So-Called Harmonic Balance

[Michael Pearce]

In a previous post Randall Pleasant expressed the belief that so-called 'Harmonic Balance' is nothing more than 'Marketing Hype' and should be included in the 'Greatest Myths' article. I would like to take this opportunity to present a rebutal to this assertion.

I must respectfully disagree with the assessment that so-called 'Harmonic Balance' is nothing more than marketing hype. A brief explanation may be in order as to why I disagree- please bear with me if my terminology isn't spot-on. I am a researcher and sword-maker, not a physicist and am somewhat handicapped by the technical language that has evolved in the sword-making industry.

The theory of Harmonic Balance is very simple- when a sword strikes an object the sword vibrates in a wave. Every wave expressed by a solid object has Rotational Nodes where the wave reverses at either end of the object. On swords the rotational node on the blade is what is commonly referred to as the Center of Percussion. This was first recognized and described in modern times in Richard Burton's 'Book of the Sword.' Examination of antique swords has shown that overwhelmingly that the Node at the opposite end of the sword tends to be located where the sword is gripped by the strong-hand of the user. In practical terms this means that shock is not transmitted to the hand when striking with the sword. This location of the rotational nodes creates the effect that we now refer to as 'Harmonic Balance.' This has been observed in actual antiques by not merely myself but by researchers such as Peter Johnson, a well known and respected European researcher and recreator and Craig Johnson of Arms and Armor- also curator of the Oakeshott Collection. Other respected researchers/recreators such as Vince Evans have also noted this phenomonen. Harmonic Balance is independantly confirmed, demonstrable, repeatable and fully meets the standards of scientific proof.

This can be tested for quite simply- Grip the sword firmly with the unsheathed blade pointed straight up, then use your off-hand to strike the pommel firmly. You will observe a spot on the blade that vibrates markedly less than the rest of the blade- this is the 'Center of Percussion' or 'Sweet Spot.' If you feel a corresponding 'dead spot' of minimal vibration under your hand gripping the hilt then the sword is what we call 'Harmonically Balanced.'

I will agree with Mr.Pleasant on this score however- I no longer believe that swords that are 'Harmonically Balanced' cut better due to reduced loss of energy through vibration. He is quite correct that energy loss through vibration will generally be minimal and have little effect on observable cutting power in most cases. After continued study and observation I have come to believe that swords that cut better tend to be Harmonically Balanced (as defined here) rather than swords that are Harmonically Balanced tending to cut better. Generally speaking swords that are closely modelled on medieval swords tend to be Harmonically Balanced. Makers such as myself, Albion Armory, Peter Johnson, Vince Evans and others produce swords based on our observations about the design characteristics of antique swords and as a consequence we make swords that exhibit the characteristic we call Harmonic Balance- just as the antiques do.

The use of the term Harmonic Balance in marketing describes a real and important characteristic found in good quality reproductions and antiques alike. In the past it has been claimed that these swords cut better due to reduced energy loss from vibration- this was not 'hype' in the sense of deliberately misleading the customer but rather a mistake that proceeds from a false assumption. I am sure that with our continually evolving understanding of this phenomonen this will be corrected by makers- at least reputable makers of good character.

A final Note- the term Harmonic Balance is part of the lexicology of the sword-making and sword using culture- it has become a technical term widely used in the community via the internet. It is not the best term for this phenomonen but has become so widely distributed that attempts to employ more technically accurate terminology have been overwhelmed by inertia- however much I wish it otherwise we seem to be stuck with this imperfect terminology. I will say however that I didn't invent this terminology- it was already in use in the sword-making community when I became a sword-maker. It was passsed on to me in the early '90s by sword-maker Chuck Sweet, whom I believe had it from Ike Roe. Mr.Roe had observed these qualities in antiques but I cannot say with any certainty whether the terminology is one that he invented to describe an observed phenomonen or whether it was passed to him by some unknown person and subsequently verified by observation.

It will likely be evening before I am able to respond to any posts on this thread- please be patient!

