On the Tuning of Chromatic Harmonicas

Background

The musical scale consists of 12 half steps or semitones, which (for the key of C) are:

A major scale is just some of those:

You can dig into the exact frequencies of chords and half step, do Just Intonation or Equal Tempered. For example is D 9/8 or 10/9 the frequency of C? But it turns out I can't hear the difference. I'm not sure if my ears aren't trained at all, or are trained to ignoring the difference, but the upshot is for me it doesn't matter and I might as well treat all half steps the same. The piano I grew up on was tuned so C was a little above Bb.

Diatonic Harmonicas

A diatonic harmonica (a normal blues harp with Richter tuning) has 10 holes. Each can be blown (breathe out) or drawn (breathe in). It covers 3 octaves:

The distinctive blues sound that harmonicas make is called a bend. For example, Swing Low Sweet Chariot. The player, by doing something with their mouth, can make the note bend lower than the normal tone. They never bend up. Some notes can be bent further than other notes. Usually bends are on draws, but sometimes they can be on blows too. I originally figured bends had something to do with specialized reeds. Nope.

Reeds, valves: there's a comb-shaped block inside the harmonica, and the holes are the spaces between the comb's teeth. The teeth keep the air from one hole getting to the other holes, the air can only go out the top or bottom of the harmonica. There are metal plates on both sides of the comb with reeds covering the holes. The bottom (or top) plate has a draw reed on the outside of the plate fixed at the end away from your mouth and free to vibrate at the end near your mouth. The other plate has a blow reed on the inside of the plate fixed near your mouth and free to vibrate away from your mouth. When you blow, the free end of the blow reed away from your mouth flaps back and forth through its plate, making sound. The draw reed on the outside of its plate and free end pointing towards your mouth mostly sits there, but it does bend out some and let out air. Reeds act like springs, the further they are bent the more force is trying to bend them back to straight. The length and weight of the reed and strength of the springing force determine the pitch of a reed. A half-valve is a flap of leather or plastic on the inside of the draw plate totally covering the draw hole (the draw reed is on the outside of the plate). When you blow, the valve covers the hole completely and no air gets out. When you draw, the valve gets sucked out of the way into the hole, leaving the draw reed free to vibrate. A valve for draws would be on the outside of the blow plate (the blow reed is inside). Valves assure all your air gets used on the reed that is vibrating, not just passing out the other side of the hole uselessly, so you don't have to breathe as hard to play. Bends are some interplay between the two reeds, but valves prevent that by isolating one of the reeds.

It turns out there's a bend rule: If the blow and draw are different, then the higher note can bend down to within about half a step of the lower tone. I don't know how it works, but I have a guess. The rate of vibration of a reed alone is determined by how strong the springing force is when it's bent pushing it back to straight. The more bent it is, the more force. Each reed is tuned to have a particular frequency. When you draw and the draw reed is vibrating and the blow reed is just stitting there, the draw reed is causing rapid changes in air pressure (which is sound) which is a force pushing the blow reed back and forth at that same frequency. It's not the blow reed's frequency, but the blow reed isn't bending much so the force from its bending is mostly irrelevant. But if you can change it somehow so that the blow reed vibrates more and the draw reed less, then the bending strength of the blow reed gets more relevant and the bending strength of the draw reed less, so the frequency moves towards the blow reed's frequency. That's my guess for why bends work.

The bend rule predicts that the number of half steps you can bend each note on a harmonica are:

On a Richter, hole 3 draw (normally B) can bend to a Bb, A, or Ab. The difference isn't how hard you pucker your lips at all. It's the shape of the cavity formed by the tongue. Bb I need a tiny cavity with my tongue curled and close to the harmonica. A, still curled, further back. Ab, tongue flat against the bottom of my mouth, big cavity with the back of my tongue constricting the throat about level with the back molars or further back. Hole 2 can bend to F# or F: same thing, F needs a big cavity. Hole 1 from D to C#, you can get a much deeper C# with a big cavity than a little one. Generally the lower holes and bigger bends need bigger cavities and the upper ones, smaller.

