Waveform Generation Using Takens Embedding for Musical Creativity
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Solution Overview
Problem
Musicians face challenges in creating original music as they often reuse tones with similar sound impressions, leading to a lack of creativity and listener disinterest, as existing methods for tone determination are based on experience and sensitivity rather than established methods, and conventional waveform amplification and attenuation only change volume without altering sound character.
Innovation Solution
A waveform generation apparatus and program that utilize Takens' plot to expand original waveforms into an n-dimensional phase space, allowing for the identification and alteration of attractors within specific areas, enabling the addition of new waveforms at corresponding times to enhance the inputted waveform, thereby generating new waveforms with resonation and attenuation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If musicians reuse tones with similar sound impressions, then consistency in sound quality is maintained, but creativity and originality are reduced
Solution Approach 1:
The patent applies parameter changes by systematically modifying waveform parameters through mathematical transformations. The waveform generation apparatus changes parameters such as frequency, amplitude, and phase by applying different functions (sine, square, sawtooth, triangle) to the same fundamental waveform data, thereby generating varied tones while maintaining sound quality consistency through controlled parameter modification.
Solution Approach 2:
The patent implements local quality by applying different waveform functions to specific portions or aspects of the same waveform data. Each function (sine, square, sawtooth, triangle) modifies local characteristics of the waveform while preserving the underlying structure, allowing musicians to maintain consistency in the base waveform while creating local variations for creativity.
2Power
If conventional amplification methods are used, then volume is increased, but sound character remains unchanged
Solution Approach 1:
The patent resolves this contradiction by changing not only amplitude parameters (for volume) but also waveform shape parameters through function application. When amplifying a waveform, the system simultaneously modifies its character by applying different mathematical functions, thereby increasing volume while also transforming sound character, unlike conventional amplification that only changes amplitude.
Solution Approach 2:
The waveform generation apparatus performs multiple functions simultaneously: it amplifies the waveform (increasing volume) while also transforming its character (changing waveform shape). This multi-functionality allows a single operation to achieve both volume increase and sound character variation, eliminating the need for separate amplification and waveform transformation steps.
3Loss of information
If Takens' plot is used to generate attractors, then sound impression extraction is achieved, but device complexity increases
Solution Approach 1:
The patent applies copying by creating simplified representations (attractors) of the original complex waveform data through Takens' plot. Instead of processing the entire complex waveform, the system generates a lower-dimensional attractor that captures the essential sound impression characteristics, thereby reducing information loss while avoiding the complexity of processing the full waveform data.
Solution Approach 2:
The patent extracts only the essential features of the waveform by generating attractors through Takens' plot. This extraction process isolates the key sound impression characteristics from the complex waveform data, achieving accurate sound impression extraction while reducing processing complexity by focusing only on the extracted essential features rather than the entire waveform.
Data Source
AI summary
In a waveform generation apparatus, a coordinates information group showing original waveform data in a two-dimensional phase space having a time axis and a wave height value axis is expanded to an n-dimensional phase space (n>2) including a time axis and a wave height value axis using Takens' embedding theorem, and converted to a coordinates information group showing attractor data. In addition, an area of the attractor data is shown, and after one of the coordinates information is specified from the coordinates information group within the shown area, coordinate values corresponding to a time axis in the coordinates information are acquired as time information. Then, composite waveform data is generated by a predetermined waveform data being added to the original waveform data, and the generated composite waveform data is outputted from a position of the original waveform data on a time axis corresponding to the acquired time information.