proportion by qingyunliuliu

VIEWS: 56 PAGES: 32

									Proportions

                                             16 PICAS




                                          Proportion
    PROPORTION
                                           equals 2:1



                               32 PICAS
    The comparative
    relation between parts,
    things, or elements with
    respect to size, amount,
    degree; a ratio.
Proportion

                                         16 PICAS

                                                                 12 PICAS




                                      Proportion               Proportion
When an object changes
                                       equals 2:1




                                                    24 PICAS
size but maintains the                                         equals 2:1
relationship between       32 PICAS
dimensions, it ‘stays in
proportion.’
                     PROPORTION
                                            16 PICAS

                                                                        16 PICAS




Unless all the dimensions




                                                        24 PICAS
of an object change
proportionally,             32 PICAS

maintaining the same
proportion, the object
will become distorted.
                                                                   Proportion 3:2

                                       Proportion 2:1
Proportional spacing




                                          kp mn
                                                         .055 em




                              72 points
In a proportional typeface,                     1 em           1⁄ em
                                                                2


the proportion (or ratio)
between letter widths
remains constant as
nominal size changes.
Likewise, space between
letters remains in
                                          kp mn
                                                    .055 em
                              48 points




proportion.
                                             1 em      1⁄ em
                                                        2
                               PAGE PROPORTIONS
                                   Mechanical

Mechanical page proportions refer to page sizes
that are dictated by:

■ Industry standards. Newspaper pages, for in-
  stance, all are a uniform size to accommodate
  national advertising.
■ Economy. By using paper in standard widths,
  printers save money. For instance, many maga-
  zines are in an 8.5 by 11 inch format, the so-
  called U.S. letter size, because it fits a standard
  size of paper and produces little waste.
■ Packaging. A pamphlet to go with a CD is
  square, not because it couldn't be some other
  shape but because it must fit the CD package.
■ Custom. Your business card doesn't have to be
  3.5 by 2 inches, but that's the customary size.
PAGE PROPORTIONS
    Mechanical




     BROADSHEET:
11½ inches by 22¾ inches
        TABLOID:
 11 inches by 11½ inches
                                                 PAGE PROPORTIONS
                                                     Mechanical

 4.25 x 5.5
  1 : 1.29
                5.5 x 8.5
 4.25           1 : 1.55
   x
 2.75
1:1.55
                                            11 x 17
                                            1 : 1.55
                                                                          U.S. LETTER SIZE
                                                                            double page spread
                                                                Letter size 2-page spread
         8.5 x 11
         1 : 1.29




                                                                      U.S. LETTER
                                                              Half-letter size double page spread
                                                                         Half-size
                                                                      2-page spread




                    U.S. LETTER HALF-SIZE
                     2-page letter-size and
         Comparison of spread
          half-letter-size proportions
                             PAGE PROPORTIONS
                                 Mechanical

A4
210mm × 297mm
                A3          A1                                420mm
     1 :√2       297mm
   (1:1.414)       ×
A5
                 420mm
 148mm            1: √2
     ×
  210mm
                (1:1.414)
   1: √2
 (1:1.414)
                             594mm × 841mm
 A2                               1: √2                                                297mm
     420mm × 594mm              (1:1.414)
          1: √2
        (1:1.414)

 A0
                                                   A4-size double page spread


                                               The A4 page, sometimes called the metric
                841mm × 1189mm                letter-size page, is based on the proportion
                      1: √2                  of 1 to the square root of 2 (1:1.414) It is the
                    (1:1.414)                only page size that replicates its proportions
                                                           when folded in half.
                     PAGE PROPORTIONS
                         Mechanical


                                             Tri-fold brochure: Limited
                                        in format by mechanical page size
                                          (8.5 x 11) and by envelope size




      TRI-FOLD BROCHURE
               1 : 2.32
Fits in 9.5 x 4 Business Envelope
                              PAGE PROPORTIONS
                                  Mechanical




                                       Locked-in formats
                                        CD covers and
ONE TIN                                  booklets are a
SOLDIER                                  double square
“Your place for guns,                     side by side
ammo and shooting supplies”
Cloverdale Plaza
Muskogee, Okla.       Zeke Mirkwood
1-708-555-1212


      Business cards fit a
   3.5-inch x 2-inch format
PAGE PROPORTIONS
      Natural

              Natural page proportions mimic propor-
              tions found in nature, either in the actual
              dimentions of plants and animals or in
              mathematics.

