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.
Splines (@[email protected])
Classical #Intercolumniation is a complex topic with myriad rules that were developed after lots of experimentation by Greek as well as Roman architects. The primary purpose of #colonnades or multiple columns was both practical (to support heavy weight) and aesthetic ("imposing effect of high relief" as #Vitruvious wrote in https://www.gutenberg.org/files/20239/20239-h/20239-h.htm#Page_78). The architects paid keen attention to the thickness of columns as well as the spacing between them. They experimented with "columns close together, … with intercolumniations a little wider, … more open still, … and farther apart than they ought to be," until they settled on column spacing "with the intervals apportioned just right." With variable spacing came the need for adjusting thickness of shafts which had to be "enlarged in proportion to the increase of the distance between the columns," without which, "the column will look thin and mean, because the width of the intercolumniations is such that the air seems to eat away and diminish the thickness of such shafts." They also wanted to avoid proportions that would make the "shaft look swollen and ungraceful, because the intercolumniations are so close to each other and so narrow." So, it wasn't just the design of an individual column that was parameterized with the single parameter µ, first mentioned in https://pixelfed.social/p/Splines/790357912719769731 and further described in https://pixelfed.social/p/Splines/790417950261292263. Intercolumniation was also codified in terms of column width (effectively parameterized by µ). Beyond the appearance, there were practical considerations. While walls (which came before columns) were made of bricks, the dominant material for columns and entablatures were stone. As such, regardless of the width of individual columns, the gap could not be increased beyond certain limits, for the spans above the column could break. Materials such as timber for beams allowed more experimentation.

