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- 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,
 1, 2, ...  , 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.
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| 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.
Figure I-1.
Scatter-plot of antiphon "Vespere autem sabbati": prominence of a particular tone.
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.
Figure I-3.
Scatter-plot of the same antiphon: significant movement between tones.
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