SPAH, August 2011 Introduction to Fourkey Tuninghome.uchicago.edu/~rmyerson/reading/fourkeyintrod.pdf · 2011-08-11 · Introduction to Fourkey Tuning A new way to get those missing

SPAH, August 2011

Introduction to Fourkey Tuning

A new way to get those missing notes!

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Desirable properties for a diatonic harmonica

(Andy Newton's wish list)

1. Chromatic completeness: All 12 notes in the chromatic scale should be playable

as straight draws or blows or as simple draw bends. (No need for overblowing.)

2. Straight major scale: At least one major scale should be playable with just

straight blow and draw notes.

3. Octave repetition: The pattern of blow and draw notes should be repeated the

same way in every octave.

4. Regularity: Notes should always get higher as we move from left to right

between holes and, within each hole, as we go from blow to draw.

(No back and forth.)

Andy Newton showed that there are only three ways to satisfy these four properties:

• a 5-hole-octave pattern that plays 4 major keys without bends (fourkey tuning),

• another 5-hole-octave pattern that plays 2 major keys (twokey tuning),

• a 6-hole-octave pattern that has no bends (chromatic tuning).

These four properties cannot be satisfied with less than five holes per octave.

Some tunings that satisfy all but one of these properties

This bebop tuning gives us two straight major scales (C and F), satisfies octave

repetition and regularity, but it is not chromatically complete because the

straight notes and draw bends do include Eb or F#.

This diminished tuning is chromatically complete, satisfies octave repetition and

regularity, but it does not have any straight major scales without bending.

diminished tuning

blows C Eb F# A C Eb F# A C Ebdraws D F Ab B D F Ab B D F

bends Db E G Bb Db E G Bb Db E

bebop tuning

blows C E G Bb C E G Bb C Edraws D F A B D F A B D F

bends Db Ab Db Ab Db

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Proving Newton's Theorem

Suppose you have a diatonic harp with all of Andy Newton's desirable properties.

Let x be any note in the chromatic scale that is played as a bend in the harp.

Let y be the next higher chromatic note that is played as a bend in the harp.

Fact: The number of chromatic notes in between the bends x and y must be even.

If x and y are in different holes then the chromatic notes between x and y include:

the draw note in the hole with x, the blow note in the hole with y,

plus the paired blow and draw notes in any holes between these two.

(Such intervening holes cannot have bends, because y is the next bend above x.)

So if y is played in the k'th hole after x then there are 2k notes between x and y.

If x and y are bends in the same hole then there are 0 chromatic notes between x and

the next bend y, but 0 is also an even number.

Thus, there must be an even number of straight notes between any two bends.

higher notes

higher blow notes:

bend notes: x y

draw notes:

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Proving Newton's Theorem (2)

Transposing if necessary, we may assume that the major scale that you can play

without bends is the C major scale, the white notes of the piano.

So your bend notes must be among the black notes of the piano.

Any child has noticed that the black keys are grouped in two clusters: a cluster of

two black notes {C#, Eb} and a cluster of three black notes {F#,Ab,Bb}.

If you pick any two black notes in the same cluster, you find that the number of

chromatic notes between them is either 1 or 3, in either case an odd number.

But we showed that your harp must have an even number of intermediate notes

between any bend note and the next higher bend note.

Thus, your harp cannot have more than one bend note in each cluster.

Then to cover the chromatic scale with only 2 bend notes per octave, you must

have 10 straight notes per octave, which requires 5 holes per octave.

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Conclusion of Newton's TheoremThere are 6 pairs of bend notes that have one in {C#,Eb} and one in {F#,Ab,Bb}.

Four pairs are separated by a fifth: {Eb,Bb} or {Eb,Ab} or {C#,F#} or {C#,Ab}.

If your bend notes are any of these pairs then you have a fourkey tuning in which

four major keys can be played without bends.

If your bend notes are either {C#,Bb} or {Eb,F#}, each separated by a minor third,

then you have a twokey tuning that can play two major keys without bends.

