(1)   ¶ A book on the imperfections of musical notes brought out by Master Johannes
      Tinctoris, licenced in law and chaplain to the King of Greater Sicily.

      ¶ Prologue
      To the most ardent young student of the art of music, Jacobus Frontin, Johannes
(5)   Tinctoris, lowliest exponent of this same art, sends his undying friendship.

      ¶ Illustrious youth, with the most praiseworthy of motives you have earnestly requested
      that I put something down in writing for you on the subject of the imperfections of
      musical notes; and I have decided that I will agree to your certainly just request straight
      away. Indeed I am moved to such an extent that, not only for your own outstanding talent
      but for all other lovers of the fine arts, if they require something from me of my opinions
(10)  on that subject, then I should not delay in producing it. Nor, I pray, should you believe
      that this is a topic of trivial enquiry for me, since I have read and heard that previous
      generations of ours have discussed the subject too little, and our contemporaries even
      less. Be so kind, then, as to accept this short piece, dedicated with my very best wishes
      to your distinguished name; and I urge you in the strongest possible terms to study its
      highly useful teachings, lest (heaven forbid) you find yourself defiled by such imperfection
(15)  of honour that what you have so laudably desired, you yourself shamelessly disdain.

      Book One
      ¶ Chapter 1
      On the definition of imperfection and the quality of notes
      As I am about to deal with this subject of the imperfections of musical notes, I
      thought that imperfection should first be defined. Imperfection, then, is the removal
(20)  of one third part of the full, intrinsic value of a note or its constituent parts. And so that
      the topic might be illuminated all the more clearly, we should preface this by noting
      that only five notes of fixed value in music are universally to be found, which are
      placed in order in this most artfully constructed single line of pentameter:
      Maxima , longa , brevis , semibrevis , minima
      ¶ Of these five notes, some are larger, others smaller. The larger notes are those that
      are positioned above the lower ones; the smaller notes are those that are positioned
(25)  below the upper ones. Moreover, certain notes are in different respects both larger and
      smaller, since they are positioned both above and below certain others. Hence we find
      that the maxima is only a larger note, because all the rest stand below it. The long is
      a smaller note with respect to the maxima, since the former stands below the latter;
      but with respect to the rest, that is the breve, semibreve and minim, it is a larger note,
      because it stands above these. The breve is a smaller note with respect to the maxima
(30)  and long, since it stands below these latter; but with respect to the semibreve and minim
      it is a larger note, because it stands above these. The semibreve is a smaller note with
      respect to the maxima, long and breve, since it stands below these latter; but with
      respect to the minim it is a larger note, because it stands above this note. The minim
      is only a smaller note, since the rest stand above it. And so we can conclude that the
(35)  maxima is a larger note relative to the long, breve, semibreve and minim; the long is
      a smaller note relative to the maxima, but a larger note relative to the breve, semibreve
      and minim; the breve is a smaller note relative to the maxima and long, but a larger
      note relative to the semibreve and minim; the semibreve is a smaller note relative to
      the maxima, long and breve, but a larger note relative to the minim; the minim is a
      smaller note relative to the maxima, long, breve and semibreve.

      ¶ Hence, smaller notes form constituent parts of larger ones; and of these parts, some
(40)  are neighbouring, others at one remove, others at two removes, and others at three
      removes. Neighbouring parts are those where between them and the notes of which
      they form such parts there is no larger part intervening. Thus longs are neighbouring
      parts of the maxima, breves of the long, semibreves of the breve, and minims of the
      semibreve. Parts at one remove are those where between them and the notes of which
      they form such parts only one larger part is to be found. Thus breves are parts at one
(45)  remove of the maxima, semibreves of the long, and minims of the breve. Parts at two
      removes are those where between them and the notes of which they form such parts
      two larger parts are to be found. Thus semibreves are parts at two removes of the
      maxima, and minims of the long. Parts at three removes are those where between them
      and the notes of which they form such parts all the other larger parts are to be found.
      Thus minims alone are parts at three removes of the maxima. From these details we
      should gather that of the maxima the neighbouring parts are longs, the parts at one
      remove are breves, the parts at two removes are semibreves, and the parts at three
(50)  removes are minims. Of the long the neighbouring parts are breves, the parts at one
      remove are semibreves, and the parts at two removes are minims. Of the breve the
      neighbouring parts are semibreves, and the parts at one remove are minims. Again,
      of the semibreve the neighbouring parts are minims.

