Creating harmony with proportions

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Desk detail, maker William Evans, Photo by Lie-Nielsen Toolworks

This is the first of many posts to come on this subject. Actually you could spend several lifetimes looking at how great designers achieved visual harmony. Anything included in a furniture design from the overall form down to the smallest carving, molding, or inlay has the potential to add layers of harmony. At its simplest harmony is pairing up two or more contrasting elements that are different, yet play off each other and somehow connect. We can’t talk about harmony without using music to illustrate. I’m not a musician so I’ll depend on those of you with more knowledge on this to keep me out of the tall grass. Harmony occurs in music when two different notes are struck and the frequency has some overlap that actually creates a third tone. Before we go too far into this it’s important to point out that for harmony to work the two elements have to be different enough that they are distinct, but close enough that they have the potential to connect. You don’t see someone playing a piano with arms totally outstretched to play at extreme opposite ends of the keyboard and you do not create harmony with one voice shouting and one voice whispering. Paired notes capable of achieving harmony are often not that far apart. Pythagoras is credited with discovering the connection between simple proportions and musical tones. A ratio of 1:2 being an octave, 2:3 being a fifth, 3:4 a fourth and so on. The ancients took this as another proof that the simple proportions they loved to use in their designs were somehow – I want to use the word natural. They very much believed that the same ratios that produced pleasing musical tones, produced a similar pleasing effect when composing a design in space. “The proportions of the voices are harmonies for the ears; those of the measurements are harmonies for the eyes. Such harmonies please very much without anyone knowing why” (Francesco Giorgi).You might easily conclude that simple whole number ratios were a product of simple tools; dividers, plumb bob, string, and simple geometry.

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 But for the ancients, they represented much more. Vitruvius, a first century Roman architect wrote extensively about how the proportions that make up the ideal human form can be expressed in simple whole number ratios. It’s thought Vitruvius was actually documenting a body of design knowledge stretching back many centuries before him.

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Vitruvian man by Leonardo, Accademia, Venice

 Again this was taken as another proof that these simple ratios connected with something deeper in our own selves. This has some strong implications for furniture design. To make it functional we need to size it to fit our bodies, i.e. comfortable height for a chair or table. To make it beautiful we can use the same proportions found in the human anatomy. If this sounds complicated with too many numbers, step back a minute. All you need for a calculator is your fingers. The simple ratios relied upon to create harmony in a design were 1:2, 2:3, 3:4, 3:5, 4:5, 3:7. These can be used to proportion linear elements like the relative heights of the different parts in a turning or they can be employed to size simple shapes like a rectangle with a height to length ratio of 3:5. In fact you could make a good case that this is a very un-mathematical approach as there are no calculations involved. Forms were roughed in using squares or simple rectangles and then elements within a form are sized using these simple ratios. Aside from the fact that they provide a palette of simple harmonic ratios to choose from, they are very user friendly. Much more on this to come.

George Walker

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About walkerg

Woodworker and writer
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9 Responses to Creating harmony with proportions

  1. Christopher says:

    George-

    Excellent, excellent information.

    I’m looking forward to future entries!

  2. Nathan Beal says:

    Thank you so much for taking the time to post these essays. This is the part of woodworking that gives me the largest struggle, and I am using the things I learn here to help me with my designing.

  3. Laurin Davis says:

    George, in regards to the statement
    harmony occurs in music when
    two different notes are struck
    and the frequency has some
    overlap that actually creates a
    third tone,

    what you are actually describing is ‘difference tones’. One often-cited example of difference tones is found in Ravel’s ‘Bolero’.

    Difference tones are also produced by certain combinations of organ pipes (although this is usually not done intentionally, as a composititional effect.)

    As you go on to suggest, harmony results from an awareness of the overtone, or harmonic, series– fundamental, octave, fifth, octave, third, fifth, etc. The relationship between the initial members of the overtone series to the fundamental can be expressed in relatively simple numeric ratios.

    Harmony based on fundamental tones and their overtones tends to work because from an acoustical perspective, the initial members of the overtone series resonate with the fundamental, rather than against it.

    In an analogous manner, design based on simple proportional ratios tends to succeed because the proportions of the design elements reinforce each other, and the overall design, rather than working against each other and the design.

  4. Jim Barry says:

    Just curious – given the differences in melody and harmony between Western and Asian music, is there also a difference in perception of what is perceived to be harmonious in furniture design across different cultures?

    • walkerg says:

      Jim,

      I’ve been asked that question many times in the past year. I have not explored this and am curious about it also. I’ve been told that Asian design also relied upon simple whole number proportions but I haven’t done any research myself. Can anyone enlighten us?

      George

  5. Torch02 says:

    One thing I think would be interesting to discuss is how these proportions work with negative space. Should intentional negative space follow these proportions or their compliments (1:2, 1:3, 1:4, 2:5, 1:5, 4:7)?

    • walkerg says:

      Torch02,

      You make a great point. I’m sure that these proportions would apply to positive and negative spaces. A carving is often more powerful if it’s next to an uncarved (negative) space. Haven’t explored this at length yet but your comment will spur me to dig deeper into this. Thanks for a great question.

      George

  6. Laurin Davis says:

    Jim,
    In regards to Chinese concepts of proportion for furniture and architecture, much of it seems to have been governed by a compendium called the ‘lu ban jing’.

    An individual craftsman or architect was expexcted to adhere to the precepts set down in the lu ban jing, but to also look for opportunities to put their personal stamp on the work being created.

    Feng shui also played in important role in terms of placement of a structure, placement of rooms within the structure, placement of furniture within rooms, and so on.

    • Jim Barry says:

      Laurin,

      Thanks for the pointer – I Googled the ‘lu ban jing’ and found some interesting reference materials on line.

      Just coincidentally, I am attending a Japanese joinery workshop this weekend at Red Rocks CC in Lakewood, Co, led by Mike Laine (http://www.woodenheart.us/) and will see what he has to offer.

      Jim

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