The Note of a Universe

If a universe is built on a pulse, it has a pitch. Every universe in this book is a Binary Pulse, 0 → 1 → 0, repeated at its own Local Pulse Tempo, and a repeated wave is a note. This part gives the shape of that wave, the harmonics it holds, and the note it sounds, ours among them.

The Shape of the Prime Pulse

The pulse jumps between two states, 0 and 1, and holds each for a Pulse Rhythm, half a Tempo. A wave that holds one level for half its cycle and the other for the rest is a square wave. Fourier showed that every repeating wave is a sum of sine waves at whole multiples of its frequency (Fourier, 1822), and a square wave has a famous sum: the fundamental, and then only the odd harmonics, each weaker in proportion to its number.

Square Pulse Spectrum G

a_h = 2 / (π · h)

Dimensional analysis:
Where (from the book): a_h [∅], h [∅]
[∅]
[∅] ÷ ([∅] × [∅]) = [∅] ÷ [∅] = [∅]
[∅] = [∅] ✓ Valid PulseCore Verified ✓

The pulse holds its fundamental and its odd harmonics alone

Where:

• a_h [∅] — the strength of harmonic h in the pulse, for odd h; for even h it is 0
• h [∅] — the harmonic's number

➢ The Fourier series of a wave that is 1 for half its cycle and 0 for the other half: a steady half, then 2/π for the fundamental, 2/(3π) for the third harmonic, 2/(5π) for the fifth, 2/(7π) for the seventh, and nothing at the even harmonics.

The pulse's own spectrum is the split of Part 4.8. There are no octaves inside the wave: the doubling is not a harmonic of the pulse but its repetition, the dimension made of the pulse itself, time. Its strongest overtones are 3, 5 and 7, the three odd primes read as space, and the next, 9, is the first composite, an etheric harmonic. The first note holds three and one in the order of its own overtones. The even harmonics a universe sounds come from its layers instead: the novas, numbered as harmonics by Data Harmonics, add 2, 4, 6 and on as they come.

A Universe's Note

Universe Note Frequency G

f₁ = 1 / ①⥂⧗⌂

Dimensional analysis:
Where (from the book): f₁ [𝕋⁻¹]
[𝕋⁻¹]
[∅] ÷ [𝕋] = [𝕋⁻¹]
[𝕋⁻¹] = [𝕋⁻¹] ✓ Valid PulseCore Verified ✓

A universe sounds one over its Pulse Tempo

Where:

• f₁ [𝕋⁻¹] — the fundamental of a universe's pulse
• ①⥂⧗⌂ [𝕋] — its Local Pulse Tempo, one full 0 → 1 → 0

➢ Ours: the Pulse Tempo is the Planck time, 5.391 × 10⁻⁴⁴ s (Tiesinga et al., 2021), so f₁ = 1.855 × 10⁴³ Hz, 143.73 octaves above one cycle a second.

A note moved by whole octaves keeps its name: an octave is the pulse doubling, and pitch is heard as the place within the octave. So any universe's note can be brought into hearing without changing it.

Octave Transposition G

f♪ = f₁ / 2^k

Dimensional analysis:
Where (from the book): f♪ [𝕋⁻¹], f₁ [𝕋⁻¹], k [∅]
[𝕋⁻¹]
[𝕋⁻¹] ÷ [∅]^([∅]) = [𝕋⁻¹] ÷ [∅] = [𝕋⁻¹]
[𝕋⁻¹] = [𝕋⁻¹] ✓ Valid PulseCore Verified ✓

The same note, moved by whole octaves

Where:

• f♪ [𝕋⁻¹] — the note brought into hearing
• f₁ [𝕋⁻¹] — a universe's fundamental
• k [∅] — a whole number of octaves

➢ Ours, moved down 135 octaves, sounds at 425.9 Hz: between G♯ (415.3 Hz) and A (440 Hz), 43 cents above G♯ and 57 cents below A. The Planck time is known to about one part in a hundred thousand, so the pitch is fixed to a small fraction of a cent. It is not the 432 Hz of a tuning tradition, which no law of physics sets.

The Prime Pulse's Note and the Lineage

Every universe's note comes from one first note. The Prime Pulse, ∅ → (0 ↔ 1), is the first completed pulse of the UniSphere, one Zinf cycle ℨ long, and every universe's Pulse Tempo is that cycle dilated by its level, ①⥂⧗⌂ = 2^L · f^L · ℨ (Chapter 1). So every universe's note is the Prime Pulse's note carried down its lineage.

