Pedal Order

[JAllen]

Good day fellow harpists,
I was recently having a discussion with a fellow musician math nerd about probability when I noticed a random correlation between the method we were using to map the different flavors of ice cream in a milkshake and pedal charts.
I pointed this out to my friend and we spent about a half a minute amusing ourselves over this before moving back to optimizing ice cream consumption.

One of the questions that arose from this discussion is why the order of pedals. We all know our pedal order to be DCB EFGA, but who arbitrarily picked that and why?
I have guestimated that it has something to do with the physical construction of the mechanism or order of sharps and flats. However, after spending my morning looking at diagrams of harp construction I see no reason on why someone might decide to put the pedals in ABC DEFG order.
The best reasoning I have so far come up with is that a recognizable pattern is created in the feet when exploring the flat side of the circle of fifths/fourths. Start inside alternating with left foot right foot on B and E; then farthest pedals, A and D, but here you must switch to a left foot right foot pattern(!); and then move inward continuing on the new left foot to right foot alternating pattern. The inverse would give you the pattern for sharps… But any arbitrary pattern for seven pedals would become memorized after several years of playing.

So, does anybody know why it is DCB EFGA?
And, while we’re at it; why four on the right and three on the left? I would say because a large number of the population is right handed and by pulling back the harp on the right shoulder at an angle limits the space for pedals on the left side of the harp…. But once again, does anybody know.

Best,
~Jenna

P.S./O.T. Does anyone know the order of pedals on a left handed harp. I have only ever seen one but was unable to dink around on it to find out. Cheers!

[catherine-rogers]

Yes, it has to do with the circle of fifths, and which pedals are most often needed and in which combinations, and keeping a symmetrical movement pattern as far as possible. As to why there are four on the right and three on the left instead of the reverse, probably a harp tech who also knows lots of instrument history like Carl would be the best person to answer that, assuming it wasn’t an arbitrary choice. With seven pedals, it can’t come out even on both sides. Even when there was an eighth “swell” pedal, it was in the middle.

[Tacye]

It is a simple circle of 5ths starting in Bb major. Which makes sense to me for a single action harp of 300 years ago, perhaps not where the circle would be started devising the instrument from scratch today.

[paul-knoke]

The pedals are arranged to allow modulation by a whole step. The most common modulations in music are between relative major and minor, by a 4th, and by a 5th, all of which require the move of just one pedal. To modulate by a whole step, another relatively common modulation, two pedals must be moved. The standard distribution of pedals allows the two pedals to mostly be in pairs on opposite sides of the harp, so both feet can be used simultaneously. For example, to get from the key of Bb to C, the B and E pedals are moved. To get from C to D, the C and F pedals are moved.

[JAllen]

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…

—

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.

—

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

[Tacye]

I think you could clean your thoughts up a lot if you took into account that when the pedal order was devised the pedals had only two positions, not three. You either had flat and natural, or natural and sharp. Most commonly the single action harp was tuned in Eb major, like fully levered harps today, but other tuning were possible and known including Ab or Bb (again like lever harps today).

The earliest reference I can find to a pedal harp in a very brief look is 1697 with Hochbrocker constructing a 5 pedal harp – my secondary source says tuned in F with pedals for BbFCGD. Your logic could give bcd to one foot and f and g to the other which I find worth noting. Adding the other two pedals they could either be tacked onto that pattern, or if I surmise the first 7 pedal harp may have been intended to be tuned in Bb (choosing a key is a balancing act between flexibility of keys and accidentals and a preference for playing open strings) running your pattern on the circle of 5ths EbBbFCGDA and the pedal order drops out immediately, simply alternating feet and centre out.

[JAllen]

Hmmm. Some tidbits here of harp history I don’t know… Thank you.
I think it is interesting to point out the tuning… I will look into this some more.

You are correct with the 5 pedal harp. My logic, for all practical purposes, collapses.
Something interesting I discovered while researching the Hochbrucker harp is that the order for the 7 pedal version was BCDEFGA as to keep the pedal rods from crossing.
I link the article http://www.beatwolf.ch/Portals/14/pdf/Report_Hochbrucker_EN.pdf
For any interested persons.

