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Nanette Hooker

Hexagons, Octagens And Dodecagons

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I have just been reading about the idea that the flight deck of the spaceship Liberator (Blakes 7) is based on hexagons.

 

Hexagons always make me think of concertinas, so I wondered why are standard concertinas hexagons? Also why was an octagen the chosen shape for Aeolas, and a dodecagon used for Edeophones? Any ideas?

 

Thoughts on the hexagon design of Liberator’s flight deck: http://www.geocities.com/ruthhelenkenyon/Libflight1.html

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I have heard it said that the hexagonal shape (and the radial reed layout) was chosen by Charles Wheatstone in order to produce an even pressure on the reeds. However, the science of that worries me (you cannot have uneven pressure in an enclosed space, surely), and would be disproved by the parallel reed layout of Jeffries and Jones. CW was too good a scientist to make elementary mistakes. I think myself CW just liked hexagons.

 

The later 8 and 12 sided designs had much more to do with marketing than anything else.

 

Chris

Edited by Chris Timson

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This is a subject that I have addressed in my soon-to-be-published paper for PICA, so I will quote from it here:

 

"With its radial internal design, the ideal shape for an English-style concertina is circular, but for practical purposes it tends towards that of a ‘squared circle’; while the traditional hexagon is the easiest to make, the octagon is better, and the dodecagon is nearest to the ideal, allowing longer-scale reeds to be used and for a larger volume of air to be contained in the bellows."

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"With its radial internal design, the ideal shape for an English-style concertina is circular,

Indeed so, but I would like to rephrase the question. Is a radial design superior to a non-radial design, and if so, why? Your point about bellows volume is well-made, but I can't see what other advantages a radial design would have. (You might just go for a bigger square box, like a Herrrington or an Accordiaphone).

 

Cheers,

 

Chris

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Hexagons always make me think of concertinas, so I wondered why are standard concertinas hexagons?  Also why was an octagen the chosen shape for Aeolas, and a dodecagon used for Edeophones?  Any ideas?

I think both myself and others have plenty of ideas. As far as I know, though, Wheatstone and his contemporaries left no record of why they chose those designs, so the rest of us can really only say why we think they are good... or not.

 

Stephen C. and Chris T. have already commented on the ideas of circularity and the radial reed layout, so I'd like to add some of my own ideas, with the caveat that they are based on my personal experience (including training as a physicist) but have not been rigorously tested by controlled laboratory experiments.

 

Regarding the desire "to produce an even pressure on the reeds", Chris says, "you cannot have uneven pressure in an enclosed space, surely." At equilibrium, that's true, but when air is flowing, it's not in equilibrium. Whether the differences in air flow with different geometries would be enough to significantly vary pressure in a concertina, I rather doubt, but I'm not sure. More relevant, and I think worth researching, is something I was told Geoff Crabb said (Geoff, can you tell us whether that's true?), that the position of the pad hole relative to the reed's orientation in the chamber is crucial. (Specifically, that the hole needs to be toward the base of the reed, not toward the tip, for the reed to sound properly.) If this is true, it suggests that there might be other significant geometric effects that are not well documented or understood. To what extent these might be affected by the grosser geometry -- circle vs. square, or radial vs. rectangular arrangement of reeds -- I don't know. Given the fact that both Wheatstone and Jeffries internal designs are quite successful, I rather doubt that there's any inherent difference in response.

 

BUT I belive I have noticed something else: It seems that on anglos with the rectangular reed arrangement, notes which are "identical" but on different buttons (e.g., the two push G's on a C/G) always seem to have slightly different tone qualities. Since I don't have a radially arranged anglo (e.g., a Linota), I don't know whether the same is true with them, but I suspect it's not. I would expect the acoustic coupling to the rest of the instrument to be more uniform with a radial reed arrangement in a more-or-less circular frame, and I think that might affect the uniformity of the sounds of the different reeds. (Similarly, one might expect greater uniformity of sound with a rectangular arrangement of reeds in a rectangular body, but see the following.)

 

So why radial-"circular", instead of rectangular-rectangular? Well, with the latter, one might expect the coupling to still be different for those reeds in the middle of a side, as opposed to those near a corner. But there are also structural reasons. A square or rectangle can be squashed, deformed into a non-square parallelogram, without changing the lengths of the sides. Other regular polygons cannot be squashed in that way, but aside from the triangle, I believe the hexagon is the regular polygon most resistant to deformation. It also has the advantage of being made of relatively few pieces, all identical. The triangle would beat the hexagon on this count, too, but it suffers from other issues, due to its projecting sharp corners. (Some people seem to consider the sharpness of the corners an issue with the square design, as well, but others consider it a non-issue. I do think that sharper bellows corners would be more prone to damage.)

