development of a meta-model for musical analysis
Important for a high quality musical performance is a good insight in the way the composition you want to play, is constructed. However, since the beginning of the 20th century, composers develop more and more their own musical language, often even diverent from one piece to another. In the end you need almost as many models as there are compositions. That’s why we want to go looking for a usable meta-model for musical analysis. This ‘universal’ analysis model should allow us – as a kind of an entrance model – to approach any composition without previous knowledge of the way it was conceived. Using some well defined procedures this model should be capable of indicating which of the existing analysis models could be most appropriate for a specific piece. We intend to use the newest insights in as diverent disciplines as linguistics, mathematics and artificial intelligence in order to get a deeper understanding of the essence of music as an art form.
The Messiaen project was started in 2003. Here we report on the results obtained so far and give directions for future research.
1. Situating the project
The title refers to Olivier Messiaen [1908 - 1992], French composer and founder of the first course in musical analysis at the Conservatoire National Supérieur in Paris]
In the western classical music tradition, a music piece survives through a score, a collection of symbols [notes] in which the composer tries to communicate his intent. As is the case with literature, painting and other art forms, the meaning of the symbols changes over time. Moreover, each time has its own rules determining how long a piece should be, or how it should be structured, what instruments should be involved etc. All these parameters are implicitly contained in the score and in such information as the period the composer lived in, the region he inhabited, the ‘school’ he belonged to etc.
It is considered particularly important for a high quality musical performance that the performer has a good insight in the way the composition he plays is constructed. It is a well known fact that a 17th century composer [e.g. Bach] composed following other composition techniques than someone from the 20th century [e.g. Schönberg]. The discipline that concentrates on extracting this information from the score is called ‘musical analysis’, or just ‘analysis’. In some [rather rare] cases we can refer to writings by the composer himself, who explains his proceedings. But in most cases the only way is to reverse engineer the thinking of the composer by musical analysis techniques: compare the piece against a pre-established model [e.g. the fugue, the sonata, the dodecaphony] in order to discover the specific characteristics of this unique composition.
However, since Schönberg [1874 – 1951] composers tend to develop their own musical language, often even diverent from piece to piece . In the end you need almost as many models as there are compositions. And you should actually ‘know’ beforehand with which composition technique a piece has been made, before you can decide which analysis model best applies.
That’s why we want to go looking for a usable meta-model for musical analysis. This ‘universal’ analysis model should allow us – as a kind of an entrance model – to approach any composition without previous knowledge of the way it was conceived. Using some well defined procedures this model should be capable of indicating which of the existing analysis models could be most suitable in order to explore a specific piece. As is the case with all meta-models, this project should allow us to re-verify [and, if necessary, correct] the existing analysis models. But perhaps it will also give us some additional insights in what is really essential or rather stylistically determined in music, which will of course be a great support in the education of musicians and can perhaps help to bring less obvious musical styles to a bigger audience. And if the model succeeds in indicating the specific characteristics of any composition whatsoever, it could even become a very valuable tool in the discussion about plagiarism.
Today this type of fundamental interdisciplinary research is almost exclusively done in only a few specialised centres: Ircam [Paris], Stanford [USA], Freiburg [Germany], Bologna [Italy], Den Haag [Holland]. As for the analysis of musical scores, their findings up till now clearly indicate the diviculty of the task, without giving much practically usable results yet. Our first results however, make us feel confident that our specific collaboration between scientists, composers and musical performers, combined with more than 100 years of expertise in music practice education, could lead us to a consistent contribution in this new field of artistic research.
2. Methodology
In order to develop this meta-model we want to use the newest insights in as diverent disciplines as linguistics, mathematics and artificial intelligence. As everybody knows, combining and generalizing models is a very typical research domain of mathematics. What’s more, since many centuries people are speaking in rather mythic wordings about the relationship between mathematics and music, referring to Bach’s number-symbolism, the often very ingenious puzzles in e.g. Renaissance music, the use of the Fibonacci series by Bartok, and so many other examples. However instead of thinking in terms of musical applications of mathematical principles, we want to see how music itself can be described in mathematical terms.
This fundamental artistic research will undoubtedly create bridges to and between diverse disciplines such as music, linguistics, Fourier analysis, data mining, compression and encryption techniques, combinatorics, structuralism, expert systems and artificial intelligence. Our mixed project group of composers, musicians, mathematicians and computer scientists has been selected in order to combine as much expertise as possible within a group of manageable size.
3. Developing a universal method for score analysis [2003 – 2004]
First thing we needed was a method with which we could approach ANY musical score. As stated before, traditional musical analysis techniques only apply to the musical forms/styles they were created for. Sometimes they can give partly useful results for other forms/styles, but none of them appears to be generic enough to become universally adoptable.
Our first tests indicated that very often the musical analyser falls back on a collection of ‘concepts’ against which he tries to compare the score , so we wanted to figure out which elements in the score trigger which ‘concepts’ . Often a lot of possibilities seem to be filtered out at first glance by specific indications in the score: the name of the composer, date or place of publication, instrumentation, the use of certain playing techniques, time or key signatures, etc. So we decided to create a test with all this information wiped out. This test score was analysed aloud by several colleagues who professionally deal with musical scores every day, while we were taking notes of their reasoning. The results were very surprising! They confirmed our first findings. But, opposite to what we hoped, the diverent test persons didn’t work following a systematic predefined plan. What’s more, depending on the ‘concepts’ they used, these professional analysts came to very diverent [and sometimes even disappointing] results. Our silent hope to distil a common method from their approaches, didn’t work out.
