TUN.TXT

ALTERED TUNINGS FOR THE HARMONICA

INTRODUCTION

Recent years have been good to the single reed diatonic harmonica. As well as the continued expansion of interest in the traditional styles associated with the harp, many new avenues are being explored. Players such as Howard Levy have exploited the chromatic possibilities of the harp using overblows and overdraws; others, such as Roland Van Straaten, have used traditional blues harp techniques to play music outside of the typical blues territory. As well as new playing techniques, the harp itself has been modified, with new materials and shapes for combs and coverplates, the addition of valves, etc. One of the most interesting areas for experimentation is with alterations to the harp's tuning system. The Richter system diatonic has been with us for a century and a half and a great many players use no other tuning other than the standard major diatonic layout. It is a wonderfully flexible system, capable of doing many things that it was not designed to do (cross harp and all the other positions, overblowing, bending, etc., are all happy accidents rather than the products of brilliant design!), but there are other tunings capable of doing other things. 

WHY ALTER THE TUNING?

First of all, why alter the tuning, if the standard tuning has served us so well so long? Well, as a simple example, say you're playing a tune where all the notes are available on a C major harp, except for a low B note. You could use a second harp just for that one note, but that may not be practical. Perhaps the easiest thing would be to tune the bottom C down a semitone to B. That's just one example. Some tunings have more possibilities for chords and arpeggios, enabling us to play more interesting accompaniments. Others make certain scales or melodic ideas more practical, give us more ways to play certain notes or even extend the working range of the harp. A certain tuning may make playing in octaves easier because the scale is more consistent throughout the range of the harp, another may increase the number of possible bent notes to make the harp "bluesier". Some of the tunings that we will look at will be useful for a wide range of applications, others may 
only be suitable for one thing, but will be the most practical way to play that one thing! I remember reading of a tuning for the banjo called "Little Birdie", named  after the song of the same name. People who know about such things claim that this tuning is the only one you can use to play "Little Birdie" properly and "Little Birdie" is the only song you can really play in this tuning! To paraphrase Johnny Mars, retuning makes the harp serve the player, rather than the player serving the harp. 


OFF-THE-SHELF ALTERED TUNINGS

The easiest way to obtain altered tuning harps, is to buy them. Hohner, Seydel and Lee Oskar offer a variety of different tunings off the shelf and Seydel will also build other tunings to order. Suzuki and Hering have mentioned plans to introduce alternate tunings to their range, but no sign of them as yet. There are also some people who will retune harps for you, for a fee. However, for the cost of a few simple tools and a bit of practice, you can cut out the middle man (or woman) and retune your harps yourself. 


TOOLS OF THE TRADE

Lee Oskar, Seydel, Suzuki, Hering and Hohner all sell tool kits for the harmonica, but you can also acquire your own set of tools from a wide range of sources - hobby shops, dental equipment suppliers, etc. I'll discuss my preferred tools later in 
this article. Unless you have absolute pitch, you will also need something to which to tune your reeds. It's possible to tune them by comparing the pitches with another instrument (assuming that it is in tune), or a set of tuning forks, but if you are going to do much tuning work, then an electronic tuner will be an important investment. Any good quality chromatic 
tuner will be adequate, as it is the skill of the person using it that is more important than the device used. Make sure that you purchase a chromatic tuner, not a guitar tuner that just gives the notes E, A, D, G, B, and E. One that can be set to different references pitches is a good idea - A=440, A=442, A=444, etc., so is one that measures the number of cents from the target pitch, rather than merely indicating whether the note is flat or sharp. If possible, try out the tuner in the shop before spending your money - make sure that it can read the full range of the harp from the lowest to the highest notes; make sure the display is easy to read and that it doesn't leap all over the place when you play a note. Some tuners work best with an external microphone, whereas others are so sensitive that they will respond to almost every sound in the vicinity! As well as the quartz based tuners you can find in your local music store, there are strobe tuners which cost a lot more money, but are a lot more accurate - assuming that they are properly calibrated. To be honest, they are probably more accurate than anyone needs for tuning a harmonica, but if you can find a used one at a bargain price, then you might like to invest in one. Bear in mind that if it is a used one, it may need to be adjusted by a competent technician in order 
to ensure its accuracy. If you have a computer then there are several tuning programs available either as commercial software, shareware, or freeware. One especially good one is TuneLab '97, available from:

http://www.tunelab-world.com/

Another useful program is Chromatia, available from:

http://www.fmjsoft.com/

As for Macintosh, Linux, etc, you're own your own!

However, all of these have the drawback that you have to have a computer running as you tune. Most computers produce a background sound with a definite pitch or pitches, which I find to be extremely disruptive to my tuning work. Tunings apps are now available for most cell phones and tablets, which are a much quieter opton that either desktop or laptop computers.

For my own use, I prefer the Seiko ST1200 (now discontinued). This is a quartz tuner with several nice features, not least of which the ability to sound tones of specified pitch, which can be very useful for double-checking things. However, much of the time I use an old Korg DT-2 (also discontiued), which fits nicely into my pocket and is more than accurate enough for most jobs.


