The «Dodeka» concept

 

A system according to reality


The desir to fix the music

The aim of the creation of a musical writing is to present the notes’ position with a maximum of clarity..


One of the principal challenges with a new method is to find a graphical concept that allows the precise presentation of the twelve semitones of the chromatic scale.


The Structure of the Lines

After diverse research, the most effective system proved to be the displaying of the notes on a staff with only four lines.



To compensate for the limited number of lines, the notes are positioned in four variants:



•On the line : C (Do) - E (Mi) - G# (Bi)

•Above the line C# (Ka) - F (Fa) - A (La)

•Between two lines D (Re) - F# (Hu) - A# (Ve)

•Under the line : D# (Xo) - G (So) - B (Si)


With this layout the reading of each note’s position is very easy and advantageously allows to place an entire octave in the four-line scale.

This arrangement brings a weighty advantage compared to the traditional system that writes the notes on a five-line scale. With this odd number the notes do not maintain their positions because the C notes are alternately on a line or between two lines.


This continuous position inversion greatly hinders the reading clarity.


With the DODEKA notation, each note keeps its position, which is the case in every octave.



Comparison between the Two Notational Systems


Traditional Method

This method that comes from the ancient musical cultures artificially gives value to certain notes by valuing a key and a harmony. At first only the notes C, D, E, F, G, A, C were present. Afterwards the B was added and symbols that allow to find the “forgotten” notes were created (sharps and flats).

This system caused aberrations: an E sharp (mi#) is an F (Fa), an F flat (Fab) is an E (Mi), a B sharp (Si#) is a C (Do), and C flat (Dob) is a B (Si) !!!

Moreover each “forgotten” note can be referred to in two ways. A C sharp can also be indicated by a D flat. In consequence, the twelve tones of the chromatic scale generate more than 24 different signs! (32 forms if we add the “cancel” symbol that nullifies the sharps and flats). By combining the different signs we can create thousands of graphical versions of the chromatic scale (and of any other musical morceau!). The illustration above is then a version among others of the base scale used to make music.


DODEKA Method

This new system of musical writing considers every note equally without favoring a melody or a key. For this, it gives a specific name to the forgotten notes. The semitone progression is clear. There are no more sharps or flats and only one way to write each note.


The DODEKA scale keeps the names of the existing notes and gives a new name to those who have none. The scale presents itself in the following name sequence:

DO – KA – RE – XO – MI – FA – HU – SO (l) – BI – LA – VE – SI – DO *


*Note : These names are based on the latinate note names as this method was first conceived in that environment. However, to be exported to Anglo-Saxon countries, it will be taken into consideration that these names be changed. They would be modeled on the Anglo-Saxon notes, consisting of only one letter of the alphabet.


The note-naming process was conceived with the following criteria:


•Only to use two letters per note: Sol becomes So.

•To find names with a specific vocable to maintain clarity.

•To favor the same vowels as their positions in the scale.

•To use consonants that are not present is the existing notes.


A Large Musical Palette

To cover a substantial tonal range, it is possible to extend the four-line modules. They can be added at will and a great clarity is still maintained.



Examples of staffs on modules of four and six octaves. The notation also allows to add fragments of additional lines to temporarily enlarge the musical space.


With this graphical system, a C is always on its line and thus quickly identifiable. The line adding allows the infinite extension of the sound space, it is then not necessary to have scales with a special layout for the lower keys anymore (like for example the F scale).


Each note has its place and the musical layout of the DODEKA scores allows to easily cover the whole range of instruments of a symphony orchestra.

Such coherence greatly simplifies the learning of music.


The Anglo-Saxon score use a letter for the notes, but unfortunately not for each note... To atribute one letter for each chromatic tone, DODEKA propose to use the letters starting from the end of the alphabet : «O» to «Z».





REVOLUTIONARY KEYBOARDS


As mentioned before, instruments with a keyboard such as the organ, the piano, etc., have a structure that replicates the traditional notational method.


