed, or borrowed, unless the chord is incomplete; otherwise it will be worthless." [I.7.36]
"The first chord of a species, particularly, must be given the name of the interval which includes within itself all the sounds of the chord." [I.6.34]
"Zarlino ... [is who] we should mainly follow. He has served as a model to posterity; it is to him we always turn in questions of practice; he is still the oracle for many musicians; and even M. de Brossard calls him 'the prince of modern musicians.'" [I.2.22]
"The fourth arises from the inversion of the two sounds which originally formed the fifth, the lower sound of the octave being transposed to the higher position. Such inversion is the principal subject of this work." [I.2.14]
"... every number multiplied geometrically always represents the same sound, so to speak, or rather gives the replicate of that sound which is its root." [I.2.9]
"... the number 7 ... can not give a pleasant interval ..." [I.2.6]
"... some ... attribute all the power of harmony to that of numbers; it is then only a matter of applying properly the operation on which one chooses to base one's system." [I.2.4]
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