Harmonic Relationships¶
Integer-Ratio Geometry
Overview¶
Harmonic relationships are based on integer multiples of a common fundamental value.
These relationships form the foundation of the Harmonic packet category.
Fundamental Concept¶
Starting with a fundamental value:
1
harmonics are generated through integer multiplication:
1
2
3
4
5
6
8
12
16
Each value remains directly related to the fundamental.
Harmonic Hierarchy¶
Fundamental
↓
2 × Fundamental
↓
3 × Fundamental
↓
4 × Fundamental
↓
5 × Fundamental
The resulting structure remains ordered and predictable.
Symmetry¶
One of the defining characteristics of harmonic structures is symmetry.
Example:
10
20
40
20
10
This produces:
- balanced packet envelopes,
- predictable timing,
- repeatable geometry.
Harmonic Packet Geometry¶
When harmonic relationships are used inside packet families, segment sizes tend to change in a regular manner.
Example:
10
20
30
40
50
The resulting envelope appears smooth and structured.
Predictability¶
Harmonic structures are highly predictable.
Small adjustments tend to produce proportional changes.
This makes harmonic families useful for:
- initial experiments,
- waveform comparison,
- geometry studies.
Relationship to Packet Families¶
Harmonic packet families are typically characterized by:
- regular spacing,
- high symmetry,
- high repeatability.
Compared to Fibonacci or Prime structures, harmonic families generally produce more ordered envelopes.
Relationship to Octaves¶
Octave structures represent a special subset of harmonic relationships.
Example:
1
2
4
8
16
32
All octave relationships are harmonic relationships.
Not all harmonic relationships are octave relationships.
Relationship to Subharmonics¶
Subharmonics represent inverse harmonic relationships.
Example:
2
3
4
5
becomes:
1/2
1/3
1/4
1/5
The mathematical relationship remains connected to the same fundamental.
Engineering Perspective¶
Harmonic relationships provide one of the simplest and most structured forms of packet geometry available within REVA.
They often produce highly ordered waveform envelopes and serve as a useful reference when comparing other packet categories.