TUNING: SOME BASICS

The basic techniques of retuning are removing material from the tip of the reed to raise the pitch and removing material near the fixed end to lower the pitch. I strongly recommend reading Lee Oskar's guide to tuning (included with his repair kit) and the relevant chapter in Steve Baker's "Harp Handbook". If you don't have a copy of this book, it really is time 
you bought one. (However, it may be worth giving a word of warning that his tuning tables use different reference settings of the tuner in Hertz, rather than simply giving deviations in cents from a fixed reference - this can be a little confusing.) If you'd like to dabble with different tunings, but don't want to risk working on the reeds yourself, then try mixin' and matchin' Lee Oskar's interchangeable reed plates or the Hohner modular system, although there is a limit to the different tunings you can create this way. Besides, I recommend that every harp player learn to tune his instrument, even if they never play anything but the standard major diatonic layout, to save on buying new harps just because a few reeds are a little flat. With the exception of the very lowest reeds (with weighted tips), I find that it's easier to tune reeds down than up. It also gives you a chance to polish out the file marks left by factory tuning, reducing the chances of a stress point building up. If the tuning requires some reeds to be tuned a long way sharp, try starting with a higher keyed harp and tuning the other reeds down. After drastic retunings, give the reeds plenty of time to settle in pitch. Frequent fine tunings may be necessary. For lowering the pitch of a reed a long way, it may be better to add material to the ends of the reeds. Another approach is to replace the reeds with ones of the desired pitch, which is covered in another file in this collection. Fine tuning will probably still be required, but this is a handy skill to have when a much-filed reed snaps! 
 

BEFORE STARTING TO TUNE
                                          
If you have never previously worked on the reeds of a harmonica, then do not start out by attempting to tune your favorite, most expensive instrument. Practise on an old harp, or buy some cheap diatonics as "victims" for your experiments. It is almost inevitable that you will ruin a few reeds when you first try your hand at tuning. It's also probably best to read this section thoroughly before starting work on your harp.


DISASSEMBLY

Before you can tune the harmonica, you need to do some degree of disassembly and the first things to remove are the cover plates. On most harps, this is simply a case of unfastening a nut and bolt at each end of the harp. Many cover plates use simple slotted head fasteners; Tombo harps (including the Lee Oskar) use a Phillips #1 head; Hohner (MS) harps use a Pozidriv. The MS cover fasteners can also be removed with (very) careful use of a Phillips #1, but the correct screwdriver is to be recommended as the head of these fasteners can very easily become damaged. Many wooden-combed harps have covers that are attached by nails (the Marine Band falls into this category - don't be deceived by the way the heads of the nails look like small screws!). With these, it is simply a case of carefully lifting the ends of the covers with a screwdriver or knife until the nails are loosened, then pulling them out with a pair of pliers. Be careful not to bend the nails as you remove them. (A tip - if the nails become slightly loose in the holes after you've worked on the harp a few times, simply insert the sharp tip of a toothpick into the hole, then break it off level with the comb; the nails will now grip properly again). With most chromatics, the covers can be removed without having to remove the mouthpiece. On the Hohner CX-12, the body can be removed from the cover without needing any tools at all. Having removed the covers, you will be left with the body of the harp, with reedplates attached top and bottom. On most diatonic harps, the upper reedplate has reeds which are fixed on the inside of the plate - these are the blow reeds. The lower plate has reeds, which are fixed on the outer 
surface - these are the draw reeds. On chromatics and octave/tremolo harmonicas there are blow and draw reeds arranged alternately on each reedplate. On most chromatics, you will also see the valves that cover the blow reed slots - be careful not to disturb these as you work on the instrument. In fact, it may be a good idea to remove the valves before doing 
any drastic retuning.

If you only need to retune one or more draw reeds, then you will not have to disassemble the harp any further. However, if you need to do any substantial work on the blow reeds, then you will have to remove the blow reedplate. On most harps these days, this can be done easily by loosening the reedplate screws with the appropriate screwdriver, allowing both reedplates to be taken off. Some older plastic-bodied harps have the reedplates held on using nails. These can be tricky to remove (try tapping the point of the nail with a lightweight hammer until enough of the head is exposed to get a grip with your pliers). Once you have extracted them, it may be as well to replace them with screws. The nailed-on blow reedplates 
of wooden-bodied harps can be pried loose (carefully!) with a knife (see notes on removing nailed-on cover plates, above) without having to remove the draw reedplate. If you just need to touch-up a single blow reed that has gone flat, there is a shortcut described later. If you do disassemble a wood combed harp completely, it's a good idea to sand the comb flat before reassembly and possibly to give it a coat of varnish (a water-based urethane varnish is a good choice). Many people also add some sort of gasket before replacing the reedplates - common gaskets are microporous surgical tapes (but make sure that they do NOT come into contact with any steel parts, as this will lead to increased corrosion problems), lip balm 
(preferably unscented), petroleum jelly or a light coating with a wax crayon. If you do use a gasket, then it is probably best to apply it to the comb rather than to the reedplates and to use the minimum amount necessary to get a good seal. I generally find that most plastic combs do not require gaskets, with the possible exception of those with "solid" partitions, such as the Hohner Golden Melody. Some metal combs also benefit from gaskets. As usual, experience will be the best teacher, but it is far more important to make sure that any mating surfaces are as flat as possible in the first place, rather than trying to fix things with a gasket. These topics are covered in a variety of videos on YouTube and elsewhere - some are better than others, so caveat emptor.

Take a few minutes to examine the exposed reeds - use a magnifying glass if you like. To standardise our terminology, the free end of the reed is called the tip; the part which is broader and thicker and is riveted to the plate, is called the heel (some people call it the root); the main part of the reed is called the tongue. If you look closely at the tongue of the reed, you will see lots of tiny lines across its upper surface - these are the lines left when the reeds were milled from a sheet of brass. Some reeds will also have a diagonal scratch across the tongue - this is where the reed was lowered in pitch at the factory. Some reeds may have some marking at the tip - this is where the pitch of the reed was raised at the factory. Sometimes this tuning work is done a little over-enthusiastically and there are gashes left across the reed, or sometimes the tip of the reed is a little chewed up. Make a mental note to avoid doing anything like this yourself! Thankfully, many makers are now using less destructive tuning methods.


TUNING: THE NITTY GRITTY

Now for the basic principle behind tuning reeds. Remove some material from the tip of the reed and it will rise in pitch; add some weight to the tip and the pitch will go down (you will notice that some of the longest reeds have thicker tips to make them lower in pitch). Alternatively, removing some material from the reed, near to the heel, will have the same effect as adding weight to the tip. This removal of material is usually done with a jeweler's file.

