Introduction: Music Notation's History
Any musician or composer charmed by a melody finds himself confronted with the intense desire to durably capture music.
Dodeka's conceptual approach of its alternative music notation is based on the reality of music. A brief historical overview of the traditional musical notation is conducted in this section, so as to underline the useless complexities and aberrations of the traditional system. From this short analysis, a good and coherent approach for music theory is presented, introducing the concept at the core of Dodeka.
The Desire to Fixate
The need to transcribe music onto something physical had dawned at the beginning of music, which seems to go back to around 5000 to 6000 years before Christ. In fact, it is mentioned in the Bible in the book of Genesis that music quickly accompanied the development of humanity.
With such an ancient origin, it is conceivable that many musical language systems were introduced around the world. But, in those ancestral times, means of printing did not exist. Potential notational systems were therefore inevitably limited to regional and temporal use. More than 3000 years BC, the Egyptians already had the means to transcribe and record the melodies of their cultic songs. Such transcription systems must also have been used later on by the cantor schools and the Jewish musicians who played biblical Psalms. Traces of one of these notational systems were discovered on Sumerian tablets of the ninth century BC. The coding, consisting of five symbols, was obtained with cuneiform characters placed on the left side of religious poems.
In Greek and Roman Times
The systems used in the Middle East have presumably transited to the Greek world and generated the “cata pycnose” system. It seems that this concept consisted in dividing the scale in twenty-four semitones per octave. If this is the case, the forefathers perhaps had a much more precise and more coherent system than ours...
History tells us that around 600 BC, the Greeks used the letters of the alphabet to transcribe musical notes. The letters were topped with a sign that indicated the note’s length. Around 400 BC, Pythagoras’ works shed light on the mathematical aspect of music. He (re)discovered that taut strings make harmonious chords when their lengths are defined by multiples of two, three or four. His works set musical theory in a simple arithmetical framework.
With the Roman conquest, the musical writing system developed by the Greeks was taken over and then consisted of 1620 symbols! In about 500 AD, the Greek letters were replaced with Latin letters, in which upper case or double letters were signalling different octaves.
However, since the system was based on a subjective approach of sound, the musical scale was truncated. A way to annotate forgotten notes was to be subsequently invented. The harmonies of the Gregorian chant thus helped to create a “soft B” located a semitone below the B value. It is from this distinctive feature that the “flat” tone originated.
In the middle Ages
Around year 1000, an Italian Benedictine monk named Guido d’Arezzo devoted his life to prayer, as well as to the study and teaching music. In order to help his students, he gave new names to the notes based on a stanza of a hymn to Saint John the Baptist. The first stanza is:
‘So that can
Resonate the cords
Distended by our
The wonders of
Remove the sin
Of your impure
Oh Saint John’
The two-first letters of each sung line gave the notes' names creating at that time the following notes: UT (which was to become Do [C]), Re (D), Mi (E), Fa (F), Sol (G), La (A).
However, the alphabetical system has its own limits. It makes the reading of more complex melodies difficult. To overcome this difficulty, the Italian copyists inserted coloured lines, first on the F note, then on the C (UT) and finally on the A. At that time, the number of lines and colours were variable. The tradition was to use the letter G as a reference. Once ornamented, this sign was to become the famous treble clef.
Since the end of the twelfth century, the use of the quill pen simplified the graphics and brought along the characteristic form of square notation: the dots became squares and rhombi, and lines linked the notes. This graphics were generalised in manuscripts and was maintained until the fourteenth century.
The Traditional System
As mentioned in the preceding historical reminder, the development of the notational system was elaborated within centuries, following an empirical process. In fact, the traditional system was originally built from a melodic suite that lacked several notes. In order to take account of the discoveries and extensions of musical styles, this system had to be gradually enlarged.
Because this progression was not foreseen, it brought about a plethora of additions, which resulted in a complex system. It is kind of like if we had built a cathedral based on blueprints drawn for a small house. Musical notation was thus never liberated from its great defect, which is to want to write a musical composition from a melody with a well-defined harmony.
This uncomfortable situation can be compared to the condition of people who would talk to each other by always using the same sentence. To express themselves, the interlocutors would continually have to use expressions and additions meant to correct and deform the initial text. This is exactly what happens with the current notational system: its basis is forged on a specific musical form from which it is very difficult to escape.
In order to convince oneself of this system’s complexity, let’s conduct a few experiments on a piano. This instrument’s keyboard is a material reflection of the standard musical notation.