However, some elements returned in several interviews. The four base parameters [pitch, time, dynamic, timbre] are examined on macro as well as on micro level. The moments ‘something important’ happens on one or more of them [a series of notes returns, a new chord appears, a rhythmic ostinato stops, etc.] are considered to be the key moments of the piece. This resulted in our working hypothesis: segment the score each time one or more parameter changes or recurs, and study the relationships between these segments. In order to test this hypothesis some 100 scores, a representative selection qua genres, styles and historical periods, have been digitized .
4. “Patterns in changes” and “Changes in patterns” [2004 – 2005]
Very soon we found out that we should not only indicate when ‘something important happens’, but also ‘how important’ this event is. This is achieved by 2 very simple, yet powerful algorithms. In order to facilitate further research, both algorithms were implemented in “OpenMusic”, a Lisp-based open source environment for musical applications, developed at Ircam [Paris]. A Finale™ plug-in is written to allow easy transfer from Finale™ into OpenMusic .
Preparing the score
Each parameter of the score is represented as a series of data, called events, each consisting of two elements: the name of the event preceded by its time coordinate [expressed in milliseconds ]. Pitch events are expressed in midicents [6000 = C4, 6100 = C#4 etc.], durations in milliseconds and dynamics in MIDI velocities [0 … 127 from softest to loudest]. Timbres are just numbered in the order they occur in the score, the same number for the same timbre. As you can see, each event name is an element from a finite collection of possible names. Important is to stress that this number is only an identification, its numeric value is of no importance [pitch value 6100 is not ‘more’ than pitch value 6000, only diverent]!
Analysing changes – the algorithm value-changes
Figure 1: for each note we determine how many notes ago
the same note occurred, or a * when it is a new one; then for each
recurring note we verify how many diverent notes occurred in between;
finally,we change * by the first next number
Analysing the changes is very simple [see fig. 1 and 2]. Each event gets a weight, representing the number of diverent names that occurred since the last time the name of this event occurred, or, put diverently, its effect of surprise . Names that occur for the first time get the highest weight of the recurring names + 1. Finally, in order to be able to compare weight series, they are normalised between 0 and 1 [all weights divided by the highest occurring weight].
Figure 2: the algorithm value-changes expressed in mathematical terms. [ai] is a row of numbers representing the events. p is the function assigning to each event from the row the rank of the previous identical event. hi is the number of events between the one on position i and the previous identical event, while gi is the number of diverent events between the one in position i and the previous identical event. This number is the weight we assign to position i. The last formula makes sure that events occurring for the first time get a weight, too.
Analysing patterns – the algorithm find-patterns
One of the main issues when dealing with musical patterns is the diviculty to express them quantitatively. Of course, a series of events that recurs identically is very easy to recognise. But what to do with widely used musical transformations such as variations, inversions, retrogrades, augmentations, …?
Figure 3: all traditional variants of this fugue theme from Bach’s
The algorithm find-patterns defines a pattern as a series of events for which the algorithm value-changes produces the same series of weights: a pattern of changes. This allows for the detection of exact repetitions, but also transpositions, augmentations, inversions etc [see figure 3]. Retrogrades are not detected [see figure 4], what could seem a constructive minus, but definitely makes sense from an auditive [musical?] point of view .
Figure 4: this retrograde from Bach’s “Musikalisches Opfer” produces
Pattern detection with find-patterns is also pretty straightforward. For each event we calculate a weight series, as if this event was the first event. This produces a triangular matrix as in figure 5. For each position we collect all other positions that start with the same [at least 2] weights and keep the position with the longest match. This defines a pattern. Each diverent pattern gets a unique number, but patterns that are a subset of another one, get the number of the longer pattern.
Figure 5: for each event we produce a series of weights as if the event were the beginning of the row. This table shows the result of applying the algorithm ‘find-patterns’ to the decimals of the number π.
The result is a series of pattern numbers with their starting time, for which we can calculate the value-changes too, producing a weight for each pattern : changes in patterns.
Segmenting the score
For each parameter the score can now be segmented based on its value-changes: for each event B look up the previous event A with the same or higher weight; the fragment going from A till B is a segment for that parameter [see figure 6].
5. A score as a multi-dimensional distribution [2005 – 2006]
Since we wanted to get more grasp on the harmonic context of a musical score, the following base parameters were added:
- sound: each position in time gets a number, based on the combination of pitches, dynamics, durations and timbres at that moment
- sonance [i.e. the highest partial needed to analyse a sound as a chord]: express all pitches in the sound as frequencies, calculate their root [i.e. their highest common denominator ], divide each frequency by this root and reduce the results to their lowest octave ; the sonance is the highest result obtained.
- root: the succession of roots modulo 1200 [i.e. reduced within one octave] represents the harmonic rhythm.
Now for each of the 7 musical base parameters [sound, sonance, root, pitch, duration, dynamic, duration and timbre], their patterns and the lengths of their patterns, plus their respective value-changes, the evolution of 5 characteristics can be analysed segment by segment [makes 7 * 3 * 2 * 5 = 210 evolutions] and plotted as a graph underneath the score [see figure 6]:
- the parameter itself
- its diversity: number of diverent values used within each segment
- its variety: number of diverent values / total number of values within each segment
- its modus: most used value within each segment
- its ambitus: highest – lowest value within each segment
Figure 6: the value-changes for the pitches of this melody are calculated [a];
then for each resulting segment [b] the diversity is calculated [c],
giving us the evolution of the pitch-diversity of this melody.
Correlations
At first glance Pearson’s Correlation Coefficient between all these graphs seems to turn around 0, suggesting correlations are insignificant. But if we replace the name of the event with a number indicating the order in which this name first appeared, correlations all of a sudden turn out to be very significant, especially for thematic music! This is due to the fact that, as stated before, our numbers are just identifications and hence have no quantitative meaning.