      ¶ And so, there is just one note that forms only a whole, that is the maxima; three
      notes that form both a whole and a constituent part, that is the long, the breve, and
      the semibreve; and just one note that forms only a constituent part, that is the minim.
(55)  Moreover, of these five notes three both imperfect and are imperfected in relation to
      the quality of prolation, tempus, and both kinds of modus, that is to say the long, the
      breve, and the semibreve; only one note is imperfected but does not imperfect, that is
      to say the maxima; and only one note imperfects but is not imperfected, that is to say
      the minim. For smaller notes imperfect larger notes, with the result that larger notes
      are imperfected by smaller notes. Hence it is that the long imperfects the maxima,
(60)  and is imperfected by the breve, the semibreve, and the minim. The breve imperfects
      the maxima and the long, and is imperfected by the semibreve and the minim. The
      semibreve imperfects the maxima, the long, and the breve, and is imperfected by the
      minim. The maxima is imperfected by the long, the breve, the semibreve, and the
      minim, and, because it does not have any larger note, it imperfects none. The minim,
      on the other hand, imperfects the maxima, the long, the breve, and the semibreve, and
      because it does not have any smaller note, it is imperfected by none, as is shown in
(65)  the present example:

      [Example1]

      ¶ Chapter 2
      On the imperfection of rests
      And since there are four of these five notes to each of which one individual rest
      specially belongs, of the same value as that of its own note, that is to say the
      long , the breve , the semibreve , and the minim , one
(70)  must be aware that all rests can imperfect, but cannot be imperfected, as is shown here:

      [Example 2]

      ¶ Hence, whatever number and type of notes a long, a breve, a semibreve, and a minim
      can imperfect, so their rests can do likewise in both number and type. And thus a long
      rest will be able to imperfect a maxima; a breve rest a maxima and long; a semibreve
      rest a maxima, long, and breve; a minim rest a maxima, long, breve, and semibreve,
      as is shown here:

      [Example 3]

(75)  ¶ Chapter 3
      On the thirteen general rules of imperfection
      First, therefore, dealing in general terms with this topic of imperfection in musical
      notes, I intend to set out thirteen general rules.

      ¶ First general rule
      The first general rule is that imperfection can occur in four ways: first, with respect
(80)  to the whole only; second, with respect to all or some constituent parts, or any one
      part only; third, with respect to the whole and some constituent parts, or any one part
      only; fourth, with respect to the whole and all constituent parts at once, as is shown
      here:

      [Example 4]

      ¶ Second general rule
      The second general rule is that when a note is imperfected with respect to the whole,
(85)  this is done by its neighbouring part; and when it is imperfected with respect to its
      parts, wither this is with respect to its neighbouring parts, and in that case it is done
      by its parts at one remove; or else it is with respect to its parts at one remove, and in
      that case it is done by its parts at two removes; or else it is with respect to its parts at
      two removes, and in that case it is done by its parts at three removes, as is shown here:

      [Example 5]

      ¶ Third general rule
      The third general rule is that it makes no difference whether a note is imperfected by
      a part either as a single unit or as separate elements, or else by a number of parts
(90)  brought together either as a single unit or as separate elements, as is shown here:

      [Example 6]

      So that this may be understood more clearly, it should be noted that a certain note
      may imperfect as a part functioning in a single unit, as here:

      [Example 7]

      Certain notes imperfect as a part in separate elements, as here:

      [Example 8]

      A certain note may imperfect as a number of parts brought together into a single unit,
      as here:

      [Example 9]

(95)  And certain notes imperfect as a number of parts in separate elements, as here:

      [Example 10]

      ¶ Fourth general rule
      The fourth general rule is that to imperfect is the particular characteristic of a smaller
      note, but to be imperfected is the particular characteristic of a larger note, since neither
      a larger note can imperfect a smaller note, nor can a note imperfect one of like value
      to itself. Hence it follows that neither will a smaller note be able to be imperfected by
      a larger note, nor will any note be able to be imperfected by one of like value to itself,
      as is shown here:

      [Example 11]

(100) ¶ Fifth general rule
      The fifth general rule is that every note which is imperfected from in front is
      necessarily imperfected before a larger or smaller note, because like before like
      cannot be imperfected, as is shown here:

      [Example 12]

      As a result of this same rule it should be noted that no note will be able to be
(105) imperfected before a rest of its own value, just as before a note of like value, as is
      shown here:

      [Example 13]

      ¶ Sixth general rule
      The sixth general rule is that no note can be imperfected with respect to the whole
      unless it is intrinsically perfect. Similarly, with respect to constituent parts, no note
      will be able to be imperfected unless those particular parts are intrinsically perfect,
      since otherwise a one-third part would not be found which is subtracted through
(110) imperfection from the whole or the constituent part, as here:

      [Example 14]

      ¶ Seventh general rule
      The seventh general rule is that however many times a note can be divided into three
      equal parts, the same number of times it can be imperfected; and so it will arrive at
      its smallest value. For example, the long in perfect minor modus, perfect tempus and
      major prolation is worth 27 minims, and these 27 make up a number divisible into
(115) three equal parts, that is into 3 times 9. Let one third part of this be taken away, and
      there will remain 18. But 18 can once again be divided into three equal parts, that is
      into 3 times 6; if a one-third part of this is taken away, that is 6, 12 will remain. And
      these 12 also make up a number divisible into three parts, that is into 3 times 4; let a
      one-third part of this be taken away, that is 4, and 8 will remain. But 8 cannot be
(120) divided into three equal parts. Hence this long will remain standing at this value, which
      is its smallest, that is to say 8 minims, as is shown here:

      [Example 15]

      ¶ Eighth general rule
      The eighth general rule is that a note which imperfects can be placed before or after,
      according to the wishes of the composer. If this note is placed before, the note which
      is imperfected is said to be imperfected 'from in front', and if it is placed after, the note
(125) which is imperfected is said to be imperfected 'from behind', as is shown here:

      [Example 16]

      ¶ Ninth general rule
      The ninth general rule is that if a single smaller note is found before a larger note
      which is imperfectible by it, provided that the correct quantities have been completed
      or that there are no other notes preceding, then it imperfects that larger note, as here:

      [Example 17]

      But if, on the other hand, a smaller note is found after a larger note which is
      imperfectible by it, whether or not there follows another larger note which is also
(130) imperfectible by it, then it imperfects that preceding larger note, as is shown here:

      [Example 18]

      Equally, if several smaller notes are found set up in imperfect number before a larger
      note which is imperfectible by them, provided that the correct quantities have been
      completed or that there are no other notes preceding, then they imperfect that larger
      note in whatever number they are, or are able to do so. And if there are still any
      remaining, also imperfect in number, then these will carry over to the next closest
      location that they will be able to occupy, as is shown here:

      [Example 19]

(135) If, on the other hand, several smaller notes are found set up in imperfect number after a
      larger note which is imperfectible by them, whether or not there follows another larger
      note which is also imperfectible by them, then they imperfect that preceding larger note
      in whatever number they are, or are able to do so, or in whatever number removes the
      imperfection in quantity. And if any are still remaining imperfect in number, then these
      will carry over to the next closest location which they will be able to occupy, as is shown
      here:

      [Example 20]

(140) ¶ This rule, however, as given above, allows of an exception in the case of three signs,
      that is to say the dot of separation, the filling-in of notes, and the ligature: for if a dot of
      separation is attached to a group of smaller notes which otherwise, according to the above
      rule, would imperfect some larger note, then they will not imperfect it, but rather they
      will carry over to the next closest location which they will be able to occupy, as here:

      [Example 21]

      And if smaller notes which otherwise, according to the above rule, would imperfect some
(145) larger note are filled in, then they will not imperfect this larger note, but rather they will
      be cross-grouped with other notes similarly filled in, as is shown here:

      [Example 22]

      On the other hand, if smaller notes which, following this same rule, would otherwise
      imperfect some preceding larger note are ligated with another larger or like-value note
      following, which along with the smaller notes cannot imperfect that preceding larger note,
      then they do not imperfect it, but rather are counted together with these following notes,
(150) as is shown here:

      [Example 23]

      ¶ Tenth general rule
      The tenth general rule is that if one single, or several smaller notes are found set up in
      imperfect number either before or after a larger note which cannot be imperfected by
      them – for instance if this larger note is itself before a note of like value or its rest, or if
      it has a dot of perfection attached, or if it has already been imperfected by other notes as
(155) far as possible – then these smaller notes carry over to the next closest location which
      they can occupy, as is shown here:

      [Example 24]

      ¶ Eleventh general rule
      The eleventh general rule is that if a dot of separation is attached to some note on behalf
      of that note only, before a note of like or smaller value, then the former note will imperfect
(160) the first larger note that it can, unless it has partner notes before it, as is shown here:

      [Example 25]

      If, on the other hand, a dot of separation is attached to some note, before a note of smaller
      or like value, on behalf not only of that note but of others, then that note, counted along
      with these others, will also imperfect the first larger note that it can, provided likewise
      that they do not have any partner notes before the note to which the dot is attached, as is
      shown here:

      [Example 26]

      ¶ Twelfth general rule
(165) The twelfth general rule is that a note to which a dot of separation is attached can be
      imperfected, as is shown here:

      [Example 27]

      On the other hand, a note to which a dot of perfection or augmentation is attached is never
      imperfected. And the reason for this is as follows: perfection and imperfection are
      opposites; but opposites cannot exist simultaneously in the same subject; and so it is
(170) impossible for one and the same note to be simultaneously perfect and imperfect, as here:

      [Example 28]

      By the same reasoning, since according to arithmetic, and music which is subordinate to
      it, addition and subtraction are opposites, and since, moreover, augmentation is a kind of
      addition and imperfection a kind of subtraction, it is impossible for one and the same
      note to be simultaneously augmented and imperfected, as is shown here:

      [Example 29]

(175) Perhaps some people will say that Tinctoris is presuming too much, in asserting that an
      augmented note cannot be imperfected, since De Domarto, in the tenor of his Patrem in
      the irregular fifth tonem and Barbingant in the tenor of his song L'omme bany, have done
      the opposite, as is shown here:

      [Example 30]

      To such people I would reply that, although Busnoys and a number of others have
      imitated these composers, I do not presume to censure anyone on the basis, as it were,
      of envying a person's reputation, but rather to demonstrate that they have erred by
(180) holding to our friend Truth to the best of my ability. I also name those at fault, lest our
      youngsters, deceived by false opinion because of the undying fame that the former have
      created for themselves through their most beautiful composition, imitate them in this
      respect, thinking that everything they accomplish is perfect, which is far from being the
      case. For, as the wise put it, nothing is perfect in all respects.

      ¶ Thirteenth general rule
(185) The thirteenth general rule is that any note which can be both imperfected and altered,
      such as the long, breve and semibreve, if it is altered, will be able to be imperfected only
      with respect to some of its parts, that is to say only so many parts that the smaller notes
      imperfecting the larger note do not reach the intrinsic value of the latter, as is also
      demonstrated in this example:

      [Example 31]

      Book Two
(190) ¶ Chapter 1
      On the imperfection of musical notes on an individual basis
      Now that we have dealt in general terms with the imperfection of musical notes,
      it is fitting that we deal in due order with the imperfection of each note on an
      individual basis. First, then, let us begin with the maxima, which is the foremost
      and chief of all the other notes, so that we may thus proceed from greater to smaller.

(195) ¶ Chapter 2
      On the imperfection of the maxima in perfect major modus
      The maxima in perfect major modus can be imperfected with respect to the whole,
      for in this case it is worth three longs of which one, being a one-third part of that
      maxima, will be able to be taken away, as is shown here:

      [Example 32]

(200) ¶ On the imperfection of the maxima in perfect minor modus
      Furthermore, the maxima in perfect minor modus can be imperfected with respect to
      two neighbouring parts, or one only, because in this case the long, which is its
      neighbouring part, is worth three breves. Hence for each long one breve, being a one-third
      part of the former, will be able to be taken away, as is shown here:

      [Example 33]

