Manipulating Tuning on Fretted Instruments in Real-Time

One of the most difficult things about playing a fretted instrument, especially in an ensemble, is tuning. Due to a variety of factors-- such as a relatively fixed scale length, fixed fret placement, and non-uniform metal-string inharmonicity--even a well-set up fretted instrument will always be, at best, only vaguely close to in-tune over its entire range with respect to twelve-tone equal temperament. Discrepancies of up to ± 4-10 cents are common even in the best of cases.

There are various systems and modifications, including the Earvana™ nut and the Buzz Feiten Tuning System™, which aim to get the guitar closer to the equal-tempered ideal. There are even guitars with bent frets aimed at correcting the problem. However, even if you found a guitar that would be 100% in equal-tempered tuning over the entire fretboard, there would still be times when you would want to pull certain notes one direction or another to tune them with the other instruments in the ensemble. Often when instrumentalists tune chords and ensemble passages, they will gravitate toward just, or resonance/overtone-based, tuning of the chords. In other words, especially with more harmonically complex chords and structures, even perfect equal temperament wouldn't quite get you there, in some situations.

Fortunately, there are many things a fretted instrumentalist can do to manipulate tuning in real-time. Good tuning is a part of good listening and good technique, and NOT exclusively a part of good setup/maintenance. In other words, tuning doesn't stop when you've finished twisting the pegs until all the green lights come on-- it is only beginning.

When tuning, as with most other aspects of musicality, the most important thing is to listen. If you learn to relish good tuning and to make tuning a priority, much of the rest will take care of itself. Good tuning, in a majority of musical situations, is so preferable to the alternative that the ear, and the hands, will find a way to make it a reality. However, there are a few things I consistently find myself doing, in almost every performance, to improve and enhance the tuning--and therefore the sound of the ensemble. I figured it would be worth it to touch on a few of those here.

To raise pitch:

There are, fortunately, many ways to raise pitch a few cents. I am ignoring the obvious ones-- like pulling back on a vibrato arm or twisting a tuning key-- in favor of the ones that are most useful in real-time performance.

• Bend the string slightly in either direction. This one is the most obvious, and also the most easily implemented. The fact that you can tune individual notes in chords this way is advantageous.
• Bend the neck slightly backward, as if to create a backbow in the neck. This works well on open strings and relatively well on entire chords. You can simply exert backward pressure with the fretting hand, or you can grab the headstock with the picking hand. Obviuously, you will want to be careful with this maneuver, but within reason it's safe for your instrument.
• Exert pressure on a string behind the bridge or nut with the picking hand. This one typically has few advantages over one of the methods listed above, but can be useful in certain circumstances or for a special effect. If one note in a chord needs to be raised by a fairly large amount, this can be a good choice to avoid collisions by simple bending.
• On an instrument with a floating vibrato, exert pressure on the bridge with the palm of the fretting hand. This one can sometimes be harder control. It could likely be mastered with practice.

To lower pitch:

While raising pitch is fairly easy, lowering pitch is quite another matter. I have found only two practical ways to lower pitch of a tone in real-time without use of the tuning keys or vibrato arm, which, in most cases, is impractical.

• Bend the neck slightly forward, as if to create an upbow in the neck. The same tips and cautions apply to this method as apply to its analog in the "to raise pitch" section above. Disadvantages, apart from possible strain on the instrument, include an inability to tune individual notes in a chord.
• Compress the sounding length of the string using a stiff backward motion of the fretting finger. To accomplish this maneuver, you are basically jamming your fretting finger into the fret in a motion that moves the finger toward the bridge of the instrument. Imagine that you are stretching the length of the string between your finger and the nut, and therefore slackening the string a bit between your finger and the bridge--which, of course, is exactly what you are doing. The object is to decrease tension on the sounding length of the string (i.e., the length between the fret depressed and the bridge) a little bit. Consequently, the more rigid the string material and the higher the tension on the string, the less you will be able to alter tuning in this manner. It works particularly well on nylon- or gut-stringed instruments, but can still be used to some effect on steel-string guitars and basses. On steel-string guitars, it tends to work more easily on the wound strings than on the plain strings. The greater the strength of the motion of the fretting finger toward the bridge, the more the sounding length of the string will be slackened, and the greater the drop in pitch. With practice, it can be perfected to allow the player to tune individual notes within chords.