In regards to using the circle of 5ths as reasoning behind the pedals. This has always bothered me since simply changing modes would shift your pattern. This is why I continually look to the order of sharps/flats. However, it is definitely worth noting that the order does drop out running the alternating pattern on the Ionian mode starting at Eb moving around in fifths…

[balfour-knight]

Well, I probably should not post my opinion on the order of the pedals, but here goes, for what it is worth!

Please take a good look at the strings of your harp. It is obvious that from the red string, C, and up two notes, there is a group of three notes, C-D-E. Now look at the black (or blue) string, F. Here is another group, this time four notes, F-G-A-B. Why are the pedals not in this obvious order?????? C-D-E for the left foot, then F-G-A-B for the right foot just makes sense, like the levers on a lever harp. Even the Dilling harp uses this sensible order for the “ditals” or combination levers which affect all the notes of one pitch, like on a pedal harp!

Imagine this pedal order, since the harp is a diatonic instrument which is based on the Key of C. The order of the sharps ascending would be F-C-G-D-A-E-B. Right foot on F, left foot on C, right foot on G, left foot on D, and so on, back and forth, ending with the right foot on B. The order of the flats is the exact reverse of this! Wouldn’t this be convenient and make so much more sense than the order we have to work with? Also, to modulate a step, as has been suggested, this alternation of the feet would be very nice! Diminished chords could be made up instantly just by looking at the strings and pedals, without having to transpose into the pedal order that is standard now.

I have played the pedal and lever harps for years professionally. But if I could have had this nice C order of the pedals, life would have been so much sweeter! I also play by ear, in addition to having a Masters degree in music, think in C, before thinking in all the other keys, and it just makes sense, like on the lever harp, to have the C order for the pedals. I even believe I am beginning to prefer the lever harp over the pedal harp now that I have my new FH 36S from Dusty Strings!

Wishing all of you a wonderful holiday season,
Balfour

[Deette Bunn]

Interestingly, I read the original question just before I started to do a 6 week run of Peter Pan, which I have played twice before. I would swear that the original scoring and key signatures were chosen with the harp clearly in mind and everything fits nicely, the pedaling is organized, and the glissandos take advantage of all the enharmonics available. BUT, it was also written for a woman cast as Peter Pan. This production decided to cast a young man. . .and all of the songs Peter sings have been transposed and then shift back to the original key when someone joins him. Consequently, all the pedaling, instead of being in lovely pairs – one on each side of the harp – has now been shifted to one side of the harp, most of the enharmonic options have been eliminated, and perfectly demonstrates Paul Knoke’s excellent explanation of why the pedals are set up the way they are.

[JAllen]

Hey everyone.
Once again, thank you to all for your input and interest.

Balfour. I like your order! I agree, it would be awesome if pedals were in a nice easy CDEFGAB. That is even one of the orders I stumbled upon while overthinking my above post of mathematical permutations… It makes complete sense for all the reasons you give, plus it would be waaayyy easier to teach to students just starting on the pedal harp. The one issue I have with this order is that both feet must move left to right while moving around the circle of fifths, and right to left while moving around the circle of fourths. I prefer the more symmetrical approach as modulating is more similar to: middle pedals…Now, outside pedals… Okay, inside pedals….(or the inverse for order of flats) and the feet move in mirror as we modulate, instead of moving with the idea of, okay, now we are in the key of D and in order to get to E I need to move both feet to the right one pedal… I also think that might cause one to fell unbalanced while playing. I know I dislike resting on my B and A or D and E. Granted, that is a big assumption considering I’ve never tried that pedaling method and I’m sure with enough practice one could get used to almost anything.
In regards to the Dilling harp, the levers are designed in a manner that is perpendicular to the performer. Plus, all the levers can be easily manipulated by one hand (I am presuming that key changes are generally made with the right hand?). In this case I would believe that having the order of levers CDEFGAB makes sense as the levers are moving away from you. Plus they are closer together and you don’t have to worry about more than one limb (typically) attempting to change keys…

I agree completely with Deette Bunn’s and Paul Knoke’s explanations. (I hope the run of Peter Pan wasn’t too horrible transposed… I feel your pain). Making it so that modulations, especially via whole step, move across the feet so we have one pedal in each foot. Our current pattern fulfills this requirement. But so does DCE BFGA or CDE FBAG…

