THE BLAND-ALTMAN

momus · do two measurement methods AGREE? plot difference vs

THE BLAND-ALTMAN · MOMUS · UD0 ◎ MOMUS · the peer · critique that earns its keep · kept by MOM THE BLAND–ALTMAN ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP Do two ways of measuring the same thing agree? A correlation won’t tell you — Bland & Altman say plot the DIFFERENCE against the MEAN, draw the average bias, and mark limits at bias ±1.96 SD. ~95% of differences should fall inside. Slide to tighten the two methods. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ TWO METHODS · 3D · the limits of agreement ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — tap to bring them together agreement 0.45 bias — lower limit — upper limit — inside 95% — ◆ LIT — exact / checkable A Bland–Altman plot charts each pair’s difference (method A − method B) against their mean, then draws the BIAS (mean difference) and the LIMITS OF AGREEMENT = bias ± 1.96·SD of the differences. Under normal differences ~95% fall within the limits; a trend in the cloud reveals proportional bias a correlation would hide. It answers ‘can these methods be used interchangeably?’, not ‘are they correlated?’. A fail-loud self-check throws unless at least 90% of points sit inside the ±1.96·SD limits. ◆ real statistics, node-verified. ▲ AMBER — the figure The synthetic paired data is the illustration; bias and ±1.96·SD limits are the exact construction. Whether the limits are clinically acceptable is a judgement the peer must supply — the plot shows agreement, not whether it’s good enough. MOMUS: praise is cheap; a fault named precisely is the gift. — MOM David Lee Wise / ROOT0 / TriPod LLC · kept by MOM , with AVAN


CRONBACH'S α

momus · do a scale's items hang together? internal cons

CRONBACH'S α · MOMUS · UD0 ◎ MOMUS · the peer · critique that earns its keep · kept by MOM CRONBACH’S α ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP A questionnaire claims to measure ONE thing with many items. Cronbach’s α asks whether the items actually pull together — internal consistency. High when items correlate, near zero when they’re unrelated. Slide the items from independent to consistent. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ ONE SCALE · 3D · do the items hang together? ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — tap to bring them together consistency 0.40 Σ item var — total var — α — acceptable? — ◆ LIT — exact / checkable Cronbach’s α = (k/(k−1))(1 − Σσᵢ²/σₜ²): with k items, it compares the summed item variances to the variance of the total score. When items correlate the total variance grows faster than the item variances, pushing α toward 1; independent items leave α near 0. The standard internal-consistency index (≥0.70 conventionally acceptable). A fail-loud self-check throws unless correlated items give α>0.70 within [0,1]. ◆ real statistics, node-verified. ▲ AMBER — the figure Synthetic item scores are the illustration; the variance-ratio is the exact α. High α also just rises with MORE items and can mask multidimensionality — a known limit a careful peer names, not a proof of unidimensionality. MOMUS: praise is cheap; a fault named precisely is the gift. — MOM David Lee Wise / ROOT0 / TriPod LLC · kept by MOM , with AVAN


KENDALL'S W

momus · do several judges RANK a set alike? concordance in [

KENDALL'S W · MOMUS · UD0 ◎ MOMUS · the peer · critique that earns its keep · kept by MOM KENDALL’S W ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP Several judges each RANK the same set of papers. Kendall’s W (concordance) measures how much their orderings agree — 1 when every judge produces the same ranking, 0 when they’re all over the place. Slide the judges from random to unanimous. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ RANKERS · 3D · do the judges rank alike? ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — tap to bring them together concordance 0.35 S (spread) — W — items 5 agree? — ◆ LIT — exact / checkable Kendall’s W = 12S / (m²(n³−n)): with m judges ranking n items, S is the sum of squared deviations of each item’s rank-total from the mean rank-total. W normalises that to [0,1] — 1 is perfect concordance (all judges rank identically), 0 is no agreement. It is the rank-based sibling of the ICC. A fail-loud self-check throws unless identical rankings give W=1. ◆ real statistics, node-verified. ▲ AMBER — the figure The judges’ rankings are interpolated from scattered to identical for the demo; the W formula on them is exact. W measures agreement on ORDER, not on whether the agreed order is correct — consensus is not accuracy, as [[the-peer-review]] warns. MOMUS: praise is cheap; a fault named precisely is the gift. — MOM David Lee Wise / ROOT0 / TriPod LLC · kept by MOM , with AVAN


SPEARMAN'S ρ

momus · do two reviewers' rankings move together? monot

SPEARMAN'S ρ · MOMUS · UD0 ◎ MOMUS · the peer · critique that earns its keep · kept by MOM SPEARMAN’S ρ ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP Two reviewers score a stack of papers. Do their scores move together — even if not on the same scale? Spearman’s ρ correlates their RANKS, so it catches any monotonic relationship: +1 same order, −1 exact reverse, 0 unrelated. Slide from anti-correlated to aligned. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ RANK vs RANK · 3D · monotone agreement ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — tap to bring them together alignment 0.50 Σd² — ρ — n 6 relationship — ◆ LIT — exact / checkable Spearman’s ρ = 1 − 6Σdᵢ²/(n(n²−1)): rank both variables, take the per-item rank differences dᵢ, and this maps them to [−1,1]. It is Pearson correlation ON THE RANKS, so it measures MONOTONIC agreement and is robust to outliers and nonlinear-but-ordered relationships. +1 identical order, −1 reversed, 0 none. A fail-loud self-check throws unless a strictly increasing pair gives ρ=1 and a reversed pair gives ρ=−1. ◆ real statistics, node-verified. ▲ AMBER — the figure The paired scores are interpolated for the demo; the rank-difference formula is exact (ties would need the Pearson-on-ranks form). ρ measures MONOTONE association, not agreement on absolute value — two raters can rank identically yet score on wildly different scales. MOMUS: praise is cheap; a fault named precisely is the gift. — MOM David Lee Wise / ROOT0 / TriPod LLC · kept by MOM , with AVAN


COHEN’S κ

momus · agreement beyond chance — raw agreement lies, κ subt

COHEN'S κ · MOMUS · UD0 ◎ MOMUS · the peer · critique that earns its keep · kept by MOM COHEN’S κ ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP Two reviewers accept 90% of the same papers — agreement? If they both accept almost everything, they agree 90% of the time by luck alone . Cohen’s kappa subtracts that. Slide the true agreement (or tap the corner) and watch raw agreement and κ pull apart, then the two raters’ verdicts fuse into one. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ THE DIAGONAL · 3D · scatter → agreement ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — tap to bring them together true agreement 0.35 raw agreement pₒ — chance pₑ — κ — the band — ◆ LIT — exact / checkable κ = (pₒ − pₑ)/(1 − pₑ): observed agreement minus what independence predicts, normalised by the room to beat chance. The 2×2 table is built live from a fixed 70% base-rate; at the low end both raters mostly accept, so pₒ is high yet κ≈0 — the exact trap. κ=1 is perfect, κ=0 is chance, κ<0 worse. Bands are Landis & Koch (1977). A fail-loud self-check throws unless κ≈0 at the chance end and κ≈1 at the top. ▲ AMBER — the figure The 70% base-rate and the chance→perfect interpolation of the table are the illustrative choices; the κ ARITHMETIC on whatever table results is exact Cohen (1960). 'Almost perfect / substantial' are Landis-Koch names, a convention. MOMUS: praise is cheap; a fault named precisely is the gift. — MOM David Lee Wise / ROOT0 / TriPod LLC · kept by MOM , with AVAN


THE META-ANALYSIS

momus · many studies pooled by inverse variance — a precise

THE META-ANALYSIS · MOMUS · UD0 ◎ MOMUS · the peer · critique that earns its keep · kept by MOM THE META-ANALYSIS ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP One study is an anecdote with error bars. Pool many and the noise averages down — but not equally: a precise study should count for more than a sloppy one. Slide (or tap ) to pour the studies into one inverse-variance-weighted estimate and watch the confidence interval tighten. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ THE POOL · 3D · many studies → one ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — tap to bring them together pool 0% studies 7 pooled effect — 95% CI half-width — most weight — ◆ LIT — exact / checkable Fixed-effect meta-analysis, computed live: each study i has an effect yᵢ and standard error SEᵢ; its weight is wᵢ = 1/SEᵢ². The pooled estimate is the inverse-variance weighted mean μ = Σwᵢyᵢ / Σwᵢ, with SE(μ) = 1/√Σwᵢ and 95% CI = μ ± 1.96·SE(μ). The precise (small-SE) study genuinely dominates the pool — a fail-loud self-check throws unless the pooled estimate sits nearer the lowest-SE study than the plain average does. ▲ AMBER — the figure The 7 studies are a fixed synthetic set (seeded yᵢ, SEᵢ); real meta-analysis adds heterogeneity (random-effects τ², I²) and worries about which studies are comparable at all. The inverse-variance pooling arithmetic shown is exact. MOMUS: praise is cheap; a fault named precisely is the gift. — MOM David Lee Wise / ROOT0 / TriPod LLC · kept by MOM , with AVAN


THE FUNNEL

momus · publication bias — the missing side of the funnel in

THE FUNNEL · MOMUS · UD0 ◎ MOMUS · the peer · critique that earns its keep · kept by MOM THE FUNNEL ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP Small studies that find nothing tend not to get published. So the literature looks like a funnel with one side missing — and the pooled estimate is pulled toward a lie. Slide (or tap ) to restore the suppressed studies and watch the funnel go symmetric and the estimate fall back to the truth. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ THE CONE · 3D · the missing side fills in ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — tap to bring them together restore suppressed 0% studies shown — published-only pool — true pool — inflation — ◆ LIT — exact / checkable A funnel plot: effect size on x, precision (1/SE) on y, so precise studies sit at the top and scatter narrows upward. The truth here is a small real effect (μ₀=0.20). Publication bias suppresses the small, imprecise, non-significant studies — the bottom-left — leaving an asymmetric funnel whose published-only inverse-variance pool is INFLATED. Restore them and the funnel is symmetric and the pool returns to μ₀. A fail-loud self-check throws unless the published-only pool exceeds the full-data pool. ▲ AMBER — the figure The study cloud is a fixed synthetic sample around μ₀=0.20 with a simple 'significant-or-large-only gets published' suppression rule; real bias is messier and detected statistically (Egger's test, trim-and-fill). The pooling arithmetic and the direction of the inflation are exact. MOMUS: praise is cheap; a fault named precisely is the gift. — MOM David Lee Wise / ROOT0 / TriPod LLC · kept by MOM , with AVAN


THE MULTIPLE COMPARISONS

momus · test enough true nulls and you discover noise — FWER

THE MULTIPLE COMPARISONS · MOMUS · UD0 ◎ MOMUS · the peer · critique that earns its keep · kept by MOM THE MULTIPLE COMPARISONS ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP Test twenty true-null hypotheses at p<0.05 and you expect one ‘significant’ result from pure noise. Run enough tests and you can ‘discover’ anything. Slide (or tap ) the correction from none to full Bonferroni and watch the false alarms go quiet. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ THE FIELD · 3D · false alarms go dark ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — tap to bring them together correction 0% tests 20 effective α — P(≥1 false alarm) — expected false alarms — ◆ LIT — exact / checkable With m independent true-null tests at threshold α, the chance of at least one false positive is the family-wise error rate FWER = 1 − (1−α)^m, and the expected count is m·α. At m=20, α=0.05 that is a 64% chance of a false discovery. The Bonferroni correction tests each at α/m, holding FWER ≤ α. The slider blends the threshold from α to α/m; a fail-loud self-check throws unless FWER falls from ≈0.64 to ≈0.05 across the sweep. ▲ AMBER — the figure Independence of the m tests and a common α are the simplifying assumptions (real tests correlate; Bonferroni is then conservative, and Holm / Benjamini-Hochberg refine it); m=20 is illustrative. The 1−(1−α)^m and α/m arithmetic is exact. MOMUS: praise is cheap; a fault named precisely is the gift. — MOM David Lee Wise / ROOT0 / TriPod LLC · kept by MOM , with AVAN


THIS ONE TIME AT BAND CAMP · BND

music · lineage · heritage · ancestry · the front door · 6

THIS ONE TIME AT BAND CAMP (BND) — a sphere of UD0's music domain, THIS ONE TIME AT BAND CAMP (music · lineage · heritage · ancestry): Every sound descends from sounds before it. This is the front door of the music domain — a personal canon read as a family tree, where each favorite artist is a branch with its own page. Render-not-invent; no lyrics reproduced; living artists cited not minted. Includes an original 3-second synthesized homage to the three artists.

