Solar Time Instrument — 12-Month vs 13-Month System

Scientific Basis — Formula Set Behind This Instrument

This simulator is not driven by random visual guesses. The clock, calendar, solar markers, lunar phase, audio tones, sky dome and harmonic overlays are all generated from explicit constants and formulas. The values below are the backbone used by the running JavaScript model.

1. Base Time Constants

• NORMAL_SECOND_MS = 1000
• TARGET_13_MONTH_SECOND_MS = NORMAL_SECOND_MS
• DAY_SECONDS = 86400
• MS_PER_DAY = 86400000
• NORMAL_YEAR_DAYS = 365
• NEW_YEAR_DAYS = 364 = 13 × 28
• LUNAR_CYCLE_DAYS = 29.530588
• KNOWN_NEW_MOON_UTC_MS = 2000-01-06 18:14 UTC

The experimental system keeps the normal physical second. What changes is the interpretation of the day boundary and the year geometry: the day begins at local sunrise, and the solar year is mapped onto 13 equal months of 28 phase-days.

2. Sunrise-Locked Solar Time

The experimental clock shows elapsed physical time since today’s local sunrise:

solarDisplaySeconds = (currentTimeMs - sunriseMs) / 1000
solarDisplaySeconds = positiveModulo(solarDisplaySeconds, 86400)

Face geometry is fixed to the physical solar-day interpretation:

solarHour = solarDisplaySeconds / 3600
faceAngleDeg = -180 + (solarHour / 24) × 360
handAngleDeg = faceAngleDeg + 90

• 00:00 = sunrise / left horizon
• 06:00 = upper arc
• 12:00 = right horizon
• 18:00 = lower night side

3. Solar Declination, Equation of Time and Daylight Length

The Sun model uses a compact astronomical approximation suitable for visual simulation. It is observer-dependent through latitude and longitude.

declination = 23.44° × sin((2π / 365.2422) × (dayOfYear - 81))

B = (2π / 364) × (dayOfYear - 81)
EoT_minutes = 9.87 × sin(2B) - 7.53 × cos(B) - 1.5 × sin(B)

solarNoonShiftHours = (standardMeridianDeg - longitudeDeg) / 15 - EoT_minutes / 60
solarNoonHour = positiveModulo(12 + solarNoonShiftHours, 24)

Sunrise and sunset come from the solar hour-angle equation. The simulator uses -0.833° for the apparent sunrise/sunset altitude, including the usual solar-disc/refraction correction.

cosH = (sin(altitude) - sin(latitude) × sin(declination)) /
       (cos(latitude) × cos(declination))

daylightHours = 2 × acos(cosH) × 180/π / 15
sunriseHour = solarNoonHour - daylightHours / 2
sunsetHour  = solarNoonHour + daylightHours / 2

Twilight bands are calculated with the same equation using altitude thresholds -6°, -12° and -18° for civil, nautical and astronomical twilight.

4. Analemma / Equation-of-Time Trace

The analemma layer plots Equation of Time horizontally and solar declination vertically. It is a visual trace of why clock noon and apparent solar noon do not stay identical through the year.

x = (EoT_minutes / 16) × 34 × visualBoost
y = -(declinationDeg / 23.44) × 38 × visualBoost

5. 13-Month Solar-Phase Calendar

The calendar follows the solar-year phase and then maps that phase into 364 equal positions.

solarYearPhase = (nowMs - yearStartMs) / (nextYearStartMs - yearStartMs)
solarPhaseDay = floor(solarYearPhase × 364)
month = floor(solarPhaseDay / 28) + 1
day = (solarPhaseDay % 28) + 1

This avoids pretending that 13 × 28 is a normal civil year. It is explicitly a phase map of the solar cycle.