Holes 7..10 on a Richter bend on blows instead of draws. Same thing: it's the size of the cavity. Getting a bend out of hole 10 needs a tiny cavity, with the tongue almost against the roof of the mouth near the top teeth.

There's also something called overblows that produce a distinct note about a semitone higher than the high note. On a Richter, the easiest is hole 6 blow, which goes up from a G to a Bb. Hole 5 overblow is an F# and hole 4 overblow is an Eb. It doesn't require blowing very hard. It's cavity shape again. I've only done hole 6 so far. Hole 6 draw needs the tongue near the front teeth. Hole 6 overblow has a bigger cavity of a certain shape, nearly at the roof of the mouth about level with the front molars. Drawing with that shape does do quite an Ab bend, but it's bigger than my normal Ab bend shape. I'm going to ignore overblows from here on.

Augmented Tuning

If a diatonic harmonica had augmented tuning (every hole a major third above the previous hole), with a minor third between blow and draw, every pitch would be reachable either directly or through a bend. This exists. The Seydel configurator calls it plain "augmented":

Every draw can be bent two semitones, or just a semitone. Three holes per octave, so it covers 3.3 octaves. No three-hole chords at all. Tongue-blocked octaves are possible (only for some notes, unless you consider bent tongue-blocked octaves possible).

Diminished Tuning

A harmonica could also use diminished tuning, with a minor third between consecutive holes, and draw a whole step above blow. This exists, the Seydel configurator calls it plain "diminished":

A C-scale needs bends for E and G. 4 holes per octave, so it only covers 2.5 octaves. Tongue-blocked octaves are possible (probably excepting bent notes). 2/3 of tones are reachable directly, and the remainder are bent a semitone where that's all the bending the hole supports, so this is probably the easiest diatonic tuning for playing all semitones.

Diatonic Antiharp

Timing myself, I can sustain a blow note for about 50 seconds, but a draw for about 36. On several harmonicas I've found draws to be less airtight. So, how come we prefer bends on draws, seeing how bends usually take even more air than plain notes? One possibility is that bends push moisture into the instrument, while draws air it out, so leaning heavily on blows over draws might clog up the reeds with moisture.

Well, one way to find out would be to try it and see. You could simply reverse all blows and draws on a Richter diatonic, producing an antiharp:

This is exactly the same as a normal harmonica, with the exact same bends even, except draw bends are replaced with blow bends and vice-versa, and overdraw hole 6, et cetera.

I tried it by swapping the top and bottom reed plates in a Hohner Special 20. (You can do that.) It turns out blow bends need a bigger resonance chamber (mouth cavity) than draw bends. Lower notes need a bigger cavity than high notes, I think the cavity length has to double when you drop an octave. I don't think blow bends were a full octave bigger than draw bends, it was more like a third or a fifth. So the bends on holes 1..3 are difficult to impossible with blow bends, because your mouth just isn't big enough even though they're easy with draw bends. And the draw bends on holes 7..10 are also more difficult because it's hard to make your mouth cavity that tiny.

So, the antiharp is a bad idea, on both the high and low end. Perhaps holes 4..6 would be better as blow bends (giving them a bigger mouth cavity). Or perhaps not. Overblows on 4..6 would become overdraws, so they would get smaller mouth cavities.

I tried swapping reedplates on a Seydel Sampler too. Didn't work. The rivets away from the mouth got in the way.

Chromatic Harmonica and Sliders

A chromatic harmonica avoids the diatonic problem of skipping some notes by splitting each hole horizontally into two holes vertically, and having a slider (a button you can press that slides a cover over the holes that determines whether the upper or lower holes are open). Rather than blow reeds in the top plate and draw in the bottom like a diatonic, both plates have a blow and a draw reed next to each other per hole, and the slider determines whether the top plate or bottom plate is being used. That gives you four modes per hole instead of two: blow, draw, blow slide, draw slide. The slider button has a spring keeping it out, so it takes work to push the slide in and keep it in, favoring the two nonslider modes.