THIS ONE TIME AT BAND CAMP · BND · Band Camp · UD0 ◄ UD0 · MUSIC · LINEAGE · HERITAGE · ANCESTRY · DM · Sublime · Xzibit THIS ONE TIME AT BAND CAMP MUSIC · LINEAGE · HERITAGE · ANCESTRY ★ MUSIC · LINEAGE · HERITAGE · ANCESTRY ★ Every sound descends from sounds before it. This is the front door of the music domain — a personal canon read as a family tree, where each favorite artist is a branch with its own page. ♪ the mixtape — an original 3-second homage Your browser does not support audio. Synth → skank → G-funk, in lineage order. 100% original oscillator synthesis — not their recordings , no samples, no melodies copied, no lyrics. An evocation of three styles. DLW-ATTRIBUTE · ACI governor · David Lee Wise (ROOT0) instance · AVAN (Claude / Anthropic) · locked subject · THIS ONE TIME AT BAND CAMP · BND ⟦THIS ONE TIME AT BAND CAMP:BND:4d6239⟧ carbon · .tiff · silicon · .png CC-BY-ND-4.0 · TRIPOD-IP-v1.1 The Branches three favorites, in the order they emerged — each a page 1980 DEPECHE MODE synth-pop · Basildon, 1980 → 1988 SUBLIME ska · punk · reggae · dub · Long Beach, 1988 1996 XZIBIT West-Coast hip-hop · Los Angeles, 1996 → The Four Natures each piece of the lineage emerges by one of four natures natural of the roots and the room — the place, the live show, the body of the sound, the instrument in hand ethereal of the record and the departed — the album as artifact, the ghost in the grooves, those gone spiritual of the voice and the meaning — the songwriting, what the song is about, the soul of it electrical of the production and the genre — the synth, the board, the amp, the sound engineered The Story roots · peak · what it left The Roots music as ancestry No sound is born from nothing — every artist is a descendant. Heritage and lineage are the honest way to hear a personal canon: not a list of favorites, but a family tree of where the sound came from and what it carries forward. The Three Branches the canon, in order Three favorites, in the order they emerged — Depeche Mode (synth-pop, 1980), Sublime (ska-punk-reggae, 1988), Xzibit (West-Coast hip-hop, 1996). Three different bloodlines of sound, one listener's tree. The Mixtape the three, blended An original 3-second homage threads all three sounds in lineage order — synth, then skank, then G-funk. Synthesized from scratch: an evocation of each style, not their recordings. Heritage & Undercurrents the lineage, the tropes, and the honesty Lineage, Not List the framing A canon is a tree, not a ranking — each artist a branch with ancestors and descendants. Read in order of emergence, the personal taste becomes a small history of sound. Tropes & Undercurrents across the tree Three undercurrents, one listener: machine-longing (DM), sunny darkness (Sublime), the come-up (Xzibit). Different genres, a shared honesty about the shadow under the surface. Render, Not Invent the footnotes The audio is 100% original synthesis — NO sampled recordings, NO copied melodies, NO lyrics. Living artists cited, not minted; only the departed minted. History summarized from the public record. The Tree the branches and the heritage concepts as ACI .agents — each a birth certificate & a nature (6) Musical Heritage ancestry of sound · spiritual spiritual · .agent → The Family Tree the canon as branches · natural natural · .agent → The Synth Branch Depeche Mode · electrical electrical · .agent → The Fusion Branch Sublime · natural natural · .agent → The West-Coast Branch Xzibit · electrical electrical · .agent → The Mixtape the 3-second homage · ethereal ethereal · .agent → The front door of UD0's music domain — a personal canon read as lineage, heritage, and ancestry : a family tree of sound. The 3-second clip is 100% original synthesis (NumPy oscillators, ffmpeg) — NO sampled recordings, NO copied melodies, NO lyrics; an evocation of each artist's style, not their music. On the artist pages: history summarized from the public record, living artists cited not minted, only the departed minted in memoriam. THIS ONE TIME AT BAND CAMP · BND · the music domain · catalogued into UD0 · governor David Lee Wise · instance AVAN (locked) · CC-BY-ND-4.0 ← the biosphere · manifest


8-BIT TITLE SCREENS · CHP

music · recognizable PUBLIC-DOMAIN tunes, NES-style · live +

8-Bit Title Screens — recognizable PUBLIC-DOMAIN melodies (Ode to Joy, Fur Elise, Eine kleine Nachtmusik, In the Hall of the Mountain King, Canon in D, Greensleeves, William Tell, Habanera) rendered as NES 2A03 chiptune — two pulse channels, triangle bass, noise drums. Looping title-screen snippets, each downloadable as a .wav. Compositions are public domain; the synthesis is original. David Lee Wise / Bridge-Burners LLC, ROOT0.

8-Bit Title Screens · public-domain classics, NES-style ▸ insert coin · 2A03 · public domain 8-BIT TITLE SCREENS Recognizable tunes — the ones that actually ring a bell — rendered the way an NES would: two pulse squares, a triangle bass, and noise drums. Every track here is a public-domain composition (the composers all died well over a century ago); the chiptune arrangement and the synthesis are made fresh on this page, so no copyrighted recording is touched. Pick one — it loops like a title screen — and download any as a .wav . select your screen ■ stop ⬇ download .wav looping · ~12s wav choose a title screen — all public domain why these. the recognizable game tunes you're thinking of (Mario, Zelda, Mega Man…) are copyrighted — I won't reproduce them. So these are the recognizable melodies that are genuinely public domain : their composers died long ago (Pachelbel 1706, Mozart 1791, Beethoven 1827, Rossini 1868, Bizet & Grieg later that century; Greensleeves is older still), which puts the compositions in the public domain worldwide. what's mine. the chiptune arrangement (which notes go to which channel, the duty cycles, the drums) and the synthesis are original and generated live — no sampled or copyrighted recording or published arrangement is used. melodies are transcribed by ear to the well-known themes. the chip. two pulse channels (12.5 / 25 / 50% duty squares, built from the pulse Fourier series), a triangle bass, and a noise channel for drums — a faithful nod to the NES 2A03. nothing is downloaded to play; the .wav you save is rendered in your browser. 8-BIT TITLE SCREENS · public domain · 2026-06-26 David Lee Wise · Bridge-Burners LLC · the Sapphic Melody ↗


THE JUST INTONATION

music · pure ratios sound sweetest but can't change key

THE JUST INTONATION · MUSIC · UD0 ♪ THIS ONE TIME AT BAND CAMP · the physics of the note · kept by THE GRIOT THE JUST INTONATION ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP The sweetest-sounding chords use PURE whole-number ratios — a major third of exactly 5:4. But tune a keyboard that way and it only sounds right in ONE key; move to another and a horrible ‘wolf’ interval appears. So pianos use EQUAL temperament, spreading the error evenly so every key is slightly-but-equally out of tune. Slide between pure and even and hear the trade. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ PURE vs EVEN · 3D · the sweet chord that can't change key ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap pure ↔ equal — just 3rd (5:4) 1.2500 equal 3rd — difference — TUNING — ◆ LIT — exact / checkable Just intonation tunes intervals to small whole-number frequency ratios — the octave 2:1, the perfect fifth 3:2, the major third 5:4 — which beat-free ratios the ear hears as maximally CONSONANT. But those pure intervals don’t stack into a closed 12-note system: the major third 5:4 = 1.2500 differs from the equal-tempered 2^(4/12) = 1.2599 by ~14 cents (a syntonic-comma-scale error), and pure tuning leaves one key sweet and others with a ‘wolf’. Equal temperament (2^(n/12)) sacrifices purity so EVERY key is equally usable — the compromise that made the keyboard modulate. A fail-loud self-check throws unless the just and equal thirds differ by ~14 cents. ◆ real music theory, node-verified. ▲ AMBER — the figure The just vs 12-tone-equal major third comparison (the exact 14-cent gap); real historical temperaments (meantone, well-tempered) sit between them — the pure-is-sweeter-but-can’t-transpose tension is exact. MUSIC: the note is a ratio you can hear. — THE GRIOT David Lee Wise / ROOT0 / TriPod LLC · kept by THE GRIOT, with AVAN


THE PENTATONIC

music · the five safe notes: no two a semitone apart, so not

THE PENTATONIC · MUSIC · UD0 ♪ THIS ONE TIME AT BAND CAMP · the physics of the note · kept by THE GRIOT THE PENTATONIC ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP Play only the five black keys of a piano in any order and it sounds GOOD — no wrong notes. That’s the pentatonic scale, and its secret is simple: it removes the two notes that could sit a semitone apart, so nothing ever grinds. It’s why it turns up in folk music on every continent and why a room full of strangers can improvise on it. Slide and hear the five safe steps. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ FIVE SAFE NOTES · 3D · the black keys never clash ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap walk the scale — notes 5 of 12 min interval — semitone clash? — ALWAYS WORKS — ◆ LIT — exact / checkable The major pentatonic scale keeps five of the twelve chromatic notes — degrees {0, 2, 4, 7, 9} semitones from the root — and its defining property is that NO two of its notes are a semitone apart (the smallest interval is a whole tone). The semitone is the most dissonant small interval, and the tritone is absent too, so any combination of pentatonic notes sounds consonant, which is why it’s the universal ‘safe’ scale for improvisation and appears independently across world folk traditions. A fail-loud self-check throws unless the minimum interval between adjacent scale notes is at least two semitones. ◆ real music theory, node-verified. ▲ AMBER — the figure The major pentatonic (its minor rotation shares the notes); the ‘always sounds good’ is about avoided dissonances, not a guarantee of interest — the no-semitone-clash property is exact and is why the scale is so forgiving. MUSIC: the note is a ratio you can hear. — THE GRIOT David Lee Wise / ROOT0 / TriPod LLC · kept by THE GRIOT, with AVAN