6. Lunar Phase Model

Lunar phase is calculated from a known new-moon reference and the mean synodic month length.

daysSinceReference = (currentUtcMs - knownNewMoonUtcMs) / 86400000
lunarDay = positiveModulo(daysSinceReference, 29.530588)
lunarPhase = lunarDay / 29.530588
illumination = 0.5 - 0.5 × cos(2π × lunarPhase)

The lunar distance indicator is intentionally approximate and visual:

anomalisticMonthDays = 27.55455
anomalisticPhase = positiveModulo(daysSinceReference + 4.1, anomalisticMonthDays) / anomalisticMonthDays
distanceKm = 384400 - 21000 × cos(2π × anomalisticPhase)

7. Astronomical Sonification

The audio engine converts very slow astronomical cycles into audible tones by octave transposition. The original periods stay stable; simulation speed changes motion and smoothing, not the core pitch mapping.

Sun period   = 365.2422 × 86400 seconds
Moon period  = 29.530588 × 86400 seconds
Earth period = 86400 seconds
baseHz = 1 / periodSeconds

while baseHz < 220:  baseHz = baseHz × 2
while baseHz > 1600: baseHz = baseHz / 2

• SCHUMANN_BASE_HZ = 7.83
• AUDIO_MIN_HZ = 220
• AUDIO_MAX_HZ = 1600

Detuning and modulation are linked to the same solar/lunar geometry:

eotDetuneCents = clamp(EoT_minutes × 0.9, -18, +18)
seasonalDetuneCents = (daylightHours / 24 - 0.5) × 22
moonDetuneCents = sin(2π × lunarPhase) × 12
earthDetuneCents = sin(2π × earthPhase) × 4

centsToRatio(cents) = 2^(cents / 1200)

8. Harmonic Relation Search

The simulator compares frequency ratios against a small harmonic reference set:

• 1:1 unison
• 6:5 minor third
• 5:4 major third
• 4:3 fourth
• 3:2 fifth
• 13:8 calendar relation
• 7:4 septimal
• 2:1 octave

ratio = max(freqA, freqB) / min(freqA, freqB)
centsError = abs(1200 × log2(ratio / targetRatio))
relationScore = max(0, 1 - centsError / 36)

9. Schumann Drift Model

The Schumann layer is modeled, not streamed from live geophysical sensors. Its slow drift follows day/night, solar altitude, seasonal daylight length and EoT.

schumannHz = 7.83
           + sin(2π × earthPhase) × 0.035
           + (altitudeNorm - 0.5) × 0.055
           + (daylightNorm - 0.5) × 0.035
           + clamp(EoT_minutes / 16, -1, 1) × 0.018

10. Procedural Sky Engine

The sky is deterministic. It does not use random live feeds, so it stays stable during fast-forward, date jumps and cockpit mode.

seed = 0x5A1A2026
state = (state × 1664525 + 1013904223) >>> 0
random = state / 4294967296

starCount = 420
radius = sqrt(random) × 0.94
angle = random × 2π
x = cos(angle) × radius
y = sin(angle) × radius

11. Cosmic / Deep-Space Audio Layer

The cosmic field profile adds a filtered noise floor, low sub oscillator, stereo drift and rare pulses, all controlled by the live astronomical audio model.

subOscillator = 28 Hz
pulseOscillator = 44 Hz
plasmaBandpassStart = 380 Hz

plasmaGain = 0.02 + harmonyScore × 0.04
plasmaFilterHz = 180 + solarBrightness × 900
breath = 0.5 + 0.5 × sin(performanceTime × 0.00012)
subGain = 0.03 + breath × 0.08 + phaseLockScore × 0.06
subOscHz = 24 + harmonyScore × 10
stereoPan = sin(performanceTime × 0.00005) × 0.75

A transient pulse may occur only when the harmonic score is high:

bucket = floor(Date.now() / 120000)
if bucket changed and harmonyScore > 0.75:
    pulseGain ramps 0.0001 → 0.12 → 0.0001

Validation Logic

The live statistics are intended as operator checks. The most important one is simple and auditable: experimental solar time = current time − today’s local sunrise. Sunrise, solar noon, sunset, twilight, Moon phase, harmonic score and audio modulation are then derived from the formula set shown above.

Purpose

This project is not a replacement for civil time standards. It is a scientific simulator for exploring sunrise-locked days, seasonal daylight variation, solar-year phase, Moon rhythm, Equation of Time, harmonic relations and observer-dependent astronomical geometry in one coherent instrument.