Chordophone Tuning via Monotonic Mapping to Limit String Tension
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Solution Overview
Problem
Existing methods for tuning chordophones to alternative musical scales with fewer degrees risk damaging the instrument due to changes in string tension and sound quality, particularly when transitioning from 12 TET to 10 TET.
Innovation Solution
A monotonic surjective mapping is applied to map N-M degrees of the original scale to the same degree of the alternative scale, maintaining the frequency range and minimizing tension changes, using a computer-implemented method to determine string frequencies.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If the strictly monotonic method is used to tune chordophones to alternative scales with fewer degrees, then the frequency range of the instrument is increased, but the total tension of the strings increases significantly causing risk of instrument damage
Solution Approach 1:
The patent applies parameter changes by mapping multiple degrees of the original scale to the same degree in the alternative scale, thereby adjusting the frequency assignments to maintain string tensions within safe limits while still achieving tuning in alternative scales with fewer degrees
Solution Approach 2:
The patent implements beforehand cushioning by establishing tension limits before tuning and using the monotonic surjective mapping to ensure that no string exceeds these pre-determined safe tension thresholds, preventing instrument damage before it can occur
2Adaptability or versatility
If the strictly monotonic method is used to tune individual strings to higher frequencies in alternative scales, then the alternative scale tuning is achieved, but individual string tension increases causing risk of string breaking
Solution Approach 1:
The patent changes the frequency assignment parameters by mapping N-M degrees of the original scale to the same degree in the alternative scale, allowing alternative scale tuning while controlling individual string tension increases to prevent breaking
Solution Approach 2:
The monotonic surjective mapping acts as an intermediary between the original scale and alternative scale, mediating the frequency transitions to ensure that no individual string experiences excessive tension that would cause breaking
3Adaptability or versatility
If string tensions are changed significantly in alternative scale tuning, then the alternative scale is achieved, but the operating point of strings changes resulting in deterioration of instrument sound
Solution Approach 1:
The patent carefully controls parameter changes in frequency assignment to achieve alternative scale tuning while minimizing deviations in string tensions, thereby maintaining the operating points within ranges that preserve the original sound quality and timbre characteristics
Data Source
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AI summary
The object of the invention is a method of tuning chordophones in alternative musical scales with a reduced number of degrees relative to the standard tuning based on monotonic surjective mappings. The tuning method is characterized in that when the original scale has N degrees and the alternative scale has M, where M<N, then when tuning an instrument in the alternative scale, N-M degrees of the original scale are mapped to the same degree of the alternative scale as another degree of the original scale. The method allows for stable tuning of a chordophone (such as a piano) without the risk of breaking strings or damaging the instrument.