If you have no bends at all, then you need six holes per octave (chromatic tuning).

blows C Eb F G A C Eb F G A

draws D E F# Ab B D E F# Ab B

bends C# Bb C# Bb

blows C D F G A C D F G A

draws C# E F# Ab B C# E F# Ab B

bends Eb Bb Eb Bb

blows C D E F# G# Bb C D E F#

draws C# Eb F G A B C# Eb F G

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Pentatonic scales instead of chords

In fourkey tuning, the blow notes form a pentatonic scale, which is the simplest

melodic scale and consists of 5 consecutive notes in the circle of fifths.

The draw notes are also a pentatonic scale, one semitone lower, one hole to the left.

Blows, Draws, & Bends on a C fourkey

CF G

Bb

Eb

E

C# BF#

D

A

Ab

Thus the fourkey's straight notes form

a sequence of 10 consecutive notes

in the circle of fifths.

Any major scale is a sequence of

7 consecutive notes in the circle of fifths.

So four different major scales can fit within

the straight notes of a fourkey harp...



bends Eb Bb Eb Bb

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In a fourkey, the first major position has 5 blow and 2 draw notes.

Key of C on C fourkey

D

[Eb] A

E

CF

[Bb]

G

[C#]

[Ab]

B[F#]

blows C D F G A C D F G A C D

draws C# E F# Ab B C# E F# Ab B C# E

bends Eb Bb Eb Bb Eb

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The second major position has 4 blow notes and 3 draw notes.

Key of G on C fourkey

[Eb] A

[Ab]

C[F] G

[C#] BF#

[Bb] D

E




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The third major position has 3 blow notes and 4 draw notes.

Key of D on C fourkey

[Eb]

[Ab]

[C][F] G

[Bb] D

A

E

C# BF#




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The fourth major position has 2 blow notes and 5 draw notes.




Ab

C#F#

Key of A on C fourkey

[Eb]

[Bb]

[C][F]

D

[G]

A

E

B

Advantages of Fourkey Tuning

1. Four different major scales available with NO BENDING required!

2. Some positions offer fewer breath changes for smoother playing. Major scales have 5 blow notes in 1st position, 5 draw notes in 4th position.

3. The complete 12-note chromatic scale is available with only 2 ordinary draw bends. Even the most complex scales will never need more than two ordinary draw bends and no overblows ever required.

4. By choosing the right positions, those bends can be made to fall on infrequently used notes or on “blue” notes. In 4th position, for example, the bends fall on the flatted 5th and the flatted 9th.

5. A NEW SOUND for diatonic harp. Purity of tone! (Wow factor!)

6. Stylistically versatile, Pop, Motown, “Smooth” Jazz, bebop, and blues scales are readily available!

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3rd position blues

4th position blues

Key of C Fourkey Harp

5th Position Blues

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Eb MajorF dorian

Bb mixolydian

F MajorG dorian

C mixolydian

Bb MajorC dorian

F mixolydian

C MajorD dorian

G mixolydian

Key of Eb Fourkey Harp

All these “ii-V-I’s” before you’ve even bent your first note!15

Disadvantages of Fourkey Tuning

You can’t find them at your local music store or order them on Amazon and they are a major PITA to make yourself if you’re trying to retune a Richter harp! Best left to master customizers like Pat Missin, or order direct from Seydel:

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Disadvantages of Fourkey Tuning

LOSS OF RANGE! Barely two octaves fit on a 10 hole harp. Seydel currently

does not offer a 12 hole version.

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In Seydel's Solo Pro 12 configurator, highest possible blow note in hole 1 is D#4.

The lowest blow notes available in holes 10, 11, 12 are B5, D#6, F#6 respectively.

For a 12-hole C-fourkey, we'd need these blow notes to be A5, C6, D6.

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With 5 holes per octave, a 10-hole standard fourkey harp has barely two octaves.

First position

blows C D F G A C D F G A1 2 3 4 5 6 7 8 9 10


bends Eb Bb Eb Bb

Second position



bends Eb Bb Eb Bb

Third position



bends Eb Bb Eb Bb

Fourth position



bends Eb Bb Eb Bb

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Some prefer a modified fourkey layout that starts at the 3rd-position tonic

and adds a high 3rd-position tonic by raising the highest draw a semitone.

