The Big Bad Wolf Tone

A wolf can be evident on any kind of bass of any size.  The worst one we have ever encountered at Quantum Bass Center, in fact, was on an entry-level German plywood.  The wolf tone was strobing so badly that we could not play even the open A string arco - the string skipped around and would not oscillate!  The culprit turned out to be its nylon tail wire - we swapped it out for a thin, stainless steel stranded cable, and the bass played normally.  
A lot of fractional (small-size) basses that have a terrible, cardboard-like tone are actually impacted by a really severe wolf.  The single more important thing to know about wolf tones is that HAVING ONE IS NOT A BAD THING.  Usually.  Unless it is so severe that it interferes with ordinary playing.  Virtually every fine double bass has a wolf.  In actual fact, HAVING NO WOLF IS MORE OF AN INDICATOR OF TROUBLE.  When we are presented with a bass that has very poor response, gray tone, and poor projection, we have most often discovered the bass is so out of adjustment that there is NO wolf tone, and on improving the adjustment, a bit of a wolf appears along with better tone and response.
In a large percentage of workshop basses on the market today, enclosure design (the size and shape of the bass body AKA sound cavity) is not based on the best physics.  These instruments are designed to be aesthetically attractive and economical to build - however, thanks to dealer competition, there is a large-scale disconnect between bassists and the workshops building their instruments.  Dealers are known to mask the actual source of the basses, so they can maintain priority access to workshops they prefer, and knowingly mis-label instruments with their store name and their own model numbers to evade MAP pricing.  This not only permits a majority flow of poorly-engineered basses to market, but disallows any responsibility for their design on the part of the dealer or the workshop.  Bassists are led to believe the workshops know what they are doing - and then if the basses don’t work properly, assume it’s because of their playing insufficiencies.  It's time to change all that, but today we are dealing with one bit of the fallout of this larger problem - unmitigated wolf tones.
What is a wolf tone?
It’s a phenomenon that occurs in the body of the bass when it’s being played, resulting in a wild oscillation on one given pitch (with 3/4 basses, most commonly A or B-flat).  Sometimes, the pitch drops out completely (strobing).  Though it’s been described in many ways, and is variously said to be the result of tension in the assembly of the instrument, faulty graduation, and numerous other causes, a wolf behaves like phase cancellation, and I believe we can study it the same way speaker cabinet engineers do (hence the topic of incomplete/insufficient engineering of workshop basses keeps resurfacing).  One of the misfortunes we bassists have to cope with is the deeply-rooted paradigm that a bass is a big violin.  Violins do, technically, have wolf tones, but they are rarely audible enough to be a problem - so why should a bass wolf be a problem?  Our gargantuan, hairy wolf tones, resulting from the faulty engineering of basses being built as giant violins, are evidence that we have to treat them at the cause by methods unique to the bass.
Some factors affecting the wolf tone, in order of user-modifiable/typically accessible luthiery features:
Soundpost placement - this is the easiest change to make on a stringed instrument which will affect the wolf; however, the desired tone and response are often sacrificed in deference to controlling the wolf note.  Other, more systemic methods are preferable, and moving the sound post can then be minimized.
Your bow - yep.  It’s unfortunate, because it’s really hard to find a bow that plays the way you want it to, and it may place you in the position of having to modify your bass or live with an exacerbated wolf.  Using a different bow will probably not completely eliminate a wolf, but it will affect it.
Your bow hair - I am not making this up.  Your bow hair constantly creates overtones from the string.  At some phases of the natural aging and wear of your bow hair, it interacts with the string in such a way as to make the wolf more prominent.  You can sometimes control this by using more rosin, less rosin, or different rosin.  Your bow sometimes tunes to a discernable pitch when you tighten the hair, and sometimes that pitch excites the wolf.  If your bow was just rehaired with a different color hair and you suddenly notice a wolf, yep, that was the bow hair.  It will change as the hair plays in.
Afterlength tuning - this is often the most effective solution, and frequently benefits the tone of the instrument as well.  For most basses, I currently like the afterlength to be tuned to two octaves plus a fourth above the open string.  There are other tunings that work, and the tuning chosen should match the bass.  The afterlength most often will not tune on all four strings with a standard tailpiece, but hitting 2 or 3 in tune will mitigate most wolf tones.  A notable improvement in overall tone can be gained with a harp-shaped tailpiece properly matched to the bass and its string length.