I spoke to my teacher about this and we looked at some prints from the Encyclopédie or Dictionnaire Raisonné des Sciences, des Arts et des Métiers that she has. You can check out an image some of the prints Here.
You can see that the pedals (shown from the bottom of the harp) are in our current order, DCB EFGA (notated in solfège). This means that our order has been standard since 1751.
I also stumbled across US patent 786275A from 1905 by Per Erik Ekman for the improvements on the harp. You can check it out Here.
From my brief skimming of diagrams I see no reason one could not make a harp with a different order… Halfway tempted to call up a harp manufacturer to see if it is possible…

Best,
Jenna

[Tacye]

Another interesting order to add to the consideration is this of an Egan Royal Portable harp -ABCD on the left and EFG on the right or AEBFCGD depending on how you look at it. (Makes much sense to me for being tuned in Eb)

http://keimages.ram.ac.uk/emuweb/php5/media.php?irn=22356
More images for this on here:
https://www.ram.ac.uk/museum/item/25404

The double action Egan Royal Portable has ditals which run FGAB on the left CDE on the right or FCGDAEB. This looks to me like an arrangement designed for Cb tuning.
http://webapps.fitzmuseum.cam.ac.uk/explorer/index.php?qu=egan&oid=77335

[Biagio]

Great thread for many reasons! Seemingly we have in the mix some purely historical reasons and some very logical ones, and the latter seemingly based on how the open strings are assumed to be tuned. Even more interesting to me, albeit a divergent topic lies the question of tradition – the music expected to be played and the techniques used.

The pedal harp has been dominant for most of the last century (some would say it still is) so it is logical that a good deal of recent “tradition” relates to this instrument: from how sharping devices are arranged to the way strings are named. With the recent renaissance of interest in so-called Celtic harps that has also led to some rethinking – contrast for example Balfour’s remarks on C tuning versus Tacye’s assumption of Eb for lever harps.

Wire players however often have no sharping blades and mostly tune to G, transposing if needed; and many have two paired Gs in the lower mid range. Paraguayans on the other hand often have an extra string in the octave tuned to Bb….

This is fun to consider – that the oldest stringed instrument is still evolving!

Biagio

[balfour-knight]

Hello, harp friends! I am reviving this “old” blog because it is very interesting to ponder over.

My continuing thoughts about the pedal order include wondering “what was the order of the five-pedal harp?” If one looks at the keyboard, the five sharps (or black-keys) are in the order C-D and F-G-A. It would make sense that this order was used for the five pedals on the harp. When the harp gained seven pedals, then it would make sense for the B to be placed before the C and the E to be placed before the F, giving the order B-C-D, E-F-G-A. Why then was the order reversed on the left side to give D-C-B?

I know that one works from the center outward, and that the half-steps come first (B to C and E to F). If one thinks this way, a better understanding of the current pedal order just makes sense. We all had to learn it that way, and we have to accept it in order to play the pedal harp.

Thanks for bearing with me once more, my friends! Hope all of you are having a great day and Fall season. It is perfectly gorgeous here in our North Carolina mountains!

Best wishes,
Balfour

[Biagio]

Gudd’ay friends,

Gosh, I cannot help mesel’ commenting here, with abject apologies to any I might offend. To whit: play the harp that is front of you.

If we all committed to only one style of harp where would be?

No offense but I personally consider the pedal harp to be an engineering abortion of extravagant cost when one can make beautiful music on a diatonically tuned wire harp.

Just kidding…On the other hand,one can’t play Debussy on a clarsach😂

Guess we are just stuck with the design; but I must say that open C tuning makes a deal of sense to me for both, if one wishes to play folk and concert music.

But heck, why not have several harps, suited to the music and venue?

Biagio

Hugs,

[balfour-knight]

So good to hear from you, Biagio! That C order on the wire harp makes the most sense to me, too, my friend. I enjoy my Dusty most of all, but, like you say, I can’t play the great French harp music on that harp!

I hope some of you can shed some light on the history and pedal order of the five-pedal harp before the seven pedals came into use. This is fascinating stuff, especially to an old almost-retired harpist who has time to wonder about all this, ha, ha!

Hope to see some of you at the Camac Festival in November–we can’t wait!

Best to all of you,
Balfour

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