The white keys correspond to the notes present on the score, while the black keys refer to the forgotten notes, signalling a pitch modifications on the main notes, namely a flat for a lower semitone and a sharp for a higher semitone.
A beginner can easily play the C major scale by successively pressing each white key one after the other. With a little more work, s/he will also be able to easily play a musical composition in that key.
Of course, this situation is totally fine for a first contact with music, as well as for those who stick to C major and minor harmonies. But what is the price to pay?
Sadly, the price to pay is high. In fact, as soon as the musician wishes to explore other harmonies, s/he is terribly penalised. The “prefabricated” melody brought about by the system becomes a huge obstacle full of aberrant complexity.
The problem with the current system is that every musical composition is based on a musical tune!
An absurd complexity
As the illustrations below show, the transposition of a semitone from a song as easy as “Happy Birthday” will end up being a painful exercice for the beginner. With the change of tone, the notes will be partly on the black and white keys.
To depart from the established basic key, the keyboard and the notational system must use many corrections, creating as many variants as there are keys. To avoid correcting each note, accidentals are in some cases assigned at the beginning of the sheet music, what is usually called at the clef. Following these instructions, the musician has to keep the corrections in mind while playing, which significantly increases the difficulty of the task. For instance, the F sharp scale comprises six sharps that have to be taken into account for each related note! This absurd situation leads to an unbelievable amount of possible writings and twelve different fingerings for the exact same musical composition!
What a system, what a terrible language! And the nightmare is only the beginning. These artificial hindrances also affect the universe of musical harmonies. In this system, each chords of every scale has twelve variants, while in reality they only correspond to one unique musical structure.
Examples of complications
Although there is only a semitone of difference between the two partitions, the way the song is written is completely different. And yet it is the same melody.
A Misleading System
The traditional system and its complexity contains yet another sly effect: it lies! For it is not without consequence that the founders of the notation system have favoured a subjective melody. At that time, without knowing it, they have tied a melodic form that betrays the mathematical standards of music.
On a score, as well as on the keyboard of a piano, the notes C and D are set out with the same space as the E and F. But nothing could be more incorrect! In reality, the space between a C and a D is of one tone, whereas between an E and an F there is only one semitone of difference. This is certainly an unintentional “lie," however, it has terrible consequences. It, in fact, creates a distortion between real music and written music. As a result, what is written in the traditional system is different from what is played, creating a gap between the theory and the reality of music.
This gap is at the base of what differentiates the composers who play and improvise “by ear” and those who perform scores more “literary”. The traditional system has involuntary created two categories of musician with different approaches to music.
A Lack of Hindsight
Unfortunately few musicians are aware of the complexities and aberrations of the traditional system. Even when the DODEKA method is presented, some musicians, generally those who are the most bound to music theory, experience great difficulties to see the useless complexities of the traditional system. Their understandings of music was constructed through the “eyes” of the system and it is not easy to show them that the path could have been so much shorter.
The current musical theory appears to be like a fortress with unnecessary high fortifications. Most learners quickly give up against its walls, while a minority, determined enough, overcome the obstacles and obtain the admiration of others. But how many musicians of quality are lost because of this absurd complexity?
The Basis of a Good Alternative to Standard Music Notation
Now that the absurd complexity of the current notational system has been delineated, it is possible to outline the needed criteria for an alternative music notation, that is coherent and logical. Crafting a good approach is relatively simple. Simply dismantle a piano and a clear and logical vision of music is observable.
The Rule of Sound
Beyond its emotional and subjective expressions, music is and remains a set of sounds governed by frequencies and mathematical laws. These laws can be easily observed with strings instruments, where the production of sound depends on the length of strings. In reality, a string, stretched between two points, produces a certain sound when it vibrates according to a certain frequency.
For example, an A sound (A4) can be produced by making a string vibrating at 440 beats per second (440 Hz). If this same string is cut in half and the remaining part keeps vibrating, a sound with a frequency twice as fast (880 Hz) will be obtained. The sound will be higher in tone, corresponding to A of one higher octave (A5). If, in contrary the initial string, vibrating at 440Hz, were to be multiplied by two, the string’s vibration rate would slow down by half, producing a lower A sound (i.e. A3).
The experiment can be taken further. The initial string can be divided following simple mathematical fractions, such as three-quarters (3/4) or two-thirds (2/3), to produce musical values that are appreciated by the human brain. Surprisingly, a string cut with a 1.333 ratio makes a fourth, while one cut with a ratio of 1.5 makes an accurate fifth. Such observation illustrates the relationship that exists between musical sounds and the fractioning of strings, but most of all, it underlines the uniform aspect of music.