(205) ¶ On the imperfection of the maxima in perfect tempus
      Furthermore, the maxima in perfect tempus can be imperfected with respect to five,
      four, three or two parts at one remove, or one only, for in this case the breve, which is
      its part at one remove, is worth three semibreves. Hence for each breve one semibreve,
      being a one-third part of the former, will be able to be taken away, as here:

      [Example 34]

(210) ¶ On the imperfection of the maxima in major prolation
      Furthermore, the maxima in major prolation can be imperfected with respect to eleven,
      ten, nine, eight, seven, six, five, four, three or two parts at two removes, or one only,
      because in this case the semibreve, which is its part at two removes, is worth three
      minims. Hence for each semibreve one minim, being a one-third part of the former, will
      be able to be taken away, as is shown here:

      [Example 35]

(215) ¶ Chapter 3
      On the fifteen methods of imperfecting the maxima
      And since in numerous pieces of music all the mensural quantities are perfect, and in
      other pieces one or more perfect quantities are mixed throughout with one or more
      imperfect, the result is that there are fifteen methods by which the maxima can be
      imperfected.

      ¶ The first method of imperfecting the maxima
(220) The first method is with respect only to the whole; and this occurs in perfect major modus,
      imperfect minor modus, imperfect tempus and minor prolation, as is shown here:

      [Example 36]

      ¶ The second method of imperfecting the maxima
      The second method is with respect only to the neighbouring parts; and this occurs in
      imperfect major modus, perfect minor modus, imperfect tempus and minor prolation,
(225) as is shown here:

      [Example 37]

      ¶ The third method of imperfecting the maxima
      The third method is with respect only to the parts at one remove; and this occurs in
      imperfect modus of both kinds, perfect tempus and minor prolation, as is shown here:

      [Example 38]

      ¶ The fourth method of imperfecting the maxima
(230) The fourth method is with respect only to the parts at two removes; and this occurs in
      imperfect modus of both kinds, imperfect tempus and major prolation, as is shown here:

      [Example 39]

      ¶ The fifth method of imperfecting the maxima
      The fifth method is with respect only to the whole and the neighbouring parts; and this
      occurs in perfect modus of both kinds, imperfect tempus and minor prolation, as is
      shown here:

      [Example 40]

(235) ¶ The sixth method of imperfecting the maxima
      The sixth method is with respect only to the whole and the parts at one remove; and this
      occurs in perfect major modus, imperfect minor modus, perfect tempus and minor
      prolation, as is shown here:

      [Example 41]

      ¶ The seventh method of imperfecting the maxima
      The seventh method is with respect only to the whole and the parts at two removes; and
(240) this occurs in perfect major modus, imperfect minor modus, imperfect tempus and major
      prolation, as is shown here:

      [Example 42]

      ¶ The eighth method of imperfecting the maxima
      The eighth method is with respect only to the whole, the neighbouring parts, and the parts
      at one remove; and this occurs in perfect modus of both kinds, perfect tempus and minor
      prolation, as is shown here:

      [Example 43]

(245) ¶ The ninth method of imperfecting the maxima
      The ninth method is with respect only to the whole, the neighbouring parts, and the parts
      at two removes; and this occurs in perfect modus of both kinds, imperfect tempus and
      major prolation, as is shown here:

      [Example 44]

      ¶ The tenth method of imperfecting the maxima
      The tenth method is with respect only to the whole, the parts at one remove, and the parts
(250) at two removes; and this occurs in perfect major modus, imperfect minor modus, perfect
      tempus and major prolation, as is shown here:

      [Example 45]

      ¶ The eleventh method of imperfecting the maxima
      The eleventh method is with respect only to the neighbouring parts and the parts at one
      remove; and this occurs in imperfect major modus, perfect minor modus, perfect tempus
(255) and minor prolation, as is shown here:

      [Example 46]

      ¶ The twelfth method of imperfecting the maxima
      The twelfth method is with respect only to the neighbouring parts and the parts at two
      removes; and this occurs in imperfect major modus, perfect minor modus, imperfect
      tempus and major prolation, as is shown here:

      [Example 47]