So there are a few techniques to experiment with to help hone your real-time tuning and intonation. It bears repeating that intonation is not a one-time adjustment on an instrument, but is rather the art or practice of real-time tuning adjustment during the course of performance. A fretted instrument may not have the ease nor range of tuning manipulation that, say, a violin might-- but its tuning is equally far from the fixed nature of a keyboard instrument. A skilled guitarist or electric bassist can, with a bit of care and listening, create beautifully tuned unisons and harmonies with other soloists.

Progressive steps to DIY for musicians and recordists

If you use electronic gear in the making or recording of music, you will have to eventually deal with the realities of maintenance and repair. Depending on the amount (and type) of gear you own, this can quickly turn into an expensive proposition.

Vintage gear, while typically exceedingly well-made and durable, is old, and will need maintenance and the occasional repair. Exactly how much and how often depends, of course, on condition, age, and how well it has been treated over its life.

Modern gear, while typically new, often uses cheap components, boasts shoddy craftsmanship, and employs any number of modern production methods designed to make manufacturing expedient. Unfortunately, these modern construction techniques often compromise durability and repairability.

Some new gear, often referred to as "boutique" gear, will combine the old-style construction techniques (and, ideally, most of the component quality of the best vintage gear) with the newness of the modern gear. For these items, you will likely be set for awhile, provided you care for them. But for the rest of it, periodic maintenance and repair is inevitable.

You needn't be afraid of nor intimidated by the prospect of learning to work on this stuff yourself. Most solid-state gear can be worked on safely by following the most minimal and obvious of precautions (i.e. don't work on the item with it plugged in). Most tube gear requires a bit more care and caution, but a healthy respect for the levels of voltage and current present is what you need to keep you safe-- there is no need for fear.

I will outline here a few simple projects that will put you on your way to doing most simple-to-moderate repairs on your musical gear yourself, saving yourself time and lots of money while perhaps having a bit of fun in the process.

As with most things, having the proper tools will make your job infinitely easier and more enjoyable. The tools needed to have an easy time of music electronics projects are relatively inexpensive-- you can get going for around $100, maybe a little more, maybe a little less (depending on the soldering iron you choose and what you already have laying around). Here are some essentials:

• Good soldering iron with temperature control (Weller WES51 and Hakko 936 recommended for quality and cost-effectiveness). This will set you back about $75-90 if you shop around. The Circuit Specialists CSA-1A is supposedly a re-badged Hakko 936 available for less than $40 and represents a good, cost-effective option. Avoid inexpensive Radio Shack irons and the like. Trust me. This is the most important tool you will buy, and a cheap iron will make soldering effectively several times more difficult.
• Vacuum desoldering pump. About $5-15. I use one called a "Soldapullt."
• A few alligator-clip test leads. I've never needed more than 3-4 at a time. They usually come in a package of 5-10 for a few bucks
• Decent digital multimeter. Needs not be expensive-- $20-30 is fine. If you're going to get really serious, an expensive Fluke multimeter really is better. For just the occasional maintenance job, an inexpensive 15-range or better meter that reads at least 500VDC is more than adequate.
• a wooden or plastic chopstick or similar for probing around in a piece of gear for mechanical disturbances/cold solder joints. DO NOT use a pencil or anything with carbon or metal in/on it. Free, usually.
• Phillips and flat-headed screwdrivers of a few sizes (one each large/small is good). You probably already have these. Cordless electric screwdriver or electric drill is a godsend.
• Needle-nose pliers and wire cutters. You probably have these, too.

Optional but handy for various applications:

• Cordless electric drill. Handy for chucking screwdriver bits into to get chassis out in a hurry. Also essential for drilling holes in aluminum chassis for pedals or scratch-builds.
• Wire stripper. Just costs a few bucks at a hardware store, but will likely be one of your best purchases. Makes stripping wire easy and worry-free, and keeps you from the frustration of accidentally nicking wire in the process.
• A small 'parts drawer' with various values of caps and resistors. I bought a "parts assortment" of resistors for a few bucks that has saved me many trips to the store and many days waiting on mail order. It's also handy to have a few capacitors around.
• Component lead bender. Hoffman sells these. Basically it's a little piece of plastic that costs a couple bucks that helps you bend component leads neatly at right angles.
• Variac. This is a variable transformer that allows you to reduce the voltage coming out of the wall (and all voltages in the gear you are working on in proportion). Useful for firing up an amp with old caps and re-forming them. Can be expensive. I don't have one, but if you have a retired engineer dad with one in the basement, it certainly would be handy to snag it. Maybe grab that oscilloscope next to it, too, and also the signal generator-- both will come in handy as you get more experienced.