              Leonardo Da Vinci (1452-1519) outlined
              the natural proportions of the circle and
              square in the human body. Le Corbusier
              (1887-1965) developed an elaborate design
              system based on human proportions and
              the Golden Section.
       PAGE PROPORTIONS
                Natural
Pages derived from a circle and square




                          Double ISO page    Perfect square
                             1 : 2.828




                              ISO page
                              1 : 1.414
                                            Double square
                                                1:2
PAGE PROPORTIONS
      Natural



           The square is seldom used in magazine
           design, and it is considered too static
           for newspaper designers, who avoid
           using square pictures or square story
           packages. But many designers find
           working on a square to be a rewarding
           and satisfying process. The square de-
           sign provides a solid, restful feel.
The grid made up of squares is the basis for modern design
                                             3




                                  2              4




                                             6
Medieval scribes used this system to place
text blocks on a page. The text block and
the page are the same proportion.
                                                                                                                   1 at the vertex. The last casualties are listed on the bottom line of West Panel 1 above the date 1975.
                                                                                                                     Each name is preceded (on the west wall) or followed (on the east wall) by a symbol designating
                                                                                                                   status. The diamond symbol denotes that the serviceman’s or servicewomen’s death was confirmed.
                                                                                                                   The approximately 1,300 men whose names are designated by the cross symbol were in missing or
                                                                                                                   prisoner status at the end of the war and remain missing and unaccounted for. In the event a service-
                                                                                                                   man’s remains are returned or he is otherwise accounted for, the diamond symbol is superimposed
                                                                                                                   over the cross. If a man returns alive, a circle, as a symbol of life, will be inscribed around the cross.
                                                                                                                      The names and inscriptions were gritblasted in Memphis, Tennessee, using stencils produced
                                                                                                                   through a photographic process. The names were arranged chronologically and typeset in Atlanta,
                                                                                                                   GA from a computer tape of the official Vietnam casualty list. The names are approximately .53
                                                                                                                   inch in height, and .015 inch depth, typeset in Optima. There are a total of 58,209 names as of
                                                                                                                   Memorial Day 1997. Approximately 2,500,000 people visit each year, making the Vietnam Veterans
                                                                                                                   Memorial the most visited in Washington, D.C.


                                                                                                                   The Memorial’s History
                                                                                                                     The memorial was established by the Vietnam Veterans Memorial Fund, Inc. (VVMF), a non-
                                                                                                                   profit, charitable organization incorporated on April 27, 1979, by a group of Vietnam veterans led
      The Vietnam Veterans Memorial                                                                                by Jan C. Scruggs, a wounded and decorated former infantryman, from Columbia, MD. The VVMF
          Each of the walls is 246 feet 8 inches long. They meet at an angle of 125.12 degrees. They point         wanted Vietnam veterans to have a tangible symbol of recognition from the American people. By
      exactly to the northeast corners of the Washington Monument and the Lincoln Memorial. The                    separating the issue of the service of the individual men and women from the issue of U.S. policy in
      walls are supported throughout their entire length by 140 concrete pilings driven approximately 35           Vietnam, VVMF hoped to begin a process of national reconciliation. Significant initial support came
      feet to bedrock. At their vertex the walls are 10.15 feet in height. The stone for the walls, safety curbs   from U.S. Senators Charles McC. Mathias, Jr., of Maryland and John W. Warner of Virginia.
      and walkways is black granite quarried near Bangalore, India. All cutting and fabrication was done             On November 8, 1979, Senator Mathias introduced legislation to authorize a site of national park
      in Barre, Vermont. The variations in color and texture are a result of different finishing techniques,       land for the memorial. The first significant financial contributions to launch the national fund rais-
      such as polishing, honing and flame treatment.                                                               ing campaign were raised by Senator Warner. More than $8,000,000 was raised , all of which came
          The list of names begins at the vertex of the walls below the year of the first casualty, and contin-    from private sources. Corporations, foundations, unions, veterans groups, and civic organizations all
      ues to the end of the east wall. It resumes at the tip of the west wall, ending at the vertex, above the     contributed, but most importantly of all, were the more than 275,000 individual Americans who do-
      year of the last death. With the meeting of the beginning and ending, a major epoch in American              nated the bulk needed to build the Memorial.
      history is signified.                                                                                          On July 1, 1980, Congress authorized a site of two acres in Constitution Gardens near the Lin-
          Each of the walls is composed of 70 separate inscribed panels. The largest panels have 137 lines         coln Memorial. In October of that year, VVMF announced a national design competition open to
      of names; the shortest have one line. There are an average of five names per line. Each panel is             any U.S. citizen over 18 years of age. By December 29, 1981, there were 2,573 registrants, and the
      numbered from 1 to 70 at the base of each panel, with West Panel 1 and East Panel 1 meeting at the           competition became the largest of its kind ever held in the United States. By the deadline of March
      vertex, leading out to East or West Panel 70.                                                                31, 1981, 1,421 design entries had been submitted. All entries were judged anonymously by a jury
          The names of the first casualties appear on the top of East Panel 1 below the date 1959. The             of eight internationally recognized artists and designers, who had been selected by VVMF. On May
      chronological listing by casualty date of the names proceeds left to right, line by line, down each          1, 1981, the jury presented its unanimous selection for first prize, which was accepted and adopted
      panel, and then to the top line of the panel to its right, as though the panels were pages in a book,        enthusiastically by VVMF.
      until East Panel 70, where the sequence of names begins on West Panel 70, proceeding to West Panel             The winning design was authored by Maya Ying Lin of Athens, Ohio, who at the time was a 21


