The dualo principle

The dualo principle

Harmony simplifier

The dualo principle

Harmony simplifier

A mathematical approach to harmonic objects

A mathematical approach to harmonic objects

The dualo principle in one minute

  • The thirds are arranged vertically:
    The notes are alternately distributed on each keyboard, major thirds inwards and minor outwards.
  • The semitones are arranged horizontally:
    On the same line, sharps and flats are located by moving respectively towards the inside and the outside of the instrument.

The dualo principle
in one minute

The thirds are arranged vertically:
The notes are alternately distributed on each keyboard, major thirds inwards and minor outwards.

The semitones are arranged horizontally:
On the same line, sharps and flats are located by moving respectively towards the inside and the outside of the instrument.

Detailed explanation

Detailed explanation

The dualo principle is a concept for arranging notes in the plane. This arrangement of the notes uses the traditional staff (or stave) as a support with the dualo key to indicate the relative pitch of the notes (degrees) and not their absolute one.

The dualo principle is a concept for arranging notes in the plane. This arrangement of the notes uses the traditional staff (or stave) as a support with the dualo key to indicate the relative pitch of the notes (degrees) and not their absolute one.

By default, the first degree is on the right on a space, but it could quite be represented on the left and / or on a line (according to the tonic and the octave chosen on the du-touch, the first degree will be located on the left or the right keyboard).

The degrees alternate on each side, one per line of keys on the du-touch’s keyboard, one per finger (from index to little finger) of each hand.

Degrees

Degrees

By default, the first degree is on the right on a space, but it could quite be represented on the left and / or on a line (according to the tonic and the octave chosen on the du-touch, the first degree will be located on the left or the right keyboard).

The degrees alternate on each side, one per line of keys on the du-touch’s keyboard, one per finger (from index to little finger) of each hand.

Major thirds inwards
Minor thirds outwards

The dualo principle ranks even degrees on the same side, odd degrees on the other. Thus, the thirds are stored vertically on the keyboard.

There are two types of thirds: the major thirds and the minor thirds, a semitone separates them. Thus, the semitones are arranged horizontally on the keyboard (sharps inwards, flats outwards).

This orientation is the same on the entire keyboard, which can be seen as a vector space generated by the major and minor thirds.

Major thirds inwards
Minor thirds outwards

The dualo principle ranks even degrees on the same side, odd degrees on the other. Thus, the thirds are stored vertically on the keyboard.

There are two types of thirds: the major thirds and the minor thirds, a semitone separates them. Thus, the semitones are arranged horizontally on the keyboard (sharps inwards, flats outwards).

This orientation is the same on the entire keyboard, which can be seen as a vector space generated by the major and minor thirds.

More generally, here are the intervals, which remain equally identical for any fundamental note; we say that the keyboard is isomorphic.

Intervals

Intervals

More generally, here are the intervals, which remain equally identical for any fundamental note; we say that the keyboard is isomorphic.

Therefore, chords are represented by simple shapes, symmetrical from one keyboard to another. Here are the main examples:

Therefore, chords are represented by simple shapes, symmetrical from one keyboard to another. Here are the main examples:

Triads

(three-tone chords with two consecutive thirds / fundamental + third + fifth)

Tetrads

(four-tone chords with three consecutive thirds / fundamental + third + fifth + seventh)

Triads

(three-tone chords with two consecutive thirds / fundamental + third + fifth)

Tetrads

(four-tone chords with three consecutive thirds / fundamental + third + fifth + seventh)

Scales

(here a major scale, with the color code of the keyboard of the du-touch: tonic in orange, other notes of the scale in green)

From two tetrads, it is possible to build a scale (of 7 notes). By having a chord on each keyboard (and therefore in each hand), just play their individual notes, following the degrees, to reconstruct this scale.

In addition, the backlit keys of the du-touch can highlight a scale among the most common modes (major, minor, dorian, etc.), or you can draw your own scale.

