Hiwatt = Lowatt compared to this 1000w tube amp

John at Champ Electronics in Nottingham England has prototyped a 1000w tube amplifier using the beastly 813 tube. The 813s have a staggering plate voltage of 2500V DC and the quartet puts out an astonishing 1015w RMS.

I'm not certain what the musical application for this would be, but for the sake of all our hearing, I think it should be kept out of J. Mascis's hands at all costs.

The Nuances of Timbre

There is a popular saying that usually comes up at least once when anyone is discussing anything related to the recording or reproduction of music: "Garbage in equals garbage out."

In other words, no matter what type of processing or sweetening occurs (and no matter how expensive or vibey any one piece of gear is that the audio passes through), the output will always retain something of the fundamental character of the input signal.

High-fidelity stereo enthusiasts and recordists both understand this (though the latter works tirelessly to contradict it as much as possible), but electric guitarists often seek miracles from the knobs on their equipment. It's not uncommon to hear ill-informed statements such as: "Any subtle difference between cheap thing X and expensive thing Y can be compensated for with EQ on the amp." Substitute "pickups," "wood," "strings," or virtually anything else (including the amp itself) for "thing" in the statement above, and you have a statement which has probably been made on an internet forum somewhere. I contend that this manner of thinking is fundamentally misguided as it places too much burden on something that influences but one of several factors that shape the timbre, or sound, coming from an instrument or setup.

To explain why, it helps to understand what timbre (often called "tone" by guitarists) actually is.

Timbre is influenced by three main factors: Overtone content, transient envelope, and formants. Let's discuss them one at a time.

• Overtone content refers to frequencies that are present which are mathematically and harmonically related to the actual pitches being played. Pure sine waves excepted, all musical tones contain various overtones. Overtones are frequencies which are harmonically related to the fundamental frequency and proceed in a very specific order called the overtone series. Which overtones are present, and in what proportions relative to one another and to the fundamental, is instrumental in determining the timbre of an instrument or setup. Fourier's Theorem states that all periodic waveforms can be expressed as the sum of multiple sine waves. Here is a cool java applet that allows you to experiment with the effect of altering the ratios of harmonic overtones, and also to examine the overtone content present in various popular waveforms such as square, sawtooth, etc.

• Transient envelope concerns the question of "what happens at the very beginning of the note?" With most instruments, there is an instantaneous burst of energy at the very beginning of a tone, often with a strong noise component, that is instrumental in determining our perception of its timbre. The precise nature of this transient is very important to the manner in which our ear parses the tone. A saxophone note with the transient removed would scarcely sound like a saxophone anymore at all-- in fact, it might be confused for a violoncello, or something else entirely.

• Formants are frequencies present in the sound which are not directly correlated with the pitches being played. In other words, if a system has a formant at 400 Hz, it may be present whether you play a Bb, an F#, or any other tone. Formants can result from acoustic resonances such as standing waves in cabinets, rooms, or sounding chambers of instruments, or from other things. The best illustration of the effect of manipulating formants is what happens when an audio tape is played back at double speed. Vocalists, rather than sounding like humans with a higher vocal range, sound like "Alvin and the Chipmunks." This is caused by the transposition of formants to an unrealistically high range--which, of course, also accounts for both the peculiar guitar sound in Les Paul's "Lover" and the decidedly un-pianolike piano solo in the Beatles' "In My Life."

An EQ filter, particularly the type found on the average guitar amplifier or mixing console, can simply boost or attenuate spectral content which is already present. If a particular overtone or formant is present, it may be boosted or cut (usually along with several surrounding frequencies). However, an equalizer is not designed to add overtones or formants that were never in the source material to begin with, and it certainly cannot alter transient envelope.

Furthermore, hardware EQ filters are imperfect and imprecise devices. While it is beyond the scope of this article to explain in depth, suffice it to say that all hardware equalizers alter the phase of certain components of the input signal. In other words, EQ filters will delay certain components of a complex waveform by fractions of a cycle with respect to other elements, which leads to very unnatural sounds at extremes of equalization. However, even if this were not the case, trying to sculpt fine nuances of timbre out of shelving or peaking equalizers of the design typically found in guitar amplifiers would be analogous to trimming your fingernails with a chain saw.

For these reasons, their capability as shapers of timbre or as compensators for timbral deficiency is actually severely limited.

Describing sounds verbally can be elusive. There are many adjectives used ("punchy," "bright," "warm," "dark," "thin," "dull," "smoky," and "fat," etc.) which can certainly connote certain audible characteristics. This is all well and good, but it pays to beware of overly reductionist thinking.