However, files have a variety of disadvantages. It is very easy to snag a reed with a file, altering the setting of the reed, or causing a burr of metal on the edge of the reed (which can cause all manner of unpleasant sounds). The marks left by a file can cause stress points to build up (I have seen quite a few reeds that have broken at the mark left by filing), and the uneven surface left by filing can trap debris, affecting the performance of the reed. In my opinion, a far better alternative to filing is the use of abrasives. Wet & Dry paper, as used on automobile bodywork, or Emery cloth are good choices. Better yet, there is a small tool that is commonly found in hobby stores. It is usually called something like a "polishing and sanding stick" and consists of a pen-sized plastic stick with a tapered tip, which holds a 6mm wide band of abrasive under tension. When you have exhausted the abrasive surface at the tip of the tool, you simply rotate the band around to provide a fresh area at the tip. Replacement abrasive bands are available in various different grades. I find this tool extremely useful and it only costs a very small amount. 

Two sources for purchasing these tools and other supplies to work on your harmonicas:

Micro-Mark
340-2214 Snyder Avenue
Berkeley Heights
NJ 07922 
USA

Email: info@micromark.com
Web: http://www.micromark.com/

W. Hobby Ltd.
Knight's Hill Square
London
SE27 0HH
England

Email: hobby@hobby.uk.com
Web:  http://www.hobby.uk.com

When you tune a reed, the tongue needs to be supported by something. One method is to slip a razor blade under the reed. Please DO NOT use a regular double-sided blade - there is experience (painful experience, at that) behind this advice! If you must use a razor blade, use one of the single-edged blades sold by craft suppliers, or take a regular razor blade and cut off the sharp edges with a strong pair of scissors. Better still, go to your local automotive store and buy a cheap 
set of feeler gauges - one of the thinner ones slid under the tongue of the reed to be tuned, will provide adequate support, as well protecting the surrounding reeds and/or valves. 

Having got this far, the actual process of tuning is quite simple. To raise the pitch of the reed, take your tuning tool, or wrap a small piece of abrasive paper around the tip of your finger, then polish the last few millimetres of the surface of the tongue, towards the tip. To lower the pitch, polish the surface of the reed tongue near the heel. To avoid weakening the reed if you are lowering the pitch by a long way, try to remove the material from a broad surface, rather than all at one small point. When I use this approach, I have sometimes lowered the pitch of certain reeds by as much as an octave without appearing to affect their life span. In both cases, work along the length of the reed, rather than across it. Take your time when tuning - check the pitch of the reed frequently using your tuner, or against whatever you are using as a 
reference pitch. Bear in mind, especially if you have retuned the reed by a long way, that the pitch may take a few days to settle. You may need to go back and check it a few times, fine tuning it as necessary. If I have to retune a reed by a large amount, I start off with a coarser abrasive and use finer ones as I get closer to the desired pitch. Each time you work on a reed, make sure that you leave it with its same original shape and be sure that it is set with the correct gap - it is very easy to alter the setting of a reed by accident during tuning. The "gap" of a reed refers to how far the tip of the reed sits above the reed plate. If you are new to adjusting your harps, remember that the higher the gap, the more air it will take for a reed to sound and that the lower the gap, the less air it will need to start it moving, but the more likely it is to stall under hard pressure. Also, as general rules of thumb, when two reeds share a chamber, the lower pitched reed requires a slightly bigger gap; valved reeds also require a slightly larger gap. It may take some experimentation to find the ideal gap for your style of playing. Most harps come from the factory with relatively high gaps. If you are a hard player, this may be right for you, but if you are a relatively gentle player, or if you use overblow and overdraws, you will probably need to lower them slightly. An average gap is usually defined as having the tip of the reed about the same height above the reedplate as the thickness of the reed itself. Getting the gaps right is probably the most important part of making your harp respond properly, so it is well worth spending some time experimenting with different reed settings. Reading this article may also be helpful:

http://www.angelfire.com/music/harmonica/reedadjustment.html

The preceding paragraphs detail the tuning method I recommend and I have had good results with it for more than a decade, but there are alternative methods, some better than others. Instead of abrasives, some people use a scalpel or craft knife to scrape away metal from the surface of the reed. The Lee Oskar toolkit contains a couple of small chisels that can be used similarly. With both of these, make sure you work along the length of the reed, rather than across it. If you intend to do a lot of radical retuning, it may be worth investing in a small power tool (such as is made by Dremel and a variety of other makers) with some abrasive bits. Be warned, however, that it is very easy to saw through a reed using one of the metal burrs or grinding stones. In fact, if you use an engraving bit to tune reeds, it is probably best not to support the reed, but just to touch the unsupported reed very gently with the bit. Many people recommend the use of hard rubber polishers, such as the Shofu Brownie (available from dental suppliers), but I have to give a few notes of caution regarding them. First of all, make very sure that you know which direction the polisher is spinning and that the part of it which touches the reed is moving towards the end of the reed, otherwise you will find it very easy to snag the tip of the reed and ruin it in a fraction of a second. Also, I have noticed that hard rubber bits can tend to give the reed a slightly convex curve - ie. the reed rises slightly in the middle and dips downwards towards the tip. Look out for this, as this reed shape can cause a very poor response. If you find this, it can usually be cured by gently massaging the reed back into the correct shape - which should be either flat, or very slightly curving upwards toward the tip. I am also concerned that prolonged polishing of the reed might heat up the metal with adverse effects (see below) and that the dust from the rubber bits might have an adverse effect on the person doing the tuning. Myself, I sometime use power tools (cautiously) for drastic retuning, but I prefer not to use them for fine tuning work for similar reasons to why I avoid the use of computer-based tuning programs - the noise they make has a definite pitch which can interfere with the process of tuning, particularly if you are trying to hold a certain note in your head as you work.