Now that we have the tools, what will we do with them?

First, start making some cables. Quality bulk cable and connectors can be ordered from Redco. Starting with single-conductor instrument cables is a good idea. Making cables will give you practice stripping delicate wire without damaging it or causing shorts, and will also give you good practice soldering. Before beginning, I suggest watching or reading one of many soldering tutorials available on the web.

Building cables is a fairly low-stakes game. There is nothing to shock you, and if you mess up stripping a wire or soldering, you can just cut an inch off the cable and start again. If it's a total loss, parts are inexpensive. If it's a success, you have built something immediately of use to you (the bulk cable and connectors sold by Redco are first-rate quality-- the cables you make will be superior to all but the most high-end boutique cables). If the single-conductor-shielded instrument cable is a success, try an XLR microphone cable next, which can be a bit more challenging. You may also wish to replace the speaker in a guitar amplifier.

With the skills learned from cable-making, try and tackle a simple fuzz, overdrive or boost pedal kit. I recommend the kits from build your own clone. They come with all parts and instructions, and they even offer a simple kit called the "Confidence Booster" for first-time builders. The Confidence Booster is free with the purchase of another kit! If you totally butcher the Confidence Booster, you can return your purchased kit and keep the mangled parts free of charge. Building effects pedals-- especially simple fuzz, boost, or overdrive pedals-- is fun and safe. You are dealing with low voltages and low currents, so there is zero chance of electrocution. None of the parts are that expensive individually, so if you fry a few things it usually won't set you back much. You will learn to be careful with soldering temperature, you will learn some peculiarities of circuit-board soldering, and you will deal with some planning and mechanical assembly. There will likely be some 'growing pains,' but the end result is usually very satisfying.

At this point, you may wish to work on a tube amplifier of some sort. Tube gear requires a brief and obligatory note about safety: Nearly all tube gear will have electrolytic capacitors capable of storing deadly amounts of power even with the gear off and unplugged. For this stuff, you need to learn to identify and discharge the caps (a very easy process that has been outlined countless times on the web-- It doesn't need repeating here). For starters, never work on a live (i.e. on and running) amp. If you do, you should keep one hand in your pocket at all times to keep from forming a path to ground across your heart. If you are inside a live amp, do not work barefoot on a concrete floor, do not wear any jewelry, have someone around to look on just in case, etc. This is mostly common-sense type stuff, and most of it doesn't come into play until the more sophisticated projects, but it bears repeating.

Start with the simple jobs. Since you have already located the electrolytic caps and discharged them, and since they often need replacing in older gear anyway for maintenance, you may want to start with a cap job. I recommend starting on an amplifier with discrete, as opposed to can-style multi-section capacitors. Amps with tag-board or point-to-point construction are infinitely easier to work on than amps with printed circuit board construction.

If your cap job or other simple maintenance is a success, try building a small kit-form guitar amplifier like a clone of a tweed Fender Champ. This will teach you a lot about what does what in tube audio gear, and will equip you with a lot of the knowledge necessary to diagnose and repair gear in the future. This project tends to be rather expensive, but the end result is often worth the expense.

The best advice for learning to maintain your own gear is to read a lot and get your hands dirty. I recommend downloading (for free) the NEETS manuals, or the Naval training series paid for by the U.S. Navy. Most of what you need to learn about electronics is spelled out in these modules.

There is also a lot of good advice on several internet fora dedicated to music electronics. Often, there are friendly and knowledgeable people on these sites that seem to enjoy walking a first-timer through a project and answering questions.

Working on stuff is fun, tweaking gear for maximum performance is musically satisfying, and you can save a pile of money working on your stuff. The information is out there and the tools are cheap, so go for it!

the time relationship between pitch and rhythm (and harmony and polyrhythm): Part II

If you haven't yet read Part I, I recommend glancing at it here before reading this installment.