      4                                                                                                                                                                                                                         5


The system still produces an attractive page,
with generous margins. A wide edge margin
is sometimes called a scholar’s margin.
                                                                                                             1 at the vertex. The last casualties are listed on the bottom line of West Panel 1 above the date 1975.
                                                                                                               Each name is preceded (on the west wall) or followed (on the east wall) by a symbol designating
                                                                                                             status. The diamond symbol denotes that the serviceman’s or servicewomen’s death was confirmed.
                                                                                                             The approximately 1,300 men whose names are designated by the cross symbol were in missing or
                                                                                                             prisoner status at the end of the war and remain missing and unaccounted for. In the event a service-
                                                                                                             man’s remains are returned or he is otherwise accounted for, the diamond symbol is superimposed
                                                                                                             over the cross. If a man returns alive, a circle, as a symbol of life, will be inscribed around the cross.
                                                                                                                The names and inscriptions were gritblasted in Memphis, Tennessee, using stencils produced
                                                                                                             through a photographic process. The names were arranged chronologically and typeset in Atlanta,
                                                                                                             GA from a computer tape of the official Vietnam casualty list. The names are approximately .53
                                                                                                             inch in height, and .015 inch depth, typeset in Optima. There are a total of 58,209 names as of
                                                                                                             Memorial Day 1997. Approximately 2,500,000 people visit each year, making the Vietnam Veterans
                                                                                                             Memorial the most visited in Washington, D.C.


                                                                                                             The Memorial’s History
                                                                                                               The memorial was established by the Vietnam Veterans Memorial Fund, Inc. (VVMF), a non-
                                                                                                             profit, charitable organization incorporated on April 27, 1979, by a group of Vietnam veterans led
The Vietnam Veterans Memorial                                                                                by Jan C. Scruggs, a wounded and decorated former infantryman, from Columbia, MD. The VVMF
    Each of the walls is 246 feet 8 inches long. They meet at an angle of 125.12 degrees. They point         wanted Vietnam veterans to have a tangible symbol of recognition from the American people. By
exactly to the northeast corners of the Washington Monument and the Lincoln Memorial. The                    separating the issue of the service of the individual men and women from the issue of U.S. policy in
walls are supported throughout their entire length by 140 concrete pilings driven approximately 35           Vietnam, VVMF hoped to begin a process of national reconciliation. Significant initial support came
feet to bedrock. At their vertex the walls are 10.15 feet in height. The stone for the walls, safety curbs   from U.S. Senators Charles McC. Mathias, Jr., of Maryland and John W. Warner of Virginia.
and walkways is black granite quarried near Bangalore, India. All cutting and fabrication was done             On November 8, 1979, Senator Mathias introduced legislation to authorize a site of national park
in Barre, Vermont. The variations in color and texture are a result of different finishing techniques,       land for the memorial. The first significant financial contributions to launch the national fund rais-
such as polishing, honing and flame treatment.                                                               ing campaign were raised by Senator Warner. More than $8,000,000 was raised , all of which came
    The list of names begins at the vertex of the walls below the year of the first casualty, and contin-    from private sources. Corporations, foundations, unions, veterans groups, and civic organizations all
ues to the end of the east wall. It resumes at the tip of the west wall, ending at the vertex, above the     contributed, but most importantly of all, were the more than 275,000 individual Americans who do-
year of the last death. With the meeting of the beginning and ending, a major epoch in American              nated the bulk needed to build the Memorial.
history is signified.                                                                                          On July 1, 1980, Congress authorized a site of two acres in Constitution Gardens near the Lin-
    Each of the walls is composed of 70 separate inscribed panels. The largest panels have 137 lines         coln Memorial. In October of that year, VVMF announced a national design competition open to
of names; the shortest have one line. There are an average of five names per line. Each panel is             any U.S. citizen over 18 years of age. By December 29, 1981, there were 2,573 registrants, and the
numbered from 1 to 70 at the base of each panel, with West Panel 1 and East Panel 1 meeting at the           competition became the largest of its kind ever held in the United States. By the deadline of March
vertex, leading out to East or West Panel 70.                                                                31, 1981, 1,421 design entries had been submitted. All entries were judged anonymously by a jury
    The names of the first casualties appear on the top of East Panel 1 below the date 1959. The             of eight internationally recognized artists and designers, who had been selected by VVMF. On May
chronological listing by casualty date of the names proceeds left to right, line by line, down each          1, 1981, the jury presented its unanimous selection for first prize, which was accepted and adopted
panel, and then to the top line of the panel to its right, as though the panels were pages in a book,        enthusiastically by VVMF.
until East Panel 70, where the sequence of names begins on West Panel 70, proceeding to West Panel             The winning design was authored by Maya Ying Lin of Athens, Ohio, who at the time was a 21