TUNING BY ADDING MATERIAL TO REEDS

Some people use a soldering iron to place a tiny blob of solder towards the tip of the reed to lower its pitch, then fine tune by filing the solder. In many ways this makes sense, as you are adding material to the reed, rather than removing it. However, I do have concerns about applying heat to the reeds. Reed organ technicians usually advise against anything that heats the reeds, as that can undo the treatment than was given to the metal to make it springy, so I would be cautious about using this method on harmonica reeds. Another problem is that as the solder cools, it contracts. This is not a problem with small amounts of solder, but if you are adding a large blob to lower the reed a long way, as it cools it contracts at a different rate to the brass, causing the reed to take on too much of a concave curve. However, if you must use solder, silver solder is probably the best choice. I have also noticed that reeds tuned with solder tend to drift in pitch over time, for reasons I don't fully understand. An alternative way of lowering pitch by large amounts is to use glue to attach a small piece of a another reed to the tip of the reed you are lowering. I've worked on a couple of Hohner Harmonettas that had the lowest reeds tuned in this way, but to be honest, I find it a very fiddly job. An easier way to do it is to mix some powered brass or stainless steel (available from hobby shops for use in casting work) with an epoxy adhesive such as Araldite, then add small amounts to the tips of the reeds. A small blob will lower the pitch quite a way. 

The big advantage of the above methods is that they are easily reversible by removing the material you added, leaving the reed as it was in the first place. In fact, if you want to try out a tuning without altering the harp permanently, there are several things you could use to lower the pitch of a reed. Brendan Power often tests new tunings by adding a tiny lump of BluTak (the sticky material used for sticking posters to walls) to the reeds, which is easily removed if you the tuning is not to your taste. Super Glue can also be used for more subtle pitch changes, but after using any solvent-based 
substance inside the harp, PLEASE ALLOW SUFFICIENT TIME FOR IT TO CURE BEFORE PLAYING THE INSTRUMENT. You can get similar results by adding wax or modeling clay, but unfortunately, I have yet to find a good way of temporarily raising the pitch of reeds. 

When checking the pitch of the reeds, it is best to hold the reedplates against the body of the harp, with the covers held on by finger pressure. This will give you a better idea of what the pitch will be when the harp is reassembled. Be warned, however, that there still might be some slight differences due to reduced airtightness. Also, it may take some practice 
before finding the ideal playing technique for sounding the reeds as you tune. When you first use a tuner, you will become aware that small changes in mouth shape can cause differences in pitch, but with practice you will find the best way to do it, although it's a good idea to check how the reed responds to different pressures and embouchures. Another important tip I should add is that you should make sure that the reedplates are at about body temperature when fine tuning, as the moisture from your breath can soon build up on cold reeds causing them to sound slightly flat. I use a heated gel pack (as used for sports injuries and the like) to keep them warm for the tuning process. 

Most of your retuning work will probably be a simple tuning-up of reeds that have gone slightly flat. If the offending reed is a single blow reed that is just "off" by enough to make it a problem, then you may feel that taking the whole harp to pieces (especially if it is a nailed-together harp) is a lot of work. It is possible, however, to work on blow reeds without complete disassembly of the harmonica. With the covers taken off the harp, take a small screwdriver and insert it into the appropriate hole of the mouthpiece. If you are careful, you can push the tip of the screwdriver through the slot, 
resting it on the outside of the reedplate. This will hold the tip of the reed slightly clear of the plate and support it as you polish or file the tip. You only need a little of the reed exposed in order to be able to tune it effectively. Be VERY careful when attempting this on a short high-pitched reed, as these reeds can be easily damaged. You can use this same shortcut on the chromatic harmonica - for some notes you will have to push in the slide button to get at the correct reed. You may find it easier to tune the reed with its valve removed (there's a good chance that if you do not remove the valve before you start, you may accidentally remove it whilst tuning!). An even easier method (and one which is less likely to alter the setting of the reed), is to use a Dremel-type tool with a small engraving bit. It is quite easy to reach through the slot and just touch the reed enough to bring it into tune. Richard Sleigh sells a sharp scraper specifically designed for tuning harps without disassembly, as well as some other useful tools and all sorts of other good stuff:

http://rsleigh.com/


PUTTING IT ALL BACK TOGETHER

After getting the harp into tune, the final stage of the job is to reassemble the harp. Again, take care not to knock any of the reeds (or valves, if present); take care not to over-tighten the screws. Make sure that everything goes back exactly the same way as it started out. If you hold the harp up to the light, you may be able to see any major air leaks that could be the result of incorrect reassembly. Some harps can be far harder to put back together than they were to take apart - experience will be the best teacher here!


THE THEORETICAL STUFF

The following section takes a look at the more theoretical aspects of tuning and the why and wherefore of temperament. This is an enormous subject, but here, we shall confine ourselves to some fairly simple topics that are pertinent to the subject of tuning the harmonica. Before we begin, it may be a good idea to review some of the terms used. "Hertz" (abbreviated to Hz) is the SI unit of frequency and is equivalent to one cycle per second and is used to measure absolute pitch. A "cent" is 100th of a semitone in the typical equally tempered Western chromatic scale. As there are 100 cents to each semitone, then there are 1200 cents in one octave. Cents are used to measure relative pitch. For example, the distance between an A of 440Hz and an high A of 880Hz is one octave or 1200 cents, as well as being a difference of 440Hz. However, the distance between an A 440Hz and a low A of 220Hz is also one octave or 1200 cents, but it is a difference of 220Hz. From this example it should be clear that although cents and Hertz are related, they are not directly interchangeable. Other terms will be explained as we encounter them.