[Stacy Clifford]

This can be tested for quite simply- Grip the sword firmly with the unsheathed blade pointed straight up, then use your off-hand to strike the pommel firmly. You will observe a spot on the blade that vibrates markedly less than the rest of the blade- this is the 'Center of Percussion' or 'Sweet Spot.' If you feel a corresponding 'dead spot' of minimal vibration under your hand gripping the hilt then the sword is what we call 'Harmonically Balanced.'

Going by the definition and experiment you described here, how would you expect a sword which was not "harmonically balanced" to behave when struck? Would there only be one point of minimal vibration, with the corresponding theoretical opposite point being out in space past the end of the sword somewhere? I'll be very interested to see George's comments on this and where this discussion leads, but I think you've at least given us a more respectable explanation of the term than we've seen elsewhere.

[Michael Pearce]

Thank you, Stacy! Typically in swords that are not 'Harmonically Balanced' the Node of Rotation near the base of the sword can be anywhere from just ahead of the guard to just ahead of the pommel- actually anywhere but under the strong hand. I suppose it is theoretically possible for the lower node to be below the pommel but I have never seen this in practice.

BTW- a correction from a reader- The COP was identified prior to Burton's book. The COP is identified in Capt. Settimo Del Frate's "Instructions for the fencing of the Sabre and Sword of Prof. Giuseppe Radaelli" of 1876

"The sabre is also divided in two centers, namely, the center of gravity and center of percussion. The center of gravity is the place on the blade where half the mass the weapon is on each side of the point. The center of percussion is the part of the blade which produces greater effect in the blow of the edge." Book I, Ch II, Sec 3.

Thanks to the contributer of this information!

[Jeffrey Hull]

I respect the arguements of both parties in this discussion.

Now, I have one simple, perhaps even simplistic thing to say, which may be construed as supportive of one party rather than the other.

However, this statement is meant simply to state something glaringly obvious to me, as I have had the experience of replacing the grip and/or modifying the hilting of 6 production swords (one of which I also shortened its blade) and 3 production daggers:

As long as you have a grip of solid hardwood, totally secured in place, and hilting well-secured to the blade and tang, so basically no gaps anywhere either seen or unseen, then I have found that a sword is noticeably adept for practice-cutting compared to those which lack such standards, and that any vibrations, harmonic or otherwise, become a non-issue, because any noticeable vibration becomes, frankly, non-existent. Why should I worry otherwise if the weapon proves to hold up well in practice thereafter?

I would observe that a tightly and strongly gripped & hilted sword tends to ring when its flat is struck by a dowel or whatever. What this means to me is that I filled all the gaps properly when reworking the thing -- or amazingly, that a modern sword-maker actually did so properly. What it means to others is for them to say.

You may even call my assertion simple-minded. Yet it stems from finding the *harmonic balance* issue somewhat wearisome -- though I admit it has significance to the sword-wielder. (And admittedly, I do not seem to weary of the seperate edge-to-edge parrying issue, so my apologies to those who feel passionately about vibrational considertions of weaponry.)

However, what I mean to express about swords and vibrations is that of what works -- which means correctly working/reworking a weapon so that said issue is neutralised altogether. Plain and simple.

[Michael Pearce]

Tightly fitted swords ring nicely- but I've handled a lot of repros that are tight but still transmit shock into the hand which is unpleasant and in swordsmanship these vibrations can cause momentary loss of control and a need to re-grip the blade- not a good thing! The most extreme example of bad 'harmonics' happened in a theatrical performance I witnessed years back. A fellow did a hard stop-block on the flat of the blade and the swords wooden handle literally burst apart in his hand. This sword was tight enough to ring, but other than that it was by no means a good sword- more of the 'beveled metal bar' variety of sword. As said, though- that is an extreme example that I have never seen duplicated. A lot goes into making a good sword and proper Node location is only one of many aspects to consider- If the sword doesn't have this quality in my opinion it's not a good sword regardless of whatever other qualities it possesses. This is just my opinion of course, and it needs a lot more than that to meet my definition of a good sword but this is the 'deal killer' for me. But then I'm a sword-design geek- what else would you expect? <img src="/forum/images/icons/grin.gif" alt="" /> Anyway I've stated my rebuttal, and I invite the reader to investigate this for his-or-her self and form your own opinion.