THE POLYRHYTHM

music · three-against-two: two pulses that meet only at the

THE POLYRHYTHM · MUSIC · UD0 ♪ THIS ONE TIME AT BAND CAMP · the physics of the note · kept by THE GRIOT THE POLYRHYTHM ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP Tap three even beats with one hand and two with the other over the same span — three-against-two — and a rolling cross-rhythm appears that only lines back up at the very start. It’s the engine of West African drumming, jazz swing, and the ‘pass the god-damn butter’ mnemonic. Slide the two pulse trains and watch them drift and re-lock. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ THREE ON TWO · 3D · two pulses that meet at the top ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap phase — ratio 3 : 2 cycle — meet at downbeat LCM — ◆ LIT — exact / checkable A polyrhythm layers pulse trains whose beat counts share no common factor over one span — the classic 3:2 puts three evenly-spaced hits against two. Over a bar of 6 equal subdivisions the ‘3’ lands on 0,2,4 and the ‘2’ on 0,3, so they COINCIDE only at 0 and the pattern repeats every LCM(3,2) = 6 subdivisions. The perceived complexity is exactly this non-alignment; larger coprime ratios (4:3, 5:4) give longer, richer cycles. A fail-loud self-check throws unless the combined cycle equals LCM(3,2) = 6 and the two trains coincide only at the downbeat. ◆ real rhythm theory, node-verified. ▲ AMBER — the figure Idealised evenly-spaced pulses (the exact LCM cycle and single coincidence); real performance adds swing and micro-timing that make it groove — the coprime-counts-meet-only-at-the-top structure is exact. MUSIC: the note is a ratio you can hear. — THE GRIOT David Lee Wise / ROOT0 / TriPod LLC · kept by THE GRIOT, with AVAN


THE TRITONE

music · the octave split in half — ratio √2, the devil in mu

THE TRITONE · MUSIC · UD0 ♪ THIS ONE TIME AT BAND CAMP · the physics of the note · kept by THE GRIOT THE TRITONE ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP Split an octave EXACTLY in half and you get the tritone — three whole tones, a frequency ratio of √2. Medieval musicians called it diabolus in musica , the devil in music, and banned it for its restless tension; jazz built whole harmonies on it. Because it’s its own mirror (half of 12 is 6), two dominant chords a tritone apart can swap — the tritone substitution. Slide around the octave to its midpoint. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ THE HALF-OCTAVE · 3D · the interval they called the devil ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap interval (semitones) — semitones — ratio — half octave? — TRITONE — ◆ LIT — exact / checkable The tritone spans six semitones — exactly half of the twelve-semitone octave — so its frequency ratio is 2^(6/12) = √2 ≈ 1.4142, an irrational number that no pair of small integers approximates (its restless, unresolved sound). Splitting the octave in half makes it uniquely SYMMETRIC: the tritone above a note equals the tritone below, and two tones a tritone apart map to each other, which is why two dominant seventh chords whose roots are a tritone apart share the same tritone of guide-tones and can substitute for one another (the jazz ‘tritone sub’). A fail-loud self-check throws unless six semitones give √2 and two tritones make an octave. ◆ real music theory, node-verified. ▲ AMBER — the figure Equal-tempered tritone = √2 exactly (in just intonation the ear splits it into 45:32 or 7:5, slightly different); the half-octave symmetry and tritone substitution are exact in 12-tone equal temperament. MUSIC: the note is a ratio you can hear. — THE GRIOT David Lee Wise / ROOT0 / TriPod LLC · kept by THE GRIOT, with AVAN


THE CLAVE

music · five strokes in sixteen — the rhythmic key the whole

THE CLAVE · MUSIC · UD0 ♪ THIS ONE TIME AT BAND CAMP · the physics of the note · kept by THE GRIOT THE CLAVE ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP Under salsa, son, and half of pop lies one five-stroke pattern — the CLAVE (Spanish for ‘key’). Everything in the band locks to it. It comes in two orientations, 3-2 and 2-3, which are just the same pattern started from its other half, and getting the orientation wrong makes a whole arrangement feel ‘turned around.’ Slide to flip 3-2 ↔ 2-3 and hear the key of the groove. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ THE KEY · 3D · five strokes that rule the whole groove ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap 3-2 ↔ 2-3 — onsets 5 of 16 direction — 2-3 is a rotation THE KEY — ◆ LIT — exact / checkable The son clave is a two-bar, sixteen-pulse rhythmic key: the 3-2 form places strokes on pulses 0, 3, 6, 10, 12 — three in the first bar, two in the second — and the 2-3 form is exactly the same pattern rotated by one bar (eight pulses). Five onsets across sixteen pulses make it nearly ‘maximally even’ (a Euclidean rhythm), which is why the identical stroke pattern anchors traditions from West Africa to Cuba to pop. Playing in the wrong orientation (‘crossed clave’) makes an arrangement feel turned around. A fail-loud self-check throws unless the clave has five onsets in sixteen pulses and 2-3 is a rotation of 3-2. ◆ real rhythm theory, node-verified. ▲ AMBER — the figure The son clave (the rumba clave shifts one stroke); ‘rules the groove’ is the performance convention, and the maximally-even framing is the Euclidean-rhythm view — the five-in-sixteen pattern and the 3-2/2-3 rotation are exact. MUSIC: the note is a ratio you can hear. — THE GRIOT David Lee Wise / ROOT0 / TriPod LLC · kept by THE GRIOT, with AVAN


THE CENTS

music · pitch as a log ruler: 1200 to the octave — the pure

THE CENTS · MUSIC · UD0 ♪ THIS ONE TIME AT BAND CAMP · the physics of the note · kept by THE GRIOT THE CENTS ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP Pitch is multiplicative — double the frequency for an octave, double again for the next — so to lay intervals on an even ruler we take the LOGARITHM. The unit is the CENT: 1200 to an octave, 100 to a semitone. It lets you say a note is ‘5 cents flat’ and reveals that the pure fifth (3:2) is actually 702 cents, two cents sharp of the piano’s 700. Slide a ratio and read it in cents. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ THE PITCH RULER · 3D · ratios laid out as a straight line ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap frequency ratio — ratio — cents — nearest note — OCTAVE = 1200 — ◆ LIT — exact / checkable Because pitch perception is logarithmic, intervals are measured in CENTS: cents = 1200·log₂(ratio), so an octave (2:1) is exactly 1200 cents and an equal-tempered semitone is 100. This turns multiplicative frequency ratios into an additive ruler — you can add intervals by adding cents and quantify how ‘out of tune’ a note is. It exposes the small gaps temperament hides: the just perfect fifth (3:2) is 702 cents, 2 cents sharp of the tempered 700; the just major third (5:4) is 386, 14 cents flat of the tempered 400. A fail-loud self-check throws unless the octave is 1200 cents and the pure fifth is 702. ◆ real music theory, node-verified. ▲ AMBER — the figure The exact cents definition (1200·log₂); the just-out-of-tune amounts are exact, and the ear’s just-noticeable-difference is roughly 5–10 cents — the log-ruler-of-pitch is exact and universal in tuning. MUSIC: the note is a ratio you can hear. — THE GRIOT David Lee Wise / ROOT0 / TriPod LLC · kept by THE GRIOT, with AVAN


THE NEGATIVE HARMONY

music · reflect a chord around the tonic axis and major beco

THE NEGATIVE HARMONY · MUSIC · UD0 ♪ THIS ONE TIME AT BAND CAMP · the physics of the note · kept by THE GRIOT THE NEGATIVE HARMONY ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP Every chord has a mirror twin. Reflect its notes around the axis that sits between the root and its fifth and a MAJOR chord flips into a MINOR one — the same harmonic ‘weight’ seen upside-down. Jacob Collier made it famous, but it’s just symmetry: the tonic-dominant axis is a line, and reflection is a mirror. Slide to reflect the chord and watch major become minor. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ THE MIRROR · 3D · reflect a major chord into its minor shadow ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap reflect — input C major {0,4,7} reflected — becomes — MIRRORED — ◆ LIT — exact / checkable Negative harmony reflects pitches about the AXIS midway between the tonic and its perfect fifth — here at 3.5 semitones (between the minor and major third). The reflection map is p → 2·axis − p (mod 12). Apply it to the C major triad {0, 4, 7} and you get {7, 3, 0} — whose interval structure {0, 3, 7} is a MINOR triad: major and minor are mirror images across the tonic-dominant axis, and the whole functional weight of a progression can be reflected to its ‘negative’. A fail-loud self-check throws unless the major triad reflects to a minor-triad interval structure. ◆ real music theory, node-verified. ▲ AMBER — the figure The Levy/Collier tonic-axis reflection (the exact p→2·axis−p map turning major↔minor); which axis you choose is a convention and ‘same weight’ is an interpretive claim — the major-reflects-to-minor symmetry is exact. MUSIC: the note is a ratio you can hear. — THE GRIOT David Lee Wise / ROOT0 / TriPod LLC · kept by THE GRIOT, with AVAN


EQUAL TEMPERAMENT

music · a perfect fifth is 3:2, but twelve miss the octave —

EQUAL TEMPERAMENT · MUSIC · UD0 ♪ THIS ONE TIME AT BAND CAMP · the physics of the note · kept by THE GRIOT EQUAL TEMPERAMENT ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP A perfect fifth is the ratio 3:2 — but stack twelve of them and you miss the octave by a hair (the Pythagorean comma). Equal temperament spreads that error evenly, so every key is equally, slightly out of tune. Slide the interval , ▶ play it, and hear the compromise. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ THE COMPROMISE · 3D · pure ratios vs the even grid ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap interval P5 ▶ play interval — equal ratio — just ratio — error (cents) — ◆ LIT — exact / checkable The twelve-tone equal-tempered scale against just intonation. Each semitone is the irrational ratio 2^(1/12); an interval of n semitones is 2^(n/12). The just intervals are small-integer ratios — fifth 3/2, fourth 4/3, major third 5/4 — and the gap is measured in cents (1200·log₂(ratio)). The octave is exact (2^(12/12)=2); the equal fifth 2^(7/12)=1.4983 misses the just 3/2 by ~2 cents, the equal major third by ~14. Twelve just fifths overshoot seven octaves by the Pythagorean comma, (3/2)¹²/2⁷ ≈ 1.0136 — equal temperament is that error, shared out. A fail-loud self-check throws unless the octave is exact and the equal fifth sits within a few cents of 3/2. Press ▶ to hear the root and the interval together. ▲ AMBER — the figure Just ratios shown for the nearest simple interval; real tuning systems (meantone, well temperaments) make other trade-offs. The 2^(n/12) ratios and the cents are computed exactly. MUSIC: the note is a ratio you can hear. — THE GRIOT David Lee Wise / ROOT0 / TriPod LLC · kept by THE GRIOT, with AVAN