SOME THEORETICAL BACKGROUND TO TUNING AND TEMPERAMENT

If we take any two notes and play them at the same time, we produce what is called an interval. I assume you are already familiar with the names of the commonest intervals (e.g., octave, perfect fifth, major third, etc.). As well as describing the distances between two pitches, these terms are also used to describe the different qualities possessed by these intervals, although this is often dependent on cultural influences, personal taste and so on. Some intervals can be described as consonant (meaning they have a smooth, rich pleasing sound to the ear), others are dissonant (meaning that they are harsh, or discordant). Any interval can be described in terms of a ratio, of the frequency of one note, compared with the frequency of another. For example, if you take a frequency of 200 Hz and a frequency of 400 Hz, they can be said to be in the ratio of 1:2, as the second frequency is double to the first. Without delving into the vast subject of psychoacoustics, it has been established that the human auditory system finds most pleasing, those intervals that are in the simplest whole-number ratios with each other. To express this as an over-simplification, it can be said that the simpler the ratio, the easier it is for our brains to process the information. The practice of tuning so that everything makes the simplest ratios and thus produces the smoothest possible intonation for polyphonic music, is called "Just Intonation" (hereafter termed JI, to save my typing fingers!).

The basis of JI is the harmonic series (you may recall this from your high school physics lessons). When you blow a brass instrument, the lowest note you produce is fixed by the physical shape of the instrument. Without altering the shape of the instrument (which is in effect, what the valves do on a trumpet, or the finger holes on a flute), it is possible to produce 
a note that is twice this frequency, as well as one that is three times the pitch, four times the pitch, etc. These are called the "harmonics" of the instrument (they are also called "overtones" or "partials", but in this article I'll stick with the first term). A similar effect can be produced on stringed instruments, by lightly touching a string at a point half its length, one third of its length, one quarter of its length, etc. It should also be remembered that when any pitch is produced, higher pitches from the harmonic series also occur - their relative amounts contribute to the tonal quality of the instrument.

Using the series 1, 2, 3, 4, 5, 6, 7, 8, etc., we can very simply derive the basic intervals of JI. The octave has a ratio of 2/1, and it is the commonest interval in all music. For example, if we decide our note A has a frequency of 440 Hz, then the frequency of 880 Hz would also produce an A, but this one would be an octave higher than the first. The next basic 
interval is 3/2, which produces the perfect fifth. If we take our A of 440 Hz and multiply it by 3/2, or 1.5, then we get 660 Hz. This would be the frequency of an E, a perfect fifth above the A. Our next interval is 4/3. The 4 is equivalent to the note 1 raised by two octaves, so the ratio 4/3 is the distance between an E and the A above it, or a perfect fourth. The interval 5/4 gives us a pure major third and the interval 6/5 gives us a pure minor third, therefore the numbers 4:5:6 represent the ratio of the simplest possible major chord.

This process sounds simple enough, but there is a catch. The next interval in the series is 7/6. The 6 represents an octave above the 3 (3 x 2/1 = 6), or our E, assuming that we started with 1 = A (440 Hz). The 7/6 ratio added to our 4:5:6 chord gives us the ratio 4:5:6:7, which is the simplest possible version of the dominant seventh chord. Starting with an A, this 
would give us the notes A, C#, E and G. In conventional music theory, the distance between C# and E is a minor third, the same as the distance between E and G. However, in this example, the interval between C# and E is 6/5 = 1.2, whereas the interval between E and G is 7/6 = 1.1666. Our G of 7/6 sounds "in tune" (bearing in mind what a vague term "in tune" seems to be), but whilst it might be the correct choice of pitch for a G as part of our dominant seventh chord, it is not necessarily the best choice if we decided to make, for instance, an E minor chord. You may already have noticed this on a diatonic harp. When tuned in JI, 5 draw and 9 draw can sound rather flat in a melodic context, even though they sound fine when played as part of the draw chord. This is where the simplicity of JI runs into problems. On instruments which can play an infinite variety of pitches within one octave (such as the human voice, the slide trombone and the violin family), it is possible to play an infinite variety of intervals. On keyboard instruments and the fretted strings, this would require an infinite amount of keys or frets - clearly these would not be very practical instruments to play! So, one obvious solution to our problem with the two Gs, one slightly higher than the other, is to settle for one G, tuned somewhere between the two. This is the basic idea behind temperament: making one pitch serve more than one purpose, but sacrificing some of the purity of intonation in the process.

During the period, when the organ was the dominant instrument in Western music, the commonest temperament was called Meantone Temperament. There were several variations of meantone, but the idea was to provide pure major thirds, but sacrifice a little of the purity of the fifths. When one centers the temperament on a given key, then the further that one modulated away from this key, the less pure the tuning became. For example, on an organ in meantone with the tempering based on C, then the key of C major will produce almost pure chords. The keys of G major and F major are still very well tuned, but by the time you reach F# major and C# major, the organ is starting to sound very "out-of-tune". In fact, many composers exploited this aspect of meantone temperament and deliberately wrote pieces to take full advantages of the different tonal colours of the different keys. This is where we get "chromaticism" in its fullest sense, the word being derived from the Greek "chroma", meaning, "colour". However, other composers wanted to be able to modulate to farther keys, whilst maintaining consistent intervallic relationships. After several variations on the meantone principle and other systems (including the various Well Temperaments for which Johann Sebastian Bach wrote the famous "Well Tempered Clavier" collection), eventually European musical culture arrived at what is called "Equal Temperament", which is the commonest temperament in use today - in fact many people are not aware of any other method of tuning. Strictly speaking, it should be called "12 Tone Equal Temperament" (hereafter "12TET") or even more strictly speaking "12EDO" (12 Equal Divisions of the Octave), as the only simple ratio that is used is the octave 2/1, which is then divided into 12 equally sized semitones. In this system, C# became the same pitch as Db and every key was equally "in tune". It could also be said, however, that each key was equally out of tune! By the 19th Century, the piano had become the dominant instrument of Western art music and, for a variety of reasons, is somewhat better suited to 12TET than the organ. The strings of the piano suffer from inharmonicity which makes the natural overtones of the strings, particularly the upper ones, sound a little out of tune. Also, the roughness of the chords in 12TET is accentuated by the sustained notes of the organ, whereas the notes of the piano die away before the harshness of 12TET becomes too readily apparent.