Prime Pulse Note G

f_ℨ = 1 / ℨ

Dimensional analysis:
Where (from the book): f_ℨ [𝕋⁻¹], ℨ [𝕋]
[𝕋⁻¹]
[∅] ÷ [𝕋] = [𝕋⁻¹]
[𝕋⁻¹] = [𝕋⁻¹] ✓ Valid PulseCore Verified ✓

The first note: one over one Zinf cycle

Where:

• f_ℨ [𝕋⁻¹] — the frequency of the Prime Pulse
• ℨ [𝕋] — one Zinf cycle, 0 → 1 → 0 at the floor of the UniSphere, ≈ 2.283 × 10⁻¹⁰⁶ s

➢ f_ℨ ≈ 4.38 × 10¹⁰⁵ Hz, 350.93 octaves above one cycle a second; brought into hearing, 244.5 Hz, a B 17 cents flat.

Lineage Note G

f₁ = f_ℨ / (2 · f)^L

Dimensional analysis:
Where (from the book): f₁ [𝕋⁻¹], f_ℨ [𝕋⁻¹], f [∅], L [∅]
[𝕋⁻¹]
[𝕋⁻¹] ÷ ([∅] × [∅])^([∅]) = [𝕋⁻¹] ÷ [∅]^([∅]) = [𝕋⁻¹] ÷ [∅] = [𝕋⁻¹]
[𝕋⁻¹] = [𝕋⁻¹] ✓ Valid PulseCore Verified ✓

A universe's note is the first note carried down its lineage

Where:

• f₁ [𝕋⁻¹] — the note of a universe at level L
• f_ℨ [𝕋⁻¹] — the Prime Pulse's note
• f [∅] — the heritage factor of the lineage, 1.018 for ours
• L [∅] — the level

➢ Each level lowers the note by one octave, which keeps its name, and by the heritage factor, 1200 · log₂ f ≈ 30.9 cents for ours, which does not. Down 202 levels our lineage falls 202 octaves and 6,242 cents more, 207.2 octaves in all, from the Prime Pulse's B, 17 cents flat, to our G♯, 43 cents sharp. Within a universe its novas add exact whole-number harmonics of its note; across levels the notes are lower octaves of the first note, bent by f, so a lineage is a slow descent in pitch, 31 cents a generation, around the circle of the octave.

The names in this part, B and G♯ and A, and the figures in hertz, depend on the second, a human unit, and on the convention that A is 440 Hz; another unit of time would give the same notes other names. What is physical is in the ratios: the odd harmonics of the pulse, the whole-number harmonics of the novas, the octave each level descends, and the drift of the heritage factor. Read in those terms the note of a universe carries no human choice at all.

A Child's Note

A child universe takes its Tempo from its Null Well's mass, ①⥂⧗′⌂ = ①⥂⧗⌂ · (M∅ / M_P)^½ (Part 6.5; Constants of a Child Universe, Chapter 1), so its note follows from its parent's.

Child Note G

f₁′ = f₁ · (M_P / M∅)^(1/2)

Dimensional analysis:
Where (from the book): f₁′ [𝕋⁻¹], f₁ [𝕋⁻¹]
[𝕋⁻¹]
[𝕋⁻¹] × ([𝕄] ÷ [𝕄])^([∅] ÷ [∅]) = [𝕋⁻¹] × ([𝕄] ÷ [𝕄])^([∅]) = [𝕋⁻¹] × [∅]^([∅]) = [𝕋⁻¹] × [∅] = [𝕋⁻¹]
[𝕋⁻¹] = [𝕋⁻¹] ✓ Valid PulseCore Verified ✓

A heavier well gives a slower Tempo and a lower note

Where:

• f₁′ [𝕋⁻¹] — the child's fundamental
• f₁ [𝕋⁻¹] — the parent's fundamental
• M_P [𝕄] — the parent's Planck mass
• M∅ [𝕄] — the mass of the Null Well the child is born in

➢ Each lineage of universes is a sequence of notes: a well four times heavier than another seeds a child an octave lower. The pitch class of each child, its place within the octave, is set by the square root of its well's mass in Planck units.

The Chord of the Novas

A universe does not stay one note. Data Harmonics (Part 3.6) numbers its layers as harmonics of its pulse: the Null Nova Harmonic 1, the Data Nova Harmonic 2, the physical layer Harmonic 3, spacetime Harmonic 4, and the Harmonic Novas after them. Each nova adds its harmonic of the universe's own note, so a universe builds a chord as it builds its layers: the fundamental at its Pulsecore, the octave as it pours out its data, the twelfth as it becomes physical, the double octave with spacetime, and the Harmonic Novas filling the series as its life closes.

What the note is, and what it is not, should be plain. No instrument hears a universe; its note is the frequency of its pulse, read as music. Its physical content is in the spectrum, the odd harmonics of the pulse and the whole harmonics of its layers, and that is what Part 4.8 reads as dimensions. The note itself is that structure made audible.

Links to Binary Pulse Theory

• Chapter 1: the Pulse Tempo and the Pulse Rhythm, 0 → 1 → 0 and its half; the Constants of a Child Universe.
• Part 3.6: Data Harmonics numbers the layers as harmonics, the chord of the novas.
• Part 4.8: the odd harmonics of the pulse and the prime axes of the dimensions.
• Part 6.5: a child's Tempo from its well's mass, and so its note.