In the previous episode, we talked about the relationship between rhythm and single tones, and how a series of impulses at regular intervals, when speeded up, would generate a tone.

But what about multiple tones? What is harmony? If we have simultaneously-occurring tones that sound consonant, why do they sound consonant? What is the mathematical relationship of their oscillating impulses? Finally, what would happen if we slowed these tones down to low-frequency oscillations of audible impulses-- what would the rhythms sound like?

Interestingly, there can be rhythmic harmony of varying density just as there can be tonal harmony of varying density. The essence of harmony and its density lies in low-prime mathematical ratios.

The first prime ratio of significance is the 2:1 ratio. In tonal harmony, this creates a simple perfect octave. For example, a tone of 880 Hz juxtaposed with a tone of 440 Hz creates a 2:1 ratio of vibrations resulting in the perfect consonance of two A naturals one octave apart. In rhythmic harmony, it creates a simple division of the pulse. For example, if a series of impulses at 120 beats per minute were identified as quarter notes, a second series at 240 bpm would be perceived as eighth notes-- a 2:1 ratio.

Where it begins to get more interesting--and harmonic--is with the next prime ratio of significance: the 3:2 ratio. Two tones with a vibrational ratio of 3:2 will produce a just-tuned perfect fifth. For example, one tone at 220Hz and another at 330Hz will produce an open fifth of A natural and E natural above. When slowed down and heard rhythmically, the 3:2 ratio gives us the very common "three-against-two" polyrhythm--typified by a triplet in duple time. The actual consonant ratio is best perceived when the "3" pulse and "2" pulse are occurring simultaneously, of course.

The basis of the Euro/Western conception of tonal harmony reaches its overtone-based limit with the next prime ratio of significance: the 5:4 ratio. Two tones with a vibrational ratio of 5:4 will produce a just-tuned major third, which incidentally is about 14 cents narrower than an equal-tempered major third. Two tones at 220Hz and 275Hz will produce A natural and C# above. When slowed down and heard rhythmically, it creates the slightly more elusive "five against four" polyrhythm, typified by squeezing 5 beats into the space normally occupied by four. Again, the rhythmically consonant ratio--much more complex this time--is most clearly perceived when the "5" pulse and "4" pulse occur simultaneously.

While certain non-western/European music, including much music of Asia, Africa, and the Americas (including the blues!) utilize higher ratios such as 7:6 and even beyond, the European 5-limit concept of tonal harmony from which modern equal temperament was derived is based strictly on 3:2 and 5:4 ratios reckoned in different directions to create the tones which have been approximated on the equal-tempered keyboard. For more reading on the subject, I highly recommend the book Harmonic Experience by W.A. Mathieu. For this reason, I'll focus here on the most common 3:2 and 5:4 ratios.

In the following examples, I have tuned two oscillators of the trusty Moog Model D to as close an approximation as is practical of just-tuned consonances. When tuning for just consonances, it is desirable to hear the higher tone 'lock' with the corresponding partial frequency (overtone) of the lower tone. The partial frequencies of the overtone series are generated themselves by low-prime ratios, and are the basis of harmony. For this reason, just consonances often possess a rich, otherwordly quality compared to the imperfect consonances created by the series of compromises that is equal-tempered tuning.

An important note: the Model D's one flaw for our purposes (though it is hardly a flaw in its character as a musical instrument!) is the fact that its three oscillators are imperfectly clocked not electronically synched with one another. What this means in real-world terms is that there might be some tuning drift which can result in phasing between the two oscillators. Interestingly, what manifests as a sweeping, oscillating comb-filtering effect when applied to harmonically related tones (not unlike a 'phaser' effect) manifests itself in rhythm as one oscillator "turning the beat around" on the other at regular intervals, or dropping a beat here and there. I have tried to work around this by selecting short enough audio examples that illustrate the polyrhythm without confusing dropped beats.