 

So there you have it, a raft of rampant speculation from yours truly. As for the spaceship Liberator ("Aarh, matey, let's go 'liberate' another spaceship." :D), I suspect the designer/author/whatever just has a hexagon fetish. There are engineering purposes for which hexagons have advantages -- e.g., the strength and resistance to distortion and fracture of a hexagonal grid, -- but furniture construction doesn't seem to be one of them, or we'd see more of it in the stores. But I love the term "partly organic" (used on the page you linked to). Sort of like "partly pregnant"? :unsure:

 

Edited to correct a typo.

Edited by JimLucas

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Stephen C. and Chris T. have already commented on the ideas of circularity and the radial reed layout . . .

Actually, I was thinking not only of the radial reed pan, but also the radial arrangement of the levers. The English concertina is a very logical design, the radial arrangement of the reed pan makes it possible to fit more reeds, within a circle of a given size, than is possible with parallel chambers, and the radial arrangement of the levers makes it possible to come closer to the mechanical ideal where all the levers should be of the same length. Also, because the reeds play the same note on press or draw, and are more or less in order of note, it is possible to make the reed pan tapered, from deep in the bass to shallow at the top.

 

Given the fact that both Wheatstone and Jeffries internal designs are quite successful, I rather doubt that there's any inherent difference in response.

Though even Charlie Jeffries used the radial arrangement when he built English concertinas.

 

So why radial-"circular", instead of rectangular-rectangular?

radial-"circular" = Wheatstone's design (English)

 

rectangular-rectangular = Uhlig's design (German)

 

It all depends on which type of concertina you choose to play, but the radial design allows you to put more into a smaller space.

 

Even Wheatstone's built some square concertinas, no doubt to special order, around 1900, both the English shown below and their own system for the Paget Trio, but I would expect to find that they are still of radial design internally. (Anybody got one ?)

post-7-1095388577.jpg

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Most strange that no-one seems to have made a pentagonal concertina yet. I would have thought it a most suitable shape for anglos and duets?

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Most strange that no-one seems to have made a pentagonal concertina yet. I would have thought it a most suitable shape for anglos and duets?

Well, I don't know about 5 sides, but a Dipper Hayden duet has 10, presumably that would be twice as good!

 

Chris

 

haydp.jpg

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Most strange that no-one seems to have made a pentagonal concertina yet. I would have thought it a most suitable shape for anglos and duets?

How about this one?

post-7-1095429410.jpg

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Ah - and another double anglo.... I should probably stop cruising my oddities files.... I've gotta pack for the NESI!

post-7-1095429712.jpg

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Most strange that no-one seems to have made a pentagonal concertina yet. I would have thought it a most suitable shape for anglos and duets?

How about this one?

German makers have sometimes built pentagonal concertinas, but all of the examples I have seen (and the second of Richard's illustrations is of a concertina that I own, the third is one that he has) are deliberately made to resemble houses, with a pitched roof, and even down to having doors and windows.

 

However, the shape serves no useful purpose and is only a cosmetic variation on the square (or rectangular) German model. Indeed, German makers have built concertinas in some very imaginative shapes, like this very militaristic "Pickelhaube" (German helmet) one:

post-7-1095440197.jpg

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Is that a real concertina!

 

If so, the points would be excellent for sinking wraggle fingers sailing boat :lol: . Or indeed protecting your seat in a busy session during trips to the bar or toilet.

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Is that a real concertina!

It is indeed !

 

Both it, and the first of the three house-shaped ones (posted by Richard) were flights of the imagination of a maker called Raum, in Klingenthal. They are in the collection of the Musik- und Wintersportmuseum Klingenthal.

 

If so, the points would be excellent for sinking wraggle fingers sailing boat  :lol: .   Or indeed protecting your seat in a busy session during trips to the bar or toilet.

Well you certainly wouldn't try to pick it up & play it the wrong way around ! :(

 

Edited for typo.

Edited by Stephen Chambers

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Any attempt to supply answers to the various questions that arise concerning concertina design can become very complex as to the reasons why certain features were adopted. In the absence of any documentary evidence other than that contained in Patent original or improvement applications etc. or the resistance by some to accept family lore, one can only suggestion why the concertina appeared and evolved in its various forms. The true answers are usually very simple being based on costs, size, appearance, demand or the manufacturing abilities available at various times. I offer the following after almost a lifetime of close association with concertina manufacture as my understanding for some of the reasons and where possible the basis for that understanding. Many players concept of the instrument often does not go beyond the type that they are familiar with and because of this the differences and limitations of each type have to be considered.