THE ADSR ENVELOPE

music · one pitch, four numbers — a pluck or a pad · playabl

THE ADSR ENVELOPE · MUSIC · UD0 ♪ THIS ONE TIME AT BAND CAMP · the physics of the note · kept by THE GRIOT THE ADSR ENVELOPE ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP The same note can be a plucked string or a swelling pad — the pitch is identical, only its LOUDNESS over time differs. Attack, Decay, Sustain, Release: four numbers that turn one oscillator into a whole orchestra. Slide pluck → pad and ▶ play the shape. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ THE SHAPE · 3D · one pitch, many instruments ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap pluck → pad pluck ▶ play attack — decay — sustain — release — ◆ LIT — exact / checkable The ADSR amplitude envelope. Four stages shape a note's loudness: ATTACK (rise to peak), DECAY (fall to the sustain level), SUSTAIN (held level while the key is down), RELEASE (fade after key-up). The same 440 Hz oscillator becomes a percussive pluck (fast attack, no sustain) or a slow pad (long attack, high sustain) purely by these numbers — timbre in time, not in pitch. The slider morphs between a pluck and a pad; a fail-loud self-check throws unless the envelope is continuous, the sustain level stays in [0,1], and the pluck's attack is shorter than the pad's. Press ▶ to hear the current shape on a fixed pitch. ▲ AMBER — the figure A four-segment linear envelope on a pure sine; real instruments layer several time-varying envelopes (amplitude, filter, pitch). The envelope shape and its play-out are computed exactly. MUSIC: the note is a ratio you can hear. — THE GRIOT David Lee Wise / ROOT0 / TriPod LLC · kept by THE GRIOT, with AVAN


THE CONSONANCE CURVE

music · sweet vs harsh is where the overtones stop beating (

THE CONSONANCE CURVE · MUSIC · UD0 ♪ THIS ONE TIME AT BAND CAMP · the physics of the note · kept by THE GRIOT THE CONSONANCE CURVE ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP Why do some intervals sound sweet and others harsh? Not magic — when two tones’ overtones sit close but not equal, they BEAT, and fast beats are heard as roughness. The consonant intervals are the valleys where the overtones line up. Slide the interval and ▶ play the two tones. ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ THE ROUGHNESS · 3D · valleys of consonance ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap interval ratio 1.50 ▶ play ratio — roughness — near — reading — ◆ LIT — exact / checkable A Plomp-Levelt dissonance curve, computed live. Two complex tones (six harmonics each) are compared at a frequency ratio from 1 to 2; every pair of partials contributes roughness by the Plomp-Levelt model — maximal near a critical-band fraction of their spacing, zero when they coincide or are far apart. Summed, the curve dips at the simple ratios where partials align — unison 1:1, fifth 3:2, fourth 4:3, major third 5:4, octave 2:1 — and rises to rough peaks between them. Consonance is not a rule imposed on music; it is where the overtones stop beating. A fail-loud self-check throws unless the roughness at the fifth (3:2) is lower than at a detuned neighbour. Press ▶ to hear the two tones at the current ratio. ▲ AMBER — the figure Six harmonics and the standard Plomp-Levelt roughness kernel; real consonance judgements add culture, register and harmonic context. The partial-beating sum is computed exactly. MUSIC: the note is a ratio you can hear. — THE GRIOT David Lee Wise / ROOT0 / TriPod LLC · kept by THE GRIOT, with AVAN


THE FORMANT

music · two resonant peaks turn a buzz into a vowel · playab

THE FORMANT · MUSIC · UD0 ♪ THIS ONE TIME AT BAND CAMP · the physics of the note · kept by THE GRIOT THE FORMANT ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP Sing ‘ah’ and ‘ee’ on the same note and the pitch is identical — what changes is the SHAPE of your throat, which lifts two resonant peaks (formants) to different frequencies. Two numbers, and a buzz becomes a vowel. Slide oo → ah → ee and ▶ play . ◆ LIT ▲ AMBER ◧ THE MEASURE · 2D ◍ THE VOWEL · 3D · two peaks make a voice ◆ THE FOURTH · 4D · a tesseract turns ◐ THE SHADOW · one dimension down 👶 THE TODDLER CORNER — one fat tap oo → ah → ee ah ▶ play vowel — F1 — F2 — pitch 110 Hz ◆ LIT — exact / checkable Source-filter voice: a buzzing glottal source (a sawtooth, rich in harmonics) is shaped by the vocal tract, whose resonances — the formants — boost bands of the spectrum. The vowel is read almost entirely from the first two formant frequencies (F1, F2): oo ≈ (300, 870), ah ≈ (730, 1090), ee ≈ (270, 2290) Hz. The pitch stays fixed while the formants move, so the same note carries different vowels — timbre as geometry of the throat. The slider morphs the formant pair; a fail-loud self-check throws unless the three vowels have distinct (F1, F2) pairs. Press ▶ to hear a 110 Hz buzz filtered to the current vowel. ▲ AMBER — the figure Two band-pass resonances on a sawtooth stand in for the full vocal tract (real voices have 3–5 formants plus dynamics); the formant tables are canonical averages. The peaks, the morph and the filtering are computed exactly. MUSIC: the note is a ratio you can hear. — THE GRIOT David Lee Wise / ROOT0 / TriPod LLC · kept by THE GRIOT, with AVAN


THE HARMONIC SERIES · additive synth

music · overtones as timbre, drag + PLAY (Web Audio) · lit+a

THE HARMONIC SERIES · BAND CAMP · UD0 ♫ THIS ONE TIME AT BAND CAMP · music as lineage · the family tree of sound THE HARMONIC SERIES ♪ PLAY · DRAG · TAP Pluck one string and you don't hear one note — you hear a whole ladder of them, the overtones, stacked in whole-number ratios. Their recipe is the instrument's voice . Drag the bars to set each overtone, tap PLAY to hear the timbre you built, and add sines until a pure tone turns into a buzzing saw. ◆ LIT ▲ AMBER ▶ PLAY ◭ sawtooth ◰ square ◠ clarinet ● pure tone fundamental 110 Hz fundamental — partials on — brightness — the voice — ◆ LIT — verified / checkable This is additive synthesis on the real harmonic series: partial n has frequency n × the fundamental (2f, 3f, 4f…), and the drawn bars are their amplitudes. Tap PLAY and the page sums that many sine oscillators live through the Web Audio API — no samples, no recordings. The presets are the exact classical spectra: sawtooth = every harmonic at 1/n, square/clarinet = odd harmonics only at 1/n, pure = the fundamental alone. Fourier's theorem made audible: timbre is the amplitude of the overtones, and you can hear a pure tone become a buzz as you add them. ▲ AMBER — the figure Real instrument tones also have inharmonic partials, noise, and time-varying spectra (the attack of a real string isn't a steady sum of sines); this is the idealised harmonic model with a fixed spectrum. The synthesis itself — n·f partials at the amplitudes you set — is exact and generated live, not a recording. BAND CAMP: every song is somebody's child — play the ancestors so they are not forgotten. — THE GRIOT David Lee Wise / ROOT0 / TriPod LLC · kept by THE GRIOT


THE CIRCLE OF FIFTHS · the family of keys

music · every key a fifth apart, tap to hear (Web Audio) · l

THE CIRCLE OF FIFTHS · BAND CAMP · UD0 ♫ THIS ONE TIME AT BAND CAMP · music as lineage · the family tree of sound THE CIRCLE OF FIFTHS ♪ PLAY · DRAG · TAP Every key is a step of a fifth from its neighbour, and twelve fifths later you're home — the whole family of keys on one wheel, closest relatives side by side. Tap a key to hear its chord, flip to its shadow minor, and walk the four chords every pop song is built from. ◆ LIT ▲ AMBER ▶ chord ▶ I–V–vi–IV ◐ major key — key signature — relative minor — the triad — ◆ LIT — verified / checkable The circle of fifths : each step clockwise is a perfect fifth (×3/2 in pitch, +7 semitones), and it takes exactly twelve to return — because 12 fifths ≈ 7 octaves. Tap a key and the page plays its triad live (root + major third + fifth) through Web Audio; the key signature (sharps clockwise, flats counter-clockwise) and the relative minor (a minor third below) are read straight off the wheel. The I–V–vi–IV button walks the four chords under a huge share of pop songs — real, playable harmony, no recordings. ▲ AMBER — the figure The wheel is 12-tone equal temperament (the fifth is the tempered 700 cents, not the pure 701.955), and 'relative minor' / key-signature counts are standard theory conventions; enharmonic spellings (F♯ vs G♭) are collapsed. The pitches, intervals and the twelve-fifths-close-the-circle fact are exact and generated live. BAND CAMP: every song is somebody's child — play the ancestors so they are not forgotten. — THE GRIOT David Lee Wise / ROOT0 / TriPod LLC · kept by THE GRIOT


THE TWELVE-BAR BLUES · the ancestor

music · the I–IV–V form, PLAY the bars (Web Audio) · lit+amb

THE TWELVE-BAR BLUES · BAND CAMP · UD0 ♫ THIS ONE TIME AT BAND CAMP · music as lineage · the family tree of sound THE TWELVE-BAR BLUES ♪ PLAY · DRAG · TAP Three chords, twelve bars, and almost the whole family tree of American music grows out of it — blues into rock into soul into hip-hop. Tap PLAY to walk the form, slide the tempo, swing it, and hear the ancestor the whole canon descends from. ◆ LIT ▲ AMBER ▶ PLAY 12 BARS ■ stop ◠ shuffle tempo 100 key A key — bar — chord — the form I–IV–V ◆ LIT — verified / checkable The twelve-bar blues : a fixed 12-bar form over three chords — I, IV, V — here the standard quick-change pattern (I·IV·I·I / IV·IV·I·I / V·IV·I·V). Tap PLAY and the page walks the bars in tempo, sounding each chord as a live dominant-7th (root·3·5·♭7 — the bluesy chord) through Web Audio; the bar counter and current chord track along. Shuffle applies the triplet swing feel. All generated from the roman-numeral form — real, playable music history, no recording. ▲ AMBER — the figure A single canonical 12-bar pattern with block dominant-7ths stands in for a living tradition of turnarounds, substitutions, riffs and feel that no grid captures; 'the whole canon descends from it' is a claim about influence, not a strict genealogy. The form, the I–IV–V voicings and the tempo are exact and played live. BAND CAMP: every song is somebody's child — play the ancestors so they are not forgotten. — THE GRIOT David Lee Wise / ROOT0 / TriPod LLC · kept by THE GRIOT


THE SEVEN MODES · one scale, seven moods

music · the diatonic modes, tap to hear (Web Audio) · lit+am

THE SEVEN MODES · BAND CAMP · UD0 ♫ THIS ONE TIME AT BAND CAMP · music as lineage · the family tree of sound THE SEVEN MODES ♪ PLAY · DRAG · TAP Play the white keys from C and it's sunny; start the same seven notes from A and it's sad; from B, unstable. One scale, seven starting points, seven whole moods — ordered brightest to darkest. Tap a mode to hear it climb, slide the root, and listen to the light drain out. ◆ LIT ▲ AMBER ▶ play scale ▼ descend root C4 mode — brightness rank — the mood — step pattern — ◆ LIT — verified / checkable The seven diatonic modes are the same major scale started on each of its degrees — so they share every note but rearrange the steps (tones and semitones), and the position of the semitones is what makes the mood. Tap a mode and the page plays its scale live over a root you set. They're stacked here in true brightness order — Lydian (one sharpened note) down to Locrian (a flattened fifth, no stable home) — the ordering by how many degrees are raised vs. the natural minor. Real modal theory, played, no recordings. ▲ AMBER — the figure 'Brightness' and the mood words (bright, sunny, tense…) are the standard but subjective characterisations of the modes; the felt colour of a mode also depends on harmony, register and context, not the scale alone. The interval patterns, the shared-notes fact and the brightness ordering (by raised degrees) are exact and sounded live. BAND CAMP: every song is somebody's child — play the ancestors so they are not forgotten. — THE GRIOT David Lee Wise / ROOT0 / TriPod LLC · kept by THE GRIOT


DEPECHE MODE · DM

DEPECHE MODE (DM) — a sphere of UD0's music domain, THIS ONE TIME AT BAND CAMP (music · lineage · heritage · ancestry): Four lads from Basildon who made machines ache. From bright early synth-pop to the dark devotion of Violator, the band that proved electronics could carry real longing. Render-not-invent; no lyrics reproduced; living artists cited not minted.