Solo Tuned Chromatic

Chromatics typically have 12 holes and typically have this layout (solo tuning) covering 3 octaves, where the slide always raises the non-slide notes by a semitone:

The neighboring C notes are usually tuned slightly differently so if you blow both at the same time you get a slow vibration known as a tremolo.

I found its tongue-blocked octaves were good for The Entertainer. I've also seen it used with vamping, like Chattanooga Choo Choo. It can also play one note at a time, but that's surely easier with something like a diminished Irish tuning (with predictable blow/draw options allowing phrases to be more legato) or the obvious augmented tuning (with no repeated semitones, so more octaves and smaller jumps between notes).

Usually chromatics are valved, which means bends are impossible. But some chromatics are valveless, so bends are possible, or half-valved, so bends are possible on draws.

If bends are allowed, the predicted bends for a solo-tuned chromatic harmonica are:

If I were designing the layout for a harmonica, I'd try to avoid neighboring notes differing by a half step or whole step or dimininished fifth, I'd try to pack notes in, and I'd try to avoid repeating notes. I would make bends as big as possible. The standard chromatic, with repeated neighboring notes and bends often disallowed, seems to me a very odd design choice.

This layout came from an earlier diatonic harmonic (US patent 863960, from 1907), where the goal was to cover every note of the scale, unlike the previous Richter tuning. It has a nice side effect for a technique not used much nowadays: playing octaves by tongue-blocking. Octaves by tongue-blocking require the pattern to repeat each octave. There are seven distinct notes in the C scale, and only two modes (blow and draw) in a diatonic harmonica, so three notes have to be one mode and four the other, requiring four holes per scale. Each octave must repeat the same pattern for octave-playing to work. If the original harmonica had been chromatic, with 4 modes not 2, this could have been done in 2 holes, or 3. If you want all 12 semitones you can still do tongue-blocking octaves in 3 holes on a chromatic. But if you start with a solo tuning designed for a diatonic and extend it to a chromatic by the slider blindly raising everything a semitone, you get solo chromatic tuning.

Even so I think it is odd the slider goes up a semitone instead of down. That's done (Pat Missin calls it Irish Tuning.) You can swap slide and nonslide on any chromatic harmonica by keeping the button on the same side but flipping the slider so the away side is now front facing, so the slider's top holes are now on the bottom and bottom holes now on the top. Except my Forerunner 2.0 has a tiny hole in the slider for the spring, and it's only on the top of the slider. I don't have any drills or punches on hand capable of adding the extra tiny hole in the metal slider. Boo.

Richter Tuned Chromatic

There actually WAS a popular chromatic that wasn't solo tuned. Perhaps the most popular chromatic ever: the Hohner 260 Chromonica. It was 10-holes, Richter-tuned like a diatonic, and the slider shifted it up a semitone. It was fully valved.

Or, if you're me, you use tweezers to pull all the valves off so it can do bends and overblows, and you flip the slider around making it a C# harmonica that can bend down to C. It's easier to think of as a C harmonica that can bend down to B. This does 3 holes per octave. It can do all the normal diatonic stuff, like Amazing Grace, and the normal chromatic stuff, like The Entertainer, and crosses that aren't reachable on either, like Gershwin's Summertime, or George Washington Bridge with chords. I got one for $15.00 plus shipping off eBay, but they have fragile wooden combs and usually have a smell of cigarette smoke that you can't ever remove.

