The main idea of serial music is that elements of the row are all equal in rights and governed by the order in which they appear. To abolish the notion of hierarchy between sounds, Schoenberg used serialism, but applied it to only one of the four fundamental parameters (pitch, duration, timbre, dynamics): the pitch. Using the twelve tones of the chromatic scale, Schoenbergian serialism reveals itself to be also dodecaphonic, which is why we often associate the twelve tone technique with serialism.

Technically, the tone-row is composed of twelve tones of the tempered chromatic scale, set in an order defined by the composer but each tone can appear once and only once in the row. The number of possible rows is very high, in mathematical terms, it is a permutation of 12 elements, 12! (1x2x3x4. … x12) So 479,001,600 possibilities. The composer, once the row has been defined, can use it in various forms:

• - prime form (Grundgestalt) , so without change
• - retrograde , the prime form is taken backwards (from the last note to the first)
• - inversion : prime form turned upside-down.
• - Retrograde inversion combination of the two previous changes

Each of these forms can also be transposed to the other eleven degrees of the chromatic scale, bringing the number of possible forms of the same row to 4+4×11=48. The composer may play several tones of the row simultaneously (in vertical form, so “chords”) or horizontally, but change registry, or overlay different speeds. We can clearly see that the possibilities are almost endless, but more important, the row can not be regarded as a theme in a classical meaning, as it is not easily recognizable melodically, but is more like a succession of intervals.

One can deduce important conclusions from the foregoing :

• 1. Serial does not mean dodecaphonic: the tone-row may be composed of less than twelve sounds (in Stravinsky for instance), more than twelve sounds (in microtonal music) or affect other parameters than the pitch (the rhythm for example).
• 2. Serial does not mean atonal: Some series can be chosen to evoke a tonal character
• 3. If works written by Schoenberg with his “method of composition with twelve tones which are not related” are basically atonal, dodecaphonic and serial, this is only a special case of atonality and serialism.

We have only spoken of Schoenbergian dodecaphonic serialism but we could also speak of dodecaphonic serialism in Western tonal music, also based on the twelve tones of the chromatic scale. Here are some examples you might find surprising : we can find a twelve-tone row in the recitatives of Mozart’s Don Giovanni , or at the beginning of Liszt’s Faust Symphony or in the fugue of Strauss’ Also sprach Zarathustra … Amazing, isn’t it?

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Atonal: having no established key (Collins). Atonality is a state in which all the rules and tonal functions are suspended. No more tonic, dominant, disappearance of consonance-dissonance axis, etc, in fact it represents the simple end of the laws on which has been based all Western music since the Baroque period (even middle ages, since modal system is not atonal). In an atonal system, the twelve tones of the chromatic scale are considered as equal, and the dissonance is not an episodic thing anymore.

It is difficult to date precisely the emergence of atonality because the atonal system did not appear suddenly but is a result of a slow evolution of the tonal system. We could see its roots in the Wagnerian chromaticism and since the mid-nineteenth century, and atonality gradually invaded the harmonic and contrapuntal writing. One of the most striking examples of the late nineteenth century is perhaps the prescient Bagatelle without tonality of Franz Liszt, composed in 1885.

But soon a character quickly became a key figure in the atonal world: Arnold Schoenberg. Upon his sextet Transfigured Night written in 1899, his path was defined. But we have to wait until 1908 and his second quartet to speak of conscious and systematic atonality which culminates in 1912 with Pierrot Lunaire. As for Schoenberg, the abolition of rules, the total freedom of the latter work has raised the question of the coherence of this new atonal world. He quickly felt the need to organize this chaotic world with new rules. The dodecaphonic system was born.

If Arnold Schoenberg and the Viennese School characterize the early atonal music, they are not the only ones to seriously blow the tonal system. Indeed, the French Impressionists were already deviating from this system and other composers have used atonal elements in their writing: for example Arthur Honneger, Bela Bartok or Stravinsky who, even after refusing almost all his life this system, introduced serialism into his works after Schoenberg’s death.

I would like to recall a word of Pierre Boulez, which is a good definition of this period: “The atonality is essentially a transitional period, being strong enough to break the tonal universe, not being coherent enough to generate a non-tonal one.” (« L’atonalité est essentiellement une période de transition, étant assez forte pour briser l’univers tonal, n’étant pas assez cohérente pour engendrer un système non tonal. »). In the next post, we will focus on the construction of a coherence in the atonal universe through dodecaphonism.

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Indeed, these signs do not appear in the neumatic notation (I might say almost not: some neumes contain them) and we have to wait until the 12th century and the Notre-Dame School before polyphonists precised the length of notes in ternary melismas. Here begins the notation said mensural. The length of the note is not set but determined by the context: 1 or 2 beats for short ones and 2 or 3 beats for long ones.