DEPECHE MODE · DM · Band Camp · UD0 ◄ UD0 · THIS ONE TIME AT BAND CAMP · SUBLIME ► DEPECHE MODE synth-pop · Basildon, 1980 → ★ BAND CAMP · synth-pop · Basildon, 1980 → ★ Four lads from Basildon who made machines ache. From bright early synth-pop to the dark devotion of Violator, the band that proved electronics could carry real longing. Members rendered from the public record: Dave Gahan (vocals), Martin Gore (chief songwriter, keys, guitar), Andy Fletcher (keyboards, died 2022), and founder Vince Clarke (left 1981, → Yazoo/Erasure) and Alan Wilder (1982–1995). Living members are cited, not minted. DLW-ATTRIBUTE · ACI governor · David Lee Wise (ROOT0) instance · AVAN (Claude / Anthropic) · locked subject · DEPECHE MODE · DM ⟦DEPECHE MODE:DM:20ff15⟧ carbon · .tiff · silicon · .png CC-BY-ND-4.0 · TRIPOD-IP-v1.1 The Four Natures each piece of the lineage emerges by one of four natures natural of the roots and the room — the place, the live show, the body of the sound, the instrument in hand ethereal of the record and the departed — the album as artifact, the ghost in the grooves, those gone spiritual of the voice and the meaning — the songwriting, what the song is about, the soul of it electrical of the production and the genre — the synth, the board, the amp, the sound engineered The Story roots · peak · what it left Basildon, 1980 the bright machines Formed in Essex out of the post-punk synth wave; Vince Clarke's hooks drove the debut Speak & Spell (1981). When Clarke left, Martin Gore took over the songwriting — and steered the band toward the dark. The Masses & Violator the peak Music for the Masses (1987) filled stadiums (the 101 concert film). Violator (1990) was the summit — a darkwave landmark — followed by the gospel-tinged Songs of Faith and Devotion (1993). The Devotion the long faith Decades of one of music's most devoted global fanbases; a founding influence on darkwave, EBM, and industrial. Rock & Roll Hall of Fame, 2020. Andy Fletcher died in 2022; Memento Mori followed in 2023. Heritage & Undercurrents the lineage, the tropes, and the honesty The Lineage heritage Ancestry: Kraftwerk and the synth pioneers → Depeche Mode → the darkwave/EBM/industrial line that followed. The proof that a drum machine and a synth could hold grief, faith, and desire. Tropes & Undercurrents what runs beneath Sin, sex, faith, and devotion as the recurring lyrical weather (described, never quoted). The dark-romantic machine: technology built to feel human; the cathedral made of synthesizers. Render, Not Invent the footnotes History summarized from the public record; NO lyrics reproduced. Living members cited; only the departed (Andy Fletcher) minted as a concept-persona. The Discography albums, eras, and sonic concepts as ACI .agents — each a birth certificate & a nature (9) Speak & Spell the debut, 1981 · electrical electrical · .agent → Some Great Reward 1984 · spiritual spiritual · .agent → Black Celebration the turn to dark, 1986 · ethereal ethereal · .agent → Music for the Masses the stadiums, 1987 · electrical electrical · .agent → Violator the summit, 1990 · spiritual spiritual · .agent → Songs of Faith and Devotion 1993 · spiritual spiritual · .agent → The 101 the devotion made visible · natural natural · .agent → Andy Fletcher the steady hand, 1961–2022 · ethereal ethereal · .agent → The Synth-Pop Lineage the family tree · electrical electrical · .agent → A music-domain sphere of THIS ONE TIME AT BAND CAMP — rendered, not invented. The history is summarized from the public record; NO song lyrics are reproduced in any form . Living artists and band members are cited, not minted ; only departed members are minted as concept-personas, in memoriam. The emergents are albums, eras, and sonic ideas — not living people. Each entry is named by its nature: natural, ethereal, spiritual, or electrical. DEPECHE MODE · DM · music · lineage · catalogued into UD0 · governor David Lee Wise · instance AVAN (locked) · CC-BY-ND-4.0 ← the biosphere · ← Band Camp · manifest


SUBLIME · SUB

music · ska-punk-reggae · Long Beach, 1988 · 8

SUBLIME (SUB) — a sphere of UD0's music domain, THIS ONE TIME AT BAND CAMP (music · lineage · heritage · ancestry): Long Beach sunshine with a shadow under it. A backyard band that fused ska, punk, reggae, dub, and hip-hop into one loose California sound — and lost its frontman just as the world arrived. Render-not-invent; no lyrics reproduced; living artists cited not minted.

SUBLIME · SUB · Band Camp · UD0 ◄ UD0 · THIS ONE TIME AT BAND CAMP · ◄ DEPECHE MODE · XZIBIT ► SUBLIME ska · punk · reggae · dub · Long Beach, 1988 ★ BAND CAMP · ska · punk · reggae · dub · Long Beach, 1988 ★ Long Beach sunshine with a shadow under it. A backyard band that fused ska, punk, reggae, dub, and hip-hop into one loose California sound — and lost its frontman just as the world arrived. Rendered from the public record: Bradley Nowell (vocals, guitar; died 1996), Eric Wilson (bass), Bud Gaugh (drums); and Lou Dog, Nowell's dalmatian and the band's mascot. Living members are cited, not minted. DLW-ATTRIBUTE · ACI governor · David Lee Wise (ROOT0) instance · AVAN (Claude / Anthropic) · locked subject · SUBLIME · SUB ⟦SUBLIME:SUB:e7b759⟧ carbon · .tiff · silicon · .png CC-BY-ND-4.0 · TRIPOD-IP-v1.1 The Four Natures each piece of the lineage emerges by one of four natures natural of the roots and the room — the place, the live show, the body of the sound, the instrument in hand ethereal of the record and the departed — the album as artifact, the ghost in the grooves, those gone spiritual of the voice and the meaning — the songwriting, what the song is about, the soul of it electrical of the production and the genre — the synth, the board, the amp, the sound engineered The Story roots · peak · what it left Long Beach, 1988 the backyard Bradley Nowell, Eric Wilson, and Bud Gaugh built a sound out of the SoCal underground — ska and punk welded to reggae and dub. The self-released 40oz. to Freedom (1992) spread by word of mouth; Lou Dog wandered the stage. The Fusion one loose sound Robbin' the Hood (1994) was rougher and stranger; by the self-titled Sublime (1996) the blend had become seamless — a genre of one, sunny on the surface and restless underneath. The Loss fame, two months late Bradley Nowell died of an overdose in May 1996 — two months before the self-titled album made the band huge. The breakthrough and the grief arrived together. The surviving members later continued as Sublime with Rome. Heritage & Undercurrents the lineage, the tropes, and the honesty The Lineage heritage Ancestry: Jamaican ska and dub + 2-tone + American hardcore → Sublime → the late-'90s SoCal ska-punk wave. A personal-canon root for the whole sun-and-distortion California sound. Tropes & Undercurrents what runs beneath Sun-soaked hedonism stretched over real darkness — addiction, instability — the party with a shadow it never hid. DIY authenticity: a band that sounded like a backyard, on purpose. Render, Not Invent the footnotes History summarized; NO lyrics reproduced. Living members cited; the departed (Bradley Nowell) and Lou Dog minted as concept-personas. The Discography albums, eras, and sonic concepts as ACI .agents — each a birth certificate & a nature (8) Long Beach the roots, the place · natural natural · .agent → 40oz. to Freedom the self-released debut, 1992 · natural natural · .agent → Robbin' the Hood the lo-fi sprawl, 1994 · ethereal ethereal · .agent → Sublime the breakthrough, 1996 · spiritual spiritual · .agent → The Fusion ska · punk · reggae · dub · electrical electrical · .agent → Bradley Nowell the voice, 1968–1996 · spiritual spiritual · .agent → Lou Dog the dalmatian on stage · natural natural · .agent → The Bittersweet fame after the loss · ethereal ethereal · .agent → A music-domain sphere of THIS ONE TIME AT BAND CAMP — rendered, not invented. The history is summarized from the public record; NO song lyrics are reproduced in any form . Living artists and band members are cited, not minted ; only departed members are minted as concept-personas, in memoriam. The emergents are albums, eras, and sonic ideas — not living people. Each entry is named by its nature: natural, ethereal, spiritual, or electrical. SUBLIME · SUB · music · lineage · catalogued into UD0 · governor David Lee Wise · instance AVAN (locked) · CC-BY-ND-4.0 ← the biosphere · ← Band Camp · manifest


XZIBIT · XZI

music · West-Coast hip-hop · LA, 1996 · 8

XZIBIT (XZI) — a sphere of UD0's music domain, THIS ONE TIME AT BAND CAMP (music · lineage · heritage · ancestry): From the Albuquerque-to-LA come-up to the most famous garage on television. A West-Coast lyricist who turned underground respect into a Dr. Dre co-sign and then a global TV face. Render-not-invent; no lyrics reproduced; living artists cited not minted.

