Thank you for the responses!!

These have led me to the following explanation I have been pondering on all day. I post this for any other interested parties and because I am a bit of a math music nerd at heart.

I believe my following thought will corroborate with all the above explanations…

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We have 7 pedals (and the occasional 8th for swell) that we must place around the base of the harp. Assuming that most harps will not have a swell pedal we still have 7 pedals that we must distribute around the base of the harp. This means we have 7 Permute 7 ways of distributing the pedals. This is equal to 7 factorial which is another way of writing 5040. That is a lot of possibilities.

How might we narrow this down?

It makes sense to separate the pedals into two different sets since human beings have two separate feet. Therefore, let us split 7 as evenly as possible into 2 sets: 3 and 4. But which pedals should we assign to which set?

Let us assume that the set of three shall be handled primarily by the left foot and the set of four will be handled primarily by the right foot. This is presumably because most harps will be constructed to be pulled back to the right shoulder resulting in a (slight!) angling of the harp meaning that there is less room for pedals on the left side of the harp. We will then assume to leave a gap between the two sets of pedals for a swell pedal which is out of the way and easy for both feet to reach.

Now, it would make sense to separate out the pedals as symmetrically by some sort of order. That way our harpists will not be required to play primarily with one foot. This is where the circle of fifths/fourths comes in. The circle is built, no matter what mode, with the order of flats being BEADGCF and the order of sharps being the opposite (FCGDAEB). Let us use the order of flats simply because the harp is tuned in all flats (C flat major). Separate out this order so that we have four pedals on the left and three on the right without favoring one foot over the other an you will get EDC on the left and BAGF (notice that I alternated the pedal distribution: B on right, E on left, A on right, etc. It you were to start on the left (B on left…) you would be forced to place two pedals in a row and get BAG on the left and EDCF on the right, note the CF together).

This cleans up our 5040 possibilities a lot! We know that EDC should be on the left, only 6 ways to arrange those pedals. And BAGF are the pedals we should place on the right, only 24 possibilities!

The total number of ways to combine the left and the right possibilities is 144! That is almost small enough to warrant listing them all out!

However, we can still yet define our sample to an even smaller set:

Assume that we still want the left foot and right foot to move in similar symmetric patterns as the instrument modulates through the circle. That means if the right foot pedals B and B is close to the center, then the next pedal, E should be (approximately) equidistant from the center.

There are only 12 ways to do this:

DCE BFGA

DCE BGAF

CED ABGF

CED FABG

DEC GBAF

DEC FGBA

EDC FGAB

EDC GABF

CDE BAGF

CDE FBAG

ECD AGBF

ECD FAGB

Now it would make sense to start the pattern close to the center, where the pedals are easiest to reach and rest your feet on…

That leaves us with DCE BFGA, DCE BGAF, CDE FBAG, and CDE FBAG

One pattern in particular stands out:

DCE BFGA Has the most consistent pattern (start inside then progress inward without having to double back) and the pedals are almost in order moving outward. If we were to swap the B and the E….

Voila! We have DCB EFGA, our symmetry is maintained, and while we may have sacrificed by placing two right foot pedals in a row, the pedals are in order as you move out from the center: BCD on the left and EFGA on the right.

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This is quite possibly a long, and even painful, method to come to the same conclusion but I feel like it has somewhat sound reasoning of why we use the current symmetric pattern over another…

Please let me know if you think this is in anyway interesting, helpful, amusing or completely overthought.

Best,

Jenna