Front View of a #Peripteral (#Sexastyle) #Colonnade with #IonicColumns arranged in #Eustyle #intercolumniation.

Ever since prehistoric architects at #Stonehenge designed rock columns and labored to lift the heavy rocks atop them, humanity has been fascinated with columns and entablatures, whether they were known by that name or not, and the designs have continued to evolve.

#Vitruvius described five classes of temples, designated as follows: "#pycnostyle, with the columns close together; #systyle, with the intercolumniations a little wider; #diastyle, more open still; #araeostyle, farther apart than they ought to be; #eustyle, with the intervals apportioned just right." So, what does it mean to have "intervals apportioned just right?"

Aside from the subjective aesthetic criteria mentioned in https://pixelfed.social/p/Splines/802974815166948953, such as avoiding columns that "look thin and mean" and shafts that "look swollen and ungraceful," there were practical considerations, such as the gap being too wide to support heavy stone entablatures.

There was also the practical matter with intercolumniation that was noo narrow. "When the [temple] matrons mount the steps for public prayer…, they cannot pass through [narrow] intercolumniations with their arms about one another, but must form single file; then again, the effect of the folding doors is thrust out of sight by the crowding of the columns, and likewise the statues are thrown into shadow; the narrow space interferes also with walks round the temple."

So, intercolumniations of 2 column diameters (4µ) or less, as in #pycnostyle and #systyle, were considered too narrow. Likewise 3 column diameters (6µ) or more, as in #diastyle and #araeostyle, were too wide. The consensus sweet spot was 2.25 diameters (4.5µ) between column shafts at the bottom (6.5µ axis-to-axis), except for the two middle columns where the spacing was 3 column diameters (8µ from axis-to-axis).

The image shows this variable intercolumniation.

Floor Plan of https://pixelfed.social/p/Splines/802974815166948953 showing #intercolumniation.

Greek architects classified temples and public buildings based on number of columns in front, number of columns in both front and rear, as well as interior columns.

The simplest buildings are those with walls on three sides, and partial walls called #antae (singular #antis) in front, flanked by just two columns.

Buildings with 2 columns in front are #distyle, 4 columns are #tetrastyle, 6 are #sexastyle, 8 #octastyle, 10 #decastyle, and those with 12 columns would be #dodecastyle.

The classifications are refined further. Those with 2 columns flanked by antae are called #inAntis. These never have any columns in the back or sides.

Tetrastyle buildings with 4 columns only in the front are #prostyle, and those with 4 columns in both front and back are #amphiProstyle.

Sexastyle buildings like those in the previous post are called #peripteral.

Octastyle buildings with densely arranged internal rows are called #dipteral, and when some internal columns are removed, the sparse structure is called #pseudoDipteral.

Decastyle buildings are also called #hypaethral. With 10 columns in front and rear, these are noteworthy for their width. In fact, they are so wide that they don't have a roof in the middle, which is open to the sky. Only the four sides have roofs supported by columns.

In addition to the number columns, there is a further classification based on #intercolumniation. #Vitruvius described five classes of temples, designated as follows: "#pycnostyle, with the columns close together; #systyle, with the intercolumniations a little wider; #diastyle, more open still; #araeostyle, farther apart than they ought to be; #eustyle, with the intervals apportioned just right."

The building in my previous post (shown without walls) has 6 columns in front and back — so, it is sexastyle. It is also known as a "Peripteral Eustyle," with column "intervals apportioned just right."

#Vitruvius defined the single parameter called #module or µ, which is the radius of a column at its base [https://pixelfed.social/p/Splines/790357912719769731].

#Vignola divided µ into 12 parts for the #Tuscan and #Doric orders, and into 18 parts for the #lonic, #Corinthian and #Composite orders. To make it easier to move between the orders, it is helpful to choose a value for µ that is a multiple of both 12 and 18. We could start with module µ = 36, which is the least common multiple of 12 and 18.

However, in classical design, it's a lot easier if minor grid lines are multiples of 8 (as in music 'octaves' and poetry 'octets'). So, I use a grid with minor grid marks at 8 and major grid marks at 32, which leads us to choose µ = 144 as that is the least common multiple of 12, 18, 8, and 32.

This value of µ = 144 is still abstract because we haven't chosen a physical unit like mm or inch, but it does not matter at this point. Once the model is constructed with the chosen value of µ, it can be scaled up or down in software to get the desired column width or order height in physical units.

The total height of columns for the same µ are in the ratio 7:8:9:10 for the #Tuscan, #Doric, #Ionic, and #Corinthian, with #Composite the same as Corinthian. When µ = 144, the diameter is 288. So the height of the Ionic column is 288*9 = 2592 units.

The #pedestal, #column, and #entablature are always in 4:12:3 ratio across all orders. So the height of the Ionic pedestal is 864 and height of the entablature is 648, and the total height of the order is 4104 units.

Remember that in the Ionic order, µ is divided into 18 "parts". So each part is 144/18 = 8 units. With this we can convert between µ and parts in either direction.

Total order height of 4104 units is then 4104/8 = 513 parts. If you are trained in computer science, you will grow despondent that it is 513, not 512. Let go, and everything will be all right.

The pedestal is the easiest component, and we start with that.

This is a sketch of the complete #IonicOrder, excluding #intercolumniation and #arches, which came later.

Different people have different abilities and different levels of mathematical knowledge. I make few assumptions about the minimum knowledge one must possess to follow my posts. At a minimum, one must understand ratio, proportion, similar, congruent triangles, Pythagoras, and basic properties of circles, including radius, diameter, circumference, tangents, secants, and chords.

No trigonometry or calculus is assumed, but people who have a knowledge of differentiable continuity, maxima, minima, and inflection points will have increased appreciation of the nuances of some designs featuring smooth curves and surfaces.

I start with first principles, even if it might be a little boring for people with advanced skills. The most basic requirement is that one must be able to mark points on a 3D grid, draw a straight line between two points, and draw a circle or arc from the center. The CAD tools should help with the rest, for example, to find a point of tangency, draw a circle through three arbitrary points, or tangential to three curves (if possible).

There are three components in the #Ionic order. Starting at the bottom is the #pedestal (which is optional), the #column, and the #entablature. Each of these three components has three subcomponents:
— Pedestal has #basement, #dado, and #cap.
— Column has #base, #shaft, and #capital.
— Entablature has #architrave, #frieze, and #cornice.

The pedestal, column, and entablature are always in 4:12:3 ratio. If all components are present, the total order height is divisible by 19. If there's no pedestal, the total height is divisible by 15.

The entire order is parameterized by a SINGLE parameter — the radius of the column at its base. #Vitruvius called the radius a "module" (µ) — an abstract unit of measure independent of physical units.

Components of Ionic column and entablature also have classic and modern variations.

I’m no DaVinci. #art #furry #procreate #vitruvianMan #vitruvius #werewolf

De vraag van Bruno Latour “waar kunnen we landen” beantwoorden we niet achter onze bureau daarom gaan we vanuit het programma #MooiNL #OpPadmet #Vitruvius in het voorjaar 2023. Volg ons op https://www.denationaleomgevingsvisie.nl/mooi+nl/default.aspx