This method becomes standard and gets broader in the 13th century: form and layout specify new lengths. New types of notes are invented: squares, rounds, filled or hollowed as well as new queues (with a hook for example).

In the beginning of the 14th century, the rhythmic notation became highly elaborated (use of different colors, of signs such as circles or points) and reached a peak at the end of the same century, to finally become progressively simplified. Features from this period are still observable, for example, C and C barre, as well as numeric combinations, which became fractions indicating bars.

In the 17th century a new character appeared: the bar line, and changed everything. A new way of counting was then introduced, not 1-1-1-1 anymore, but 1-2-3-4, and therefore set the duration of notes according to the figuring.

From this time, and despite the many treaties offering an improvement in the rhythmic notation, this one has remained almost unchanged. Thanks to the non-harmonic music, the debate has recently been revived, but the proposed new types are still very experimental.

So, this is the end of our little story of musical notation, but I already promise a post following this exciting saga: I will show you soon some examples of musical notation not exactly like any other!

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Little by little, the use of this line increased, then became ink-drawn and marked with a letter corresponding to the note assigned to this line. This letter is thus the ancester of our modern keys. A bit later, a second line was added, representing the quint, then a third one, in the middle of the two first. People thus realized that each note had its own place on the “staff”. During the XIIth century, the use of a fourth line was spread, later, in the XIIIth century, a fifth one was added.

The use of the “key” fixed all intervals between notes once and for all. Yet, remained the problem of B, which was mobile and was either a half-tone lower than C or a half-tone higher than A. It had thus to be differentiated: B forming a half-tone with C was represented by a square and the other B, by a circle. This was specified, either just after the key (our actual key signature), or in the text (the origin of accidentals).

From the XIIIth century, people started using natural signs (then confused with sharps) and flats for other notes than B: F and C-sharp, and in the XIVth century, G and rarely D-sharp (does not this order remind you something?). At the beginning of the XVIth century E-flat appeared. At the end of this same century was invented chromatism, the flat-natural-sharp system has thus become without limit. It can be said that in the XVIIth century, the classical notation was fixed and won’t be subjected to many changes.

At this stage, musical writing perfectly informs on note pitches and can become a real vector of music propagation. Rhythmic notation evolves the same way, but I will come to this in a next post.

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The first manuscripts in which neumes are written down, date from VIIIth and IXth centuries and come from Aquitaine. Neumes are a set of signs written above the text, indicating the direction of melodic curves and enabling the cantor to remember a melody already memorized.

In a general manner, neumes are graphic elements inspired from accents used by grammarians. The first forms of neumes were said aligned and took the form of grave or acute accents.
The etymological origin of the word “neume” is ambiguous. Indeed, it can signify πνεύμα “pneuma” (breath) as well as νεύμα “neuma”, the sign. One could think that, as a sign, the neume represented the choirmaster’s signs.

Little by little, the number of neumes used increased to reach a total of 8 (Punctum and Virga, Clivis (or Flexa), Podatus (or Pes), Climacus, Scandicus and Salicus, Torculus, Porrectus) to which were added special neumes (Quilisma, Stropha or Strophicus, Pressus, Bivirga, Trigon, Oriscus for example) informing about ornamentation or interpretation. Other conventional signs came to complete this notation, leading to the classic list of neumes. This notation well describes the rhythm and gives coarse indications on the melodic line, but not on the pitch or intervals. The musical notation thus was not a vector of propagation, which remained mainly oral, and was more like an aide-mémoire.

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For several thousand years, music was mostly handed down verbally without leaving a written trace. Regardless, since the origin of writing, it is possible to find some localized attempts of musical notations. A Babylonian tablet dated from the 16th century BC attests these attempts and lets us see a musical notation based on writing (alphabetic letters and grammatical accents).

By the 6th century BC, the Greeks posed the problem of notation a bit further. Alypius, whose introduction to music came to us partly, let us to get a precise idea of what the greek notation was at this time.

The greek system involved two signs for each degree of a given mode: one corresponding to an instrumental notation and another to a vocal notation.

The instrumental notation was composed of sixteen fixed signs, sorted into two octaves. In accord with theory, each sign could take three positions. According to its position, either natural, reversed (seen as in a mirror) or flattened, you had to play the sound either natural, either a half tone, or a quarter tone higher.

The vocal notation was less organized, simply constituted by the 24 letters of the greek alphabet, from alpha to omega. The Greeks, as we do, wrote musical signs above the text and the syllabs gave their length to sounds, thus avoiding use of rhytmical signs. Originally, rhythmic and metric were thus mixed together. Indeed, the vocal music occupied such a place that only the verbal aspect of musical rhythm remained. With the development of instrumental music, the rhythmic emphasized and became a discipline of its own. The greek notation system turns out to be a complex alphabetic system, mainly dealing with sounds height.

See you soon for the next part!

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