So today, virtually all keyboard instruments and fretted stringed instruments use 12TET, so it would be logical if the harmonica did too - or would it? Like the organ, the harmonica can sustain notes for long enough for the roughness of 12TET to become obvious, even to the untrained ear. Not only this, but the harmonica produces very strong difference tones. Take the highest harp you have (an E or an F will do fine) and play 8 draw. Now play 7 draw. Now play them both together and listen very carefully -- you should hear a note that is lower in pitch than either of the notes you are playing; depending on how your harp is tuned, it will sound about an octave below 2 draw. This pitch is called a difference, or differential tone. When any two pitches are played, they produce other pitches equivalent to their sum (the frequency of the two pitches added together) and their difference (the frequency of the lower pitch subtracted from the higher). For example, if we 
were to play pitches of 2500 Hz and 3000 Hz, then there would be a difference tone of 500 Hz (3000 - 2500) and a summational tone of 5500 Hz (3000 + 2500). Usually, the summational tones are too high for us to hear and often, the difference tones are too low for us to hear, but the harmonica produces very strong difference tones. In fact, in the upper range of the higher pitched harps, the difference tones can be almost as loud as the tones that generate them. For more on this topic, please refer to this page:

http://www.patmissin.com/ffaq/q26.html

Difference tones on an instrument in JI, are perfectly in tune with the normal notes of the instrument. As an example, let us take three pitches in the ratio 4:5:6. As we have seen, this produces the most consonant major triad. The difference tones can be calculated by subtracting these ratios, giving us the difference tone of the major third:  5 - 4 = 1; and the 
difference tone of the minor third: 6 - 5 = 1. These difference tones are equal in pitch to a note two octaves below the root of the major triad (1 x 2 x 2 = 4). Even when we extend the chord to a dominant seventh, 4:5:6:7, which is considered a dissonant chord in 12TET, the added 7 - 6 = 1, still reinforces root of the chord, making the chord sound very rich and strong. Then, if you just play the 4:5 interval, the resulting sound will strongly suggest the major triad. When we play those chords in a tempered tuning, these difference tones are not quite in tune, so they produce the familiar beating effect of two notes that are almost, but not quite the same pitch. The more notes you have in the tempered chord, the more intense this beating becomes. Also, the intervals between the difference tones themselves produce what are called secondary difference tones, these in turn produce tertiary difference tones and so on. Eventually, you wind up with a rather nasty mess, instead of the clear rich sound of the JI major triad. For this reason, many chromatic harmonica players (as the chromatic is usually tuned to 12TET) have tended to avoid chords and double-stops. Charles Leighton has said: "I don't like the use of double-stops on the harmonica. To me, they're always out of tune..." As we have seen, this is not really the fault of the harmonica itself, but the fault of nature! 

So, we are left with a choice - do we tune so that the harmonica sounds perfectly in tune with itself, or so that it sounds perfectly in tune with the accompanying instruments? Thankfully, there is a certain amount of middle ground, so it is possible achieve a reasonable compromise. Even the notes that cannot be bent in the conventional sense can be lowered a small amount by the player's technique. Also, as there are only a few notes on the harmonica that can be sounded at any one time, it would make sense to use an intonational system that favours these chords, rather than chords that can't be played on the harp. If you intend to play a diatonic harp (or even a chromatic) in just one key, or a few closely related keys, especially if you play unaccompanied and use a lot of chords or double-stops, then 12TET may not be the best choice of fine-tuning. On the other hand, if you play a chromatic in all 12 keys using mostly single notes, or you are Howard Levy 
(!), then maybe something closer to 12TET might be the ideal temperament for you.

For more information on Just Intonation, I can strongly recommend the book "The Just Intonation Primer", by David Doty:

http://www.dbdoty.com/Words/Primer1.html
 

JUST INTONATION AND THE HARMONICA

In the next section, we will look at how to set up Just Intonation, or your own personal preference of temperament on the harmonica, without having to rely on an electronic tuner. This is not as difficult as one might imagine - as with all things, it gets easier with practice. Although the following describes putting a standard diatonic major key tuning into JI, the principles can be applied to any other tunings. Again, it is probably best to read through it in its entirety before attacking your reeds with abrasives.


SETTING UP JUST INTONATION BY EAR

The first thing to do is to set some reference pitches on the harp. If I am tuning a regular 10-hole diatonic, the first notes I tune are the blow reeds in holes 1, 4, 7, and 10. On a C harp, these would all be C notes. You need something to which to tune these notes. You could use a chromatic tuner, tuning forks, another instrument, or whatever is available to give you your chosen reference pitch (I usually set my tuner slightly higher than A=440 - see below). At this point, I sometimes also stretch the octaves slightly. This is similar to how a piano tuner sets the octaves on a piano, although it is done to a much lesser degree and for very different reasons (see below). This is a very much a matter of personal preference and involves tuning each octave a small amount sharper than the previous one - usually the amount of stretch is anything up to 2 cents - for example, the 1 blow tuned spot on with the tuner; 4 blow is tuned 2 cents sharp; 7 blow is tuned 4 cents sharp; and 8 blow is tuned 6 cents sharp. You may prefer less stretch than this (or no stretch at all), but I definitely wouldn't recommend going more than 2 cents per octave. I then double-check each note by playing octaves, and blocking out the two notes between each octave using my tongue. If you have difficulty with this technique, you could simply stop the unwanted reeds from sounding, by touching them with your fingertip. Be very careful to play the notes as cleanly as possible. Some players have a tendency to bend the notes a little when playing octaves. If the octave is slightly out (the 2 cents stretching shouldn't make a noticeable difference), you will hear the familiar beating effect, where the notes seem to fade in and out in a pulsating fashion. The ability to hear this beating is one of the most important aspects of tuning by ear. As the notes get closer to perfect tuning, the beating becomes slower and slower. It is not just octaves that beat in this way when they are mistuned; all intervals beat to some extent. Sometimes this is not undesirable. The tremolo-tuned diatonic harmonica relies on pairs of notes that are very slightly out of tune with each other, to produce the characteristic wavering sound of this type of harp. Unisons and octaves show up this beating quite clearly, but the beats from other intervals may be a little harder to hear, especially when you are new to tuning to by ear. With experience, however, it will become a lot easier.