(260) ¶ The thirteenth method of imperfecting the maxima
      The thirteenth method is with respect only to the parts at one remove and the parts at two
      removes; and this occurs in imperfect modus of both kinds, perfect tempus and major
      prolation, as is shown here:

      [Example 48]

      ¶ The fourteenth method of imperfecting the maxima
      The fourteenth method is with respect only to the neighbouring parts, the parts at one
(265) remove, and the parts at two removes; and this occurs in imperfect major modus, perfect
      minor modus, perfect tempus and major prolation, as is shown here:

      [Example 49]

      ¶ The fifteenth method of imperfecting the maxima
      The fifteenth method is with respect to the whole, the neighbouring parts, the parts at
      one remove, and the parts at two removes all at the same time; and this occurs in perfect
(270) modus of both kinds, perfect tempus and major prolation, as is shown here:

      [Example 50]

      ¶ Chapter 4
      On the imperfection of the long in perfect minor modus
      The long in perfect minor modus can be imperfected with respect to the whole, for in
      this case it is worth three breves, of which one, being a one-third part of that long, will
      be able to be taken away, as is shown here:

      [Example 51]

      ¶ On the imperfection of the long in perfect tempus
(275) Furthermore, the long in perfect tempus can be imperfected with respect to two
      neighbouring parts, or one only, because in this case the breve, which is its neighbouring
      part, is worth three semibreves. Hence for each breve one semibreve, being a one-third
      part of the former, will be able to be taken away, as is shown here:

      [Example 52]

      ¶ On the imperfection of the long in major prolation
(280) Furthermore, the long in major prolation can be imperfected with respect to five, four,
      three or two parts at one remove, or one only, for in this case the semibreve, which is its
      part at one remove, is worth three minims. Hence for each semibreve one minim, being
      a one-third part of the former, will be able to be taken away, as is shown here:

      [Example 53]

      ¶ Chapter 5
      On the seven methods of imperfecting the long
(285) And since in numerous pieces of music, under major modus of either kind, perfect
      mensural quantities of minor modus, tempus and prolation are set up, and in other
      pieces one or more perfect quantities are mixed throughout with one or more imperfect,
      the result is that there are seven methods by which the long can be imperfected.

      ¶ The first method of imperfecting the long
(290) The first method is with respect only to the whole; and this occurs in major modus of
      either kind, perfect minor modus, imperfect tempus and minor prolation, as is shown
      here:

      [Example 54]

      ¶ The second method of imperfecting the long
      The second method is with respect only to the neighbouring parts; and this occurs in
      major modus of either kind, imperfect minor modus, perfect tempus and minor prolation,
      as is shown here:

      [Example 55]

(295) ¶ The third method of imperfecting the long
      The third method is with respect only to the parts at one remove; and this occurs in major
      modus of either kind, imperfect minor modus, imperfect tempus and major prolation, as
      is shown here:

      [Example 56]

      ¶ The fourth method of imperfecting the long
      The fourth method is with respect only to the whole and the neighbouring parts; and this
      occurs in major modus of either kind, perfect minor modus, perfect tempus and minor
(300) prolation, as is shown here:

      [Example 57]

      ¶ The fifth method of imperfecting the long
      The fifth method is with respect only to the whole and the parts at one remove; and this
      occurs in major modus of either kind, perfect minor modus, imperfect tempus and major
      prolation, as is shown here:

      [Example 58]

      ¶ The sixth method of imperfecting the long
(305) The sixth method is with respect only to the neighbouring parts and the parts at one
      remove; and this occurs in major modus of either kind, imperfect minor modus, perfect
      tempus and major prolation, as is shown here:

      [Example 59]

      ¶ The seventh method of imperfecting the long
      The seventh method is with respect to the whole, the neighbouring parts, and the parts at
      one remove all at the same time; and this occurs in major modus of either kind, perfect
(310) minor modus, perfect tempus and major prolation, as is shown here:

      [Example 60]

      ¶ Chapter 6
      On the imperfection of the breve in perfect tempus
      The breve in perfect tempus can be imperfected with respect to the whole, because in this
      case it is worth three semibreves, of which one, being a one-third part of that breve, will
      be able to be taken away, as is shown here:

      [Example 61]