Tail wire material - a rigid (solid) metal wire, instead of a cable, is frequently seen on mass-market basses, and is often a major cause of an unneccessary wolf tone.  The solid wire was traditionally used on some viol-type instruments, and suits the low-tension setup of gut strings.  IMHO a solid tail wire is not generally compatible with a modern, steel-string setup, and as a result, we see things such as fractional plywood basses having terrible tone and/or a wolf, which dramatically improves by changing the tail wire to a stranded cable.
Steel/metal end pin - around here, we are not only fans of wood endpins because of the angled-endpin setup.  A steel endpin vibrates like a tuning fork, and not necessarily on the pitch you want!  Who needs that?  One of the first and easiest things anyone can do to reduce an unwanted wolf is to pull the steel endpin, or at the very least, saw off the excess length that extends into the bass.  If you find, to your chagrin, that your bass has been fitted with one of those non-removable endpins, I can’t recommend more strongly having it replaced with a grownup’s endpin (or button if you don’t require an endpin).  The non-removable endpin does not offer a single benefit to the function of the double bass, and impertinently supposes the bassist lacks the sense to keep up with his own endpin.  It’s like putting a governor on your accelerator.  If you (like most bassists) don’t care for being bossed around by an aluminum tube, you will want that thing off there. OFF. OFF.  There are adjustable all-wood endpins, and carbon-fiber endpins are very easy to come by.  I don’t try to influence players to replace all the world’s steel end pins, but to customize them, at least, when there is a problem with a wolf.  Of course it begs the question of whether a different endpin would improve a bass that is not having problems.
Tailpiece mass (should be matched to the instrument).  Has a large effect on the wolf as well as the overall tone and response of the instrument.  Good makers take the time to match the tailpieces to their new basses, and good shops take the time to match/customize tailpieces even when setting up stock instruments!  No one type of tailpiece is a panacaea - some basses respond well to low-mass, plastic or all-wire tailpieces, but others need more mass.  Often, a bass with a thinner, more flexible top responds best to the stability offered by a more massive tailpiece.  This can be tested by clamping weights to the existing tailpiece while playing.
Bridge placement - a bridge that is as little as 2mm out of place can dramatically affect the wolf, as it changes the relationship between the bridge, the sound post, and the bass bar.  If the bridge is tilted toward the fingerboard (very common), it messes up the afterlength tuning.  Some basses are hyper-sensitive to bridge placement.
Open seam (evident if the wolf appears on multiple pitches, especially adjacent pitches).  Though the seam may not be buzzing, it is oscillating to some degree.  
Top crack - a crack in the top plate of your bass is likely to cause the appearance of a wolf.  This is an often-overlooked factor, because the player is much more likely to notice the crack than a change in the wolf note.  However, if you are searching and searching for the cause of a new wolf, there may be a top crack that is very hard to see and may not be buzzing.  A “mystery buzz” coinciding with the new appearance of a wolf tone is an indicator of a hairline top crack.  Around here, we use a stethoscope to locate mystery buzzes.
Sound post fit - either too loose or too tight, or a gap, can contribute to a wolf.
Training the wolf, or “playing it out”.  Once the bass is properly adjusted, spending several minutes a day training it is really the most organic way to control a wolf.  Start by playing the wolf note on its absolute worst spot, at full volume, close to the bridge, and letting it strobe as much as it wants to, for as long as you can stand it.  Alternate this with playing the wolf note pitch cleanly, without letting it strobe - this can be achieved with bow placement (usually very close to the fingerboard) and at a lower volume, as if you are showing the bass the “right” way to make this pitch.  I find it useful, with ordinary playing, not to allow the wolf note to strobe unless it’s undergoing its daily “training” procedure.  When you come across the wolf note while playing, back off and get the bass to play the note “right”.  Typically, improvement will be noticed in as little as three hours, though it can take as long as 6 months of daily “training” to get to a point where the wolf does not interfere with your comfort level of everyday playing.  I am not making this up.  If even electric guitars, with comparatively few parts and no resonance cavity, show well-documented improvement with playing, the bass will also do so.  