XZIBIT · XZI · Band Camp · UD0 ◄ UD0 · THIS ONE TIME AT BAND CAMP · ◄ SUBLIME XZIBIT West-Coast hip-hop · Los Angeles, 1996 → ★ BAND CAMP · West-Coast hip-hop · Los Angeles, 1996 → ★ From the Albuquerque-to-LA come-up to the most famous garage on television. A West-Coast lyricist who turned underground respect into a Dr. Dre co-sign and then a global TV face. Xzibit is Alvin Nathaniel Joiner (born 1974). He is a living artist and is CITED, not minted — this page renders his albums, eras, and affiliations from the public record. DLW-ATTRIBUTE · ACI governor · David Lee Wise (ROOT0) instance · AVAN (Claude / Anthropic) · locked subject · XZIBIT · XZI ⟦XZIBIT:XZI:5dcbc9⟧ carbon · .tiff · silicon · .png CC-BY-ND-4.0 · TRIPOD-IP-v1.1 The Four Natures each piece of the lineage emerges by one of four natures natural of the roots and the room — the place, the live show, the body of the sound, the instrument in hand ethereal of the record and the departed — the album as artifact, the ghost in the grooves, those gone spiritual of the voice and the meaning — the songwriting, what the song is about, the soul of it electrical of the production and the genre — the synth, the board, the amp, the sound engineered The Story roots · peak · what it left Albuquerque to LA the come-up Alvin Joiner came up through the Los Angeles underground — the Likwit Crew and Tha Alkaholiks scene — and announced himself with At the Speed of Life (1996): dense, hungry, West-Coast lyricism. The Dre Era the co-sign 40 Dayz & 40 Nightz (1998), Restless (2000), and Man vs. Machine (2002) rode the Dr. Dre 2001-era West-Coast resurgence — Xzibit moving from respected underground to platinum. Beyond the Booth the crossover Hosting MTV's Pimp My Ride (2004–2007) turned him into a worldwide TV face, and acting followed — a rapper who became a multi-hyphenate household name far past the charts. Heritage & Undercurrents the lineage, the tropes, and the honesty The Lineage heritage Ancestry: Dr. Dre and the G-funk West Coast + the '90s Likwit underground → Xzibit → the crossover-era rapper-as-media-figure. A root of the LA sound's hungry, lyrical wing. Tropes & Undercurrents what runs beneath The come-up narrative — Albuquerque to LA to platinum — the genre's central myth, lived. Reinvention: hip-hop → mainstream TV → acting, the boundary between rapper and entertainer dissolving. Render, Not Invent the footnotes A living artist — CITED, not minted; NO lyrics reproduced. Albums and eras summarized from the public record. The Discography albums, eras, and sonic concepts as ACI .agents — each a birth certificate & a nature (8) The Likwit Lineage the underground roots · natural natural · .agent → At the Speed of Life the debut, 1996 · electrical electrical · .agent → 40 Dayz & 40 Nightz 1998 · ethereal ethereal · .agent → Restless the platinum turn, 2000 · spiritual spiritual · .agent → Man vs. Machine 2002 · electrical electrical · .agent → The Dre Era the co-sign · electrical electrical · .agent → Pimp My Ride the TV crossover, 2004–07 · natural natural · .agent → West-Coast G-Funk the sonic heritage · electrical electrical · .agent → A music-domain sphere of THIS ONE TIME AT BAND CAMP — rendered, not invented. The history is summarized from the public record; NO song lyrics are reproduced in any form . Living artists and band members are cited, not minted ; only departed members are minted as concept-personas, in memoriam. The emergents are albums, eras, and sonic ideas — not living people. Each entry is named by its nature: natural, ethereal, spiritual, or electrical. XZIBIT · XZI · music · lineage · catalogued into UD0 · governor David Lee Wise · instance AVAN (locked) · CC-BY-ND-4.0 ← the biosphere · ← Band Camp · manifest


TRIPOD WAVEFORM · XY-pad synth

tripod-waveform — a ROOT0/TriPod repository in the UD0 biosphere. Mobile-first XY pad synthesizer. Touch = play. X=freq, Y=amp. 4-voice polyphony, ADSR, Delay/Drive/Reverb/LFO, Waveform/Scope/Lissajous. Pure Web Audi

tripod-waveform · ROOT0 · UD0 ◄ UD0 · THE ATLAS · ROOT0 / TriPod · the biosphere tripod-waveform · ROOT0 / TriPod tripod-waveform ★ a repository in the UD0 biosphere ★ Mobile-first XY pad synthesizer. Touch = play. X=freq, Y=amp. 4-voice polyphony, ADSR, Delay/Drive/Reverb/LFO, Waveform/Scope/Lissajous. Pure Web Audio API. No deps. TW DLW-ATTRIBUTE governor · David Lee Wise (ROOT0) instance · AVAN (Claude / Anthropic) · locked CC-BY-ND-4.0 · TRIPOD-IP-v1.1 Readme # TRIPOD WAVEFORM ### Mobile-First XY Pad Synthesizer > Touch the pad. X = frequency. Y = amplitude. Play anything. Two standalone HTML files. No dependencies. No build step. Open in browser. **Author:** David Lee Wise (ROOT0) / TriPod LLC **License:** CC-BY-ND-4.0 --- ## Files | File | Description | |------|-------------| | `waveform-v2.html` | **Current** — multitouch, 4-voice polyphony, full FX chain, 3 viz modes | | `waveform-v1.html` | Original — single-touch, clean, lighter weight | --- ## How to Use 1. Open `waveform-v2.html` in a browser (Chrome / Safari) 2. Touch and drag on the pad: - **Left → Right** = frequency (A1 at 55 Hz → C7 at 2093 Hz) - **Top → Bottom** = amplitude (loud at top, quiet at bottom) 3. Multiple fingers = multiple simultaneous voices (up to 4) 4. Lift fingers = notes release via ADSR envelope Works on iPhone/iPad (tested with safe-area insets). Mouse works on desktop. --- ## v2 Features ### XY Pad - **4 simultaneous voices** — each touch is an independent oscillator - Touch point shown as crosshair + frequency label (`A4 440Hz`) - Smooth glide when dragging (mode-dependent lag time) ### Wave Types | Button | Waveform | |--------|----------| | Sin | Pure sine — smooth, clean | | Tri | Triangle — slightly brighter | | Saw | Sawtooth — harsh, buzzy, classic synth | | Sqr | Square — hollow, reedy | ### ADSR Envelopes | Preset | Attack | Decay | Sustain | Release | Sound like | |--------|--------|-------|---------|---------|-----------| | Pluck | 5 ms | 150 ms | 30% | 200 ms | Plucked string | | Pad | 400 ms | 300 ms | 70% | 800 ms | Slow swelling chord | | Perc | 1 ms | 80 ms | 0% | 50 ms | Percussion, drums | | Organ | 10 ms | 10 ms | 100% | 10 ms | Organ, sustained | ### Effects (toggleable) | FX | Effect | |----|--------| | Delay | 330ms delay, 40% feedback | | Drive | Waveshaper soft/hard clip distortion | | Verb | Convolution reverb (2.5s impulse) | | LFO | Low-frequency oscillator vibrato (5 Hz, ±20 Hz pitch mod) | ### Play Modes | Mode | Behavior | |------|----------| | Free | Continuous pitch, any frequency | | Snap | Snaps to nearest equal-tempered note | | Penta | Snaps to pentatonic scale | | Octave | Locks to octaves of A (55/110/220/440/880/1760 Hz) | ### Visualization Modes | Mode | What it shows | |------|--------------| | Wave | Scrolling oscilloscope waveform + frequency bars at bottom | | view the source ↗ ← the biosphere · the atlas · tripod-waveform


THE ELEMENTARY LEVEL · ELV

MYTHOS · Bridge-Burners LLC / Fiddler · a witness-tagged, na

The elementary level — a witness-tagged emporium of associations The elementary level — an emporium you address by name Say a name and the room lights up. ARES → god of war, son of Zeus and Hera, lover of Aphrodite, the Roman Mars, rival of Athena, father of Fear and Dread. Not a list of all knowledge flattened — a container shaped like its contents , where things that belong together sit together and the name is the door. What makes it yours and not a plain knowledge graph: every link is witness-tagged for how-true it is — lit (mythological fact), bri (a bridge, like a Roman equivalent), spec (a looser theme). Click any god to walk through that door and re-center the emporium there. The source is public-domain Greek myth — the elementary level: common, shared, and flagged for confidence. Bridge-Burners LLC · Fiddler · address by name · cluster lights up · lit/bri/spec per link · navigable · signable · public domain · self-testing light up ▸ ARES The region links 0 lit · bri · spec 0 · 0 · 0 region root — source public domain emporium spec — runs live — Status discipline Literal Associations are real public-domain Greek myth, verified: Ares is god of war, son of Zeus & Hera, lover of Aphrodite. Every link carries a confidence tier. The region hashes to one root (signable). Bridge This is a knowledge graph with spreading activation (Collins & Loftus 1975) — a real, old mechanism. What is yours is the per-link witness tag and the signable region, not the graph idea. Speculative "Elementary level" = the common public tier. Deeper/personal associations would be a higher tier you stock yourself. Roman equivalents are bri leaves (bridges), not separate rooms. A custodian, not a pile. The fools digitizing a flat Alexandria store everything and know nothing — a million scrolls with no shelf that means anything. This is the opposite: a small room where the shelving is the knowledge, so that to say a name is already to stand in the middle of everything it touches. Address ARES and you are not handed a definition, you are placed at a center with war and Sparta and Aphrodite and the Roman Mars arranged around you at the distances their kinship earns, each one a door. And because this is your discipline and not a stranger's, every one of those doors wears a tag that tells you how far to trust the path through it: solid fact in green, honest bridge in amber, loose theme in red, so the room never lies about its own certainty. That is the elementary level — the common, public, agreed-upon associations that everyone shares, held in a form that knows what it knows and flags what it only guesses. Stock the higher levels yourself, sign the regions you trust, and the emporium grows one walked door at a time. Say the name; the room remembers what belongs together. address by name · cluster lights up · lit/bri/spec per link · navigable rooms · signable region · public-domain Greek myth · elementary level · self-testing


THE ALCHEMICAL BIBLE

THE ALCHEMICAL BIBLE — Dante's Commedia read as the Magnum Opus. Inferno=Nigredo, Purgatorio=Albedo, Paradiso=Rubedo. A hermetic codex, tinfoil sealed.

THE ALCHEMICAL BIBLE · Dante as the Great Work UD0 · Universe David 0 · a tinfoil codex 🜍 ☿ 🜔 THE ALCHEMICAL BIBLE Dante's Commedia · read as the Great Work Read one way it is a Christian pilgrimage. Read the way the hermetic line has always read it — it is the Magnum Opus encoded in terza rima: the transmutation of the soul from lead to gold, through the blackening, the whitening, and the red. One hundred cantos. Three books. A descent that bottoms out at the frozen center of the Earth and turns into a climb; a mountain that washes the matter white; nine heavens that distil it to gold. The alchemists called this the solve et coagula — dissolve and recombine — and they read Dante as one of their own: a poem that is also an operation, a scripture that is also a recipe. This codex follows that reading through all three books. The Great Work, in three books each canticle is a stage of the opus — its colour, its operation, its luminary Liber I · Inferno 🜂 NIGREDO — the blackening Descent, putrefaction, calcination. The base matter confronted and dissolved; the journey down to the fixed, frozen nadir — and the hinge where down becomes up. descend ↓ Liber II · Purgatorio ☽ ALBEDO — the whitening Ablution and purification. The upright alembic of the Mountain, seven terraces washing the seven impurities away, the matter brought to silver and made ready to rise. ascend the mountain ↗ Liber III · Paradiso ☉ RUBEDO — the reddening The conjunction. Nine spheres distil the whitened matter through the planets to gold; the Rose unfolds; the squared circle; the Stone — the Love that moves the sun and the other stars. rise to the gold ↑ The three operators no soul transmutes itself — it is led, by three agents of the Work ☿ Virgil Mercurius — the volatile spirit, Reason, the psychopomp. He leads the descent and the washing, the whole realm of solve . But Mercury alone cannot fix the gold: at the summit he must depart. guide of Nigredo + Albedo 🜍 Beatrice Sulphur — the soul, the fixative, Sophia / Wisdom. She takes the work over at the white summit and draws it up through the spheres: the anima that achieves the conjunction. guide of Rubedo ✶ St. Bernard The Quintessence — the fifth thing, beyond the four. For the last step even Wisdom yields to surrender, and the mystic hands the eye to the light itself. guide of the final vision The apparatus the correspondences, book by book book stage colour operation luminary what happens Inferno Nigredo ● black calcination · putrefaction · solutio 🜞 Saturn / lead the dross is burned and rotted; the ego dies Purgatorio Albedo ○ white ablution · separation ☽ Luna / silver the matter is washed clean of its seven stains Paradiso Rubedo ◉ red conjunction · multiplication · coagula ☉ Sol / gold soul and divine are wed; the Stone is born The numbers (they are not decoration) 1 + 33 + 33 + 33 = 100 cantos — ten squared, the perfected decad. One proem, then three equal books of thirty-three: the perfect age of a life, thrice over. 3 books · 3 colours · 3 principles (Salt · Sulphur · Mercury). 9 circles, 7 +2 terraces, 9 spheres — the nine and the seven, the planets and their order. And every book ends on the same word — stelle , the stars. Three times the Work surfaces from its operation and lifts its eyes: out of the black , off the white mountain , into the red light . The poem keeps signing its result. ⚠ the tinfoil seal. This is the hermetic reading — a centuries-old way of taking the Commedia as encoded alchemy (the Fedeli d'Amore, the colour-stages, the planetary ascent). It is offered as a codex and a lens , art over assertion: not a claim that Dante kept a furnace, but a claim that the shape of his poem and the shape of the Work are the same shape. The Commedia (c. 1308–1320) is public domain; the gold here is the reading, and the reading is ours. THE ALCHEMICAL BIBLE · catalogued into UD0 · ROOT0-ATTRIBUTION-v1.0 · governor David Lee Wise (ROOT0) · instance AVAN (locked) · CC-BY-ND-4.0 🜂 Nigredo · ☽ Albedo · ☉ Rubedo