Rules

There are lots of possible tunings. Enough that it becomes an art rather than mathematics. Mostly it comes down to what rules you want to enforce, what goals you want to meet. Here are some rules (many are contradictory):

• Have a hole/mode for every possible semitone.
• Have a way to include every semitone if you allow bends.
• Don't repeat semitones.
• Cover lots of octaves.
• Have a hole/mode for every possible note in the C scale.
• Have as many 3-hole major and minor chords as possible.
• Avoid intervals that are a halfstep, wholestep, maybe diminished fifth.
• Have a variety of intervals, including the occasional half step and whole step.
• Favor intervals useful for a particular key.
• Allow lots of big bends.
• Simple rules for the interval for blow/draw and nonslide/slide.
• Avoid needing to go down a hole when going up the scale.
• Preserve the CEGCE blow DGBDF draw of Richter tuning.
• Have tremelos.
• Allow tongue-blocked octaves (requires notes to repeat an octave up).
• Have useful tongue-blocked intervals.
• Easy transposition to different scales.
• Play legato.
• Flexibility: many ways to play each note. (Or at least some notes ... if one note has only one option but the next has three, you can still probably get your phrase to do what you want.)
• The slider can be pushed in occasionally, or kept in and let out occasionally. Make both approaches useful and complementary.
• Have draw bends on low notes and blow bends on high notes.

Tunings

The Obvious Augmented Tuning

All modes advance by major thirds, draw is two semitones above blow, slide is one semitone below nonslide. 11.1 in Pat Missin's "Altered States", covered by many patents back to at least 1979. y

This is the most obvious layout for a chromatic harmonica (at least if you have no a-priori reason for the slider to go up a semitone rather than down a semitone, otherwise going up a semitone works too). Each hole covers four consecutive semitones. Every pitch is covered exactly once. Three holes per octave, four octaves in a 12-hole harmonica. Tongue-blocked octaves work. All draws can bend down a semitone (if you allow bends).

This is key-agnostic, and the pattern is very simple, so once you learn a scale you've learned three scales, and you can learn all 12 scales by learning 4 patterns. Each octave is 3 holes, 12 notes covers four octaves. The pattern repeats every octave so this does support tongue-blocked octaves. You do have to use the slider to play a C scale. Some pitches are not reachable without the slider even through bends.

Compact Chromatic Tuning

I tried laying out my own tuning. More compact than solo. No repeated notes or whole steps. Every semitone covered. (So far, the obvious augmented tuning achieves this, even if Solo does not.) Every mode (blow, draw, slide blow, slide draw) forms a major or minor chord. I'll call this the compact layout. Slider does not uniformly shift up, it always shifts by a semitone but sometimes it is up and sometimes down. It uses 3 holes per octave not 4, and covers 4 octaves not 3 (there is no capping high C#). All octaves have the same pattern, so it allows playing tongue-blocked octaves.

The predicted slides for the compact layout are

I actually got one of these made. It isn't very airtight, especially on draws, bends even moreso, so bends aren't very useful on it. (On my EastTop Forerunner I can do 36 seconds draw, 50 seconds blow. On this I can do 11 seconds draw, 26 seconds blow.) I flipped the slider so slide and non-slide are reversed. That way F# is the easiest key to play, since do mi sol are blow and only fa and ti need the slider. It has the range to play Solfeggietto, in Am or G#m, but it's almost exclusively draws in those keys. (If I build further tunings, I'll attempt to rearrange Hohner Chromonicas myself.)

It starts on C#. That's annoying at least for beginner songs, you really want the tonic of the bottom octave. Fortunately I'm not playing it in C anyhow. I've flipped the slider so blow/draw are F#, G# major instead of D, E minor. I can't bend the bottom two holes, I think my mouth isn't big enough for the cavity required. I haven't found any song so far where intervals make sense ... it's always a mistake to play more than one note at a time.

If you have a harmonica with the obvious augmented tuning, and a slider that slides a half-hole to choose either the top or bottom reedplate, you can make this compact minor/minor tuning just by changing the slider: choose top-bottom-bottom (repeating each octave) rather than top-top-top. If you prefer major/major, just flip the slider to Irish so it chooses bottom-top-top.

If sliders can be flipped to Irish, there's only three alternative sliders possible: 100, 101, 110 (top-top-top is 111). If you consider 4-hole octaves, there's 7 more: 1000, 1001, 1010, 1011, 1100, 1101, 1110. You could probably 3d-print all 10 alternative sliders.