Multidimensional distribution
As a result of having analysed all scores the same way, they now can easily be compared . Each of the 210 evolutions is displayed as a normalised frequency-graph [how often does each value appear within a graph? see figure 7] and this distribution is described with the standard statistics "mode" , "median" , "trimean" , "mean" , "range" , "semi-interquartile range" , "standard deviation" , "skew" and "kurtosis" , with the addition of the diversity and the variety of the parameter throughout the score [see figure 8].
Figure 7: the pitch-diversity from figure 6 expressed as a normalised frequency-graph:
for each value in graph 6b we count how many times it occurs; it is then plotted as
[value, number of occurrences / total number of values]
Figure 8: the standard statistics for the distribution from figure 7
A few conclusions jump out immediately:
- maximum overall pitch-diversity grows with music history. When in the Early Baroque it reaches its maximum of 12, the maximum overall duration-diversity starts growing, till it reaches a maximum in the middle of the 18th century, where the overall velocity-diversity starts growing till somewhere halfway the 19th century, where the overall timbre-diversity also starts growing. This mechanism seems to stop around 1950, where other distribution types seem to make their entrance
- range of pitch-pattern-lengths seems to grow slowly till J.J. Fux [ca 1700], and then diminishes; in other words with Fux we find the shortest and the longest patterns at the same time.
- maximum overall sonance seems to grow less than expected throughout music history and is apparently characterised by a fluctuation that is synchronised with the alternation between more Apollinic and more Dyonisic styles.
- mode of sonance indicates the harmonic system used [5.0 for the classical triad system]
- distribution of pitch-diversity [among others] seems to be a possible identifier for a lot of composers or styles
Further investigation learns that these 210 distributions [each described by 11 statistics] plus all their correlations create a multi-dimensional space in which composers and styles seem to form specific clusters. Even a simple calculation of [Euclidian] distance allows to recognise many of them. More specific techniques from multi-variate statistics and machine learning, such as Principal Component Analysis and Cluster Analysis, will undoubtedly reveal much more in a near future.
6. What’s next?
So far it seems we have succeeded in creating a universal analysis method, allowing us to model ANY score mathematically in a standardised way without loosing essential artistic information . Now we can start doing numeric analyses within this multi-dimensional space. Afterwards we’ll have to reconnect these results into artistic insights. This will certainly give us a better understanding of diverences between styles and composers. Perhaps we will even be pointed to musical relationships we’ve never been conscious of before? We don’t know yet, but it’s a fascinating journey!
Tom Deneckere and Peter Swinnen
Published in "Brave new interfaces" 2007, VUB press, ISBN 978 90 5487 416 4 pp. 237-251.
" P - TRAINS "
Ann Eysermans [2009-2010]
a:e graphic score phosphorescent
a:e graphic score ASCII
a:e graphic score Matrix
a:e graphic score HTML
[*] De piekuurtrein 7209 [die vertrekt vanuit Herentals om 7:43u en als eerstkomende haltes Wolfstee, Bouwel en Nijlen heeft] vertrekt om 7:57u vanuit Kessel, komt in Lier aan om 8:03u, vertrekt om 8:04u, komt aan in Mechelen-Nekkerspoel om 8:18u en vertrekt daar om 8:19u, komt in Mechelen aan om 8:22u en vertrekt daar terug om 8:25u, komt aan in Vilvoorde om 8:34u en vertrekt om 8:35u, komt aan in Brussel Noord om 8:45u en vertrekt daar om 8:47u, komt vervolgens aan in Brussel Centraal om 8:50u en vertrekt om 8:51u, komt tenslotte aan in Brussel Zuid eindstation om 8:54u. De totale reistijd [Kessel-Brussel Zuid] bedraagt 57 minuten. De trein vertrekt. Spoor naar nieuwe lucht, pulsaties die anders klinken, voor diegene die ze horen wil. Vrij rechte lijnen, je weet niet eens waarnaartoe; het 'niet' krijgt iets bijzonders. Naaste velden, waar klanken oplichten: een zachte galm, die geschiedenis wordt - voor zover men niets meer ziet, slechts licht nog hoort... Tegenspoor, je rechte evenwijdig met je vorige. Landschappen vervagen, worden fosfor-groener. Verder en vertraagd, vertraagt en nog. Naar het punt dat eindpunt heet, maar niemand weet iets méér... Het noodhamerkastje: zichtbaar. Zoals het hoort. Ik kijk ernaar. Maar niemand die het ziet...
text route
Binnen het BOAB onderzoeksproject "Messiaen Weerspiegeld" waarin ik gedurende vier jaar als assistent heb meegewerkt, onderzoek ik nu de correlatie tussen muziek, treinen en fosforescentie. Het project heeft de naam "P - TRAINS" en een eerste fase is reeds uitgewerkt: van een piekuurtrein [met het nummer 7209] naar miniaturen voor orgel en tape, van stoppende en voorbijrijdende treinen naar een geluidsinstallatie, alle elementen die samenkomen in een collage [tape], een fosforescerende grafische partituur, enz... Analyses en een gedetailleerde uitwerking van het compositorisch verwerken van de Piekuurtrein 7209 - gegevens, worden hieronder uiteengezet.
Composities en Installaties
* "P - TRAINS: music boxes"
* "P - TRAINS: graphic score"
* "P - TRAINS: collage"
* "P - TRAINS: 7209-morse-route"
* "P - TRAINS: accellerations"
* "P - TRAINS: miniatures for organ: Miniature 3 [with tape]" [live]
* "P - TRAIN: recording and recordings"
* "P - TRAINS: mystery train"
* "P - TRAINS: miniatures for organ"
* "P - TRAINS: Atomary Counterpoint Residus"
ACR 01
ACR 02
ACR 03
ACR 04
ACR 05
ACR 06
ACR 07
ACR 08
ACR 09
ACR 10
ACR 11
ACR 12
ACR 13
ACR 14
ACR 15
ACR 16
ACR 17
ACR 18
ACR 19
ACR 20
ACR 21
ACR 22
ACR 23
ACR 24
ACR 25
Uitvoeringen
- "P - TRAINS: miniatures for organ"
Maandag 30 november 2009 in de Finisterrekerk, 12.45u, Nieuwstraat, Brussel.
orgel: Iris Eysermans
- "P - TRAINS: music boxes"
Zondag 21 februari 2010, "Music on the Spot", Concertgebouw Brugge.