      ¶ On the imperfection of the breve in major prolation
(315) Furthermore, the breve in major prolation can be imperfected with respect to two
      neighbouring parts, or one only, for in this case the semibreve, which is its neighbouring
      part, is worth three minims. Hence for each semibreve one minim, being a one-third
      part of the former, will be able to be taken away, as is shown here:

      [Example 62]

      ¶ On the three methods of imperfecting the breve
(320) And since in numerous pieces of music, under major or minor modus of either kind,
      perfect tempus and major prolation occur together, and in other pieces imperfect tempus
      with major prolation, or the reverse, perfect tempus with minor prolation, are mixed
      together, the result is that there are three methods by which the breve can be
      imperfected.

      ¶ The first method of imperfecting the breve
(325) The first method is with respect only to the whole; and this occurs in major or minor
      modus of either kind, perfect tempus and minor prolation, as is shown here:

      [Example 63]

      ¶ The second method of imperfecting the breve
      The second method is with respect only to the neighbouring parts; and this occurs in
      major or minor modus of either kind, imperfect tempus and major prolation, as is shown
      here:

      [Example 64]

(330) ¶ The third method of imperfecting the breve
      The third method is with respect to the whole and the neighbouring parts at the same
      time; and this occurs in major or minor modus of either kind, perfect tempus and
      major prolation, as is shown here:

      [Example 65]

      ¶ Chapter 7
      On the single method of imperfecting the semibreve
      The semibreve can be imperfected by just one method, which is to say with respect only
(335) to the whole; and this occurs in major prolation under any kind of modus and tempus,
      because in this case it is worth three minims, of which one, being a one-third part of that
      semibreve, will be able to be taken away, as is shown here:

      [Example 66]

      ¶ Chapter 8
      On the three signs of imperfection
      Finally, because there are certain fixed signs by which notes are recognized as being
      imperfected, I consider it necessary to say a few words about these. And so, it should be
(340) known that there are three signs which indicate that an imperfectible note is imperfected,
      which is to say imperfection by number, filling-in of the note, and separation by dot.

      ¶ On the first sign of imperfection
      As regards the first: whenever smaller notes are found set up in imperfect number either
      before or after a larger note, it is a sign that the first larger note which is imperfectible by
(345) them is to be imperfected, unless the smaller notes are to be cross-grouped beforehand
      with partner-notes, as is shown here:

      [Example 67]

      ¶ On the second sign of imperfection
      As regards the second: whenever a whole note is filled in, it is a sign that it is imperfected
      by a one-third part of its full value; and if only a half of the note is filled in, it is a sign
      that it has been imperfected by a one-third part of half of its value. Also, smaller notes
(350) which in this way imperfect larger notes should be filled in just as the latter are; nor does
      it matter whether the smaller notes precede or follow the larger, or whether the former
      and latter are immediately juxtaposed or placed with other notes in between, as is shown
      here:

      [Example 68]

      If, however, three like notes have been filled in to indicate imperfection, whether they are
      placed immediately after one another or not, then the middle note imperfects the first
      from behind, and the last from in front, as neighbouring parts brought together in a
      single unit, as is shown here:

      [Example 69]

(355) And since the filling-in of notes indicates not only imperfection, but also cross-grouping,
      sesquialtera and dupla proportion, I have comprehensively explained in my Proportionale
      Musices how to identify readily which of these four indications should be adopted,
      whenever such filling-in of notes is encountered in some piece of music. For this reason
      I am not saying anything on the subject in the present treatise.

      ¶ On the third sign of imperfection
(360) As regards the third: whenever a dot of separation is added to any note on behalf of that
      note only, or on behalf of both it and other notes, it is a sign that the first larger note
      which is imperfectible by them is to be imperfected, unless the smaller notes are to be
      cross-grouped beforehand with partner-notes, as is shown here:

      [Example 70]

      ¶ Chapter 9
      The conclusion of this work
      And this should be enough said on the imperfection of musical notes. If anything therein
(365) is found to have been set down imperfectly, I pray that all those perfected in this divine art
      may be willing to perfect it as with a more perfect love, so that God, the great Lord of all
      knowledge, who knows no need of imperfection, may deem them worthy to be rewarded
      with his most perfect blessing.

      The End.