A very similar alternative is major/minor and minor/major:

This one's actually old, it's in Joseph E Murphy's US patent 882575 from 1906. Except he had blow slide and draw slide reversed, meaning that bends are on blow not draw when the slider (well, lever in his case) is engaged. I think he missed the boat here: it's a good thing to be able to do C-B-C just by pressing the slider (lever) instead of switching blow/draw at the same time.

Diatonic Spiral Tuning

But wait. Is it actually easy to play anything on that? What makes a harmonica easy to play? A diatonic has many chords laid out in a row in each mode: CEG of course with blow, but DGBDFA has two G majors, then a G major seventh, then a D minor all in a row.

There is an alternate tuning of diatonic harmonicas called spiral, which does CEGBDFA in a loop on both blow and draw, and covers an octave in 3.5 holes. The .5 means that each note alternates from blow to draw or back each octave. That layout exactly is:

Spiral tuning gives you the C, Em, G, G7, Dm, F, Am chords in each octave. You could run arpeggios on any of those chords over many octaves by switching from blows to draws and back as you go from octave to octave. Draws are always a note above blows, and blows are always a note below. It doesn't quite cover 3 octaves, it's just two and two thirds octaves. All draws can bend, usually pretty well:

That seems like it's usually an improvement over Richter in chord variety, and it has way better chords than the Compact Chromatic Tuning. Spiral Diatonic has all C Em G G7 Dm F Am chords. "Amazing Grace" is particularly well suited to spiral tuning: it wants FACE and DFAC chords in addition to the usual FAC, ACE, CEG, and GBD.

A downside of spiral tuning is you can't tongue-block octaves like you can on blows on a Richter or everywhere on a Solo or Compact Tuning (Solo requires tongue-blocking three holes, Compact only two). Another downside is that all chords are in root position only.

Compact Spiral Chromatic Tuning

So, back to the drawing board. Here's the best Compact Spiral Chromatic Tuning I came up with:

There are four patterns: one for the starting hole on BbBCC#, one for BCC#D, one for CC#DEb, and one for C#DEbE. They all have a pattern that repeats every 4 octaves. Draw, slide blow, slide draw repeat the pattern one, two, and three octaves above blow respectively. Or below not above, it could be done either way. The patterns all have two augmented fifths, one totally bendable and one nonbendable. This was the only pattern that placed the nonbendable augmented fifth mostly on accidentals, making more notes in the C scale bendable. This one has major/minor chords C#, F, Am, C, Em, G, Bm (it lacks Dm and G7). It does cover every semitone exactly once, in three holes per octave, so four octaves total (there is no capping high D). Bending isn't great, but often exists, it looks like this:

Chromatic Interval Tuning

Well wait again. What's so great about the Richter Diatonic? It's mostly the CEGCEG/DGBDFA in the lower two octaves. Those repeat a G and are missing lots of notes. It makes up for the missing notes with bends. Well why is it great if it's got repeated notes? And missing notes? Well, alternating EGC/DGB chords sound great, especially with all the bends. So maybe blues harmonica is about bends plus chords or intervals, rather than notes? If we take the bottom two Richter chords as revealed truth, can we keep them and extend them into something better that covers more chords and intervals?

Here's another tuning, maximizing useful intervals for the key of C. All semitones can be reached either directly or through bends. The pattern repeats every 2 octaves. It does not repeat intervals within an octave. There are two useful intervals in C starting with B (BD and BE), but only one ending in B (GB), so to reach both starting intervals you'd either have to repeat GB or add an F#B or G#B. Similar for CF, DF versus just FA, you'd need FAb or FBb. I added and F# and Bb, and got this:

This does not cover every semitone directly, but it does through bends. There are many repeated notes in different modes, but no repeated intervals within an octave. It covers four octaves, A through B. It covers intervals CE, CF, DF, DF#, DG, EG, EA, FA, FBb, F#A, GB, GC, AC, AD, BbD, BD, BE (though the ones with F# and Bb are only every other octave). It covers 3-hole chords C, Am, G, Em, Dm, F, D, Bm, Bb (though sometimes only every other octave). Playing the C scale up requires going up to an A, down to a B, then back up to a C every other octave, unless you bend the B to get the A. Bends are only on draws, are on every draw, and are huge:

The tone layout seems pretty arbitrary, you'd just have to memorize what is available where. Tongue-blocked octaves aren't possible in every position and mode, but they are available in some. All notes of the C scale are always available for tongue-blocked octaves somewhere: CE on blow, GB on draw, FA on slide blow, and D on slide draw.