4                                                                                                                                                                                                                         5
                                                                                                             1 at the vertex. The last casualties are listed on the bottom line of West Panel 1 above the date 1975.
                                                                                                               Each name is preceded (on the west wall) or followed (on the east wall) by a symbol designating
                                                                                                             status. The diamond symbol denotes that the serviceman’s or servicewomen’s death was confirmed.
                                                                                                             The approximately 1,300 men whose names are designated by the cross symbol were in missing or
                                                                                                             prisoner status at the end of the war and remain missing and unaccounted for. In the event a service-
                                                                                                             man’s remains are returned or he is otherwise accounted for, the diamond symbol is superimposed
                                                                                                             over the cross. If a man returns alive, a circle, as a symbol of life, will be inscribed around the cross.
                                                                                                                The names and inscriptions were gritblasted in Memphis, Tennessee, using stencils produced
                                                                                                             through a photographic process. The names were arranged chronologically and typeset in Atlanta,
                                                                                                             GA from a computer tape of the official Vietnam casualty list. The names are approximately .53
                                                                                                             inch in height, and .015 inch depth, typeset in Optima. There are a total of 58,209 names as of
                                                                                                             Memorial Day 1997. Approximately 2,500,000 people visit each year, making the Vietnam Veterans
                                                                                                             Memorial the most visited in Washington, D.C.