First position

blows D F G A C D F G A C1 2 3 4 5 6 7 8 9 10

draws E F# Ab B C# E F# Ab B D

bends Eb Bb Eb Bb C#

Second position

blows D F G A C D F G A C1 2 3 4 5 6 7 8 9 10



Third position

blows D F G A C D F G A C

1 2 3 4 5 6 7 8 9 10



Fourth position

blows D F G A C D F G A C

1 2 3 4 5 6 7 8 9 10



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Seydel configurator form for a modified fourkey harp in C

http://www.seydel1847.de/

Dealing with Fourkey Loss of Range“Missin Special” Fourkey 365

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Dealing with Loss of Range

“Missin Special” Fourkey 365

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Loss of Expressivity

Because most reeds don’t bend at all, or only bend ½ step, you may wish to add

valves for increased expression. (And you’ll get a bit more range with valves too.)

Seydel will add valves at no extra cost!

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Two major chords have one breath direction, but they're not in adjacent holes.

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draws Db E F# Ab B Db E F# Ab B

bends Eb Bb Eb Bb



bends Eb Bb Eb Bb



bends Eb Bb Eb Bb



bends Eb Bb Eb Bb



bends Eb Bb Eb Bb



bends Eb Bb Eb Bb

LeGato Tuning

Fourkey’s Big Brother!

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In LeGato tuning, 2/3 of the notes on the harp have useful enharmonic

choices. Slide out or slide in? Blow or draw? Stab up or Fall down into a

note? Choice = artistic freedom to craft long flowing lines, changing

breath direction only when YOU want to, instead of when the harp says

you have to.

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“Breath Simple”

C Major Scale =

All Draw notes, no

change of breath

direction needed!

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“Button Simple ”

C Major Scale =

All Button Out, no

change of button

position needed!

“Breath Simple” or “Button Simple” ? On the LeGato Chromatic, it’s YOUR Choice!

“Breath Simple”

C# Major Scale =

All Blow notes, no

change of breath

direction needed!

(Add A natural for

Bebop scale, still all

Blow notes!)

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C# Major Scale =

All Button In, no

change of button

position needed!

“Breath Simple” or “Button Simple” ? On the LeGato Chromatic , it’s YOUR Choice!

“Breath Simple”

Bb Major Scale =

All Blow notes, no

change of breath

direction needed!

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Bb Major Scale =

All Button In, no

change of button

position needed!

“Breath Simple” or “Button Simple” ? On the LeGato Chromatic , it’s YOUR Choice!

“Breath Simple”

Bb Bebop Scale =

All Blow notes, no

change of breath

direction needed!

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Many other “Breath Simple” scales are available. “Breath Simple” = flowing, legato lines!

Change breath direction whenever you want to instead of when the harp says you have to!

“Breath Simple”

Bb Minor =

All Blow notes, no

change of breath

direction needed!

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FOURKEY DIATONICS:

Seydel Blues Session $65.95 incl shipping available from Low

G to High A.

Seydel Session Steel introductory special $85.95 incl shipping

available only in keys of D, Eb, E, F, F#, High G.

(C to F# in modified-fourkey version)

LEGATO CHROMATICS:

Seydel Deluxe ($207.95 including shipping)

PRICING AND AVAILABILITY

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General references on fourkey tuning:

http://4keyharps.wordpress.com/

Andy Newton's 2007 articles in Harmonic Sessions magazine:

http://archive.harmonicasessions.com/aug07/Newton.html

http://archive.harmonicasessions.com/oct07/Newton.html

Slidemeister discussion

http://www.slidemeister.com/forums/index.php?topic=1205.0

Seydel's harp configurator can be found at

http://www.seydel1847.de/

Documents

SPAH, August 2011 Introduction to Fourkey Tuninghome.uchicago.edu/~rmyerson/reading/fourkeyintrod.pdf · 2011-08-11 · Introduction to Fourkey Tuning A new way to get those missing