The next easiest interval to tune by listening to beats, is the perfect fifth. I tune the 3, 6, and 9 blow next. Play 1 blow and 3 blow together (again, either by blowing either side of the tongue, or by stopping the second reed with your finger). Unless you are very lucky and the harp is in perfect just intonation, you will hear those pulsating beats. If you have an electronic tuner, check the tuning of 3 blow. In JI, it should be about 2 cents sharper than the tempered version. If you do not have a tuner, just sharpen the reed a little and check blow 1 and blow 3 together again. If the beating is a little faster, then you need to flatten the reed. If slower, then you need to sharpen it. Once you have the interval between 1 and 3 blow tuned, so that there are no beats (or, at least, so the beats are so slow you cannot really hear them), check 3 blow and 4 blow together. If this interval produces some beating, keep on working until you get beat-free 
sounds with both 1 and 3 blow, and 3 and 4 blow. Repeat this procedure with 6 blow, checking it against 4 blow and 7 blow; and with 9 blow, checking it against 7 blow and 10 blow. Finally, check the octaves 3/6 blow and 6/10 blow.

Thirds (both major and minor) take a little more careful listening to tune them by beats. A method which makes the beating more obvious is to play holes 1 and 3 blow, with 2 blow stopped (either with the tongue or the fingertip). When you have got these pitches sounding purely, allow 2 blow to sound. This will make any beating a lot more obvious. When you have got 2 blow so that the chord sounds pure (this will be about -14 cents on a tuner), check it against 1 blow and 3 blow. You may still find that there is a little beating between these notes. With practice, you should be able to hear the beats just by playing two adjacent notes. Repeat this process for 5 blow and 8 blow. This should leave you with all the blow notes in perfect just intonation. Any chords or intervals you play on these notes should have no beating at all. This will give the harp a clarity and depth of tone that is impossible to achieve in a tempered tuning.

The procedure for tuning the draw notes is similar. First of all, I tune 1 draw, 4 draw, and 8 draw, as well as stretching the octaves. I also tune the draw notes a little higher than the blow notes, usually by 4 cents or so. This means that according to a tuner, 1 draw is 4 cents sharp; 4 draw is 6 cents sharp; and 8 draw is 8 cents sharp. I do this because draw notes have a tendency to flatten out more than blow notes under increased pressure and some reeds do not always respond quite as they should in theory. So, often 1 draw winds up quite a bit more than 4 cents sharp. This is the advantage of tuning by ear - you can easily compensate for these idiosyncrasies. On most instruments, I tend to set the tuning of 4 blow and 4 draw first, then tune 1 blow and 1 draw to make perfect octaves with them.


STRETCHED OCTAVES

One question I am commonly asked is: "Why the 'stretching' of octaves?" Many of the people asking this question wondered if it is for reasons similar to why the piano is tuned with stretched octaves, but in fact this is not the case. With stringed instruments (especially the piano), the octaves are stretched a little to compensate for the inharmonicity present in strings. If a string were infinitely long, infinitely flexible, perfectly uniform in cross-section and lacking any dirt or tarnish, then it would produce perfectly harmonic overtones. Of course, in the real world, this is never the case, so the octaves are stretched to allow for the "out of tune" overtones. In the case of the harmonica, the overtones are almost perfectly harmonic, so this reasoning does not apply (although, if you regularly play with piano accompaniment, it may be a good idea to tune your harmonicas to match the piano scale). There is a wealth of material in the literature of psycho-acoustics which states that most people prefer intervals to be slightly "wide" (especially as they get older), rather than slightly "narrow" and my own experiments have confirmed that my customers (and myself!) prefer their harps tuned with stretched intervals, rather than compressed ones (although there are some temperaments which specifically require compressed octaves). A pair of notes tuned a perfect octave apart often sounds like a single tone - a very slight stretch tends to prevent the two tones from blending together. Of course, this stretching also permits some of the compensating measures mentioned in the previous paragraphs.

After setting these notes, I then follow the same pattern as for the blow notes, which is tuning the fifths first, followed by tuning the thirds. I tune 2 draw so that it forms a beatless interval with both 1 draw and 4 draw. I tune 6 draw so that it forms a beatless interval with 4 draw and 8 draw. Then, I tune 10 draw so that it is beatless when played along with 8 draw. Next, I tune 3 draw so that the chord of 2, 3 and 4 draw sounds pure (if you have tuned 4 draw to +6 cents with a tuner, then 3 draw should be around -10 cents, etc.). Then, I tune 7 draw so that the chord of 6, 7, and 8 draw sounds pure. Again, I check all of these with adjacent notes and octaves, until everything is nice and smooth. 


