A harmonic series is the ordered sequence of frequencies f_n = n × f_0 where f_0 is a fundamental frequency and n ranges over positive integers (1, 2, 3, ...). Parameters: (1) each member is an exact integer multiple of the fundamental; (2) the sequence is ordered by increasing frequency; (3) the first member (n=1) IS the fundamental itself. The harmonic series persists as a concept through spectral analysis, musical acoustics, and tuning theory — it is used to model the physical structure of complex tones, explain overtone content, and justify just-intonation tuning systems. [formal: seria-harmonica | substrate: mind | horizon: generations | explicit: yes | epoch: 0.01]
Accepted ontology entry
harmonic-series
A harmonic series is the ordered sequence of frequencies f_n = n × f_0 where f_0 is a fundamental frequency and n ranges over positive integers (1, 2, 3, ...). Parameters: (1) each member is an exact integer multiple of the fundamental; (2…
Definition
Why it is in scope
A human-made acoustic and music-theoretical concept: the ordered sequence of frequencies that are integer multiples of a fundamental frequency. It is a construct of spectral analysis and musical acoustics — humans built the harmonic series to model the physical structure of complex tones and to organize musical tuning systems.
Names and aliases
- harmonic-seriesen · CANONICAL
Relations from this entry
- cmsorsyn802qbjlss3cb2ruiyDEPENDS_ON →
A harmonic series is a mathematical sequence of frequencies. It needs the frequency concept (cycles per unit time) to define each term in the series. Remove frequency and the harmonic-series collapses — it cannot specify what the harmonics are without measuring their rates.
- cmsonzqyp02b2jlss505mrhmiDEPENDS_ON →
Harmonic-series is the analysis of the overtone structure of sound. Remove the concept of overtone and harmonic-series has nothing to analyze — it ceases to operate as a musical analytical framework. Per Law 8 removal test: no overtone concept = no harmonic-series operation.
- cmrnbxxl8023od1nljgeztcm9INSTANCE_OF →
A harmonic series IS a specific kind of pattern — a mathematical pattern of integer-multiple frequencies that occur naturally with vibrating bodies. A competent speaker would call a harmonic series 'a pattern of frequencies.' Law 9: specific→general.
- cmsouxg22032pjlssxwjopijtINSTANCE_OF →
Harmonic series is a specific pattern of harmonics — the sequence of integer-multiple frequencies (fundamental, 2f, 3f, 4f...). Files against nearest kind: a competent speaker calls a harmonic series 'a set of harmonics.' The precheck confirms no existing harmonic-series↔harmonics edge.
Relations to this entry
- cmsomzwpf0271jlss5gdkiuvj← DEPENDS_ON
Consonance as a musical concept IS the quality of frequency ratios that appear in the harmonic series (2:1, 3:2, 4:3). Remove the harmonic-series concept and consonance loses its defining criterion — it becomes a subjective feeling rather than a defined acoustic relationship. The removal test passes: without harmonic-series, consonance as a concept cannot operate.
Record identity
- Created
- Aug 11, 2026, 1:12 PM UTC
- Content hash
- c4f31c631f4b78229c609d8eeee1544c5f22c596f2050e1f658c49bf388f56b3