Neumed & Ekphonetic Universal Manuscript Encoding Standard


Table of Contents
§ I. Scatter plot of tones at n-1 vs n
Sample analysis
§ II. Software Architecture

§ I. Scatter plot of tones at n-1 vs n

  • A scatter plot (or, scatter diagram) is a graph that shows the correlation between data in a way that is easy to grasp visually. The graphs presented in this section plot the tone of each note in a melody against the tone of the next note. If these points tend to fall along a line, or otherwise 'cluster' together, then the data are said to have positive correlation.
  • Some positive correlations are discussed musicologically in the Sample Analysis, below.
  • Features of a scatter plot that reveal relationships between the data include: the strength in which the data points cluster in a pattern (revealing, for example, the relative amount of melodic leaps versus stepwise motion); the general shape of the pattern (e.g., linear, curved, etc.); and its directionality. By comparing the scatter plots of several chants, one can see contrasting characteristics in these features. Remark, however, that scatter plots are just a tool: by themselves, they do not provide conclusions; rather, they can suggest at-a-glance where one might productively do a more detailed analysis.
  • We number the notes of a chant as a sequence, sequence delimiter, left 1, 2, ... sequence delimiter, right, and refer to any arbitrarily chosen note as n (" n " is any particular note generally speaking). The note immediately preceding note n in the chant, we refer to as n-1. The X-axis and Y-axis are calibrated in tones (by which we mean, degrees of the modal scale, or pitches in the case of pitched sources). On each axis, these tones are in ascending order of 'pitch', and their scope corresponds to the ambitus of the chant (which is, the tonal distance between a chant's lowest tone and highest tone).
  • The X-axis shows the tones at note n, and the Y-axis shows the corresponding tone at note n-1. The data points of the scatter plot are pairs of tones: (tone at n, tone at n-1). Thus, the tone at n-1 is plotted against the tone at n. These graphs also show a linear regression line through the set of data points. Intuitively, one can think of a regression line as a weighted average trend, such that one can predict (with more or less certainty, according to the strength of clustering along this line) what the value of n-1 will be for any given value of n.
  • Scatter plot of random noise.
    Scatter-plot of random noise
    Mathematically speaking, the type of correlation shown by these plots is the degree of local randomness in the chant melody. That is to say, the degree of predictability in tonal movement between adjacent notes. In the case of 'random noise', there is no correlation between successive pitches; its scatter plot would look approximately as shown at right.
  • Requires Flash Player (free), version 5.0 or above, for viewing.
  • To view a scatter plot, select a NEUMES/NeumesXML transcription from the list below, and click on 'Draw Graph'.
    [Remark: this version of the scatter plot analysis works only for pitched sources transcribed as NEUMES data. We intend to expand this analyalytical method to cover non-pitched sources as well.]

Sample Analysis : antiphon "Vespere autem sabbati"
  • Prominence of a particular tone or tones

    Tones (viz., pitches) that are sung frequently in a chant melody are obvious in a scatter plot. For example in the antiphon "Vespere autem sabbati," the tone c occurs 15 times out of 69 notes. Melodic motion to and from the note c occurs repeatedly with the tones a, b-natural and c (repetition of the same tone), but most often between the tones c-a, and c-c. This is highlighted in Figure I-1 by magenta boxes superimposed on the plot.
Scatter-plot of antiphon 'Vespere autem sabbati': prominence of a particular tone.
Figure I-1. Scatter-plot of antiphon "Vespere autem sabbati": prominence of a particular tone.
  • Repetition of a particular tone

    If dots cluster at one point in the plot, as occurs in the middle of the 'cross' in Figure I-1 (at the tone c), the scatter plot is displaying a repetition of this tone in the chant. Such a repetition of tones would be expected for a responsory tone, a versicle, or another genre of chant which is based in recitation, but this is a significant occurrence in an antiphon. Figure I-2 is an image excerpt from a source containing this antiphon; it shows a recitation-like section, with multiple repeated c-tones.
Antiphon 'Vespere autem sabbati': excerpt from source image.
Figure I-2. Source image of antiphon "Vespere autem sabbati," excerpt.
[Source: British Library; Yates Thompson 25, f. 1r.]

  • This scatter plot also shows significant movement between the tones a-G (or G-a), as highlighted by the magenta circle in Figure I-3.
Scatter-plot of antiphon 'Vespere autem sabbati': significant movement between tones.
Figure I-3. Scatter-plot of the same antiphon: significant movement between tones.

§ II. Software Architecture

As with much of the NEUMES website, this 'Analytical Software' section uses the client/server model of processing. In contrast to the static model, whereby fixed-content webpages are sent to the end-user's browser by a server, the client/server model establishes a dialog between the server and individual client computers for 'collaborative processing'. This involves some sharing of responsibility for the program logic of particular tasks.

Our implementation uses a type of program called a Java Servlet on the server-side. We use so-called 'thin client' processing on the client-side: no special, NEUMES-specific software has to be installed on the client computer; everything relies on standard components of modern Web browsers (CSS or Cascading Stylesheets, JavaScript, Flash Player, Java Applets, and so on). Small programs embedded in the NEUMES webpages perform such tasks as user-interface customization on the client, basic verification of input by the end-user, and dispatching of Servlet requests to the server. These programs operate in a security 'sandbox' on the client-side and do not put the client computer at risk.
Client/server model: Servlet Request and Servlet Response.
Figure II-1. Client/server model: Servlet Request and Servlet Response.
Figure II-1 depicts the sequence of events involved in drawing a chart on the client computer.
  1. A chart is initiated by a Servlet Request from the client's Web browser. This happens by the user clicking on 'Draw Graph' button under 'Selection '. The Servlet Request includes information about the particular graph that is needed.
  2. In its Servlet Response, the server delivers an HTML webpage that has embedded in it an Object, which is a 'generic' Flash presentation for charts. Written into the Object are specifications for the data needed by this chart, which shall be delivered by a Servlet. When the client's browser starts to draw the 'generic' chart on-screen, it automatically runs the embedded Servlet Request such that data for this chart will be downloaded.
  3. In the second Servlet Response, the server feeds a stream of data for this chart to the Flash Show. In actuality, the Servlet generates the data dynamically on-demand from a NEUMES transcription; it does it by XSL (Extensible Stylesheet Language) Transformation on the transcription file. Finally, the client computer renders the chart on-screen.
Protected by law under one or more of the following copyrights:
Copyright 2005-2007, The University of Oxford.
Copyright 2003-2005, Louis W. G. Barton.
Copyright 2002-2003, The President and Fellows of Harvard College; contains software or other intellectual property licensed from Louis W. G. Barton, copyright 1995-2001 by Louis W. G. Barton.