The DODEKA method enables to profitably play every existing instrument and on piano keyboards. However, the design of the standard keyboard greatly handicaps the musicians because it reproduces the “defects” of the system (this is not the case for string instruments, brass instruments, accordions, etc.).


Only a keyboard that replicates the real form of music allows to fully benefit from a coherent system that encourages musical expression and learning.


The objective of creating the DODEKA keyboard was to set all the keys in a chromatic configuration. Thus, every note is at the same level and in succession.

The arrangement of the keys of the DODEKA keyboard corresponds exactly to the position of the strings and the mechanisms that are in the piano.


The Advantages of the DODEKA Keyboard

In a chromatic disposition, each note of the scale is side by side, there is no more established and penalizing construction. Each interval is equivalent which allows the musician to very easily control the “musical space” because the keyboard perfectly replicates what is happening in the sound universe. The semitones are always beside the next, the tones are a key away, the thirds and the fifths have the same intervals in every tonality

This configuration is an incalculable benefit for those who improvise and avoids the long-out calculations that the traditional keyboard imposes.


The DODEKA Disposition Abides with the Current Intervals

On a piano keyboard, the black keys are further back. Changing to a twelve key configuration where each key is on the same level reduced the space for each of them. But this problem was easily solved by lightly sharpening the keys. This way the fingers benefit from the available room. The DODEKA keyboard is thus similar to a standard keyboard in the disposition and the intervals of keys.





The DODEKA disposition matches a traditional keyboard; every key has the same shape as the black ones and are all one next to the other.






AN EASY READING

The interaction between the DODEKA method and keyboards comes from their structure based on the chromatic scale. Because each note precedes the next, we only need a few marks to indicate the position the score lines on the keyboard.


With these marks the keyboard mirrors the notational system of the score (if it is rotated by 90°).

These explicit links between the position of the keys and the position of the notes greatly advantage the learning of reading (and writing). For in practice, one only needs to touch the key indicated on the score in order to play the right note.


No calculation is necessary and there is no alteration at the clef, nor are there sharps and flats.



The simplicity and the coherence of the annotation theory enable novice musicians to read and play complex melodies.

On learner keyboards we can strengthen the visual link between the keyboard and the scores by using a specific color for each line. This way, the keys are the same color as the line to which they correspond.

Thus for example, the following learning colors:

1- Red: the C lines (Do).

2 - Blue: the E line (Mi).

3- 3-Yellow or green: the G sharp line (Bi).



Thus, the tinted key is the one that the musician should push when the note is on the line; both keys beside it are those above and beneath the line. Finally the isolated key in the middle is the note between the lines.


This link between the lines and the keyboard allows to situate each note with great ease.


This system is so evident that one lesson is enough to show the entire notational principle. Thereafter the study time can be entirely devoted to the teaching of music and acquiring dexterity and reading reflexes.





SCALES AND HARMONIES

As we have mentioned before, the traditional method favors a scale at the expense of others. With the DODEKA method, there are no favored scales; and on a modified keyboard, the notes are in a row. The musician then has to learn to construct a scale starting from the chromatic scale.


The Major Scale

If he wishes to play in major, he will have to select the notes corresponding to this harmony. This consists in producing the following intervals:

This structure, applied to the O key (C), corresponds to the following writing:
The empty spaces correspond to the avoided notes


The Minor Scale

If the musician wishes to play with minor harmonies, he will have to reproduce the following intervals:

This structure, applied to the O key (C), corresponds to the following writing:

Keys and Transposition

One of the most impressive advantages of the DODEKA method is to get free of the key constraint.

In the traditional system, any tonality change was extremely burdensome because there are eleven ways to play the same musical morceau. Each key change involves calculations and a rewriting of the score.


As we have seen, this also applies to scales: thus also eleven variants of major scales exist, eleven variants of minor, etc. Pianists constantly have to rework numerous variants of playing and this is only to master the basic scales.


