How Sound Works: Frequency, Resonance, Overtones

〰 What is Frequency?

Everything that vibrates has a frequency. Frequency is the number of vibrations per second, measured in Hertz (Hz). A string vibrating 440 times per second produces a tone of 440 Hz — that is the note A, the universal tuning note to which orchestras worldwide align.

• 1 Hz = 1 vibration per second
• 100 Hz = 100 vibrations per second (a deep humming tone)
• 440 Hz = the concert pitch A4
• 20,000 Hz = the upper limit of human hearing

The fundamental insight: everything vibrates. The chair you are sitting on vibrates at an extremely high frequency (the atoms vibrate). Your heartbeat is a frequency (~1-1.5 Hz). The earth itself vibrates at the Schumann resonance of ~7.83 Hz. From atom to planet — everything is frequency.

🌊 Wavelength and Amplitude

A sound wave has two fundamental properties:

Amplitude = volume

The amplitude is the height of the wave — how large the displacement is. Greater amplitude = louder sound. Measured in decibels (dB). A whisper is ~20 dB, a normal conversation ~60 dB, a rock concert ~110 dB, and the pain threshold is at ~130 dB.

Wavelength = pitch

The wavelength is the distance between two wave peaks. Short wavelength = high pitch. Long wavelength = low pitch. A bass tone of 50 Hz has a wavelength of nearly 7 meters. A whistle tone of 4000 Hz has a wavelength of only 8.5 centimeters.

Frequency and wavelength are each other's mirror: frequency × wavelength = speed of sound (~343 m/s in air). The higher the frequency, the shorter the wave — and the more complex the cymatic patterns that can be formed with it.

🔔 Resonance

Resonance is perhaps the most important concept in all of sound theory — and in Hermetic philosophy. The principle is simple but profound:

The tuning fork experiment

Place two identical tuning forks next to each other. Strike one. The other begins to vibrate on its own — without contact. This is resonance: a vibration that transfers to an object with the same natural frequency.

Why glass shatters from opera singing

A wine glass has a natural frequency. When a singer hits exactly that frequency with sufficient volume, the glass absorbs the energy and begins to vibrate more and more intensely — until the material limit is exceeded and it shatters. This is no trick: it is pure physics.

The Tacoma Narrows Bridge (1940)

One of the most dramatic examples of resonance: wind caused the Tacoma Narrows Bridge in Washington to vibrate at its natural frequency. The oscillations grew larger and larger until the entire bridge collapsed. Resonance is not an abstract concept — it is a force.

From a Hermetic perspective, resonance is the mechanism behind "As above, so below": when two systems are attuned to the same frequency, they influence each other — regardless of distance or medium.

🎹 Harmonic Overtones

When a violin plays the note A at 440 Hz, you don't hear only 440 Hz. You hear an entire series of overtones: 880 Hz (2nd harmonic), 1320 Hz (3rd), 1760 Hz (4th), and so on. These are the harmonic overtones — whole multiples of the fundamental tone.

Why does a violin sound different from a flute?

Both instruments can play the note A at 440 Hz. But they sound completely different. The difference lies not in the fundamental tone but in the composition of overtones — the timbre or tone color. A violin has strong odd harmonics, a flute has nearly pure fundamental tones. A piano has a rich, complex overtone series.

The harmonic series is mathematically identical to the ratios Pythagoras discovered on his monochord:

• 1:2 = octave (the first overtone)
• 2:3 = fifth (the second overtone)
• 3:4 = fourth (the third overtone)

Overtones are thus not merely an acoustic phenomenon — they are the physical manifestation of the numerical ratios from Module 2.

🔊 The Spectrum of Sound

The human ear hears only a small part of the total vibration spectrum. Sound extends far beyond what we can perceive:

Interesting: babies hear up to ~20,000 Hz, but as we age the ear loses sensitivity to high frequencies. By age 50, the upper limit has often dropped to ~12,000 Hz. What we cannot hear, however, still affects us — infrasound can cause physical sensations, and ultrasound is actively used in medicine.

🧠 Brainwaves as Frequencies

Our brains continuously produce electrical vibrations — brainwaves — measurable with EEG (electroencephalography). These waves correspond to specific states of consciousness:

The connection with sound? External frequencies can synchronize your brainwaves — a phenomenon called brainwave entrainment. Listen to a rhythmic sound of 10 Hz (alpha), and your brain tends to resonate along. This is the scientific basis behind drumming sessions, singing bowls, binaural beats, and mantra meditation.

The Schumann resonance of the earth (~7.83 Hz) falls precisely in the alpha-theta range — the range of relaxed alertness and meditation. Many researchers suggest that the human brain is "tuned" to the frequency of the planet itself.

★ Contemplation