Symmetric 12-TET Harmony Notation With Interval Grid
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Solution Overview
Problem
Traditional Western music notation systems are inadequate for representing atonal music and 12 ET features, as they focus on diatonic scales and pitches rather than intervals, leading to inconsistencies and the need for mental adjustments with accidentals.
Innovation Solution
The SymD notation system is designed as a 12 ET interval-oriented notation with a symmetric grid staff that explicitly represents intervallic harmony, using a symmetric grid of 5 parallel lines and 8 spaces to assign notes based on their interval relationships, eliminating the need for accidentals and providing a unified numerical naming system for notes and intervals.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If traditional Western music notation is used, then tonal music with diatonic scales can be represented, but atonal music and 12 ET features cannot be properly represented
Solution Approach 1:
The traditional staff is segmented into 5 parallel lines with 8 spaces, creating 13 distinct locations that correspond to the 12 ET notes plus an additional reference point. This segmentation allows each location to represent a specific intervallic relationship, enabling clear representation of atonal and 12 ET music without the complexity of traditional accidental-based notation.
Solution Approach 2:
The notation system transitions from pitch-based vertical positioning (traditional staff) to interval-based spatial arrangement (SymD staff). By organizing notes according to their intervallic relationships rather than absolute pitch, the system achieves versatility for atonal music while maintaining a simple, unified structure.
2Ease of operation
If traditional music notation focuses on pitches, then diatonic scales are clearly indicated, but interval relationships become unclear and require mental adjustment
Solution Approach 1:
Instead of placing notes on a staff and requiring readers to mentally calculate intervals, the SymD notation inverts the approach by directly displaying interval relationships through the spatial arrangement of notes on the 5-line staff. The staff positions themselves encode interval information, eliminating the need for mental adjustment and accidentals.
3Ease of operation
If accidentals are used in traditional notation, then out-of-scale notes can be indicated, but musicians must mentally adjust to figure out exact notes
Solution Approach 1:
The SymD notation system is self-explanatory through its structural design. The 5 parallel lines with 8 spaces create 13 fixed locations that automatically indicate both pitch and interval relationships. No additional symbols or mental calculations are needed—the staff structure itself provides all necessary information for determining exact notes and their intervallic relationships.
4Stability of the object's composition
If note locations are standardized on the staff, then consistency is maintained, but inconsistencies arise between clefs, octaves and keys due to interval spacing
Solution Approach 1:
The SymD staff design with 5 parallel lines and 8 spaces serves multiple functions simultaneously: it represents pitch, indicates interval relationships, and maintains consistency across different clefs, octaves, and keys. The universal structure eliminates the need for separate notation conventions for different musical contexts, providing both stability and adaptability.
Data Source
AI summary
The present invention relates to a symmetrical dodecaphonic harmony notation system for 12 ET based music, abbreviated as SymD notation. One of the most predominant characteristics of SymD notation is a staff of 5 lines arranged symmetrically with 8 space settings between and beside the lines for all 12 semitones and its octave in a 12 ET scale. The staff serves as a visual reference for intervallic harmony relationships in sonority and melody progressions in 12 ET music.