Example 1 illustrates 3:2. First, using a sawtooth wave on the 8' range, the oscillators are tuned nearly as possible to a just perfect fifth. I depress an "A" note, and you hear "A" and "E" sounding simultaneously. Then I switch to "Lo" range, and you will hear the 3-against-2 polyrhythm, if you listen carefully. When the two oscillators click nearly-simultaneously, that is "beat 1." Then you will hear the distinct "ONE (and) TWO AND THREE (and)" signature of the 3:2 polyrhythm.

Example 2 is a sweep of 3:2 from just below the audible range (fast enough to be rhythmically indistinguishable but still not tonal) well into the audible band (and back). For this, the keyboard is set up similarly to Example 2 from Part I.

Example 3 illustrates 5:4. Set up similarly to Example 1, we tune this time to a just major third. First on the 8' range, when I depress "A," you will hear A and C#. Then on "Lo" range, you will hear 5:4. Again, the 'flam' generated by the two oscillators sounding almost-simultaneously is "beat 1." 5:4 can be an elusive polyrhythm to hear in this context, but if you are familiar with its sound, you will be able to distinguish the particular character of this rhythmic consonance in this example.

Finally, Example 4 is a sweep of 5:4 from just below the audible range well into the audible band (and back).

So that's scratching the surface of that concept. Of course there is a lot more there if you want to dig for it. Electronic composers might enjoy creating pieces based on the ratios, where ratio-based rhythmic consonances speed up into tonal consonances, or slow down from consonances into rhythms. Some might want to explore the complex rhythms inherent in dissonances using electronic means of slowing down recorded intervals. Most importantly, it is just enlightening to know what makes the sounds we make relate to one another the way they do.

the time relationship between pitch and rhythm (and harmony and polyrhythm): Part I

Sometimes it is good to get back to basics. Sometimes it helps to pull the camera back, throw on the wide angle, and remember some of the really obvious things about musical sound-- such as:

• A tone is a rhythm happening really, really fast.
• A harmonic interval is a polyrhythm happening really, really fast.

But before we get to that, it pays to consider the question "What is a sound?"

Sound is, most literally, the rapid compression and rarefaction (de-compression) of air, which is perceived by tiny hairlike structures in our ears and decoded as sound by our brains. However, all sounds are not tones-- some are impulses and some are noise. A tone (with a definite pitch) results from an oscillation of impulses in a periodic manner. What is an "oscillation of impulses?" Anyone who has ever used an oscillating fan knows that an oscillation is a repeated movement back-and-forth at a constant speed. When air molecules compress and rarefy at a consistent interval in a regular pattern, an oscillation, or tone, is produced.

Because electronic music is all about creating electrical impulses that are analogous to (i.e. "electronically representative of") the air's compression and rarefaction, you can learn a lot about sound and vibration by playing around with a synthesizer. A good analog synthesizer can teach you a lot, particularly if it has multiple oscillators and an intuitive user interface. My favorite tool for this purpose is an old Moog Model D, as its knob-based interface makes sense to me.

On a synthesizer, an oscillator is a circuit designed to generate an AC voltage that swings positive, then negative at regular intervals to electronically represent air that compresses, then rarefies at regular intervals. This voltage can later be converted into actual vibrating air by a transducer, or speaker.

The Moog, like many analog synthesizers, has a few oscillators that can be set to oscillate in one of several ranges, including 5 audible ranges and one labeled "Lo." "Lo" is what is known as an LFO, or "low-frequency oscillator." This means it creates oscillations, or patterns of impulses, that if transduced into sound would be too slow for the ear to recognize as a tone. What do you get when you have a regular pattern of impulses too slow for the ear to recognize as a tone? You get a rhythm!

The slowest rate of oscillation that a human ear will recognize as a tone is approximately 20Hz, or 20 cycles per second. 20 or more impulses in one second, at regular intervals, creates a very low audible tone to most humans. Anything slower, and the typical ear will hear instead a series of successive impulses--A repetitive beat, in other words.

In synthesis, LFOs are typically used in conjunction with other circuits to create vibrato or other modulation effects (among others), and are not typically transduced into sound. However, if one has a synth like the Model D that allows patching of the LFO to the output, listening to what it sounds like can be pretty informative.

When a Model D oscillator is set to "Lo" and routed to the output, depressing a key causes a series of audible, electronically generated clicks, or impulses, that can be heard through the speaker. If keyboard control of the oscillator is turned on, then pressing a higher key causes the impulses to speed up in relation to one another. Depressing a lower key causes a slower series of impulses.