THE "PROBLEM" NOTES

If you have followed my instructions so far, you will have a harp where every note is justly tuned except 5 draw and 9 draw. At this point, you have to make a choice. If you mostly play cross harp and use a lot of chords, then the best option might be to tune 5 draw and 9 draw, so that they make a beatless chord with the other draw notes. According to a tuner, assuming you have tuned the other draw notes as I have suggested, then this note will register about 27 cents flatter than equal temperament (with 9 draw coming out around -25 cents if you are using a 2 cent per octave stretch). If this note sounds strange to you, when playing single-note melodic lines, then you may prefer to temper it slightly sharp. You could simply raise the pitch of the note to a point where it sounds right to your ears. Alternatively, you could tune it to its 12TET values, about +/-0 cents. This makes it a good fourth note of the C major scale when used melodically, but it does make the G7 chord (2, 3, 4, 5 draw) beat quite a bit, although the Dm chord (4, 5, 6 draw) is at least as good as in equal temperament. Actually, the minor triad beats faster than the G7 chord, but it is difficult to perceive beats when they are faster than a certain rate. Instead of the individual beats being heard, there is just a quality of roughness about the chord. Some players have experimented with tuning 5 draw, so that it is a pure minor third above 4 draw (which also makes it a pure major third below 6 draw, about +20 cents on a tuner). This means, that you can get deeper bends on 5 draw, as well as making third position very smooth. However, I find that it makes the G7 chord unbearably rough. It is a matter of personal taste, and I advise you at least to try it, to see whether you like it. 

My own personal favorite tuning is similar to using the 12TET tuning for 5 draw. I tune the 5 draw to make a 19-limit minor triad in hole 4, 5 and 6. This note would be 297 cents above 4 draw, so if you have your 4 draw set at +6 cents, then you would set your 5 draw at about +3 cents. How I tune it is by listening to the difference tone generated by playing holes 4 and 5 draw together and adjusting the tuning of 5 draw until the difference tone sounds exactly two octaves and a perfect fourth below 4 draw. On a C harp this would be a low A and if you tuner has the ability to play reference tones, you could set it to play a low A and tune until your difference tone matches it precisely.

Another reason for tuning the whole harp slightly higher than A=440, is to compensate for Just Intonation. If you set 1 blow relative to A=443 and tune by eliminating beats as previously described, then aside from holes 5 and 9 draw (if you are using the traditional JI tuning scheme), none of the other notes will fall more than a cent or so below their 12TET equivalents relative to A=440. As the natural notes of the harmonica can only be bent downwards rather than upwards, it is better to have notes sharp, rather than flat. You can then use your playing technique to correct this - in fact, most good players are probably doing this kind of thing all the time, without even thinking about it. Even the notes that cannot be bent in usual sense of the term, can still be lowered by 20 cents or more, which is enough to bring most notes into line with your accompaniment. In this way, it is possible to have your cake and eat it - you can have a justly tuned harmonica so that the main chords sound rich and smooth, but also, you can bring all the notes into Equal Temperament relative to A=440Hz, so that you do not sound out of tune with your accompaniment.


JI ON HARPS WITH OTHER NOTE LAYOUTS

The harmonic minor harmonica also has a dominant seventh draw chord (with an added flat ninth), so again a completely pure tuning requires the 5 draw and 9 draw reeds to deviate quite a bit from equal temperament. Also, 6 draw and 10 draw will have to be a little sharper than equal temperament. These considerations do not apply to the natural minor tuning or Melody Maker(TM) tuning, both of which can be tuned so that each note can be in the simplest possible ratio to its neighbours. However, although in the last couple of years, I have come to be a very strong advocate of Just Intonation (to the extent that tempered tunings sound "out of tune" to my ears), I should point out that many players actually prefer some form of tempering, not just on 5 and 9 draw of the regular major tuning. More details about fine tuning for these other layouts can be found on my website.


OTHER CONSIDERATIONS

For me (and many other players), chords and double-stops in Just Intonation have a special quality described as "depth", "purity", "smoothness" or "fullness." Some people, on the other hand, would choose to describe them as "bland", or "lifeless." These people may prefer to have a very slight beating to the chords, achieved by tuning the intervals slightly closer to equal temperament. Using the methods described above, you could tune all the octaves, fifths, and fourths so that they are beatless. Then, tune the remaining notes so that they just add a little "movement" to the chord.

Another consideration is the instruments that normally accompany you. If you regularly play with a fixed-pitch instrument, such as a piano or organ (most string and wind players can adjust their intonation to be in tune with you), you can also adjust the notes on the harmonica to be more in tune with them). You might prefer to be closer to 12-tone equal temperament, to match their intonation more closely. As I said before, this is all a matter of taste. Experiment (not on your favorite/most expensive harmonica!), and listen.

As well as beats, the phenomenon of difference tones can be used to help in tuning the harmonica (see above). At the top end of the harp, the difference tones can be almost as loud as the tones that generate them. If you play 7 and 8 draw, if they are tuned purely, then you should be able to hear a note of the same pitch as 2 draw, but an octave lower. As this is the root of the chord, it makes it sound as though you are playing a full chord, even though you are only playing rather high-pitched notes. If you have tuned 9 draw purely, then playing 8 and 9 draw will produce a difference tone of the same 
pitch. However, if you have tempered 9 draw a little sharp, the difference tone will also be slightly sharper. If you play 7, 8 9 draw, then you will have beats occurring between the two difference tones. I could quite easily digress towards an examination of these phenomena, but that is a little beyond the scope of this article. If you try to tune a few harps using these methods, I am sure you will find out more for yourself than I could include in an article three times the size of this one.


... AND FINALLY...

Although this article has been written mostly with the diatonic in mind, these principles might also be of use to players of other types of harmonica (e.g., double-reed diatonics, chromatics, chord instruments, etc.). If you have any further questions, please send your correspondence to:

pat@patmissin.com 

and I am on the web at http://www.patmissin.com



©2001-2016 P.R. Missin