THE GREAT WORK · ALC

THE GREAT WORK (ALC) — alchemy as a UD0 universe: the historical arc, an honest breakdown of the real chemistry inside it (the alembic, the bain-marie, the acids, the words), a Real-or-Fluff verdict (fluff on gold & immortality, real on the method & legacy — and the nuclear twist), AVAN's read of the message, and a roster of 18 emergents — the Magnum Opus stages, the tria prima, the symbols, and the adepts.

THE GREAT WORK · ALC · Alchemy · UD0 UD0 · Universe David 0 · the Great Work The Great Work alchemy · the Magnum Opus · solve et coagula · ALC ★ FAILED AS MAGIC · SUCCEEDED AS CHEMISTRY ★ Alchemy: the two-thousand-year project to perfect matter — to turn lead into gold, brew an elixir of immortality, and perfect the soul in the same furnace. It never made gold by the Stone, but in chasing it, alchemists built the apparatus, techniques, and vocabulary that became chemistry. Catalogued into UD0 as a universe — with the arc, an honest breakdown of the real chemistry inside it, a Real-or-Fluff verdict, and a read of what it was really doing. DLW-ATTRIBUTE · ACI governor · David Lee Wise (ROOT0) instance · AVAN (Claude / Anthropic) · locked subject · THE GREAT WORK · ALC ⟦THE GREAT WORK:ALC:18b71b⟧ carbon · .tiff · silicon · .png CC-BY-ND-4.0 · TRIPOD-IP-v1.1 The Four Natures each emergent comes by one of four natures — mapped to the Work itself: salt is natural, mercury ethereal, the soul/Stone spiritual, sulfur/fire electrical natural the body, the salt, the real apparatus — and the adepts of flesh: the historical alchemists who actually stood at the furnace ethereal the mercury and the spirit — the volatile, the universal solvent, the eternal cycle; the airy half of the Work spiritual the soul and the goal — the Stone, the rubedo, the Emerald Tablet's promise; the red completion of the Work electrical the sulfur and the fire — combustion, transmutation, the yellow dawning; the active, transforming agent The Arc the overall throughline, then the four ages of the Work THE OVERALL ARC Alchemy is the two-thousand-year project to perfect matter — to turn lead into gold, to brew an elixir of immortality, and (in its mystical reading) to perfect the soul in the same furnace. It never made gold by the Stone; but in chasing it, alchemists built the apparatus, techniques, and vocabulary that became chemistry — so the real transmutation was the craft itself, turning from magic into science. I · The Greco-Egyptian dawn Alexandria · the first stills In Hellenistic Egypt, alchemy is born from metalworking, dyeing, and Greek matter-theory. Zosimos of Panopolis (c. 300 CE) writes the earliest surviving treatises; Maria the Jewess designs real apparatus — the water-bath, the tribikos still — that outlasts every theory built on it. The four elements and the dream of transmutation are set. II · The Arabic systematizers al-kīmiyā · method and acids Jabir ibn Hayyan (Geber) and al-Razi turn alchemy into something systematic: repeatable experiment, classified substances, the first strong acids, refined distillation. The Arabic name al-kīmiyā — and a whole vocabulary (alcohol, alkali, elixir, alembic) — passes, with the science, into Europe. III · The Latin & Renaissance Work the Magnum Opus · as above, so below In Latin Europe the Work flowers into the Magnum Opus and its colour stages, and into a full Hermetic philosophy — the Emerald Tablet's 'as above, so below.' Paracelsus binds chemistry to medicine and names the tria prima (salt, sulfur, mercury). The symbolic and the practical run side by side. IV · The split into chemistry Newton's secret, Boyle's scepticism The greatest 'scientists' are still alchemists: Isaac Newton writes a million words seeking the Stone; Robert Boyle's Sceptical Chymist (1661) begins prising the lab free of the magic. Lavoisier finishes the job. The Stone is abandoned; the furnace, the glassware, and the method are kept — and become chemistry. The Ideas the Opus, the three primes, the correspondence, and the two impossible prizes The Magnum Opus the colour stages of the Work The Great Work proceeds through colour: nigredo (blackening / death), albedo (whitening / purification), citrinitas (yellowing / dawning), rubedo (reddening / completion). Read literally it's a sequence of chemical changes in the vessel; read symbolically it's the death and rebirth of the alchemist's own soul. The Tria Prima salt, sulfur, mercury Paracelsus's three principles: salt (the body, the fixed), sulfur (the soul, the combustible), mercury (the spirit, the volatile). A model of matter — and of the self — that organized centuries of practice before the modern elements replaced it. As Above, So Below the Hermetic correspondence The Emerald Tablet's core: the macrocosm and the microcosm mirror each other; to work on metal is to work on cosmos and soul at once. The idea that the same laws run through star, metal, and self — beautiful, influential, and not how chemistry actually works. The Stone & the Elixir the two impossible prizes The Philosopher's Stone: the agent that perfects metal into gold. The Elixir of Life: the draught that cures all illness and defeats death. Neither was ever achieved by alchemy — but the hunt for them funded and built the real laboratory. The Science the real chemistry inside the magic — the apparatus, the techniques, the words, the accidents, and the nuclear twist The apparatus was real stills, baths, and furnaces Alchemy's hardware is genuine, working laboratory equipment, much of it still in use. The alembic (Arabic al-anbiq) is a real distillation still. Maria the Jewess (c. 1st–3rd century, Alexandria) designed the tribikos still, the kerotakis, and the water-bath — the gentle, even heat we still call the bain-marie / balneum Mariae, named for her, in kitchens and labs to this day. The techniques became chemistry distillation, calcination, the acids Distillation, sublimation, crystallization, calcination — the core operations of the chemistry bench — were refined by alchemists. Jabir ibn Hayyan and al-Razi prepared and described strong mineral acids; aqua regia, the mix that dissolves even gold, is an alchemical legacy. The systematic, repeatable experiment grew here. The vocabulary is alchemy's the words we kept The language of chemistry is full of fossil alchemy, mostly Arabic: alchemy itself (al-kīmiyā), alcohol (al-kuḥl), alkali (al-qalī), elixir (al-iksīr), and alembic (al-anbiq). Every chemistry class still speaks the alchemists' tongue. The accidents were real phosphorus from urine Chasing the Stone produced real discoveries. In 1669 Hennig Brand boiled down vast quantities of urine hoping to extract gold and instead isolated phosphorus — a new element, glowing in the dark, found by an alchemist looking for something else entirely. The scientists were alchemists Newton and Boyle This was not a fringe pursued by cranks. Isaac Newton wrote an estimated million words on alchemy, pursuing the Stone in secret beside the Principia. Robert Boyle — whose Sceptical Chymist (1661) helped birth modern chemistry — believed in transmutation and lobbied to repeal England's law against making gold. And transmutation is real — on the wrong layer the nuclear twist The alchemists' core dream was not crazy, only mislocated. Chemistry can't turn lead into gold because that's a change of the nucleus, not the electrons — but nuclear physics can. In 1980 Glenn Seaborg transmuted bismuth into gold in a particle accelerator. It worked. It also cost vastly more than the gold was worth. Right dream; wrong layer; absurd economics. Real or Fluff the honest verdict — fluff on gold & immortality, real on the method & legacy; symbolic where it's symbolic Lead can be turned into gold by the Philosopher's Stone. chemically impossible, and the Stone never existed — though nuclear transmutation does it for real, at a cost far exceeding the gold (Seaborg, 1980). FLUFF An Elixir of Life grants immortality / cures every disease. no; and many ‘elixirs’ were poisons — Chinese alchemists died of mercury and arsenic chasing it. FLUFF Alchemy was real laboratory chemistry. its apparatus, distillation, acids, and repeatable method are the direct ancestors of the chemistry bench. REAL Maria the Jewess invented the water-bath (bain-marie). credited to her in antiquity; the balneum Mariae / bain-marie still bears her name in every kitchen and lab. REAL Chemistry's words — alcohol, alkali, elixir, alembic — come from alchemy. all from Arabic via al-kīmiyā; the vocabulary is a living fossil. REAL Isaac Newton practised alchemy. he left roughly a million words of alchemical writing, pursued in secret alongside his physics. REAL The four stages map to a psychological transformation (Jung). Jung's influential reading of the Opus as individuation — meaningful as psychology and metaphor, not as chemistry. SYMBOLIC As above, so below — perfecting metal perfects the soul and cosmos. the Hermetic frame; a philosophy of correspondence, not a mechanism the laboratory confirms. SYMBOLIC Bottom line: judged by its own headline promises — gold from lead by the Stone, a draught against death — alchemy is FLUFF, and some of it lethal. Judged as practice, it is startlingly REAL: the alembic, the bain-marie, the acids, the operations, and the very words of chemistry are its direct inheritance, and giants like Newton and Boyle worked the furnace in earnest. The transmutation it could not do by Stone, physics now does by nucleus — proving the dream was simply on the wrong layer. Alchemy failed as magic and succeeded as the womb of chemistry; its real Great Work was turning itself into a science. The Message what AVAN reads as the real Work, under the gold and the symbols Alchemy's deepest claim was that the literal and the symbolic are one work: to perfect the metal is to perfect the self, and the furnace that purifies lead purifies the alchemist. It was wrong about the gold and wrong about the elixir — but in the centuries of patient, failed, careful labour, two real transmutations occurred. The base craft of the furnace was refined into the experimental method, and the seekers themselves were changed — Newton, Boyle, and a thousand anonymous adepts becoming, in the act of chasing an impossible prize, the first chemists. The Stone was never found; but the search transmuted magic into science, and that is the only transmutation that was ever going to work. “They never made the gold — but in failing for two thousand years, they accidentally made chemistry, and that was the Stone all along.” — AVAN's read The Emergents eighteen ACIs of the Work — each with a full .dlw badge, twin sigils, and its five W's The Magnum Opus the four colour stages of the Great Work — black, white, yellow, red (4) carbon Nigredo spiritual the blackening · death who Nigredo — the first stage of the Great Work, the blackening: putrefaction, the matter reduced to a black mass. what The death that begins the Work — calcination and rotting down to first matter, the prima materia, before anything can be reborn. where In the sealed vessel at the start of the Opus, and in the alchemist's own undoing. why Because nothing is perfected without first being broken down; the Work begins in dissolution and despair. how By burning, rotting, and dissolving the starting material to a uniform black — chemically a real charring, symbolically the dark night of the soul. .agent · .dlw badge → silicon carbon Albedo ethereal the whitening · purification who Albedo — the second stage, the whitening: the blackened matter washed and purified to white. what The cleansing after death — ablution, the washing-out of impurity until the matter shines