This basically creates a slow-motion movie of exactly what happens when when we use the synthesizer (or any other instrument) to create a tone, except that when we move up to a faster rate of oscillation, we get tones instead of rhythms. The faster-in-succession the impulses, the higher the pitch.

Particularly interesting is to explore the estuary between the audible and sub-sonic ranges of oscillation. For example, selecting the lowest audible range (labeled 32' on the Moog) and depressing the lowest key on the keyboard-- and then selecting "Lo" and depressing the highest key of the keyboard-- will start to give a picture of the transition between "series of impulses" and "tone." Utilizing the tuning and pitch-bend functions can start to give an even more complete picture.

In the following example, I have set the oscillator to a square-wave (which is essentially a binary "off-on" type of impulse, very good for demonstration purposes). I first depress a "low C." You will hear a series of impulses occurring at about 150 beats per minute. Then I move up in octaves, first with a C an octave higher on the keyboard, then another couple of octaves above that until I reach the top key of the keyboard. Each octave up causes the rate of clicks to double (say, from quarter notes to eighth notes, then sixteenths, etc). At this point you can almost begin to hear the impulses wanting to blur together into a tone. To go yet another octave above, we must move now to the 32' setting (signaled by a brief pause), at which point the tone becomes obvious and clear, but very low in pitch. In fact, it is so low in pitch that depending on your speakers, it may appear an octave higher than it actually is. This is because the square waveform contains a lot of harmonics and not all speakers can reproduce very low frequencies with any linearity. Finally, I go one additional octave above for good measure.

The region at which your personal ears begin to perceive tone as opposed to rhythmic pattern can be further narrowed down by utilizing the tuning function on the synth. Using the tuning adjustment and/or the pitch bend wheel, you can find the exact point at which your ear fails to hear the distinct impulses and begins to instead hear a tone.

For another example, I set the oscillator to 32' and turn the tuning and pitch bend controls all the way down. I then set the portamento ("glide") function to its maximum (slowest) setting. This allows me, by depressing the bottom and then top keys of the keyboard, to create a sweep that goes from the sub-sonic range well up into the audible band, and back down again. Notice as the rapid clicks morph into a rising tone. Pretty cool!

In Part II, we will explore harmonic relationships between tones and their relationships to polyrhythmic patterns of impulses.

The misleading story of the guitar amp RMS "watt"

One of the greatest misconceptions among users of guitar amps is the notion that the output power of the amp-- usually (mistakenly!) referred to as "wattage"-- is somehow directly correlated to the perceived loudness of the amplifier.

In reality, the amount of voltage and current across the speaker terminals is only one of several factors that help determine how loud the amp will sound to the listener.

Amplifier manufacturers usually market amplifiers with ratings in "RMS watts." RMS stands for "root mean square" and is a statistical measure to calculate the mean, or average, amount of voltage or current delivered into a given load. First of all, it should be pointed out that there is technically no such thing as an "RMS watt." RMS is a way to measure voltage or current, not power. But the notion of an "RMS watt" prevails somehow as the standard by which amplifiers' loudness capacities are judged.

However, eschewing semantics for a moment, one might wonder: Why isn't an amp's power rating the best means of mentally estimating its capability to be loud? And what other factors should I consider?

First, it helps to understand a bit about how the human ear works. The human ear can detect a staggeringly wide range of sound pressure levels. The level of sound pressure that causes permanent hearing damage is more than a million times greater than the sound pressure produced by the faintest sound a human can hear. For this reason, the decibel is a logarithmic unit of measure. An increase of 3dB is equivalent to a doubling of sound pressure in Pascals (Pa), the SI unit of measure for pressure.

What does this mean? Well, for our purposes, it means that all else being equal, a 100 watt Marshall head is not "twice as loud" as a 50w Marshall head, as many seem to think-- it is only a scant three decibels louder.

Further complicating matters is that power ratings are taken with respect to a given "%THD," or percentage total harmonic distortion. If an amplifier is rated 100w with 1% THD, that means it develops 100w across the speaker terminals, with one percent of that power coming in the form of distortion products (i.e. stuff not present in the source input). If it is 100w with 5% THD, then 5% of the output comes in the form of harmonic distortion.