As seen with the latter experiment, all musical notes hold distinctive positions on the string, suggesting that every note is in reality unique. A C# is as unique as a C, and therefore, there are no reasons for associating the value of the latter one to the former, as the traditional system posits.
The relationship between musical sounds and the fractioning of string and the uniform aspect of music can be easily observed on guitars. Guitars’ necks have frets that define “spaces“, where strings are cut to produce musical values the human brain appreciates.
The Basis of a Good Language
In order to find a language capable of easily transcribing diverse musical compositions, it is essential to go back to the initial “alphabet” of the musical universe, being its reality. Such a new approach must reject any subjective favouritism of specific notes and keys.
To do so, it is important to represent consistently and accurately all musical intervals within an octave. In fact, when every musical intervals are successively played, an octave is divided in twelve parts.
This scale is called the chromatic scale and is composed of twelve semitones. Dodeka takes this scale at the core of its approach to simplify music notation and escape the useless complexities of standard written music notation.
Dodeka: Music Notation Redesigned
The Dodeka Stave
One of the main challenges when creating a new music system is to come up with a logical notation that keeps a maximum of clarity. For this reason, Dodeka suggests placing the chromatic scale on a new four-line structure.
After various research, the most effective and clear system to arrange the twelve semitones of the chromatic scale is on a set of four horizontal lines, in which the notes are placed in four different ways: on the line (C, E, G#); above the line (C#, F, A); between the lines (D, F#, A#); and under the line (D#, G, B).
By placing an entire octave within four lines, the Dodeka stave positions the notes in a logical and clear manner, which makes reading notes easy. In fact, this structure assigns a fixed position to every note in every octave, making notes directly identifiable. As shown in the below illustration, a C is always placed on the first and/or fourth lines.
With Dodeka, every note keeps its position in every octave. Reading a sheet music has never been so simple!
A Large Musical Palette
To cover a substantial tonal range, DODEKA offers the possibility to extend the four-line structure. Additional modules of lines can be added at will, while a great clarity is still maintained. In fact, additional lines do not affect the notes’ positions. A C is always on its line and still quickly identifiable.
The capacity of adding lines modules allows the infinite extension of the sound space. It is then not necessary to have scales with a special layout for lower keys anymore, like for example the F scale. The DODEKA’s musical layout also allows easily covering the whole range of instruments of a symphony orchestra. Such coherence and flexibility greatly simplifies the learning of music.
This graphical notation allows adding fragments of additional lines to temporarily enlarge the musical space.
Scales and harmonies with Dodeka
The DODEKA scale
To rename the semitones traditionally forgotten, DODEKA suggests using new letters, namely K, T, H, P, and V.
As mentioned earlier, the traditional method favours a scale at the expense of others. With DODEKA, there are no favoured scales and the notes on the keyboard are set out in a row. The musician has to learn how to construct any scale starting from the chromatic scale.
Major scale in C
The C Major Scale in DODEKA refers to the following sequence on the DODEKA staff and its associated chromatic basis. If one wishes to play in major C, he will have to press the keys corresponding to this harmony. This consists in producing the following intervals.
Minor scale in C
The C Minor Scale in DODEKA refers to the following sequence on the DODEKA staff and its associated chromatic basis. If one wishes to play in minor harmonies, he will have to reproduce the following intervals.
Keys and Transposition with Dodeka
One of the most impressive advantages of DODEKA is its capacity to get free from the key constraint.
In the traditional system, any tonality change is extremely burdensome, since there are twelve ways to play the same musical composition. Each key change involves calculations and the rewriting of the score, as well as the scales. As a result, pianists constantly have to rework numerous variants of playing and this only to master basic scales. This aberrant situation disappears with DODEKA. When using a chromatic scale, the structure of a scale or a musical composition is always the same for the complete range of keys.
With DODEKA, one only has to learn one single major scale to be able to play it in every key. Sequence is always the same. As shown in the illustration below, a composition 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.
A Clear Transposition
DODEKA’s ability to simplify transposition not only concerns scales, but also applies to chord notations as shown in the following illustrations.
The three-note chord of the C major type corresponds to the intervals shown below. These intervals used in the chromatic scale always form chords with similar harmonies and this is the case no matter what the starting note was.
By moving the position of the fingers of one slot, we create the K chord (C #) presented in the example mentioned on the page above.