[Jaron Bernstein]

Hmmm....I tried the "hold it and hit the pommel" vibration test on my sempach after reading this thread. The handle didn't vibrate at all. The blade (more so in the strong than the weak) wobbled like crazy. What this means I leave to you guys to figure out.

[Michael Pearce]

Sounds like your Sempach meets the definition of 'Harmonically Balanced.' More and more swords are displaying this feature- in the last few years a lot of Paul Chen products as well as the more limited production or custom makers show this. What used to be the exception is becoming more and more the rule as makers like Hanwei Works get more authentic every year. At his point I'm going to 'bow out' of the conversation unless anyone directs something to me. I want to thank the ARMA forum members for your attention, open-mindedness and politeness in this discussion. Cheers, Tinker

[Brian Hunt]

Hi Micheal,

All things are subject in one degree to another to vibrational waves. Earthquakes are vibrational waves and the destruction they bring is the end result of vibrations on everything they touch, bridges have been torn apart when the vibrational waves created by wind have caused them to shake themselves apart, so I have no problem with the concept that a sword can be affected by a vibrational wave. The question I have, is do you think the concept of a harmonically balanced weapon is one the ancients strived for, or is it just a modern theory that is being used to describe something that is the by product of a properly balanced, well made fighting weapon? As you stated, people are trying to create swords that are a more authentic representation of those that we have that have survived the ravages of time. I cannot help but wonder if the result of a harmonically balanced blade, isn't actually created due to a better distal taper, the proper balance created by a properly weighted and sized pommel, etc. The reason to place a pommel on a sword is to balance the weapon, and the size of the pommel you use helps determine where the COP ends up on the blade, too heavy of a pommel, and IMHO you can actually move the COP off the blade to a theoretical location somewhere in front of the point. Also, the more weight, or less weight you add to the end of your blade will affect the vibrations that are generated throughout your sword. I have found that a properly balanced weapon that feels alive in the hand places the COP about right where I train to cut with a sword. I have made a couple of swords (I am an amature smith) and I never worried about such a thing as vibrational nodes, but when I checked the one sword I still own that I made, it appears to be harmoniclly balanced as you described it. I didn't try for such a thing, I just used a pommel that created a well balanced weapon. Also, I just returned from Ashokan sword 2005 and I never heard any of the smiths there discuss harmonic balance, that doesn't mean that some of them don't believe in this theory, but it wan't communicated as a neccessary concern in the creation of a sword starting from raw iron ore. Also, there are other swords out there aside from western swords that don't use a pommel at all, such as the Katana, Tulwar, saber, etc. Are swords that don't have a pommel harmonically balanced, and how? As such, I would ask for a basic concept of how you strive for a harmonically balanced blade in your own construction of a sword. Please understand, I am not being hostile to you or your position, I really am just curious.

thanks

Brian Hunt.
GFS

[Andrzej Rosa]

First, I'd like to say hello to everybody. It's my first post but incredibly good aricle I read at your website made me to register and maybe draw some attention to it. It is very on topic.

must respectfully disagree with the assessment that so-called 'Harmonic Balance' is nothing more than marketing hype.

It seems that you are right here, Mr Pearce. It seems to be simple lack of understanding of what center of percussion was. It has nothing to do with vibrations. It has a lot to do with oscilations. The knowledge about what it really is was obviously lost long time ago. But now we have chance to understand it again.

The theory of Harmonic Balance is very simple

And it is, sadly, very wrong too.

when a sword strikes an object the sword vibrates in a wave. Every wave expressed by a solid object has Rotational Nodes where the wave reverses at either end of the object. On swords the rotational node on the blade is what is commonly referred to as the Center of Percussion.

