Musical Instrument Fibratio Tuning for Pythagorean Comma Correction
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Solution Overview
Problem
Existing musical instrument tuning systems, particularly those using equal temperament, fail to address the Pythagorean comma issue, leading to imperfect intervals and harmonies, especially in instruments with inharmonicity like pianos, and do not effectively utilize the golden ratio and Fibonacci sequence for improved tuning.
Innovation Solution
A fibratio tuning system that combines equal temperament with the golden ratio and Fibonacci sequence to create a fibratio curve, adjusting sharps and flats through a fibratio spiral positioned at an inflection note, using a neutral intercept to achieve improved harmonic alignment.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If equal temperament tuning is used, then all keys can be played with acceptable tuning, but perfect fifths and just intonation intervals cannot be achieved
Solution Approach 1:
The patent applies parameter changes by modifying the frequency ratios of musical intervals from standard equal temperament to fibratio-based ratios derived from the golden ratio and Fibonacci sequence. This transforms the tuning parameters to achieve both just intonation purity and golden ratio harmonics, resolving the contradiction between interval accuracy and key versatility
Solution Approach 2:
The patent creates a composite tuning system that combines multiple mathematical principles (equal temperament, golden ratio, Fibonacci sequence) into a unified fibratio tuning methodology. This composite approach integrates the advantages of different tuning systems while eliminating their individual shortcomings, achieving both perfect fifths and golden ratio harmonics
2Manufacturing precision
If just intonation is used, then perfect fifths and pure intervals are achieved, but modulation to different keys becomes problematic
Solution Approach 1:
The patent changes the tuning parameters from fixed just intonation ratios to fibratio ratios that incorporate the golden ratio and Fibonacci sequence. This allows intervals to maintain mathematical purity while providing a consistent framework that works across all keys through the universal properties of golden ratio harmonics
3Manufacturing precision
If Pythagorean tuning is used, then perfect fifths are achieved, but the Pythagorean comma creates discrepancies in octave relationships
Solution Approach 1:
The patent converts the harmful Pythagorean comma discrepancy into a beneficial feature by using the golden ratio to define new interval relationships. The fibratio tuning system acknowledges the mathematical impossibility of perfect fifths and octaves simultaneously but uses golden ratio proportions to create a harmonious compromise that eliminates the comma problem while maintaining interval purity
Solution Approach 2:
The patent changes the fundamental tuning parameters from Pythagorean 3:2 fifth ratios to fibratio ratios based on golden ratio proportions. This parameter transformation resolves the octave consistency issue by using the self-similar properties of golden ratio scaling, where each octave relationship maintains mathematical harmony without the Pythagorean comma discrepancy
Data Source
AI summary
A tuning method for a musical instrument that is offset from an equal temperament diatomic octave tuning following a fibration spiral positioned using a fibratio inflection note and a fibratio neutral crossing note for sharp adjustment at frequencies above the fibratio inflection note and flat adjustment below the fibratio inflection note.