I've been told the harmonica one of the devil's instrument (by a man who hand-builds racketts). Because it doesn't have intuitive rules, and some pitches are just impossible, so playing it requires excessive cleverness. This tuning leans into that.

The bottom notes of Richter tuning are still there. CEGCE is in blow and DGB is in draw. Further, BDF is over in slide draw, FA is in slide blow, and EG is back in draw. It doesn't capture the full chords of the bottom two scales of Richter but it does capture all the intervals, keeping DGB and BDF bendable. It makes DF#B, DFA, and FAC available alternatives in the lowest octave, too. It should allow almost all of blues and then some. It's likely fun to play. It should be good for vamping because it has a lot more useful intervals and chords available than other harmonics.

Simplest Tuning

Being hard to learn and work with is usually considered a bug, not a feature. Although sometimes it's fun to do things that are hard just for the sake of showing off that it can be done. Still, simple is good.

Here's the simplest tuning possible:

Those aren't even C in different octaves, they're all the same C. It is an utterly useless tuning. But, you have to admit, it IS the simplest tuning possible for a chromatic harmonica in C.

There's a moral to this tuning: be careful what you wish for. The best tunings aren't just perfect in one goal, they're being moderately good at lots and lots of different goals, while emphasizing some goals over others. A lot of evil in this world is simply priority inversions, where two goals are both valued but one is valued higher than the other when it should be the other way around. A lot of evil in this world actually looks evil from both directions, because the other guy thinks you are doing the priority inversion not them. So pay attention to what you're valuing vs not valuing.

Diminished Irish Chromatic

A very simple tuning: all modes follow diminished thirds, draws are two semitones above bends, slide is one semitone down.

There are only three diminished series (containing C, C#, or D), so two of the four mode are required to repeat. I like Irish tuning better than the normal raised semitone with the slider.

The advantage of using pure diminished series is it's a very simple rule and key agnostic. Once you've learned the pattern of a scale, you've learned four different scales, so learning three patterns gives you all twelve different scales. Blow and draw are separated by two semitones, so draw always has a semitone bend, so you could cover all semitones with just slide or nonslide if you include bends. Three octaves in 12 holes, same as solo tuning. Each octave has the same pattern, and is 4 holes. This does support tongue-blocked octaves.

This tuning isn't new, it's been done lots of times, the Seydel configurator lists it as "diminished" (actually I think theirs isn't Irish but you could flip the slider to make it Irish if you wanted).

Augmented Bending Chromatic

A very similar variant on the obvious augmented: all modes advance by major thirds, draw is a minor third above blow, and slide is two semitones up.

There are four augmented series, containg C, C#, D, or Eb, so have each mode do a different one. Since blow/draw are separated by a minor third, every draw has a two-semitone bend, so you can cover every semitone with draws without the slider. (I would have preferred Irish to slider going up by two semitones, but that would have skipped one series and repeated another.) You can play a C scale without bends but you sometimes have to go backwards. With bends you can play it with or without the slider.

This isn't a new tuning, Seydel configurator lists it as "augmented".

Spiral Slide Tuning

Another simple tuning: all modes advance along the C scale by thirds. Both draw and slide shift up a note of the C scale. It's the cross of spiral tuning and the diatonic slide tuning.

This supports chords C Em G G7 Dm F Am. As with spiral tuning, you can play arpeggios of any of those chords in a single mode by breathing in and out on alternative octaves. As with Brendan Power's diatonic slide, you can do ornaments or avoid rapid alternating blow/draws by using the slider button. All accidentals are reachable by bends with or without the slider. It covers three and a half octaves. It does not allow tongue-blocked octaves.