Amount of energy stored in vibration is negligible. Swords are very stiff objects so they can not vibrate much. They do not flex much in the plane of the impact so amount of energy that can be stored this way is very small when compared with the energy of impact. Center of Percussion is simply a center of impact (from old English) which resultes in pivot point around a grip of a sword. If we hit a target with a center of percussion there will be no force transfered to the grip. Sword will simply rotate around this point. It has nothing to do with vibrations. It has a lot to do with an oscilations of a pendullum.

This can be tested for quite simply- Grip the sword firmly with the unsheathed blade pointed straight up, then use your off-hand to strike the pommel firmly.

This can be tested quite simply. Hang a string with some weight at the end from a crossbar. Attach another string to the pommel. Wave your sword around and regulate the lenght of a string attached to a crossbar until a pendullum follows a blade. The point where an attached weight finally is located is in fact a center of percussion as it was understood in the old times. It can coincide with a vibrational node or it can be anywhere on, or even below the blade. In antique blades it is very uniformly located near the tip of the sword.

The only point of an article by George Turner I do not really support is his critique of a draw cuts and an effects of blade curvature, but I understand that it was regarding some specific techniques used "by some" and should not be treated as very general. Anyway, just this thing

Just remember that the 19th century arguments between the benefits of straight versus curved sabers (especially in regard to mounted combat) never got settled, which implies that neither side ever produced clear evidence of superior cutting.

vexes me a tiny bit. I mean that in countries which had good cavalry for centuries before aforementioned discussion, for example Poland or Hungary or Turkey or Tartars, there was never such a discussion. Cavalry used mostly sabers, with some exeptions which I find badly quoted time after time.

Still, it is the single best article about swords I ever read.

Best regards.

[Michael Pearce]

No worries, Brian, you don't sound hostile at all- and you've asked the $64 dollar question to boot. Did the ancients strive for this quality or is it a natural consequence of a properly balanced sword? Unfortunately it's a chicken-and-the-egg question- My belief is that it's a bit of both. HB is so common in antiques that the ancient smiths had to have produced designs that contained it deliberately. My guess is that after a couple thousand years sword-making tradition it simply never occurred to them that it was a good idea to make a sword without it. Why deliberately make a tool that it hurts to use?

For the other question- I have two tulwars dating to approx the mid 18th century. One has a more 'european' style of blade, the other is distinctly Persian. Different lengths, weight, balance etc. Both are harmonically balanced. I have had the honor to handle two different Katanas dated to prior to 1600- neither was 'tired.' Both were harmonically balanced. Most of the 19th century Katanas that I've handled aren't. Two Victorian Court swords that have passsed through my hands are HB. 19th Century military swords are a mixed bag- some are some aren't. The overwhelming majority of older eastern European sabers that I've handled are. I've handled Sudanese Kaskara of a wide variety of vintages and they all were. Similarly I've never handled an genuine and complete antique Scottish basket hilt that wasn't. Persian Shamshir are a mixed bag, but the older the sword the more likely it was to be harmonically balanced. Generally on swords from India the more elaborately decorated they are the LESS likely they seem to be to be HB! This concept seems to have been well known throughout the world- so much so that with some types of sword it's absense is the first thing after appearance that makes me look for signs that a sword is a forgery.

As for whether or not they thought about this characteristics in specific terms we'll probably never know. One can readily imagine a master Cutler trying out a Journyman's sword and Grunting, "Stings the hand- try again!" without ever particularly considering why it stings the hand- just knowing that it wasn't 'right.'

As for swords without pommels- I and some others have come to view the pommel less as a counter-weight than as a fine-tuning mechanism for several qualities of the sword, HB among them. A sword's over-all mass orginization seems to be responsible for correct Node Location. A pommel helps, but is not necessary. Profile, distal taper, the width, thickness and shape of the tang all contribute, as does the weight of the hilt.

Thank you for the excellent questions!