                                                                                                             The Memorial’s History
                                                                                                               The memorial was established by the Vietnam Veterans Memorial Fund, Inc. (VVMF), a non-
                                                                                                             profit, charitable organization incorporated on April 27, 1979, by a group of Vietnam veterans led
The Vietnam Veterans Memorial                                                                                by Jan C. Scruggs, a wounded and decorated former infantryman, from Columbia, MD. The VVMF
    Each of the walls is 246 feet 8 inches long. They meet at an angle of 125.12 degrees. They point         wanted Vietnam veterans to have a tangible symbol of recognition from the American people. By
exactly to the northeast corners of the Washington Monument and the Lincoln Memorial. The                    separating the issue of the service of the individual men and women from the issue of U.S. policy in
walls are supported throughout their entire length by 140 concrete pilings driven approximately 35           Vietnam, VVMF hoped to begin a process of national reconciliation. Significant initial support came
feet to bedrock. At their vertex the walls are 10.15 feet in height. The stone for the walls, safety curbs   from U.S. Senators Charles McC. Mathias, Jr., of Maryland and John W. Warner of Virginia.
and walkways is black granite quarried near Bangalore, India. All cutting and fabrication was done             On November 8, 1979, Senator Mathias introduced legislation to authorize a site of national park
in Barre, Vermont. The variations in color and texture are a result of different finishing techniques,       land for the memorial. The first significant financial contributions to launch the national fund rais-
such as polishing, honing and flame treatment.                                                               ing campaign were raised by Senator Warner. More than $8,000,000 was raised , all of which came
    The list of names begins at the vertex of the walls below the year of the first casualty, and contin-    from private sources. Corporations, foundations, unions, veterans groups, and civic organizations all
ues to the end of the east wall. It resumes at the tip of the west wall, ending at the vertex, above the     contributed, but most importantly of all, were the more than 275,000 individual Americans who do-
year of the last death. With the meeting of the beginning and ending, a major epoch in American              nated the bulk needed to build the Memorial.
history is signified.                                                                                          On July 1, 1980, Congress authorized a site of two acres in Constitution Gardens near the Lin-
    Each of the walls is composed of 70 separate inscribed panels. The largest panels have 137 lines         coln Memorial. In October of that year, VVMF announced a national design competition open to
of names; the shortest have one line. There are an average of five names per line. Each panel is             any U.S. citizen over 18 years of age. By December 29, 1981, there were 2,573 registrants, and the
numbered from 1 to 70 at the base of each panel, with West Panel 1 and East Panel 1 meeting at the           competition became the largest of its kind ever held in the United States. By the deadline of March
vertex, leading out to East or West Panel 70.                                                                31, 1981, 1,421 design entries had been submitted. All entries were judged anonymously by a jury
    The names of the first casualties appear on the top of East Panel 1 below the date 1959. The             of eight internationally recognized artists and designers, who had been selected by VVMF. On May
chronological listing by casualty date of the names proceeds left to right, line by line, down each          1, 1981, the jury presented its unanimous selection for first prize, which was accepted and adopted
panel, and then to the top line of the panel to its right, as though the panels were pages in a book,        enthusiastically by VVMF.
until East Panel 70, where the sequence of names begins on West Panel 70, proceeding to West Panel             The winning design was authored by Maya Ying Lin of Athens, Ohio, who at the time was a 21


4                                                                                                                                                                                                                         5


                        We can combine this ancient “grid” with a vertical mea-
                        surement system based on the line height of the body
                        text.This is known as a “ledding grid.”
                                PAGE PROPORTIONS
                                      Natural




                    1




                                    1    __
                                        √ 2 __
                                            √3
                                                  __
                                                 √4


Many of the “natural proportions” follow the           rectangle, one with a proportion of 1:√2. If we
Pythagorean Theorum in forming rectangles that         repeat the process with this “root 2” rectangle,
please the eye. Jay Hambidge, in his good The          we get one with a proportion of 1:√3. Repeat it
Elements of Dynamic Symmetry, described the            again and we get a rectangle with a proportion
“root” rectangles, so named because the propor-        of 1:√4.
tion is always 1 to a square root. Starting with       This last “root 4” rectangle is actually a double
the square, we draw a diagonal, then rotate it in      square. Remember, the square root of 4 is 2, so
an arc until the diagonal line lies horizontal. By     the proportion is 1:2, a double square.
adding a rectangle to this point, we form a new
        PAGE PROPORTIONS
              Natural

                           The “Golden Section” has
                           a proportion of 1+(√5) ⁄ 2 .
                           That works out to about
                           1:1.618. The Golden Section
                           is less useful for establish-
                           ing a page size than it is for
1                          establishing units on a grid
                           or copy block sizes.




    1
        (1+√5)÷2
     PROPORTION

 THE GOLDEN
     SECTION,
DERIVED FROM
 THE SQUARE,
  FASCINATED
   THE GREEKS
       PROPORTION
  b




   a               b        c
THE GOLDEN SECTION IS EXPRESSED AS:

           ab:bc = ac:ab
The Golden Proportion
The golden proportion can be found
  in many parts of the Parthenon
PROPORTION               a

    THE GOLDEN
        SECTION              b
     OCCURS IN
  SOME REGULAR
          SHAPES

                                 c

         ab:bc = bc:ac
PROPORTION
THE GOLDEN SECTION IS
  FOUND IN NATURE
  The spiral of the chambered nautilus
mimics the spiral created by joining golden
   rectangles with arcs drawn through
           the square portion
  The spiral of the chambered nautilus
mimics the spiral created by joining golden
   rectangles with arcs drawn through
           the square portion
                       PAGE PROPORTIONS
                   Mixing natural with mechanical


                                                     5.5"
We can design a page that fits                  4p
a classical proportion such as
the Golden Rectangle, or we
                                           4p                     4p
can build a text block of classi-
cal proportions on an industry
standard page. This example
uses half of a U.S. letter-size
page with a text block that                           25p
comes close to matching the
Golden Rectangle:                   8.5"
                                                            41p
        (41 ÷ 25 = 1.64).