Doing nothing - the most common approach of professional players.  I am really not sure how the rumour started that a wolf tone indicates some kind of defect with the bass and must be stamped out.  Maybe just the fact that wolf eliminators are on the market as a product implies it’s something players have to have.  We sell about 5 of them a year, virtually all of them mail-order to locations where a good bass luthier is inaccessible.
Scordatura - tuning your E string down to a D is a big help, and one that modern players can often live with on a long-term basis.  So is not tuning to A=440 (helps the wolf, but not your ensemble playing), or other scordature such as fifths tuning.  These are very subjective choices, but from a physics standpoint, EADG tuning is not perfectly compatible with the ‘traditional’ range of sizes and shapes in which we find many modern workshop basses.
Get a C extension - similarly, the scordatura of the low string offsets most of the problems caused by a wolf, and is pretty compatible with the top 3 strings remaining at ADG.  For most modern playing, the solution of adding a C extension is as good as it gets.
Using appliances (“Wolf elminators/modulators”) -
The use of appliances to control a wolf can be effective, although I emphasize they should be a last resort, after the bass is thoroughly and knowledgeably adjusted, and in the unlikely event the wolf is still so prominent as to interfere with ordinary playing.  The most familiar, of course, is the brass weight affixed to the afterlength.  The important thing to know about these weights is they work because they are mutes.  Who really wants less A string sound?  And, the important thing to know about USING the brass-weight wolf eliminator is that it affects the training of the bass, so it can be temporary!  If you resort to this type of appliance, try taking it off after 3 months.  Chances are, your wolf will be greatly reduced.  Although the weights are sold up to 22 grams or so, I find no advantage in using one this heavy.  We don’t stock them above 18 grams, since after having adjusted several hundred basses for wolf mitigation, we find that if it takes more than an 16-gram wolf eliminator to control the wolf, it indicates the bass is out of adjustment.  Choose the bare minimum weight that will reduce the wolf to a level that is tolerable to you.

Case in point: we had a customer who had mail-ordered a bass, and came in with 3 wolf eliminators on the strings, in different weights.  After placing the first one, he noted a wolf on a different note, and so on.  He was still hearing a wolf, and like many new players, thought it was essential to have no detectable wolf on the bass.  The first thing we did was take off all three weights so we could hear what was going on, and the player noted the wolf was hardly worse.  He’d had them on there so long the wolf was largely trained out.  Then we changed the tailwire to tune the afterlength, and the wolf was mitigated down to such a low level the customer was satisfied.  Adding one wolf eliminator, when the afterlength was incorrect, simply moved the problem to another pitch, much like squeezing a balloon just causes it to bulge in a different place.  
Other appliances that are less invasive include adding mass to the hollow behind the fingerboard, to the hollow behind the tailpiece (if changing the tailpiece is not practical), or to a location on the top plate of the bass.  Generally, a contact point that dramatically decreases a wolf, without interfering with the response of the bass, can be located on the bass side of the top about 6 inches below the southernmost point of the FF hole.  Fine bass shops can make a custom wolf eliminator that they glue to the inside of the top, and done.  I would recommend this for an older bass that is thoroughly played-in, yet still has a wolf that interferes with regular playing, and it’s unadvised to alter the original maker’s work by regraduating.
Luthiery that can affect the wolf
The carving of your bass is, to a large degree, both the problem and its solution.  Having regraduating or other carving done for the sole purpose of controlling a wolf tone is not indicated, since the wolf is a symptom of an imbalance, and not the cause.  However, it’s always worth the discussion with your high-level bass luthier, and keep in mind that if at any time you have the top off your bass for another repair, you can ask for the graduation and the bass bar to be checked and modified if indicated.  The work should be contracted from a luthier experienced in this task, since it is possible to cause a host of problems, the least of which would be a more annoying wolf. Thanks to the neverending supply of horrible school basses being repaired here at Quantum Bass Center, on which we have the opportunity to conduct unholy experiments, we find that if, at the very least, the top plate has a discernible tap tone, not too muddy, and the bass bar is not oversized, the bass will have a full tone and minimal wolf.  It’s kind of horrifying, the huge majority of workshop instruments that don’t even have this modicum of graduation.  If you are in possession of an ordinary workshop bass (that is to say, it has a brand name), there is minimal risk in having judicious regraduating done.
