Sheridan College Sheridan College
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Publications and Scholarship Faculty of Animation, Arts & Design (FAAD)
1996
A Computer-Based Editor for Lerdahl and Jackendoff's Rhythmic A Computer-Based Editor for Lerdahl and Jackendoff's Rhythmic Structures
Structures
Bruno Degazio
Sheridan College, [email protected]
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Degazio, Bruno, "A Computer-Based Editor for Lerdahl and Jackendoff's Rhythmic Structures" (1996).
Publications and Scholarship. 7.
https://source.sheridancollege.ca/faad_publications/7
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A COMPUTER-BASED EDITOR FOR
LERDAHL AND JACKENDOFF'S RHYTHMIC STRUCTURES
Bruno Degazio
The Artificial Evolution Studio ([email protected]) 192 Spadina Ave • suite 512 • Toronto • Ontario • Canada • M5T 2C2
In A Generative Theory of Tonal Music, Lerdahl and Jackendoff (hereafter L+J) discuss two forms of rhythmic structure which they call metrical structure and grouping structure. Together these constitute a basis for an analytical understanding of rhythmic structure in music.
A software based editor has been written which allows the interactive exploration of these two types of hierarchical rhythmic structures. It bears some relationship to simple time based editors found in commercial software, but represents an extension of such software to a much wider range of rhythmic features
The Metrical Structure PAitor allows the user to specify up to eight hierarchical levels, each with strong-weak beat pattern up to sixteen elements long. The pattern can also be broken arbitrarily and restarted at any point, a feature common to the higher (i.e. greater than measure length) levels of metrical structure. The software strictly enforces L+J's Metrical Well Formedness Rules 1 and 2:
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Figurc 1· regular metrical Btructure based on hierarchical duple divisions
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Figure 2 - complex mctrea created by multiple layers of S Blructurcd as 2+3
1. Every attack point must be associated with a beat at the smallest metrical level present.
2. Every beat at a given level must also be a beat at all smaller levels Metrical Well Formedness Rules 3 and 4 are implemented in a freer form:
3. At each metrical level, strong beats are spaced either two or three beats apart.
4. The tactus and immediately larger metrical levels must consist of beats equally spaced.
The relaxation of these latter two rules allows for compound metrical structures such as are found in Bulgarian folk music, and for free metrical structures such as
recitative and for specification of metrical structures impossible to notate conventionally, such as poly-compound meters where both the tactus and the measure are comprised of a recurring pattern of strong/weak beats (e.g 3+2+3).
The Metrical Structure Editor is shown in figures l and 2 above. Figure 1 shows a regular metrical structure based on a duple division at all levels.
Figure 2 shows a more complex structure where two levels employ a five beat pattern structured internally as 2+3. The user can specify a strong
weak pattern for each of eight levels of metrical structure. Two of these levels have a special status: the measure and the lactus, designated with
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Figure 3 - mclrical Hlruclur1:11 di•playcd 1111perimpu,,ed ·un a ""'fUence uf nuleM
the letters 'm' and 't' along the left edge of the editing screen. The taclus is the metrical level used, if possible, for the denominator portion of the time signatures, and usually moves along at approximately the rate of the
Degazio 396 ICMC Proceedings 1996
human heartbeat (about 60 to 140 beats per minute). The measure is the level used ror the numerator portion of the time signatures, which are shown along the top of the editing screen. These levels have a special meaning in other portions of the software as well, notably in the Selection Filter, where choices can be made based on an event's measure or tactus chamcteristics. Levels of metrical structure can be displayed in the graphic event editor as a set of 'barlines' of varying weight (figure 3).
The Grouping Structure Editor allows for the specification of three levels of grouping structure, arranged hierarchically according lo L+J's Grouping Well-Formedness Rules:
1. Any contiguous series of events, and only contiguous events, can constitute a group.
2. A piece constitutes a group.
3. A group may contain smaller groups.
4. If a group O I contains a group 02, it must contain all of 02.
- --�--- --- - - -
Grouping structure is displayed along the bottom of the graphic editor screen (figure 4), using lines with curved ends which resemble L+J's notation. Six levels of grouping structure are allowed, with the current levels designated by a small letter 'G' along the left edge of the screen. A series of notes can be designated as a group by selecting them with the mouse and choosing 'Group Notes' from the Edit Menu. Notes already grouped can be selected with the 'Select Group' command.
L+J's Grouping Well-Formedness Rules are not enforced at the time of selection; instead a separate pass can be made using the 'Check Group Structure ... " command.
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Figure -4 - graphic editor with grouping structure displayed along bottom
Two other commands allow the automatic creation of group structures. "Make Repeating Groups ... " (figure 5) creates regularly
repeating groups at the current level of grouping structure. This ••• CREATE REGULRRL Y REPEATING GROUPS •••
Start at: � I note numberl
auto-grouping uses:
§:]OPilch
� 0 uolume Siert et:
� D duration �I 1_2 __ �
� D 11rtlcul11tlon lnd 111:
l:!!:=J
D pitch class._1
2_8 __ �( cnncel )
I
RUTD-GROUPI
may be used, for example, to I>
End et: � (note number)
Group euery: E:J (ticks) Group leuel: EJ ( 1-6, D manna
current leu111)
group measures or beats, if I>
these are suitably regular. A I>
more complex command is
"Auto Group ... " (figure 6), which uses a measurement similar to that discussed by I>
James Tenney and Larry Polansksi to automatically create groups based on a
( group thl1 leue1._ )
I
REPEAT GROUP•
Figure 5 - ·create Repeating Groups ... • dialog .,..,_,Fi..,
gur-e""6"'.""·Au.-to-G".'"r_ou_p ___ -:-_.-d-lal_og ___ _, selection of intrinsic musical parameters. These include: pitch, velocity, currently implemented.
Acknowledgements
duration, articulation (i.e. onset delay) and pitch class. Only pitch weighting is
This research was carried out with the financial �istance of the Canada Council. Media Arts Section. The Artificial Evolution Studio wishes lo thank Karl Mohr for his help in the preparation of this paper.
Refereaca
(Degazio, Bruno 1988] Con rat Sen.iitive Editing in I� MIDIFOR11I Co,nP"ler Music Sysiem. Proceedings of the International Computer Music Conference: Cologne. 1989.
[Degazio, Bruno 1993) New Software Co111po.sition Tools. Fourth Biennial Arts and Technology Symposium: New London, Connecticut. 1993.
[Lerdhal. F, Jacl.endoff. R 1983] A Generative Theory o/Tona/ Music. MIT Press: Cambridge, 1983.
ITenncy,J and Polanski.LI Hierarchical Temporal Ges1al1 Perception in Music: A "Metric Space" Model. Yon: Univenity, Toronto. Ontario, 1978
ICMC Proceedings 1996 397 Degazio