Champ d'Action - productie. www.champdaction.be
Installatie: Ann Eysermans
- "P - TRAINS: graphic score"
= Grafische fosforescerende partituur die in het donker uitgevoerd wordt, na oplichting.
Zondag 21 februari 2010, "Music on the Spot", Concertgebouw Brugge.
Champ d'Action - productie. www.champdaction.be
Uitvoerders: Ann Eysermans, Serge Verstockt, Kris Delacourt.
MUZIEK - TREINEN - FOSFORESCENTIE
Gemeenschappelijke kenmerken:
- noodhamerkastje ---> fosforescentie.
- P - trein = piekuurtrein. P = phosphor.
1] Notenmateriaal:
0 = fa# resterende noten: la# en si.
1 = re
2 = re#
3 = la
4 = do
5 = sol
6 = do#
7 = fa
8 = sol#
9 = mi
Ritmisch:
[telkens + 1 zestiende noot]
0 = zestiende noot
1 = achtste noot
2 = gepunte achtste noot
3 = kwartnoot
4 = kwartnoot + zestiende noot
5 = gepunte kwartnoot
6 = kwartnoot + gepunte achtste noot
7 = halve noot
8 = halve noot + zestiende noot
9 = halve noot + achtste noot
2] Piekuurtrein 7209 Kessel - Brussel Zuid.
reistijd bedraagt: 0:57
rijperiode: maandag-vrijdag, niet 11 november.
aantal overstappen: 0.
7209: zevenduizendtweehonderdennegen
getal 7209:
---> getallen die in woorden worden omschreven: = van cijfers naar tekst.
fa - re# - fa# - mi + ritme
fa[halve noot]- re#[gepunte achtste noot] - fa#[zestiende noot] - mi[halve noot + achtste noot]
Transposities: [chromatisch van 0 t.e.m. 11]
0 = fa - re# - fa# - mi
2 = sol - fa - lab - fa#
7 = do - sib - reb - si
9 = re - do - mib - reb
- Uurtabel en haltes:
7:57u [=477 min.] Kessel
8:03u [=483 min.] Lier
8:18u [=498 min.] Mechelen - Nekkerspoel
8:22u [=502 min.] Mechelen
8:34u [=514 min.] Vilvoorde
8:45u [=525 min.] Brussel Noord
8:50u [=530 min.] Brussel Centraal
8:54u [=534 min.] Brussel Zuid
---> uren omgezet naar noten.
- Combinatie uurtabel + minuten:
combinatie 1: do-fa-sol
combinatie 2: do-sol#fa#-la
combinatie 3: do-mi-sol#-re
combinatie 4: sol-lab-re#-fa#
combinatie 5: sol-lab-do-re
combinatie 6: sol-lab-do-mib
combinatie 7: sol-lab-la
combinatie 8: sol-lab-la-do
Uren X 7209:
757 X 7209 = 5457213
803 X 7209 = 5788827
818 X 7209 = 5896962
822 X 7209 = 5925798
834 X 7209 = 6012306
845 X 7209 = 6091605
850 X 7209 = 6127650
854 X 7209 = 6156486
---> berekeningen omgezet naar noten.
3] P - TRAIN DRAWN
SPEAR-analyses:
- analyse soundfiles laimeofudre [SP.K]
Speed: 8.000X
Pitch: - 3.00 semitones
Noise: 24.OO db.
[= DIMINUTIE]
- analyse soundfiles laimeofudre [SP.L]
Speed: 0,125X
Noise: 8 db.
[= AUGMENTATIE]
- analyse treinen [opname in piekuurtrein 7209]
Speed: 0.145X
- analyse tekst laimeofudre
Speed: 2.969X
Pitch: - 2.50 semitones
Noise: 24.00 db.
[= DIMINUTIE]
---> DRAWN 1.
- analyse drawn 1.
Speed: 2.312X
Pitch: - 5.50 semitones
Noise: 5 db.
---> GB: drawn 1 + analyse drawn 1. ---> DRAWN 2.
DRAWN 2 + opname treinen [2X] + opname tractie [treinen] + beat. [P-trainbeat = opname treinen verwerkt tot beat in GB.] = P - TRAIN DRAWN.
4]7209 - akkoord GB [orgels]
Pitch:
0 = 168,421 cents
1 = 378,947 cents
2 = 589,473 cents
3 = 800,000 cents
4 = 1010,52 cents
5 = 1221,05 cents
6 = 1431,57 cents
7 = 1642,10 cents
8 = 1852,63 cents
9 = 2063,15 cents
10 = 2231,57 cents - voor teksten
11 = 2400,00 cents - voor teksten
---> telkens laatste cent-cijfer in reeks.
7209 - akkoord + transposities
Lijst van cents [volledig] telkens eerste getal.
7 = 1473,68 cents
2 = 421,052 cents
0 = 42,1054 cents
9 = 1894,73 cents
---> 2X [inzetten per toon: telkens met 2, 7, 9 of 18 tussenvakjes, zie GB]
5] MINIATUREN VOOR ORGEL
"P - TRAINS: MINIATURES FOR ORGAN"
---> analyse-systeem Messiaen Weerspeigeld: informatie?
nr.1] 7209 [THEMA]
7[fa] 2[mib] 0[fa#] 9[mi] ---> melodisch
7[halve noot] 2[gepunte achtste noot] 0[zestiende noot] 9[halve noot + achtste noot]
---> ritmisch
Mel. + ritm. aan elkaar gekoppeld, + omkeringen, afzonderlijk en
simultaan.