This aberrant situation totally disappears with a chromatic base because a scale or a musical morceau is always the same and this is the case of the complete range of keys.


Thus one only has to learn one single major scale to be able to play it in every key. The sequence of fingering is always the same.

For example, a morceau written in C major can be played in E by simply moving a line away.


As every space between the notes is the same, the construction of the musical playing does not change.


As the illustration shows, this ease of transposition also applies to note chords.


The three-note chord of the O (C) major type corresponds to the following intervals:

These same intervals used in the chromatic scale always form chords with similar harmonies and this is the case no matter what the starting note was.


Thus by moving the position of the fingers of one slot, we create the Ka chord (C sharp) presented in the example mentioned on the page above.

By moving again of one slot we increase the value of another semitone and create the D major chord.
We could of course pursue the demonstration for the whole stretch of the scale because this rule applies to every key, to every form of scale and to every harmonic construction.


With such simplicity it is even possible to read a score in one tonality and play it in another.



The Musical Architecture Is Revealed

The DODEKA method allows to bring the real structure of the chords to light. Thus with this writing system, we learn the intervals proper to each different chord. These can then be applied to every key.


In regular scores, the spaces between the notes are constantly modified by the position of the notes. An equivalent chord thus has numerous graphical forms.


But this illogicality disappears with the DODEKA notation. The graphics of the notes faithfully transcribes the intervals between notes. This allows to grasp the geometrical form of the intervals that separate the notes. Since these spaces are conform to the sound reality, it is possible to visually perceive the type of harmony that the assembling of notes will produce.


For example, the structure of the famous major chord makes two asymmetrical intervals. And surprisingly the variant of a minor chord of the same tonality makes two asymmetrical intervals as well. But the gaps are not the same and the minor version kind of contains the opposite reflection.


Thus the DODEKA notation enables to grasp geometrical structures that give “character” to musical chords.

Several chords have an asymmetrical structure (major, minor), others have symmetrical intervals (diminished, augmented, m7), others are made of a group of notes separated by the same intervals. mThis graphic vision of music is very interesting and allows to reveal the relations that exist between a group of notes and their capacity to convey impression to our psyche.



The DODEKA method conveys the structural vision of music that the traditional notation had unfortunately hidden.

With habit, it is possible to globally grasp the different chords without having to sight-read each note.


The musical chords

As we have seen, to transcribe music according to a system that is based on pieces of music (the scales), leads to an unnecessary complexity within the system itself. Moreover, this complexity also affects chords’ notation, and their current codification is not able to convey the structure of the notes in a transparent way.

The usual method of scoring chords is effectively based on the structure of the major scale defined over its five 5. As shown in the picture below, the names of the chords were defined according to the intervals appearing on the score.


A major chord may therefore have a dominant seventh (DoM7) or ninth (DoM9) ...

This archaic system does not take the effective intervals between notes into account. This is why particularly opaque.

 


The chromatic base of the DODEKA-notation helps to clarify the actual position of all the notes, and, therefore, of the intervals between them. This provides a consistency between the "live experience" of a chord and its architecture. The construction of a set of notes thus conveys the melodic impression and this in any tonality. Which shows even more how absurd it is to define the arrangements within the frozen structure of scale-system.


Thanks to its system of representation, the DODEKA-method allows to visualize the architecture of each chord in a clear way, and thus to find an immediate coherence between writing and the musical harmony.

To take full advantage of these benefits DODEKA uses a numeric definition of chords, which indicates the intervals taking place between notes. This transcribtion can be applied to all kinds of situation and to each tone as well.


According to this principle, a major chord, which would involve the notes C-E-G-C, can be set by indicating the number of intervals between the notes. In the case of the major chord, the second note of the chord is to be found right after the first four keys, the third note three keys later, and the last one appears after five keys. This specific architecture can thus be expressed by means of the three following digits: 4.3.5.

This structure can be applied to any tone, because it will always give a major chord.


The table below presents the numerical representation, within the DODEKA-system, of the most common chord.