We could adjust the bottom
margin to come even closer to
the ideal proportion, but it's
important to keep your page
dimensions simple.
                                                6p
                                                            PAGE PROPORTIONS
                                                        Mixing natural with mechanical


                                                                                                                   5.5"
                                                                                          4p
                    The Love Song of J. Alfred Prufrock                                               The Love Song of J. Alfred Prufrock

                                     By T.S. Eliot
                                                                             4p                                        By T.S. Eliot
                                                                                                                                                   4p

                       S’io credesse che mia risposta fosse                                              S’io credesse che mia risposta fosse
                       A persona che mai tornasse al mondo,                                              A persona che mai tornasse al mondo,
                       Questa fiamma staria senza piu scosse.                                            Questa fiamma staria senza piu scosse.
                       Ma perciocche giammai di questo fondo                                             Ma perciocche giammai di questo fondo
                       Non torno vivo alcun, sx’i’odo il vero,                                           Non torno vivo alcun, sx’i’odo il vero,
                       Senza tema d’infamia ti rispondo.                                                 Senza tema d’infamia ti rispondo.

Let us go then, you and I,                                                        Let us go then, you and I,           25p
When the evening is spread out against the sky                                    When the evening is spread out against the sky
Like a patient etherised upon a table;                                            Like a patient etherised upon a table;
Let us go, through certain half-deserted streets,
The muttering retreats                                                8.5"        Let us go, through certain half-deserted streets,
                                                                                  The muttering retreats
Of restless nights in one-night cheap hotels                                      Of restless nights in one-night cheap hotels
And sawdust restaurants with oyster-shells:
Streets that follow like a tedious argument
                                                                                  And sawdust restaurants with oyster-shells:
                                                                                  Streets that follow like a tedious argument               41p
Of insidious intent                                                               Of insidious intent
To lead you to an overwhelming question …                                         To lead you to an overwhelming question …
Oh, do not ask, “What is it?”                                                     Oh, do not ask, “What is it?”
Let us go and make our visit.                                                     Let us go and make our visit.

In the room the women come and go                                                 In the room the women come and go
Talking of Michelangelo.                                                          Talking of Michelangelo.

The yellow fog that rubs its back upon the window-panes,                          The yellow fog that rubs its back upon the window-panes,
The yellow smoke that rubs its muzzle on the window-panes                         The yellow smoke that rubs its muzzle on the window-panes
Licked its tongue into the corners of the evening,                                Licked its tongue into the corners of the evening,
Lingered upon the pools that stand in drains,                                     Lingered upon the pools that stand in drains,
Let fall upon its back the soot that falls from chimneys,                         Let fall upon its back the soot that falls from chimneys,
Slipped by the terrace, made a sudden leap,                                       Slipped by the terrace, made a sudden leap,
And seeing that it was a soft October night,                                      And seeing that it was a soft October night,
Curled once about the house, and fell asleep.                                     Curled once about the house, and fell asleep.
And indeed there will be time                                                     And indeed there will be time
For the yellow smoke that slides along the street,                                For the yellow smoke that slides along the street,

                                          1                                                                                 1
                                                                                          6p
 PAGE PROPORTIONS
       Musical




                    Major 4th 3:4
                                                            MAJOR SIXTH
Unison 1:1                                         Major 6th 3:5
                                                               3:5




                              MAJOR FIFTH
Major 3rd 4:5        Major 5th 2:3
                                 2:3




                                                   Octave 2:1
                                            Robert Bringhurst has outlined a
                                            set of page proportions based on
                                            the musical scale. It presents many
Minor 3rd 5:6                               interesting page shapes, but the
                     Minor 6th 5:8          page must fit the content.
                              PAGE PROPORTIONS
                                  Harmonics

                                                                         When
                                                                         pages of
                                                                         musical
                                                                         propor-
                                                                         tion are
                                                                         divided
                                                                         into two
                                                                         pages,
                                                                         they pro-
                                                                         duce “har-
                                                                         monics.”
Major 5th / Major 4th — 2:3 / 3:4    Major 3rd / Minor 6th — 4:5 / 5:6




 Minor 3rd / Major 6th — 5:6 / 3:5   Unison / Octave — 1:1 / 1:2

								
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