Eindakkoord: opeenstapeling fa-mib-fa#-mi [2X] + pedaal.
Registratie: III: Bourdon 16’, Bourdon 8’, Voix céleste 8’, Flûte harmonique 8’, Tremblant II: Montre 16’, Bourdon 16’, Bourdon 8’, Flûte 4’ Ped: Contrebasse 16’, Sousbasse 16’ III/II, Ped/I
nr.2] 7[si-reb-sib-do: 7de transpositie]
2[fa#-lab-fa-sol: 2de transpositie]
0[mi-fa#-mib-fa: origineel = 7209, 0de transpositie] [volgorde noten vrij]
9[do#-mib-do-re: 9de transpositie]
---> zestiende noten, allemaal na elkaar.
---> idem, halve toon lager, andere tessituur.
---> idem, andere tessituur.
---> idem, halve toon hoger, andere tesseituur.
---> idem, enkel 0 andere tessituur.
---> idem, halve toon lager, andere tessituur.
---> idem, andere tessituur.
---> naar pedaalnoot LA [die in het geheel van transposities NIET aanwezig is].
in pedaal: FA [+vrije combinatie van fa#,mi en mib]
MIb [+vrije combinatie van fa#,fa en mi]
FA# [+vrije combinatie van fa,mi en mib]
MI [+vrije combinatie van fa#,fa en mib]
---> = THEMA. daarna verkorting [stretto-effect]: fa-mib-fa#-mi. naar LA-pedaal.
---> in akkoorden: LA-octaaf, 4de transpositie [la-sol-sib-sol#] + samenklanken 7, 2, 0
en 9: andere volgorde [verticaal].
---> THEMA [mel. en ritm. gekoppeld] 7 - 2 [omk] - 0 - 9 [omk] + ritmisch verlengd.
Registratie: III: Bourdon 16’, Bourdon 8’, Flûte harmonique 8’, Basson hautbois 8’, Trompette 8’ II: Bourdon 16’, Bourdon 8’, Montre 8’
Ped: Contrebasse 16, Sousbasse 16’, Violonbasse 8’, Trompette 8’
III/II, Ped/II
nr.3] uurtabel in noten
757 samenklank fa-sol-fa
803 samenklank sol#-fa#-la
818 samenklank sol#-re-sol#
822 samenklank sol#-re#-re#
834 samenklank sol#-la-do
845 samenklank sol#-do-sol
850 samenklank sol#-sol-do
854 samenklank sol#-sol-do
---> zeer hoog register.
Eindakkoord: opeenstapeling 7209 met pedaal.
TAPE: GB [trein-orgelwerk] duur: 4min. 10sec.
- treinen [opname]
- analyse SPEAR treinen [opname] ---> AUGMENTATIE. [speed: X 0,145]
- 7209 - akkoord GB.
Registratie: III: Fugara 4’ II: Prestant 4’ I: Mélophone 4’, Plein jeu
Ped: Contrebasse 16’, Sousbasse 16’, Violonbasse 8’ I/II, III/II +
1: II: + Flûte 4’
2: II: + Montre 8’, Bourdon 8’
3: III: + Basson Hautbois 8’
4: II: + Bourdon 16’, Viole de gambe 8’
5: III: + Trompette 8’
6: I: + Clairon 4’
Bovenstaande samenklanken [partituur] dienen [ritmisch vrij, legato] gespeeld te worden na ongeveer 1 minuut, nadat het geluid van de voorbijrijdende trein volledig uitgestorven is. Vanaf 2 minuten: eindakkoord, in crescendo, tot en met het einde. Orgel uitzetten terwijl het akkoord wordt aangehouden.
[u
r.4][/u]
7[ARP] naar si2 [halve noot]
2[ARP] naar fa#2 [gepunte achtse noot]
0[ARP] naar mi2 [zestiende noot]
9[ARP] naar do#3 [halve noot + achtste noot]
---> ritmisch 7209!
in pedaal: 7209
uren:
757 samenklank fa-sol-fa
803 samenklank sol#-fa#-la
818 samenklank sol#-re-sol#
822 samenklank sol#-re#-re#
834 samenklank sol#-la-do
845 samenklank sol#-do-sol
850 samenklank sol#-sol-do
854 samenklank sol#-sol-do
minuten:
477 samenklank do-fa-fa
483 samenklank do-sol#-la
498 samenklank do-mi-sol#
502 samenklank sol-fa#-re#
514 samenklank sol-re-do
525 samenklank sol-re#-sol
530 samenklank sol-la-fa#
534 samenklank sol-la-do
COMBINATIE van beide reeksen, waarbij de gemeenschappelijke noten worden weggelaten;
- combinatie 1: do-fa-sol
- combinatie 2: do-sol#fa#-la
- combinatie 3: do-mi-sol#-re
- combinatie 4: sol-lab-re#-fa#
- combinatie 5: sol-lab-do-re
- combinatie 6: sol-lab-do-mib
- combinatie 7: sol-lab-la
- combinatie 8: sol-lab-la-do
Comb.1 - 7[andere notenvolgorde] - Comb.2[ARP] - 2[andere notenvolgorde] -
Comb.3[akk.] - Comb.4[akk.] + 0[andere notenvolgorde] in pedaal. - Comb.5[akk.] -
9 - 7 - 2 - 0 - 9[andere notenvolgordes] In manuaal: + Comb.6 + LA uit Comb.7 --->
naar LA-octaven.