This may not be best for jazz or blues, but it's probably good for traditional music. There's only one lower and upper interval per note, so it isn't nearly as interval-rich as the interval tuning, but that's fine for music that usually plays one note at a time. The slider is useful for fast music by being predictable and avoiding switching blow/draw on neighboring notes.

Since it's all in the key of C, it should use Just Intonation. There are several Just Intonations for notes. D could be 10/9 or 9/8 the frequency of C, ratio 80::81. (10/9 gives a good D minor, 9/8 for a good G major.) Since every note is repeated twice, once on a blow and once on a draw, the blow could use the lower and the draw could use the higher of the two (9/8 for G major) and the higher could be bent down if you want.

F could be from F major (4/3) or from G7 (21/16), ratio 64::63. If you want G7 you want the G-based D, which places the G-based F on draws, and if you want D minor or F major you want the F-based D, which places the F-based F on blows. But the G-based F is lower than the F-based F, so you can't bend the G-based F to the F-based F. So my best guess is to only do the enharmonic tunings for D. An alternative is to do it for F as well, and an alternative alternative is to do it for D F and A (80::81). Doing it for A would give a dissonant A minor on draws. Doing it for A would give you a good G9, but that's pretty obscure. You already have a good C9 just from doing D. Well not really. Because this tuning omits the Bb in C7 which is a vital part of the C9 chord.

Spiral Irish Tuning

This tuning is also spiral tuning without the slide, but the slide moves everything by a semitone down (not the usual up by a semitone, and not by the diatonic slide's up by a note of the scale). I was trying to play "The Entertainer" on a C solo chromatic, and discovered it is much easier, with decorative intervals even, if you treat it as a C# harmonica with the slider in where you let the slider out (shifting down a semitone) for ornaments. But it's rough holding the slider in all the time. The solo's repeated C's and consecutive AB's got in the way, as usual, so I'm opting for spiral instead. Although, "The Entertainer" has lots of octave intervals and this doesn't allow tongue-blocked octaves. This has chords C, Em, G, G7, Dm, F, Am, B, Ebm, F#, F#7, C#m, E, Abm.

Bends are the same as spiral slide.

This isn't new, in Seydel configurator this is "circular (1st position)" with the slider flipped.

Chord Monster Tuning

This is one of those "be careful what you wish for" tunings.

How many 3-hole chords can a harmonica pack in? Since there are 12 semitones, there are 24 major and minor chords. If an octave is 3 holes and there are 4 modes, there are only 12 reeds per octave, and each can start only one chord, so you can't have more than 12 chords per octave. 4-hole octaves would allow 16 chords per octave. But you could theoretically pack all 24 within two octaves.

Voilà:

This actually packs 28 chords in 7 holes instead of 24 chords in 6. (The extra chords are C7, A7, F#7, and Eb7). The modes are all spiral tuning, with the different modes offset by minor thirds: the spiral tunings for F, D, B, and Ab. The bad thing about this tuning is that if a chord is in one octave, it isn't in the next octave, and most songs are in a single key spanning two octaves. You can't do a C scale on this without bends. With bends, you can do it without the slider. If you want maximum chord flexibility you should probably get a melodica instead.

All draws are a minor third above their blows, so all draws can bend 2 semitones, pretty good.

Augmented Minor Fourth

If you have just majors on blow, and a minor third up to draw, then between blow and draw and the bends on draw you can reach all accidentals. All the intervals are major thirds.

If the slide is then minor-fourth-minor-fourth, it matches up with major-major-major-major every other hole, and the whole pattern repeats every 6 holes. If draw is a major third higher, bends can reach all accidentals. All intervals are minor thirds or fourths.

