Using normalized Hermite functions, we construct bases in the space of square integrable functions on unit circle (L2(C)) and l2(Z), which are related to each other by means Fourier transform discrete transform. These relations unitary. The construction orthonormal requires use Gramm–Schmidt method. On both spaces, have provided ladder operators with same properties as for one-dimensional quant...

Even though chord roots constitute a fundamental concept in music theory, existing models do not explain and determine them to full satisfaction. We present a new method which takes sequential context into account to resolve ambiguities and detect nonharmonic tones. We extract features from chord pairs and use a decision tree to determine chord roots. This leads to a quantitative improvement in...