[Jeffrey Hull]

Well, my swords do not have exploding grips. Why? Because I use hardwood and proper materials to affix and fill the thing to the tang. And by the way, the swords I own are all hand-forged and meant for fighting -- most certainly not "beveled metal bars" like the apparently inferior theatrical abomination you described. I can actually cut things with them and they are still intact thereafter.

The quality of ringing is meant to convey that the hilting has quality craftsmanship in its attaching. Quality of grip-material one uses is another matter, and actually you were conveying an example of that seperate yet related issue. Why did I bring up ringing then? Because it actually matters and demonstarbly indicates correctly to the user some more meaningful information about correct consturction (and perhaps of quality of steel) than worries about *harmonic balance*.

Of course, wielders of the swords would not have to worry about any of that if sword-makers in general would stop messing around and make every aspect of the weapons properly.

Do I have to say it: If everything is done right, then proper vibration, harmonic balance, shocky-shock, whatever becomes, frankly, rather meaningless. None of that exists in a meaningful way to make any difference, good or bad, if the materials and craftsmanship are worthy. Ask Turner, Reinhardt, and others and so forth as they seem to corroborate.

Swords do not fail because they *harmonically disbalanced*, but because some maker did not do his damned job right.

[Michael Pearce]

Andrzej- Understand that I am not here to argue the merits of George's paper- I don't know enough math to do so competently regardless. The theory that we call Harmonic Balance can and has been demonstrated in the real world in actual use of swords, and the effects have been reproduced, verified in physical tests and manipulated with predictable results. It fits all of the observable facts and it works. If my description of the phenomonen uses incorrect wording or what have you, I remind you that I am not a scientist- I am a sword-maker and an empirisist. I am quite confident in the correctness of my conclusions simply because it works and is demonstrated to work in the real world- but I always bear in mind that my knowledge is incomplete and that some of my assumptions may be incorrect. Making and testing swords according to this theory has worked very well for the last 13 years and nearly a thousand swords- I'll not be easily persuaded that the base theory as I understand it is incorrect.

[Michael Pearce]

Jeffrey- I am sorry if I have angered you, and it was certainly not my intention to slight you or your work in any way. I did not imply or even mean to suggest that your swords were sharpened metal bars or similar atrocities. I've never seen or handled your work and have no basis to form an opinion about it- and in fact haven't formed any opinion about them.
I've made my rebuttal and said my piece- I'm going to stop following this thread and let it go before things heat up any more. If anyone has questions or comments feel free to email them to me at [email]tinkerpearce@hotmail.com.[/email]

[Andrzej Rosa]

Andrzej- Understand that I am not here to argue the merits of George's paper- I don't know enough math to do so competently regardless.

You do not need math to understand it. Really. It does not even contain any expicitly written mathematical equations. Any inteligent human being is able to understand it.

The theory that we call Harmonic Balance can and has been demonstrated in the real world in actual use of swords, and the effects have been reproduced, verified in physical tests and manipulated with predictable results. It fits all of the observable facts and it works.

The problem is, that this theory is based on wrong understanding what center of percussion, so valued by our ancestors, was all about. The meaning of words change, and now we obviously invented the theory which explains in details totaly meaningles features of swords. In contraty, what is important is still lacking. Sad story, IMO.

If my description of the phenomonen uses incorrect wording or what have you, I remind you that I am not a scientist- I am a sword-maker and an empirisist.

So, I gather, you should be vitaly interested in how make swords which handle like antiques? Then read this article. You understand it first, you will be first to make well handling swords. And repeatably, too,

I'll not be easily persuaded that the base theory as I understand it is incorrect.

So, I guess, some other swordmaker will eat the cake. <img src="/forum/images/icons/wink.gif" alt="" />

Best wishes.

[Mike Cartier]

Lets keep things scholarly here Mr Pearce has presented his argument well and without malice. Remember the internet amplifies any sort of percieved feelings in a post.

I think I speak for everyone here when i say thank you to Mr Pearce for this excellent explanation and discussion. I do not agree with his theories but never the less appreciate the thoughtfull instructive discussion.