Note that the fact of higlighting intervals allows to understand the reason why chords may overlap or complement each other.






To Go Further...

The graphic system of the DODEKA method allows us to understand that music is a game of “mathematical” intervals between two axes. The first, the vertical axis, is the one for the notes and the sound frequencies. The other, horizontal, is the one for time and the rhythms. This global vision allows us to make the hypothesis that both axes are governed by the same rules and enable the communication of psychic impressions.


Thus the intervals of a major chord can also be reproduced in a rhythmical (asymmetrical) sequence. Notes and cadenza would be the spaces governed by the same rules and in which we could produce structural constructions that would be appreciated by our brain.


The Rythmical Notation

The elaboration of a new musical notation was also the occasion to make some modifications to the way of writing the music tempo. In the traditional method, the length of the notes is indicated by graphical particularities. The temporal values of eighth notes (GB: quavers) are indicated by the addition of horizontal bars. This does not simplify the reading and forces the musician to pay attention simultaneously to the position of the note’s round part and to what is above it. In complex scores, these two visual zones are difficult to decode, even more so because the musician also has to consider the alterations: sharps, flats and cancels that can modify the pitch of the note.


In addition, the traditional system also created the principle of dotted notation, where a dot following a note lengthens its duration of half its value.

With this principle, the dot can represent the duration of an eighth note, of a quarter note (GB: crotchet), or of a half note (GB: minim). Since its value is relative, we have to work out its length as we read.

All these elements are not practical and offer numerous occasions to make mistakes.




An Explicit Temporal Vision

The objective of the DODEKA method was to find a new rhythmical writing concept that allows to transcribe the temporal vision of music in a clear and practical way.


Logically the easiest way to indicate the length of a note is to give it a horizontal size proportional to its duration. This is actually the system used in programs of computer notation.


This system is most certainly less «poetic» that the traditional version that fills the scores with little symbols and graphically embellishes the notes.

However the new notation allows to directly perceive the length of the note and following a clear temporal scale.

It is thus very easy to understand that one must play two eighth notes during the length of a quarter note. Moreover, the variable value of the dot disappears and gives way to a precise indication of each time.

In practice it suffices to look at a note to simultaneously know its value and its length. This greatly helps the learning of music theory because the interactions between the notes and the musical times become evident.


A Variable Temporal Scale

In some cases, this linear notation can lengthen the scores that contain big musical sequences with long tempos (scores for orchestras).

To take this aspect into account, the notational system DODEKA has two methods. The first allows to compress the length of the long notes with the notation in half notes. This value increases the notes’ length by doubling their tempo.

The second solution consists in indicating the change to a new temporal scale in the progress of reading. This annotation redefines the notes’ temporal value. For example, this allows to make the length of half notes change to that of eighth notes.


Note

Amusingly, the manner in which the DODEKA method writes music can be found in certain interfaces of musical computer programs. In 1980, when this new method was created, musical computing was taking its first steps and there was no existing way to display scores.


Later on, technology has allowed to use the computer for composing and as a “sequencer”.


In this kind of program the position and the value of each note must enable to indicate the pitch of the note and its temporal length. This condition brought several programmers to present the notation on a grid with a chromatic base.



The correspondences between the DODEKA method and the interfaces of the modern musical programs show that this new writing mirrors the physical reality of music and that it allows to present music with more clarity.




Example of a Score

The following score is a transcription in the DODEKA method of a little composition of Johann Sebastian Bach: “Bourrées”.


This well-known morceau contains several “forgotten” notes that go past the usual C major scale.


In the traditional method, these notes have to be then noted by the addition of various alterations such as sharps or flats.


But this is not the case with the DODEKA method that clearly indicates the position of the notes. The graphics allows to easily visualize the sound spaces of the melody. On a DODEKA keyboard a novice musician can locate the position of the notes and play them without difficulty.


 

Jacques-Daniel Rochat, © 1980, ©1990, © 2005, © 2009.