By Harold Crabtree
The article of this e-book is to convey in the diversity of the abler Mathematicians at our Public colleges and of First yr undergraduates on the Universities, a topic which has hitherto been thought of too tough for any however the extra complex scholars in arithmetic, whereas even they've got in lots of circumstances did not derive extra excitement from the learn of spinning tops than is contained in filing the matter to the motion of a sophisticated piece of Mathematical equipment which instantly, although unintelligently, seems the right kind end result.
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Additional info for An elementary treatment of the theory of spinning tops and gyroscopic motion
First, the chords selected for the database and the naming convention of the played notes is presented. The naming convention used has musical meaning which is a new feature in this type of database. Finally, the content of the database organized by the polyphony number is shown. 1 Chord Selection The chords are selected taking into account the most typical chords in Western music and also different difficulty levels in the detection due to the existing harmonic relations between the notes that compose the chord.
Note that, in the recordings, these intervals can be simple or composed by one or more octaves. gr. 1)). The most consonant chord that exist, and the most typical Western music chord, is the perfect major chord (X : (1, 3, 5)). gr. M. 9 Name Intervals Perfect Major Perfect Minor Augmented Augmented-Minor Diminished Diminished Minor X X X X X X Name Suspended 4 Suspended-Augmented 4 Suspended-Diminished 4 Major-Major 7 Major-Minor 7 Augmented-Major 7 Augmented-Minor 7 Diminished-Major 7 Diminished-Minor 7 Minor-Major 7 Minor-Minor 7 Augmented-Minor-Major 7 Augmented-Minor-Minor 7 Diminished-Minor-Major 7 Diminished-Minor-Minor 7 : (1, 3, 5) : (1, 3b, 5) : (1, 3, 5#) : (1, 3b, 5#) : (1, 3, 5b) : (1, 3b, 5b) Intervals X : (1, 4, 5, 7) X : (1, 4#, 5, 7) X : (1, 4b, 5, 7) X : (1, 3, 5, 7) X : (1, 3, 5, 7b) X : (1, 3, 5#, 7) X : (1, 3, 5#, 7b) X : (1, 3, 5b, 7) X : (1, 3, 5b, 7b) X : (1, 3b, 5, 7) X : (1, 3b, 5, 7b) X : (1, 3b, 5#, 7) X : (1, 3b, 5#, 7b) X : (1, 3b, 5b, 7) X : (1, 3b, 5b, 7b) the root note, the third degree note and the fifth degree note) are included in the designed UMA-Piano database.
M. Marolt, “A connectionist approach to automatic transcription of polyphonic piano music”, IEEE Transaction on Multimedia, vol. 3, pp. 439–449, 2004. 3. P. Bello, L. B. Sandler, “Automatic piano transcription using frequency and time-domain information”, IEEE Transaction on Audio, Speech and Language Processing, vol. 14, pp. 2242–2251, Nov. 2006. 4. E. W. Ellis, “A discriminative model for polyphonic piano transcription”, EURASIP Journal on Advances in Signal Processing, vol. 8, pp. 1–9, 2007.