Registratie: III: Salicional 8’, Voix céleste 8’ II: Flûte 4’ Ped: Sousbasse 16’, Octavebasse 4’
Begin: spelen op II, zwelkast dicht
1: II: + Prestant 4’
2: Op III spelen
3: Ped: + Violonbasse 8’
4: II: + Viole de gambe 8’, spelen op II
5: II: + Montre 8’, Ped: + Contrebasse 16’
6: II/Ped
7: II: - Prestant 4’
nr.5] verticale opeenstapeling, samenklank van onder naar boven.
5457213 samenklank sol-do-sol-fa-mib-re-la#
5788827 samenklank sol-fa-sol#-sol#-sol#-mib-fa
5896962 samenklank sol-lab-mi-do#-mi-do#-re#
5925798 samenklank sol-mi-re#-sol-fa-mi-sol#
6012306 samenklank do#-sol#-re-re#-la-fa#-do#
6091605 samenklank do#-fa#-mi-re-do#-fa#-sol
6127650 samenklank do#-re-mib-fa-do#-sol-fa#
6156486 samenklank do#-re-sol-do#-do-sol#-do#
---> zetting [zoals hierboven] voor 2 manualen en pedaal.
Eindakkoord: opeenstapeling 7209. [idem miniatuur 3]
TAPE: GB: duur: 5min. 10sec.
- 7209[org.]
- 7 [org.+1642,10cents]
- 7209[org.]
- 2 [org.+589,473cents]
- 7209[org.]
- 0 [org.+168,421cents]
- 7209[org.]
- 9 [org.+2063,15cents]
COMBINATIE 7209 en 7, 2, 0 en 9. [=eindakkoord]
Registratie:III: Bourdon 16’, Bourdon 8’ II: Montre 16’, Bourdon 16’, Bourdon 8’ Ped: Contrebasse 16’, Sousbasse 16’, III/II, Ped/II
De akkoorden [de hierboven vermelde samenklanken] dienen afzonderlijk gespeeld te worden, vanaf een akkoord uit de tape hoorbaar is. +/- 4 seconden aanhouden, orgel uitzetten.
Eindakkoord: laten uitklinken, orgel uitzetten, enkele seconden na laatste akkoord.
nr.6]
uren:
757 fa-sol-fa
803 sol#-fa#-la
818 sol#-re-sol#
822 sol#-re#-re#
834 sol#-la-do
845 sol#-do-sol
850 sol#-sol-do
854 sol#-sol-do
minuten:
477 do-fa-fa
483 do-sol#-la
498 do-mi-sol#
502 sol-fa#-re#
514 sol-re-do
525 sol-re#-sol
530 sol-la-fa#
534 sol-la-do
---> 757[fa-sol-fa] - 477[do-fa-fa] - 803[sol#-fa#-la] - 483[do-sol#-la] enz...
achtste noten, elkaar opvolgend van boven naar beneden, per 3 noten.
Registratie:1: Tutti, met een langzame registerdecrescendo.
Begin: spelen op II, zwelkast open.
2: Tutti, begin: spelen op II, zwelkast open.
- as fast as possible.
---> - mogelijkheid 1: ffff > 0. Telkens blijven herhalen, dynamiek neemt af door registratie, tot er niets meer overblijft!
- mogelijkheid 2: Blijven herhalen, maar terug bij het begin gekomen, telkens 2 noten weglaten, dus tot er enkel la-do
[op het einde] overblijft. [= uitgeschreven]
nr.7] vergelijking nr.1].
7209 [THEMA]
7[fa] 2[mib] 0[fa#] 9[mi] ---> in omkering.
7[halve noot] 2[gepunte achtste noot] 0[zestiende noot] 9[halve noot + achtste noot]
---> ritmisch: blijft hetzelfde t.o.v. origineel.
Mel. + ritm. aan elkaar gekoppeld, + omkeringen, afzonderlijk en simultaan, andere tessituren in vergelijking met nr.1].
Einde: 7[si-do#-sib-do] stijgend.
2[fa#-lab-fa-sol] dalend.
0[mi-fa#-re#-fa] dalend +
9[do#-mib-do-re] stijgend. [stretto!]
eindakkoord: re-fa + LA [de niet-aanwezige noot] in het pedaal.
Registratie:III: Salicional 8’ II: Viole de gambe 8’ Ped: Contrebasse 16’, Sousbasse 16’ III/I
6] Composities en Installaties
* "P - TRAINS: miniatures for organ": de zeven miniaturen klinken in en door elkaar in diminutie.
* "P - TRAINS: collage": alle elementen [opnames, 7209-akkoorden, diminuties en augmentaties van de tapestukken en van de
collage zelf: canonisch, contrapuntisch] binnen dit onderzoek worden samengevoegd in één collage [tape], waarin eveneens een koraaltje klinkt ['traagheid' van de akkoorden <-> snelle, kortere, meer grillige structuren], in een trein gecomponeerd [2005].
* "P - TRAINS: music boxes": noodhamerbakjes [trein] worden muziekdoosjes. "En cas de danger, brisez la glace!".
* "P - TRAINS: 7209-morse-route": tekst [*] over P-trein 7209 en over artistiek onderzoek wordt in Morse-code omgezet, in augmentatie en diminutie, simultaan op halve toonafstand.
* "P - TRAINS: accellerations": opname van de piekuurtrein die aankomt [+ voorbijrijdende trein] wordt versneld.
* "P - TRAINS: graphic score": 100cm - 70cm, fosforescerend groen, acrylverf, Chinese inkt. Deze partituur bevat notenmateriaal uit het onderzoek; uurtabel, treinnummer en combinaties, treinsignalisatie; seinlicht + borden langs de sporen, grafische [wetenschappelijke] weergave fosforescentie + tekst, aanduidingen met betrekking tot 'galm', aanduidingen met betrekking tot treingeluiden en muziektekens en benamingen [Italiaanse termen]. Partituur die in een donkere kamer, door de muzikant die ze interpreteert, wordt opgelicht [volledig, of in stukjes; deze informatie kan worden gelezen na oplichting en worden uitgevoerd tot het licht volledig gedoofd is...]