At the risk of incurring the wrath of some I will say that Charles Wheatstone’s major contribution to the development of what is known as the ‘concertina’ is his ingenious design of the English system keyboard layout. Other ideas and the functional design and construction were carried out by other specialists engaged by him and later incorporated as the ‘& Co’ in the company title.

 

The hexagonal shape. I am sure that Charles Wheatstone and associates were fully aware of what their contemporaries on the European continent were doing to utilise the free reed in various instrument forms. When the decision was made to follow others and incorporate a bellows to provide the air movement through the reeds as a development to his earlier idea of the air-hungry Symphonium, the hexagonal shape was adopted primarily to provide some unique identity to the ‘new’ British instrument. I agree that the hexagon is a robust design and has *proved to be the best shape for the bellows as it resists collapse or distortion far better than any other shape, even square or rectangular but I believe that this was not necessarily a design consideration. It has been suggested that the nearest to ideal shape for the concertina both for reed accommodation and bellows volume is 12 sided. In theory yes, in practice no for ongoing structural (damage) and bellows (collapse) problems were and possibly still are common.

As suggested elsewhere the 8 and 12 sided were introduced as a marketing ploy and possibly this could be discussed at another time.

Lachenal did produce a few round ended instruments but these were fitted with 12 sided bellows. Not a success hence the rarity.

*Based on statistics of bellows repairs/replacements carried out at the Crabb workshops over a considerable period.

 

Radial reed layout. I do not also believe that the hexagonal shape originally contributed to radial reed layout. The first Wheatstone instruments that we commonly recognise as practical concertinas had only 24 keys, 12 each side arranged in the English layout and the notes sounded only when the bellows were compressed i.e. they had one set of 24 reeds, 12 at each end. A feature of these instruments was the exposed action where the pallets (pads) were decorated with mother of pearl backing discs.(See Stephen C’s avatar). For visual appearance these were placed symmetrically around the edge of the ends of the instrument and consequently the pallet holes beneath the pads and the reeds had to be relatively located. It was obviously thought logical to arrange the reeds in a radial fashion as with only 12 reeds to accommodate at each end there was plenty of available space within.

As the instrument evolved i.e. a second set of reeds installed and a larger compass included etc. the radial practice was continued with the familiar tapered reeds, this being the only way of accommodating the number of reeds without an appreciable increase in overall size The 48 key instrument having 48 reeds, two per button, at each end in the space occupied by 12 in the original. It has been suggested that the reeds are arranged on a circle which in the original was true, in fact with the introduction of many more reeds, the arrangement had to be modified to an offset circle, to successfully accommodate the different lengths of reed. I am not sure of the date when machining (routing) of the reed slots to house the reeds was introduced but I think this was a lot earlier than generally accepted, however it is known that routing (pan) machines were developed that used circular templates or settings to accomplish the installation of the reeds. Further machines were developed later by the larger makers that included settings for radial Anglo and Duet installations and eventually to include arrangements for 8 and 12 sided models..

It has also been suggested that a radial and thus circular arrangement of the pallet holes allows nearly equal length levers. This can only be applied to the earliest English designs where the keyboards occupied central positions of each end. As the compass increased upwards and the keyboards grew the lever lengths became more unequal.

Sloped reed pans, where the chambers of the small reeds are of less height than those of larger reeds were introduced much later (???) most earlier instruments being non-sloped.

Parallel or Straight reed layout. I must correct popular belief. C Jeffries did not design the parallel reed layout nor indeed the Fretwork pattern commonly found on his own make Anglo concertinas . Both the reed layout and the fretwork pattern were in use by my great grandfather, John Crabb and others long before Jeffries became involved dealing, assembling supplied parts and eventually manufacturing his own instruments. To those who may not know many of the early Jeffries were made at the Crabb workshops and supplied to Charlie Jeffries for onward sale. They were made with no name or cartouche on the outside, Jeffries stamping his name on the outside usually between the keys. Internal Crabb marks/numbers were often erased before eventual sale.

With the introduction, low price and thus popularity among the masses of the German concertina to Britain it was not long before improved chromatic models with 26 Keys or 30 keys were produced by some of the smaller British makers. With the substantial saving in the number of reeds required to cover much the same range as an English Treble in the C/G Anglo, it was found that the reeds could be fitted comfortably and parallel at each ‘end ‘of a pan working with the grain making the fitting easier and faster when using a pan machine. The Crabb machine (circa 1860) that I have and still working, originally accepted circular templates for English system and settings for the Anglo parallel reed installations.