Scales

(here a major scale, with the color code of the keyboard of the du-touch: tonic in orange, other notes of the scale in green)

From two tetrads, it is possible to build a scale (of 7 notes). By having a chord on each keyboard (and therefore in each hand), just play their individual notes, following the degrees, to reconstruct this scale.

In addition, the backlit keys of the du-touch can highlight a scale among the most common modes (major, minor, dorian, etc.), or you can draw your own scale.

Notes

When applying this principle to design a physical keyboard like the du-touch’s, here is a possible arrangement of notes (here on 3 octaves, 12 semitones per octave in equal temperament), assembled around the scale of C major by convention.

As for the degrees, we find the same note and its alterations on the same line (ex: fb, f, f #, f ##).

Notes

When applying this principle to design a physical keyboard like the du-touch’s, here is a possible arrangement of notes (here on 3 octaves, 12 semitones per octave in equal temperament), assembled around the scale of C major by convention.

As for the degrees, we find the same note and its alterations on the same line (ex: fb, f, f #, f ##).

The du-touch is the first instrument to use the dualo layout. It has been declined in two models: the du-touch Pro (released in 2015) and the du-touch S (released in 2017). Apart from the number of octaves, their respective keyboards are different as to the notes that compose them.

The du-touch is the first instrument to use the dualo layout. It has been declined in two models: the du-touch Pro (released in 2015) and the du-touch S (released in 2017). Apart from the number of octaves, their respective keyboards are different as to the notes that compose them.

Keyboard of the du-touch S

Each side of the keyboard is partially chromatic.

The keyboards are thus more complementary (e.g. Ebb = D).

Keyboard of the du-touch Pro

Each side of the keyboard is fully chromatic.

It is particularly preferred among pianists, who thus have all the notes on one side or the other; ideal for playing complex chords and their one-handed inversions.

Keyboard of the du-touch S

Each side of the keyboard is partially chromatic.
The keyboards are thus more complementary (e.g. Ebb = D).

Keyboard of the du-touch Pro

Each side of the keyboard is fully chromatic.
It is particularly preferred among pianists, who thus have all the notes on one side or the other; ideal for playing complex chords and their one-handed inversions.

On a dualo physical keyboard, it is of course possible that one or more intervals must be found on the opposite keyboard (and therefore played with the other hand); this is particularly the case for chords having as fundamental a note located at the edge of one of the keyboards. It is nevertheless possible to transpose (that is to say to shift uniformly by one or more semitones) the totality of the notes in the parameters of the instrument, in order to regain the comfort of playing an entire chord on a single keyboard.

On a dualo physical keyboard, it is of course possible that one or more intervals must be found on the opposite keyboard (and therefore played with the other hand); this is particularly the case for chords having as fundamental a note located at the edge of one of the keyboards. It is nevertheless possible to transpose (that is to say to shift uniformly by one or more semitones) the totality of the notes in the parameters of the instrument, in order to regain the comfort of playing an entire chord on a single keyboard.

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    Jules Hotrique, inventor of the dualo principle

    Mathematician and musician passionate of musical harmony, it is while re-tuning a sanza (piano with African thumbs, also known under the name of mbira or kalimba) that it comes to him the idea to arrange the harmonious notes, the thirds, next to each other. With the help of mathematics, he ends up conceiving the dualo keyboard as it exists today, and immediately decides to make an instrument with it…

Jules Hotrique,
inventor of the dualo principle

Mathematician and musician passionate of musical harmony, it is while re-tuning a sanza (piano with African thumbs, also known under the name of mbira or kalimba) that it comes to him the idea to arrange the harmonious notes, the thirds, next to each other. With the help of mathematics, he ends up conceiving the dualo keyboard as it exists today, and immediately decides to make an instrument with it…

The alternative note layouts

  • Piano, accordion and more:
    If the dualo keyboard does not suit you at first, try the other isomorphic keyboards available in the du-touch settings.

The alternative note layouts

Piano, accordion and more:
If the dualo keyboard does not suit you at first, try the other isomorphic keyboards available in the du-touch settings.