* "P - TRAIN: recording and recordings": opname piekuurtrein 7209 [tape]---> opname van deze opname, opname van déze opname, enz... tot +/- noise. [in totaal: 10 opnames] + tekst route en proza [2- en 4 bit- residuen] die hieronder stilaan vertraagt en een beetje luider wordt.
* "P - TRAINS: Atomary Counterpoint Residus" [ACR]: vooronderzoek "laimeofudre" bestaat uit 25 composities die door middel van een SPEAR-analyse worden verkort [diminutie] tot kleine stukjes noise, zodat bepaalde [opgezette] structuren [vooral contrasten in densiteit, timbre en duur] plotseling veel sneller duidelijk lijken te worden worden. Deze stukjes zijn interessante miniaturen op zich, maar kunnen eveneens als nieuw bronmateriaal gelden [ik heb ze contrapuntisch verwerkt in "Pretty Good Year", een compositie uit de 'Christmas Special 2009'].
---> terugkoppeling metamodel Messiaen Weerspiegeld:
- parametrische analyse?
- herkenbare patronen? [7209-thema?]
- conclusies?
7] TEKSTEN
---> [*] omzetting naar MORSE: ritmisch gegeven. Worden aan LA# en SI- klanken gekoppeld [overblijvende noten uit de reeks].
---> omzetting naar ASCI: nieuw notenmateriaal [cijfers].
---> omzetting naar BRAILLE: tekens worden tabulatuur voor de muziekdoosjes.
8] Beeldmateriaal
Een afbeelding van de grafische partituur [opgelicht] is omgezet naar ASCII, HTML en MATRIX. Deze beelden genereren nieuwe informatie: cijfers en nieuwe structuren die opnieuw compositorisch worden verwerkt in een volgende fase binnen dit onderzoek.
9] Fosforescentie
Fosforesceren is het licht afgeven na bestraling met licht-, röntgen- of andere stralen zonder dat hiermee gloeiing of verbranding gepaard gaat. Sommige materialen hebben merkwaardige eigenschappen; ze kunnen verschillende soorten energie absorberen, die energie opslaan en een deel ervan achteraf weer uitzenden onder de vorm van licht.
1] De energie die wordt geabsorbeerd zorgt ervoor dat de elektronen van de atomen van het absorberend materiaal geëxiteerd worden; de elektronen [die in banen rond de kern van het atoom draaien] springen van een meer inwendige naar een meer uitwendige baan.
2] Wanneer de elektronen naar hun oorspronkelijke toestand terugvallen, wordt een pakketje licht uitgezonden. De tijd die tussen 1] en 2] verloopt kan ofwel heel kort [minder dan 1/100.000 van een seconde] ofwel lang [verschillende uren] zijn. Bij een kort interval spreekt men van fluorescentie. Bij een lang interval spreekt men van fosforescentie.
[voorbeeld: wijzerplaat horloge: de kleurstofmoleculen worden geëxiteerd door het daglicht, waarna ze slechts heel langzaam hun fosforescentielicht uitzenden, wat overdag nauwelijks zichtbaar is. 's Nachts echter, kunnen we het zwakke fosforescentielicht waarnemen.]
9] Dankwoord
Mijn speciale dank aan Peter Swinnen ["Messiaen Weerspiegeld"] en Serge Verstockt [Champ d'Action]. Zonder hen zou de realisatie van dit project en de uitvoeringen, niet mogelijk zijn geweest. Dank ook aan Iris Eysermans voor de prachtige vertolking van de miniaturen voor orgel.
a:e kinkempois
a:e diesel locomotive type 55
a:e performance and installation P - TRAINS, Champ d'Action, Concertgebouw Brugge
a:e performance and installation P - TRAINS, Champ d'Action, Concertgebouw Brugge
a:e performance and installation P - TRAINS, Champ d'Action, Concertgebouw Brugge
a:e performance and installation P - TRAINS, Champ d'Action, Concertgebouw Brugge
a:e performance and installation P - TRAINS, Champ d'Action, Concertgebouw Brugge
a:e performance and installation P - TRAINS, Champ d'Action, Concertgebouw Brugge
a:e performance and installation P - TRAINS, Champ d'Action, Concertgebouw Brugge
a:e performance and installation P - TRAINS, Champ d'Action, Concertgebouw Brugge
a:e performance and installation P - TRAINS, Champ d'Action, Concertgebouw Brugge
a:e performance and installation P - TRAINS, Champ d'Action, Concertgebouw Brugge
a:e performance and installation P - TRAINS, Champ d'Action, Concertgebouw Brugge
en cas de danger brisez la glace en cas de nécessité brisez la glace en cas d' urgence brisez la glace en cas de force majeure brisez la glace en cas d' obscurité brisez la glace en cas d'été brisez la glace en cas d'impuissance brisez la glace en cas de retard brisez la glace en cas d'excès de confiance brisez la glace en cas de danger brisez la glace en cas de nécessité brisez la glace en cas d' urgence brisez la glace en cas de force majeure brisez la glace en cas d' obscurité brisez la glace en cas d'été brisez la glace en cas d'impuissance brisez la glace en cas de retard brisez la glace en cas d'excès de confiance brisez la glace en cas de danger brisez la glace en cas de nécessité brisez la glace en cas d' urgence brisez la glace en cas de force majeure brisez la glace en cas d' obscurité brisez la glace en cas d'été brisez la glace en cas d'impuissance brisez la glace en cas de retard brisez la glace en cas d'excès de confiance brisez la glace en cas de danger brisez la glace en cas de nécessité brisez la glace en cas d' urgence brisez la glace en cas de force majeure brisez la glace en cas d' obscurité brisez la glace en cas d'été brisez la glace en cas d'impuissance brisez la glace en cas de retard brisez la glace en cas d'excès de confiance brisez la glace en cas de danger brisez la glace en cas de nécessité brisez la glace en cas d' urgence brisez la glace en cas de force majeure brisez la glace en cas d' obscurité brisez la glace en cas d'été brisez la glace en cas d'impuissance brisez la glace en cas de retard brisez la glace en cas d'excès de confiance brisez la glace en cas de danger