Put the two together and you've got a lot of minor thirds, major thirds, fourths, and at least two ways to reach every pitch. Every pitch appears exactly once. I don't know of anything this tuning is good for, but that could be ignorance. You can cover the C scale without bends (except for the low D and high C) but sometimes you have to go backwards. You can also do it with bends but no slider. Although it goes out of its way to have lots of minor thirds, major thirds, and fourths, it misses many and the ones it has are repeated between blow slide and draw side and aren't often used together. It contains chords F#, F#m, D, Dm, Bb, Bbm. I tried to favor C, but it's pretty key ambivalent. It covers 4 octaves.

Each minor-fourth mode formed all majors and minors of D, F#, Bb. Those are all in the same augumented arpeggio. There are four such arpeggios: DF#Bb, EbGB, EAbC, FAC#. By making blow and draw a fifth apart, I caused them to form the same chords. The main chords most songs want (C, Am, F, G) are on three different arpeggios, so no choice of draw distance for minor-fourth will give you all of them. None of C, Am, F, G are present in this tuning, in fact the EG, BD, AC intervals aren't even present.

I don't like these augmented minor fourth tunings. But they do have big bends.

Minor Spiral Tuning

(March 2024) Non-slide is spiral tuning in F. Slide is spiral tuning in D, a minor third above that. Bends are on blows not draws.

This gives 3-note chords Gm, Bb, Dm, F, Am, C, C7, Em, G, Bm, D, F#m, A, A7 in every octave. It covers 3.3 octaves (Bb to D). Not all pitches are reachable directly (Eb, G# are missing). Eb is reachable by bends. G# requires an overdraw. Since slide G->F# isn't a useful bend, tune those reeds to make overdraw easier. Draw takes slightly more air than blow, bends take slightly more air than nonbends, so I put the bends on blow rather than draw to make bends easier. It's got tiny bends.

This might be a very good tuning. It's got a huge variety of useful chords. Scales and arpeggios are easy.

Two Hole Octaves

So, you can do an octave in three holes instead of four. Can you do it in two holes per octave? Um, yes, if you include bends.

Fourth Fifth Tuning

(February 2024) Every hole goes up by a major fifth in the key of C (except a diminished fifth from F to B). Draw is always up from blow by four notes of the C scale (so actually a diminished fifth from F to B). Slide is a third below non-slide (in the key of C).

This covers 4 octaves per 7 holes, and it takes 7 holes for the pattern to repeat. All notes of the C scale are present without bends, but playing a scale without bends requires jumping back a hole: Blow N, Slide Draw N, Slide Blow N+1, Draw N, Blow N+1, et cetera. Since draws are a fourth or diminished fifth above blows, it has big bends. Seydel's Configurator only offers 4.5 octaves, so there aren't reeds available to make a 12-hole harmonica with this pattern (that would cover 6 octaves). Not all semitones are covered without bends, but with bends all semitones are covered, usually multiple ways. It's a variant on spiral tuning.

Two Hole Scale Tuning

(February 2024) Draw is a fourth above blow (except slide blow F to slide draw A). Slide is a third above nonslide in the C scale (except draw G to slide draw A). Blow is GDGD, slide blow is BFBF.

This packs all the notes of the C scale in two holes, with G repeated, and the pattern repeats every octave. All draws can be bent and all semitones can be reached by bends.

Two Hole Chromatic Tuning

(February 2024) Draw is a fourth above blow. Slide is a minor third above nonslide. Holes advance by diminished fifths.

Every two holes is an octave, so a 12-hole harmonica would cover 6 octaves. All semitones are reachable if you allow bends. Two of the three diminished arpeggios are reachable without bends. The rules are very uniform. Tongue-blocked octaves are possible. But accidentally playing two neighboring holes always gives a diminished fifth. The draws are all a minor third apart, so their bends mostly do not overlap. Those semitones that are not a pure blow or draw can be reached by a one-semitone bend of some draw.

Having draw 2 semitones above blow instead of 5 would also cover two of the three diminished arpeggios and make the third accessible by semitone bend. It would make bend range smaller but make it easier to tune your bends correctly.

Fractions of a string and musical tones
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