The demonstration could be made for the whole stretch of the scale given the fact that this rule applies to every key, to every form of scale, and to every harmonic construction. With such ease, it is possible to read a sheet music in one tonality and play it in another.
K (C#) Chord
The architecture of music
The DODEKA revolutionary system reveals the architecture of music. It sheds light on the real structure of chords, that is, the intervals proper to each different chord. These can then be applied to every key.
In regular scores, spaces between the notes are constantly modified by the alternative position of the notes. The same chord thus has numerous graphical forms. This illogicality disappears with the DODEKA notation. The graphics of the notes faithfully transcribe the intervals between notes. This allows grasping the geometrical form of the intervals that separate the notes. Since these spaces reflect the reality of sound, it is possible to visually perceive the type of harmony that the group of notes will produce.
For example, the structure of the famous major chord makes two asymmetrical intervals. And surprisingly the sequence of a minor chord of the same tonality makes two asymmetrical intervals as well. But the gaps within the sequences are dissimilar, in the sense that the minor chord seems to reflect the opposite intervals.
From this perspective, the DODEKA notation enables to grasp the geometrical structures that give “character” to musical chords. Several chords have asymmetrical structures (major, minor), others have symmetrical intervals (diminished, augmented, m7), and others are made of a group of notes separated by the same intervals.
This graphic vision of music is very interesting and allows revealing the relationship that exist between a group of notes and their capacity to convey impression to the psyche.
Table of main chords with DODEKA (in C)
DODEKA conveys the structural vision of music that the traditional notation had unfortunately hidden. With practice, it is possible to globally grasp the different chords without having to sight-read each note.
To Go Further
The graphical system that the DODEKA system conveys underlines 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, refers to the axis of time and rhythms. DODEKA posits that both axes are governed by the same set of rules, which communicates psychic impressions.
From this perspective, 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.
Creating a new notational system provided the opportunity to revise the way music tempo was written.
In the traditional method, the length of 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 accidentals, which the pitch.
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 not appropriate, leaving many occasions for errors.
An Explicit Temporal Vision
The objective of the DODEKA method was to find a new rhythmical writing concept that enables 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. At this point, it seems important to remind the reader that DODEKA has been conceived in 1980, long before the advent of musical computer notation.
Less Poetry, More Clarity
This way of writing tempo is obviously less «poetic» than the traditional version, which fills sheet musics with little symbols and embellishes notes.
However, rather than poetry, this notational system seeks clarity. Notes are set according to a clear temporal scale, which allows perceiving directly the length of any note. It is therefore 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, one only has to look at a note to simultaneously know its value and its length. Such notation greatly helps the learning of music theory as it clearly underlines the notes’ values and their musical tempo.
A Variable Temporal Scale
In some cases, this linear notation can lengthen sheet musics of large musical sequences with long tempos, like those for orchestras for examples.
To take this aspect into account, the notational system DODEKA provides two solutions. The first one is to compress the length of long notes in half notes. By doing so, the notes’ lengths are reduced and their tempos are doubled. The second solution consists in indicating a change of tempo on sheet musics. The annotation temporarily redefines the notes’ temporal values. Such annotation allows, for example, changing the length of half notes in that of eighth notes.
Amusingly, the manner in which DODEKA writes music can be found in certain interfaces of musical computer programs. In 1980, when this new structure 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 computers as “sequencers”. In this kind of software 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 DODEKA and the interfaces of modern musical programs shows that this new notation mirrors the physical reality of music, allowing to write music with more clarity.
Later on, technology allowed using computers as sequencers for composing music. In this kind of program the position and the value of each note indicate the pitch of the note, as well as its temporal length. This condition brought several programmers to present the notation on a grid based on a chromatic base.
The correspondence between DODEKA notation and the interface of modern musical programs shows that this new writing mirrors the physical reality of music and presents music with more clarity.
Bourrées', Johann Sebastian Bach
This sheet music is a transcription in the DODEKA language of a short composition entitled “Bourrées” from the composer, Johann Sebastian Bach. The composition contains several “forgotten” notes that go past the usual C major scale.
In the traditional method, accidentals, such as sharps and flats, would have to be used to make sense of those forgotten notes. By contrast, in the DODEKA transcription, the sheet music is devoid of any accidentals and the positions of the notes are clearly indicated.
Such graphics make the sound spaces of the melody easily identifiable. Even novice musicians would be able to easily play this short composition on a DODEKA keyboard.