brisez la glace en cas de nécessité brisez la glace en cas d' urgence brisez la glace en cas de force majeure brisez la glace en cas d' obscurité brisez la glace en cas d'été brisez la glace en cas d'impuissance brisez la glace en cas de retard brisez la glace en cas d'excès de confiance brisez la glace en cas de danger brisez la glace en cas de nécessité brisez la glace en cas d' urgence brisez la glace en cas de force majeure brisez la glace en cas d' obscurité brisez la glace en cas d'été brisez la glace en cas d'impuissance brisez la glace en cas de retard brisez la glace en cas d'excès de confiance brisez la glace en cas de danger brisez la glace en cas de nécessité brisez la glace en cas d' urgence brisez la glace en cas de force majeure brisez la glace en cas d' obscurité brisez la glace en cas d'été brisez la glace en cas d'impuissance brisez la glace en cas de retard brisez la glace en cas d'excès de confiance brisez la glace en cas de danger brisez la glace en cas de nécessité brisez la glace en cas d' urgence brisez la glace en cas de force majeure brisez la glace en cas d' obscurité brisez la glace en cas d'été brisez la glace en cas d'impuissance brisez la glace en cas de retard brisez la glace en cas d'excès de confiance brisez la glace en cas de danger brisez la glace en cas de nécessité brisez la glace en cas d' urgence brisez la glace en cas de force majeure brisez la glace en cas d' obscurité brisez la glace en cas d'été brisez la glace en cas d'impuissance brisez la glace en cas de retard brisez la glace en cas d'excès de confiance brisez la glace en cas de danger brisez la glace en cas de nécessité brisez la glace en cas d' urgence brisez la glace en cas de force majeure brisez la glace en cas d' obscurité brisez la glace en cas d'été brisez la glace en cas d'impuissance brisez la glace en cas de retard brisez la glace en cas d'excès de confiance brisez la glace en cas de danger brisez la glace en cas de nécessité brisez la glace en cas d' urgence brisez la glace en cas de force majeure brisez la glace en cas d' obscurité brisez la glace en cas d'été brisez la glace en cas d'impuissance brisez la glace en cas de retard brisez la glace en cas d'excès de confiance brisez la glace en cas de danger brisez la glace en cas de nécessité brisez la glace en cas d' urgence brisez la glace en cas de force majeure brisez la glace en cas d' obscurité brisez la glace en cas d'été brisez la glace en cas d'impuissance brisez la glace en cas de retard brisez la glace en cas d'excès de confiance brisez la glace en cas de danger brisez la glace en cas de nécessité brisez la glace en cas d' urgence brisez la glace en cas de force majeure brisez la glace en cas d' obscurité brisez la glace en cas d'été brisez la glace en cas d'impuissance brisez la glace en cas de retard brisez la glace en cas d'excès de confiance brisez la glace en cas de danger brisez la glace en cas de nécessité brisez la glace en cas d' urgence brisez la glace en cas de force majeure brisez la glace en cas d' obscurité brisez la glace en cas d'été brisez la glace en cas d'impuissance brisez la glace en cas de retard brisez la glace en cas d'excès de confiance brisez la glace en cas de danger brisez la glace en cas de nécessité brisez la glace en cas d' urgence brisez la glace en cas de force majeure brisez la glace en cas d' obscurité brisez la glace en cas d'été brisez la glace en cas d'impuissance brisez la glace en cas de retard brisez la glace en cas d'excès de confiance brisez la glace en cas d'urgence brisez la glace en cas d'urgence
P-Trains performance
for phosphorescent graphic score, 4 free improvisation musicians and tape,
as an accompanying performance to the P-Trains sound installation [+-13minutes]
4 musicians are situated in a small dark room together with a small amount of audience around the P-Trains phosphorescent graphic score which is painted on a canvas, laying on the floor. A few stroboscopic light flashes enlighten the graphic score and a music tape starts to sound. While the light of the phosphor score gradually fades out during the performance the 4 musicians make an original improvisation based soundscape inspired by the graphic score and interwoven with the sounding tape. The graphic score consists out of elements from Eysermans’ investigation in trains and phosphor translated into musical instructions.
In a P-Trains performance version without tape each performer can light up a part of the score by using the flash of a camera. Each performer plays his part of the score during the unpredictable time that it is illuminated. A sounding contrapuntal play of light is created.
Tape includes:
- 7209-trainnumber-sounds and transpositions [organs]
- collage of several compositions in 'diminution' and 'augmentation'
- trainsounds: in canon [fifth] and used as beats [melodical and rhythmical]
- 'chorale' written in a P-train [Kessel-Brussel Midi]
- musicboxes: 'Miniatures for Organ' and improvisations played on musicboxes
Graphic score:
- 70cm-100cm, phosphorescent green, chinese ink
- timetables, train-numbers transformed in notes, serial composed [chords, melodies, …]
- train signs, trainlights, and graphical scientific representations of phosphorescence and text
- 7209-numbers in Braille
- decrescendo-reverb and fade-out signs
Those signs have to be interpreted by the musicians in a intuitive way and have to be played in the context of the tape.
a:e performance and installation P - TRAINS, Concertgebouw Brugge
PRODUCTION P-TRAINS MUSIC BOXES: CHAMP D'ACTION
Mucic Box 1
Music Box 2
Music Box 3
Music Box 4