 

Pallet holes and reed positions. It is evident that experiments were carried out at some time to determine the ideal position of the pallet hole in relation to the reed tongue tip and it is a *fact that for response and a preferred tonal quality of the majority of reeds in a concertina, the pallet hole should be at or towards the heel end of the reed. Obviously with very high pitched, short reeds this is not possible but their tonal quality is such that it is generally found of little consequence. On the other hand lower pitched reeds i.e. those below the range of the English Tenor benefit from the pallet hole being beyond the heel, the reeds being installed further towards the opposite side of the reed pan with consequently longer chambers whilst retaining the pallet hole at the edge of the instrument. With regard to tonal quality, placing the pallet hole above the tip of a reed results in a very reedy sound, lacking any warmth or rounded tone. As an aside this was the practice with American Organ makers to produce the ‘Vox Jubilante’ stop. If possible it is worth studying the reed and stopwork of these organs to understand how these makers achieved the different stop tonal sounds.

*Examination of larger, later English and Duet concertinas will show how the lower pitched reeds are positioned in relation to their respective pallet holes.

It is not fully understood why the majority of reeds sound ‘better’ if they and their respective pallet holes are mounted close to the periphery of an instrument and it is accepted by most that in traditional parallel reeded concertinas having reeds mounted in chambers in the middle of the reed pan i.e. 46 key Anglos, Jeffries Duets etc. that these reeds do not respond or sound as those at the edges even with the pallet holes at the heel end. Unfortunately with the demand for manageable sized instruments or the stipulation of the customer there was no alternative to these arrangements.

 

Radial versus Parallel. There are obvious advantages and disadvantages to either method of reed layout, mainly for the maker and some are given below. It is impossible to say which is superior as there are too many variables to consider. Examples of Bass-Baritone English can be found that incorporate both, the lower longer reeds being parallel and the higher, radial Of course there are good and not so good examples of instruments using either method. In the better instruments refinements would be made to ensure best performance for the required use of the instrument.

Radial:

Advantages.

Offers the ability to arrange all reeds and pallet holes around the periphery of the instrument.

Allows the greatest number of reeds to be accommodated in the preferred space available.

The instrument can be smaller than an equivalent parallel reeded model.

Disadvantages.

Great care required when installing the reeds because of the lack of space.

Reed lengths limited.

Frequent splitting between the pallet holes in older instruments.

Generally greater time taken to make therefore more expensive.

 

Parallel:

Advantages

Relatively easy and quicker installation of the reeds.

Simpler pan requiring less work in processing.

Usually reeds of a preferred length can be installed.

Less expensive..

Very rare splitting between the pallet holes

Disadvantages.

Difficulty in installing all reeds and pallet holes to the periphery in instruments of range and size dictated by the customer.

Reeds mounted on the underside of the pan in the ‘corners’ may have different tonal qualities due to shielding of two adjacent bellows sides.

Careful selection of these reeds, in size, to ensure free full vibration of the tongues with no interference from the bellows when almost closed.

 

 

 

I think that will do for now.

 

 

Geoff

 

Edited to remove picture. Too Large File

Edited by Geoffrey Crabb

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As a manufacturing engineer in a previous life I found your post really interesting. Thank you for sharing your knowledge with us.

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I am sure that Charles Wheatstone and associates were fully aware of what their contemporaries on the European continent were doing to utilise the free reed in various instrument forms. . .

 

. . . I do not also believe that the hexagonal shape originally contributed to radial reed layout.

They were indeed, Wheatstone's were selling accordions by Demian (the inventor) several years before the first concertina (shown as my avatar) appeared. Wheatstone took the fingering system of his own Symphonion and applied it to Demian's Accordion, but I do think it very important that he chose to do so in a radial form, hence the instrument was made hexagonal.

 

The first Wheatstone instruments that we commonly recognise as practical concertinas had only 24 keys, 12 each side arranged in the English layout and the notes sounded only when the bellows were compressed i.e. they had one set of 24 reeds, 12 at each end. A feature of these instruments was the exposed action where the pallets (pads) were decorated with mother of pearl backing discs.(See Stephen C’s avatar).

I'm afraid that this is a common misconception. All the known open-pallet concertinas, like the Demian accordion on which they are based, have reeds both for both press and draw. Single-action instruments were only introduced later, initially in an attempt to build a less-expensive instrument.

 

I am not sure of the date when machining (routing) of the reed slots to house the reeds was introduced but I think this was a lot earlier than generally accepted . . .

That was introduced by Louis Lachenal (for Wheatstone's) in 1848, it is why they changed from square to round-ended reed frames.

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On 9/17/2004 at 10:01 AM, Richard Morse said:

Ah - and another double anglo.... I should probably stop cruising my oddities files.... I've gotta pack for the NESI!

post-7-1095429712.jpg

Double Anglo? I want one!! It looks like some thing I’d see when I’m having a Seizure

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