If our ear perceives something as "bright," that does not always mean "more treble." It might mean sharp, pronounced transients that have been faithfully reproduced. "Fat" doesn't necessarily mean "more bass." It might mean "a modified/reduced transient envelope," such as what occurs when tube or tape saturation has brought up the level of a note's sustain relative to the level of its transient. If something is "boxy," the solution isn't always necessarily to turn the midrange knob all the way down. Sometimes the solution is to try a different speaker cabinet whose formants might be different, or even a different room--rooms can have formants, too!

Simply and anecdotally put, If one distortion pedal sounds 'warmer' than another as a result of having more pronounced second-harmonic overtone content, then this cannot be imitated by turning up the 'bass' knob on an amplifier. If one speaker sounds 'brighter' than another due to an ability to reproduce transients with greater fidelity, then all the "treble" in the world isn't going to imitate it.

When concerned about shaping the sound of your instrument or rig, it pays to be informed-- consider the role of each component of timbre in the equation. Don't always assume that filtering alone will get you there. In some ways, EQ filters are similar to light filters. A red gel on a spotlight might create a different atmosphere around the performer than if he was under white light alone, and it may even minimize or highlight some colors on his wardrobe, but it will not change his hairstyle or the shape of his face. Similarly, twisting the knobs of phase-mangling EQ filters on a guitar amplifier will create a perceptible difference in timbre, but it will not change the fundamental sound. For that, you have to go straight to the source-- garbage in equals garbage out, after all.

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!

Gear Review: The Klon Centaur

While this is not a gear review blog, occasionally I will feel that there is a piece of gear in need of review that would actually create something worth talking about. The Klon Centaur is a hotly-debated pedal. Arguably, its inception around 1994 was one of the first droplets in the flood of high-end 'boutique' overdrive pedals that exist today. It is the subject of much passionate controversy, but when I was shopping for one, I found myself wanting a few more objective, even-handed, non-sponsored reviews of the unit.

First, the facts: The Klon Centaur a buffered-bypass clean boost and overdrive pedal. It is built in a rugged cast aluminum enclosure, and battery access is through two screws you can turn with a guitar pick or coin. If the bootleg schematics are to be trusted, it is a unique circuit which uses TL072 op amps in its design and germanium diodes for clipping-- though you wouldn't know this to open it up, as the circuit board is 'gooped' in epoxy to keep prying eyes away. There is a 'boost' section and an 'overdrive' section, controlled unobtrusively by means of a seamlessly-integrated dual-gang pot labeled "Gain." The "boost" side makes use of what is called a charge pump, which increases voltage, thereby increasing headroom (and eating batteries). There is a tone control, labeled "treble," and an "output" control, as well. There is an LED status indicator, and an old-school 1/8" TRS jack for 9v power-- non-BOSS style.

The business model of Klon begs some explaining as well, as it is unique from other pedal manufacturers and is the subject of a lot of the debate about this pedal. Klon is mostly one man, Bill Finnegan. Klon pedals are available only directly, and are not usually available through any retailers. They cannot be purchased online. To purchase a pedal, you must follow these steps:

• Phone Mr. Finnegan to discuss the pedal and its suitability for your needs
• Give Mr. Finnegan your order information
• Snail-mail Mr. Finnegan a check or money order-- No credit cards or PayPal!
• Supply Mr. Finnegan with a business address for shipping-- he WILL NOT, under any circumstances, ship the pedal to the same place where you sleep, even if that place is also your business.
• Wait several weeks for your pedal to arrive.

The phone call is one of the hottest topics around this pedal. Mr. Finnegan has a headset which allows him to talk and take orders while working on pedals. When you call, before you place your order, he will ask you about your other gear, your playing style, and the capacity in which you perform (i.e., bedroom player, weekender, professional, etc). He will also answer any questions and concerns you have about the pedal. If and when he decides the pedal will be a good fit for you, he will take your order information. It is not an 'interview' per se--Finnegan is not ascertaining whether or not you 'deserve' the pedal, as is often mis-reported. From what I can tell, he is simply trying to determine whether or not the pedal will help you (and, I suspect, whether or not you intend to actually use it or to sell it for profit on eBay).

Once your order is placed, you are not placed in the queue until your payment is received. You will not receive any follow-up e-mails or calls. You will have no further contact with Mr. Finnegan unless you initiate it-- you will mail your check, and several weeks later your pedal will arrive.

