The Frequency Lab

Use headphones. The left ear hears the base frequency, the right ear hears base + beat. Your brain perceives the difference as a pulsing tone at the beat frequency. 7.83 Hz = Schumann resonance. 4 Hz = deep theta. 10 Hz = alpha. 40 Hz = gamma binding.

Chromatic tuner with Pythagorean just-intonation reference. Baseline default: A = 432 Hz. When your pitch lands within ±3 cents of the target, the display turns GREEN — locked and in tune. Yellow/orange = close (±3-10 cents). Red = far off (>10 cents). Works with voice, guitar, bass, violin, cello, ukulele, bowls, any sustained tone.

Every culture discovered that specific combinations of frequencies produce distinct psychological and spiritual effects. These aren't random — they're configurations refined over centuries of practice. Click any to hear it, or stack multiple to create layered ceremony.

A church bell produces 5 tuned partials simultaneously: hum (octave below), prime (fundamental), tierce (minor 3rd), quint (5th), and nominal (octave above). This is why a bell sounds so rich — it's a built-in chord. Click each partial to isolate it.

English change ringing: bells tuned to a descending major scale, rung in mathematical permutations. Note: 6 bells = 720 permutations (= Plato's tonal index!). 7 bells = 5,040 (= Plato's ideal citizens in Laws). This is McClain's thesis made audible.

Select multiple sets to layer. Each plays simultaneously, creating compound ceremonial space.

McClain's central thesis: the numbers in Plato's dialogues — the World Soul construction in the Timaeus, the Allegory of the Marriage in the Republic, the city plan of Atlantis in Critias, and the 5,040 citizens of Laws — are not arbitrary. They are tonal indices: integer limits that define musical scales. The same mathematical structures appear in the Sumerian pantheon, the Rig Veda, and the Hebrew scriptures. Music was the universal language of ancient cosmology.

The Demiurge constructs the World Soul from two geometric series: powers of 2 (the Even, the Female) and powers of 3 (the Odd, the Male). Together: 1, 2, 3, 4, 9, 8, 27. Note that 27 = sum of all preceding terms. This spans 4 octaves + a major 6th — the entire range of the ancient 7-string lyre. Click any node to hear it.

Between any two tones, three means exist. For the octave 6:12 (the smallest integers showing all three), the arithmetic mean = 9 (the fifth 2:3), the harmonic mean = 8 (the fourth 3:4), and the geometric mean = √72 ≈ 8.485 (the tritone, irrational — the "problem" at the heart of all tuning). The difference between arithmetic and harmonic means (9 - 8 = 1) is the whole tone 8:9.

The multiplication table of 2ᵖ × 3ᵍ generates every Pythagorean tone. Rows = powers of 3 (fifths), columns = powers of 2 (octaves). All doubles (columns) are the same pitch class. This is the mathematical engine behind all ancient scale construction. Click any cell to hear it and see its musical identity.

Adding prime 5 to the Pythagorean system creates just intonation — pure thirds. McClain's key insight: Plato's "tonal index" of 720 (= 6! = factorial 6 = 2⁴×3²×5) is the smallest number that contains all 18 tones of the complete chromatic scale as integers within the octave 360:720. This is the yantra — the complete tonal mandala.

Stack 12 perfect fifths (3:2) and you should return to the starting note 7 octaves up. But (3/2)¹² = 531,441 while 2⁷ = 524,288. The ratio 531441/524288 ≈ 1.01364 = 23.46 cents — the Pythagorean comma. This tiny gap is the mathematical origin of all temperament systems, the reason 432 ≠ 440 matters, and what Plato called the problem of "the allegory of the allegory." Click PLAY to hear the comma spiral.

Not a circle — a spiral. Each fifth (3:2) generates the next tone. After 12 steps the spiral doesn't close — it overshoots by the comma. This is why equal temperament was invented: it distributes the comma evenly across all 12 steps, making each fifth slightly flat (≈ 2 cents). Click any note on the spiral to hear its pure Pythagorean pitch vs. its tempered pitch.

The numbers Plato embeds in his dialogues are all tonal indices — limits that define musical scales:

Drop any sheet music file and it plays through the Frequency Lab's tuning engine. Import a Bach fugue at 440, retune it to 432 Pythagorean, and hear the difference instantly. Every note passes through your chosen reference pitch and temperament.

Supported formats: MusicXML (.xml, .musicxml) — the universal sheet music standard, exported by MuseScore, Finale, Sibelius, Dorico, Noteflight, Flat.io. MIDI (.mid) — binary note-on/note-off events with timing. ABC Notation (.abc) — lightweight text format used in folk music archives. Also accepts pasted ABC text directly.

Tuning system: Every note is recomputed through the selected reference pitch and temperament. Pythagorean uses pure 3:2 fifths. 5-limit just adds pure 5:4 thirds. Meantone tempers the fifths to improve thirds. Equal temperament divides the octave into 12 equal steps. Switch between them while playing to hear the difference.

Every ancient medical tradition treated sound as medicine. Modern research is catching up — FDA-approved vagus nerve stimulation, MIT's 40 Hz Alzheimer's protocol, thousands of peer-reviewed studies on music therapy. Below is a playable reference organized by body system, with evidence levels marked: ✓ VERIFIED = peer-reviewed / FDA-approved, ~ SUPPORTED = published studies with positive results, ○ TRADITIONAL = ancient practice without modern clinical trials.

Click any protocol to hear the frequencies. Evidence levels: ✓ VERIFIED · ~ SUPPORTED · ○ TRADITIONAL. This is educational reference — not medical advice.

The chakra system maps seven energy centers to specific body locations, psychological states, and frequencies. Whether viewed as literal energy anatomy or as a useful metaphorical framework for mind-body states, the frequency correspondences are widely used in sound healing practice. Evidence level: ○ TRADITIONAL — thousands of years of practice, no peer-reviewed clinical trials on specific chakra frequencies.

Note: Chakra frequencies above use the Pythagorean scale from C=256 Hz. Some traditions use different assignments. The solfeggio correspondences are a modern mapping, not historically documented.

The Yellow Emperor's Classic of Internal Medicine (Huangdi Neijing, ~200 BCE) maps five musical tones to five elements, five organs, five emotions, and five seasons. This system was used therapeutically for over two thousand years. Click to play each tone in the pentatonic scale from C=256.

Solar activity directly modulates the Schumann resonance, geomagnetic field, and your biology. Here's what the metrics mean and where to track them live.

Not speculation — published peer-reviewed findings on how geomagnetic and Schumann activity correlates with human health outcomes.