harmonic function
Satisfies Laplace's equation
A harmonic function is a mathematical function whose second derivatives sum to zero—satisfying Laplace's equation.
Such functions describe steady-state phenomena: temperature distributions in equilibrium, gravitational potentials, electrostatic fields.
Harmonic functions have the elegant property that their value at any point equals the average of surrounding values, making them smooth and without local extrema in their interior.
Boundary-prescribed harmonic solution
- subharmonicFrequency dividing the fundamental
- real-valuedHaving numerical output
- electrostaticsStudy of stationary charges
Amplified oscillation at natural frequency
- vibrationRapid oscillating movement
- standing waveOscillation with fixed nodes
- overtonesImplicit secondary meanings
- partialsIncomplete sets or components
frequency · amplitude · oscillation · waveform · natural frequency · interference · node · antinode
Sequence of tonal changes
- tonicInvigorating medicinal drink
- dominantHaving superior influence
- subdominantFourth scale degree
- resolutionFormal decision or determination
cadence · tension · release · counterpoint · prolongation · secondary dominant · predominant · suspension
Dirichlet problem
Boundary-prescribed harmonic solution
- subharmonicFrequency dividing the fundamental
- real-valuedHaving numerical output
- electrostaticsStudy of stationary charges
resonance
Amplified oscillation at natural frequency
- vibrationRapid oscillating movement
- standing waveOscillation with fixed nodes
- overtonesImplicit secondary meanings
partials · frequency · amplitude · oscillation · waveform · natural frequency · interference · node · antinode · timbre
chord progression
Sequence of tonal changes
- tonicInvigorating medicinal drink
- dominantHaving superior influence
- subdominantFourth scale degree
resolution · cadence · tension · release · counterpoint · prolongation · secondary dominant · predominant · suspension · overtones
- complex analysiscomplex numbers, modulus, complex plane, analytic, singularity
- music theorynote, notes, chord, chords, melody
- potential theoryDirichlet problem, balayage, capacity, barrier
- smooth functionssine, cosine, tangent, polynomial, exponential
- waveswave crest, shock wave, wave front, blast wave, seismic wave
- differential operatorsdel, gradient, divergence, curl, partial derivative
harmony, function, harmonize, disharmony, harmonic, harmonization, harmonizing, harmonized, functionality