When I ordered my pedal, the wait was specified as 12 weeks, and it was delivered in that time, as-promised. If the wait gets too much longer than that, Mr. Finnegan may briefly stop taking orders. Consequently, I had to wait a week to even place my order.

The website is a flash-based site that appears to not work on Macintosh computers--it does not detect the FLASH on my Mac machine or any others I have tried. However, beware, as the second Google result takes you through a back door into an obsolete site, complete with old pricing information, that was apparently never fully decommissioned.

Now, the opinions: Beginning with the Klon in its bypass state, you may notice that it has a great bypass buffer that is, in my opinion, superior to a true-bypass design, particularly if you use long cables or a lot of pedals in your chain. The buffer is transparent but can allow long cable runs, etc. and is therefore very handy.

The TL072 is hardly a glamorous op-amp, being a ubiquitous, inexpensive part with a reputation for being somewhat noisy and performing merely adequately. However, a pedal is the sum of its parts, and in this case, sonically, I don't feel anything lacking. There is a bit of noise, however, particularly if other distortion pedals are placed in the chain after the Klon. In most situations I do not find the slight hiss objectionable-- in many cases, it is not even detectable-- but in certain situations it does appear. One wonders whether this noise is attributable to the TL072, or whether it results from other aspects of the design.

As the "Gain" knob is advanced to the right through a clean or solid-state amplifier, you will notice an overdrive sound with a somewhat unique, slightly raspy character. With a clean amp, the overdrive is, in my opinion, rather unspectacular. However, when used in front of a good tube amp that is overdriven to even modest saturation, the Klon really begins to shine. Its overdrive dovetails beautifully with the natural overdrive of the amp and pushes it over the edge in a very appealing way. I do not perceive 'transparency,' as is claimed, but rather a sweetening, as the pedal's own character interacts with the amp's character. If a clean amp must be used, placing another distortion pedal after the Klon can yield suitably pleasing results, but it is most at-home driving an already-pushed tube amp even further.

Some perceive a midrange emphasis from the Klon, but I don't hear it. In my opinion, many other overdrive manufacturers (808 clones excepted) have a tendency to de-emphasize the midrange frequencies. The Klon does not--which is one of its best selling points. In a typical ensemble where distorted guitar would be used, the guitar's slice of the pie, spectrally, tends to live in the mid-band. The bass and bass drum's sustain typically occupy the lower frequencies, while the snare, cymbals and vocal sibilants occupy the upper midrange and treble frequencies. The fact that the Klon allows these mid-band frequencies to shine through, rather than attenuating them, places a natural amount of spectral information in the guitar's 'comfort zone,' allowing it to live naturally in the mix. For this reason, the Klon sounds its best to me in real-world scenarios.

The pedal is admirably constructed, looks beautiful, and battery access is a breeze. However, powering the pedal with a 9v supply is problematic. Mr. Finnegan neither supplies nor offers a proper power supply, supplying instead a pamphlet and a connector with instructions on modifying a BOSS supply. However, be careful, because installing the connector with inverted polarity will smoke the pedal-- and it will NOT be a warranty repair. Should you opt to use batteries, be advised that a low battery will cause a high-pitched squeal that comes on virtually without warning. In my opinion, powering the pedal could be dealt with more elegantly.

Finally, the ordering process is difficult and seemingly arbitrary. Mr. Finnegan is polite enough and pleasant to deal with over the phone, but I would prefer to just be able to place an online order. I typically, like many, do not even use personal checks anymore, and the snail-mail process added a few extra days to an already-long wait. As I work primarily from my home studio, I did not have a business address to ship to. I had to have the pedal shipped to a friend who owned a business across the Hudson, which made picking it up difficult and added extra expense in gas and tolls. Additionally, I did not need nor desire a conversation about my gear and pedal needs; as I have been doing this for a living my whole adult life, such hand-holding was not necessary in my case.

However, the pedal was worth all the hoops-jumped-through in the end. It is really a fantastic and unique overdrive unit. That said, there is clearly a reason the pedal routinely sells for at least $100 more than its $329 list price on eBay-- getting one takes a lot of time and is a fairly involved process. Is 12 weeks and one-click ordering (complete with online payment) worth an extra $100 (and minus a three year warranty) to you? For many it is.

Anyway, hope this sheds some light on this pedal, which in its roughly 15 years in existence has become almost as mythical as the centaur from whom it takes its name.

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.