Complicating matters significantly (and impeaching the usefulness of that measurement for our purposes) is that guitarists almost never use their amplifiers with distortion content that low. Even 10% THD or more can sound "clean" in a guitar amp-- with the soft clipping of a tube amp, the onset of distortion into significant percentages manifests itself as a gentle compression or 'fattening' before true clipping occurs.

Beyond this, guitarists often like a little (or a lot) of audible distortion in their sound, so they deliberately induce audible clipping-- likely 50% THD or more. So while a typical 1% THD power rating might be relevant in a hi fi amplifier, it is almost never terribly relevant to actual use in a guitar amplifier.

Besides output power, here is a list of a few factors that can affect a listener's perception of how loud a guitar amplifier is, in no particular order:

• Number of speakers
• Efficiency/sensitivity of speakers
• %THD tolerable to the user/listener
• Onset of core-saturation in the output transformer
• Ability of power supply to keep voltage up when amp is pushed
• voicing/frequency content of amplifier

Let's take them in order, in brief.

First, the number of speakers is critical. Addition of a second, equal speaker, provided the amp will drive the additional load, will usually net an extra 3dB in loudness, roughly equivalent to doubling amplifier power. This is the largest source of the "more watts means louder" myth. A 50w Marshall is often paired with a single 4x12 cabinet while a 100w Marshall is often paired with two 4x12s. No wonder it seems "twice as loud!" A 22w Deluxe Reverb has a single 12" speaker whereas an 85w Twin Reverb has two 12" speakers (and usually very efficient ones, at that). For this reason, 'physical size of the cabinet' is often a more accurate predictor of loudness than the RMS power rating.

Secondly, the efficiency/sensitivity of the speakers matters a lot. Not all speakers are created equally. In a loudspeaker, only a fraction of the current input is turned into sound energy; the vast majority is dissipated as wasted heat energy. Some speakers are more efficient than others. For example, a JBL D120F has approximately 102dB efficiency at 1W white noise @ 1m distance. A less efficient speaker might only have, say, 96dB efficiency at the same power and distance. Consequently, a 25w amp through the JBL could easily sound louder than a 50 or even 60w amp through the less efficient speaker, especially when set up for clean operation.

Thirdly, the farther you are pushing an amplifier past the %THD used for its power rating, the more unpredictably it will behave. Amps do not stop getting louder once they hit 1% THD. They will continue to get louder as well as more distorted, and the nature of those distortion products will influence how loud an amp seems.

How much louder it will get past that point usually has to do with one of the following factors:

Output transformers are varying sizes. Sometimes they are small and will exhibit a behavior called "core saturation." When this happens, the transformer reaches its limits and cannot allow any more current to pass through. It will distort audio passed through it. In other words, it can serve as a "bottleneck" for the power trying to get from the tubes to the speakers. Consequently, a bigger output transformer will often allow an amp to keep getting louder as it is driven into clipping.

As another factor, the power supply feeds the amp the power it needs to amplify sound. If a power transformer, rectifier, or other components within the power supply are limiting the amount of power that can actually be used for amplifying, that can put a ceiling on how loud an amp will get. So a small power transformer might also limit an amp's ability to keep getting louder past the point of rated % THD.

Finally, the voicing of an amplifier can affect how loud it sounds. The Fletcher-Munson curve indicates that certain frequencies in the speech-range appear louder to humans, as our ears are more sensitive to them. An amplifier with a lot of those mid-band frequencies will conceivably seem louder to a human than an amp containing a lot of spectral content outside of that range.

So, in other words, largely ignore the numbers. When gauging whether or not an amplifier will be loud enough (or too loud) for your needs, focus more on the number and size of the speakers-- with speaker efficiency as a secondary factor-- and then the size of the transformers. Bigger output transformers almost always equal the ability to have more headroom and give up more volume even as the tubes saturate. Big power transformers, large filter cap values, and solid-state rectifiers signal a power supply that will keep up and won't mush out before the output tubes flat-line. All of these things are better clues than the rated output as far as determining how loud the amp will be when you crank it up and bounce it off a chair. Of course, you could always just judge by the physical size of the cabinet.