Substantial benefits can be gained from, similarly, expert balancing of the mass of the neck/scroll assembly and the back of the free end of the fingerboard.  Time constraints around here, so far, have kept us from really getting into this, but there are a few luthiers knowledgable in it.  Something that is unlikely to be undertaken for the sole purpose of controlling a wolf, but worthwhile to explore when large-scale improvements are being sought for an instrument, and is likely to result in an improvement of the wolf as a side benefit.  There is a good deal of research on it here: http://www.catgutacoustical.org/research/articles/modetune/
How can a wolf affect your playing life?
Though mostly a complaint of arco players, a wolf is a wolf and does affect the bass even when played pizzicato.  If you find your bass has notes that are inexplicably hard to hit in tune or that have no sustain played pizz, chances are it’s the wolf.  And, even if the wolf is not bothering you, checking for a wolf with the bow when having the bass adjusted for tone will be beneficial.  Normally, an apt bass luthier will start checking a bass by playing pizz, and may remark right away that you have a wolf or an open seam (if there are 2 or more wolves).
There is one important effect on your bass of which you should be aware.  This might sound a little obscure, but the wolf can cause fingered notes to buzz as if there were a defect in your fingerboard.  I am not making this up!  If you have a problem with buzzing notes, particularly on the G string, and 1) this is on a fingerboard you KNOW to be dressed by a thoroughly knowledgeable bass luthier, so it was properly shaped to begin with, and 2) you are considering having the fingerboard planed because of the buzz, make sure you have the bass adjusted to mitigate the wolf first.  Here’s why - if the fingerboard buzz is caused by the wolf, no amount of scoop planed into the fingerboard will eliminate the buzz.  An unknowing luthier could take off so much ebony as to destroy the fingerboard, and it will not change the buzz one bit.  The primary location where a wolf/fingerboard buzz will present is on the wolf note.  You can test this by playing the pitch of the wolf note pizzicato, at a conservative volume, on the G string.  It will buzz even when played quietly.  It will usually be evident above the octave (not in first position).  Play the buzzing note while simultaneously holding down the note one octave below, and chances are, the buzz will be reduced or eliminated.  If so, it’s definitely a wolf and not your fingerboard.  It can also appear on the dominant or sub-dominant of the wolf note.  Say for example your wolf is on G# - if your fingerboard is buzzing on the G string, it will likely be around D#, less frequently on C#.  The buzz can extend to about a whole step on either side of its epicenter - though it may be worst on the C#, for example, it may also buzz on all notes between B and D#.  When the wolf is mitigated, the buzzing area will shrink to its central pitch, or disappear entirely.  
One wolf that will affect your playing life
The pitch of the wolf note is inherent - meaning it will stay on the same pitch whether or not the bass is in tune.  One thing we can observe changes the wolf’s pitch is the string length.  From a modern bassist’s standpoint, one wolf that can interfere with ordinary playing in a particularly annoying fashion is G natural.  Holy hell.  Just try to start the Beethoven V scherzo cleanly if you have a wolf on your open G.  Apart from the challenge of the opening pp low G, it requires heroic measures and a vise-grip left hand to land on the first dotted half note G without it being flat, in the best of circumstances.  With a G wolf, it’s practically impossible to get the attack of that G to come out on pitch.  You can plant your finger in the precise location, but there is no controlling what part of the oscillation of the wolf will sound first, and it’s equally likely to be severely sharp, flat, or no sound at all - then jump in out of tune.  Having a wolf on that ONE note in that ONE passage has probably cost more than one otherwise qualified bassist an audition!
This theory is not proved, but I am coming to the conclusion that a G wolf indicates the string length is incompatible with the size of the body cavity.  A G wolf is particularly unresponsive to most measures to dislodge it, though changes to the string length have been known to get rid of it!  If you are having a neck reset or neck graft done to your bass, remember to mention to your luthier whether you have a wolf on G, and don’t be married to its current string length.  Changing it by as little as 3/8” can shift the wolf.  Anything but G!
Please feel free to comment here if you have any questions about wolf tones!