Overtone series: Chords in nature
Fundamental tone + overtones = timbre: The overtones of A4 (440Hz) are 880Hz, 1320Hz...
The principle of chord formation: Major triads (C-E-G) precisely correspond to the 4th, 5th, and 6th notes of the overtone series
2. Musical War: Equal Temperament vs. Perfect Temperament
Equal Temperament: The "compromise solution" for the piano, where all semitones are equal (√2^(1/12))
Just intonation: Chords are purer, but modulation is difficult (a major problem in the Baroque period)
Auditory comparison: Pure tone major triads vs. Equal tone major triads (The latter is slightly "dirty")
3. Psychoacoustic tricks
The vanishing fundamental frequency: Even when only overtones are played, the brain "imagines" the fundamental frequency (the principle of telephone sound).
Binaural Beats: When listening to audio with a difference of less than 30Hz between the left and right ears, a third rhythm will be "hallucinated" (used for meditation music).
(Experiment: Play a perfect fifth with a tuning APP and observe whether the ratio of Hz numbers is 3:2)
Content planning ideas
From simple to complex: From note names to jazz improvisation, catering to learners at different stages
Interdisciplinary links: Combining mathematics, physics, and psychology to broaden cognition
Practical-oriented: Each article contains exercises/experiments that can be tried immediately
Visualization AIDS: Interval diagrams, keyboard/fingerboard annotations, sound wave spectrum diagrams