Page 213 - DCAP208_Management Support Systems

Management Support Systems

Notes
Table 1: Relative Frequencies of the 12 Semi-tones [6]-[8],[15]

Frequencies Occur in Order

Exactly 72 such scales are possible. They are given characteristic names and are serially
arranged in a table. Beauty of a raga delineation takes a new dimension when performer
sings or plays another raga by staying in the domain of the original raga. This is possible
by temporarily shifting the reference note to a new note existing in the original raga.
Hence all the remaining semi-tones will take different relative values leading to a new
raga. This is called ‘tonic-shift’. Every such shift may not give a new raga. For example,
29th melakartha raga called ‘Dheera Shankarabharana’ has the scale S, R2, G3, M1, P, D2,
N3., i.e., relative frequencies are 1 9/8 81/64 4/3 3/2 27/16 and 243/128. Shifting reference
from S to R2 makes the frequency ratios of R2, G3, M1, P, D2, N3 and upper octave S,=1, 9/
8 192/162 4/3 3/2 27/16 and 16/9 respectively. This corresponds to another new raga.
Continuing the process of shifting to various notes give raise to 4 other ragas using G3,
M1, P and D2. When reference is shifted to N3, relative frequencies give rise to both M1
and M2 in the new scale which does not correspond to any valid scale.
Formulation of the Problem
CCM being highly scientific, shows very interesting phenomena which are intriguing
researchers from a long time. One such phenomenon known as modal tonic shifting
exhibited by ragas of CCM have been investigated in the present paper using ANN. MLP
and LR models were constructed using inputs of frequencies present in all possible
heptatonic ragas of CCM. Applying TS on them, frequencies of the base pitch was shifted
to every note present in a given scale. The new scales generated were verified to evaluate
if a new valid raga was obtained. Since there are 72 scales, TS to remaining 6 notes of each
scale theoretically gives 432 combinations. But only 122 of these are valid scales. Hence a
total of 194 exemplars were used as inputs.
100% accurate results were obtained with MLP and LR models, using LM and momentum
learning, 2 HLs. Sensitivity analysis was performed to study the effects of the inputs on
target values. MLP used here was hetero-associative, supervised learning since correct
results (desired outputs) were known, so that during training the NN could adjust its
weights to match its outputs to target values. After training, NN was tested giving only
input values LR method allows user to test a network on a chosen data set Best network
weights were used to minimise CV error.

Experiments and Results
The present paper concerns with the study of an intelligent system to analyse the
performance of MLP and LR for a classification and regression problem. A case study was
taken up to study the unique phenomenon of tonic shifts in CCM. Input data consisted of
relative frequency ratios of the notes in heptatonic scales and their TS. MLP neural network
was constructed with one and two HLs and studied for online/batch processing. LM and
momentum learning rules were used. About 194 exemplars were used out of which 70%
was used for training, 10% for (CV), 20% for testing. 1000 epochs ( iterations) were used.
Classification and Regression reports were generated. Regression gave a plot of network
output and desired output for each value and correlation coefficient. Classification Report
gave the meansquared error (MSE), normalized mean-squared error (NMSE), mean absolute
error (MAE), minimum absolute error, maximum absolute error (MAE), correlation
coefficient (r) for each output and percent correct for each class. Bread boards generated for
Contd....

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