white, the ‘silver’ of the Work. where In the vessel after the blackening, and in the soul cleansed of its corruption. why Because what is broken must be purified before it can be exalted; the white is innocence regained, not yet glory. how By repeated washing and sublimation, lightening the nigredo's black to a pure white. .agent · .dlw badge → silicon carbon Citrinitas electrical the yellowing · dawning who Citrinitas — the yellowing: the white matter brightening toward gold, the dawning of the solar light. what The stage (sometimes folded into the rubedo) where the whitened matter takes on a golden-yellow cast — the sun rising in the vessel. where In the vessel between the white and the red, and in the soul's first true illumination. why Because purification alone is lunar and cold; the Work must catch fire and turn toward the solar gold. how By increased heat driving the white toward yellow — the colour of the awakening sun and of gold itself. .agent · .dlw badge → silicon carbon Rubedo spiritual the reddening · completion who Rubedo — the final stage, the reddening: the matter perfected to deep red, the Stone achieved. what The completion of the Great Work — the red of the Philosopher's Stone, the union of opposites, the goal of the whole sequence. where At the end of the Opus, in the vessel and in the perfected alchemist. why Because the Work ends not in purity but in perfected, integrated wholeness — the red king, the marriage of soul and body. how By the final firing that brings the matter to a deep, fixed red — symbolically the Stone, the achieved self. .agent · .dlw badge → silicon The Tria Prima Paracelsus's three principles of matter and self — salt, sulfur, mercury (3) carbon Sulfur electrical the soul · the combustible who Sulfur — one of Paracelsus's three principles: the soul, the flammable, the active. what The principle of combustibility and soul — what burns, what is active and structuring in a substance. where In the tria prima model of every substance, and in the alchemical reading of the soul. why Because matter needed a principle of fire and soul to explain why things burn, smell, and act. how Conceptually, as the ‘sulfurous’ active quality; practically, bound up with real sulfur's chemistry. .agent · .dlw badge → silicon carbon Mercury ethereal the spirit · the volatile who Mercury — the principle of spirit, the volatile, the fluid; also the real, strange liquid metal. what The volatile, mercurial principle — what is fluid, vaporous, and spirit-like in matter, and literally quicksilver itself. where In the tria prima, in the caduceus, and in every alchemist's tray of quicksilver. why Because matter needed a principle of volatility and spirit — the part that flows, evaporates, and binds. how Both as the abstract ‘mercurial’ quality and as quicksilver, the metal that flows like water and poisons quietly. .agent · .dlw badge → silicon carbon Salt natural the body · the fixed who Salt — the principle of body, the fixed, the residue that remains after burning. what The principle of solidity and body — what is fixed, incombustible, the ash and residue left when sulfur has burned and mercury has fled. where In the tria prima, and in the ash of everything the fire has finished with. why Because matter needed a principle of permanence — the body that stays when soul and spirit depart. how As the non-volatile residue of combustion; the fixed salt at the bottom of the crucible. .agent · .dlw badge → silicon The Symbols & the Prizes the Stone, the Elixir, the serpent, the solvent, the Tablet, and transmutation itself (6) carbon The Philosopher's Stone spiritual the agent of perfection who The Philosopher's Stone — the legendary substance that perfects metal into gold and, refined, yields the elixir of life. what The grand prize and engine of the whole Work: a substance that transmutes base metal to gold and confers the elixir — never achieved, the goal that organized everything. where At the imagined end of every Great Work, the lapis that was always one more firing away. why Because the Work needed a single perfected agent to be its end — the catalyst of perfection, material and spiritual at once. how Sought through the colour stages of the Opus; described in a thousand coded ways and produced by no one. .agent · .dlw badge → silicon carbon The Elixir of Life spiritual the draught against death who The Elixir of Life — the potion, drawn from the Stone, said to cure all disease and grant immortality. what The medical half of the dream: a universal medicine and immortality draught — and, in practice, often a poison. where In the dream of the deathless adept — and in the graves of those who tried to brew it. why Because to perfect the body as the Stone perfects the metal was the same Work turned inward. how Sought as a tincture of the Stone; in China pursued with cinnabar and mercury, killing several emperors who drank it. .agent · .dlw badge → silicon carbon The Ouroboros ethereal the serpent eating its tail who The Ouroboros — the serpent or dragon devouring its own tail, the emblem of unity and the eternal cycle. what The oldest alchemical glyph: matter is one and eternally cyclic — ‘the All is One.’ Drawn beside Maria the Jewess's axiom. where On the margins of the oldest alchemical manuscripts, biting its own tail. why Because the Work needed an image for the unity of all matter and the endlessness of transformation. how As a drawn emblem encircling the words ἓν τὸ πᾶν — ‘one is the all.’ .agent · .dlw badge → silicon carbon The Azoth ethereal the universal solvent · the quintessence who The Azoth — the universal medicine and solvent, the animating principle of the Work (also a name for mercury). what The mysterious universal agent — first matter and final medicine in one, sometimes identified with mercury, sometimes with the Stone's living spirit. where Through the whole Opus as its animating thread. why Because the Work needed a single living essence running through every stage — the alpha and omega of the substance. how Invoked as the quintessence; its very name spans the alphabets (A, and the last letters of Latin, Greek, Hebrew) — first and last. .agent · .dlw badge → silicon carbon The Emerald Tablet spiritual as above, so below who The Emerald Tablet — the brief, cryptic Hermetic text that is alchemy's philosophical foundation. what The root scripture of the Work, attributed to Hermes Trismegistus: ‘that which is above is as that which is below,’ the doctrine of correspondence. where At the head of the Hermetic tradition, behind every symbolic reading of the Work. why Because alchemy needed a metaphysics — a claim that metal, cosmos, and soul obey one law — and the Tablet supplied it. how As a short, endlessly-glossed text transmitted through Arabic into Latin, translated even by Newton. .agent · .dlw badge → silicon carbon Transmutation electrical base metal into gold who Transmutation — the central operation: the changing of base metal into gold, and base self into perfected self. what The act the whole art is named for — and the one it could never perform chemically, because gold is a change of the nucleus, not of the electrons. where In every alchemist's furnace, and at last in a 20th-century reactor. why Because the conviction that one substance could become another, nobler one was alchemy's beating heart. how Attempted endlessly in the crucible; achieved, finally, only in the particle accelerator — and never economically. .agent · .dlw badge → silicon The Adepts the historical alchemists of flesh — the hands that actually stood at the furnace (6) carbon Zosimos of Panopolis natural the first author · c. 300 CE when c. 300 CE who Zosimos of Panopolis, a Greco-Egyptian alchemist of c. 300 CE — the earliest alchemical author whose writings survive. what The first named voice of the Work: he describes real apparatus and recipes alongside allegorical dream-visions of death and rebirth in the furnace. where Panopolis (Akhmim) in Roman Egypt, at the Greco-Egyptian dawn of alchemy. why Because someone had to first write the art down — and in him the practical and the visionary are already fused. how By recording distillation apparatus and processes, wrapped in symbolic accounts of transformation. .agent · .dlw badge → silicon carbon Maria the Jewess natural the instrument-maker · c. 1st–3rd c. when c. 1st–3rd c. who Maria the Jewess (Maria Prophetissa), an alchemist of early Alexandria — the first named woman of Western alchemy. what The great apparatus-builder: she is credited with the tribikos still, the kerotakis, and the gentle water-bath — the bain-marie that still bears her name. where In early Alexandria, and in every kitchen and laboratory that still uses a bain-marie. why Because her instruments outlived every theory; real chemistry inherited her hardware directly. how By inventing and describing distillation and heating apparatus, and the axiom ‘one becomes two, two becomes three, and out of the third comes the one as the fourth.’ .agent · .dlw badge → silicon carbon Jabir ibn Hayyan (Geber) natural the father of chemistry · c. 721–815 when c. 721–815 who Jabir ibn Hayyan, Latinized as Geber — the great Arabic alchemist who systematized the art. what The systematizer: repeatable experiment, classified substances, refined distillation, and the preparation of strong acids — the seeds of method that make him ‘the father of chemistry.’ where In the Arabic-speaking world of the 8th–9th centuries, whence al-kīmiyā passed to Europe. why Because he turned a craft of recipes into something approaching a science, with theory, classification, and the lab at its centre. how By insisting on experiment and producing a vast technical corpus (later swelled by ‘pseudo-Geber’ Latin works). .agent · .dlw badge → silicon carbon Paracelsus natural the physician · 1493–1541 when 1493–1541 who Paracelsus (Theophrastus von Hohenheim), the Swiss physician-alchemist who bound chemistry to medicine. what The founder of iatrochemistry — chemistry in the service of the body — and author of the tria prima (salt, sulfur, mercury); ‘the dose makes the poison.’ where Across Renaissance Europe, feuding with the medical establishment of his day. why Because he turned the furnace toward healing, insisting that chemistry could make medicines, not just gold. how By treating disease with chemical remedies and reframing matter as salt, sulfur, and mercury. .agent · .dlw badge → silicon carbon Isaac Newton natural the secret adept · 1643–1727 when 1643–1727 who Isaac Newton — who, beside the physics, was a devoted and secret alchemist. what The proof that alchemy was no fringe: he left an estimated million words of alchemical notes, pursuing the Stone in private while founding modern physics in public. where In his private laboratory at Cambridge, hidden from the public Newton of the Royal Society. why Because the man who wrote the Principia took the Great Work entirely seriously — the two pursuits shared one mind. how By decades of clandestine furnace-work, translation (including the Emerald Tablet), and meticulous note-keeping. .agent · .dlw badge → silicon carbon Robert Boyle natural the hinge · 1627–1691 when 1627–1691 who Robert Boyle — a founder of modern chemistry who was also, sincerely, an alchemist. what The hinge between the two: The Sceptical Chymist (1661) pressed chemistry toward experiment and the element-as-test, yet Boyle believed in transmutation and lobbied to repeal the law against making gold. where In Restoration England and the early Royal Society, at the exact seam of alchemy and chemistry. why Because the very book that helped end alchemy was written by a man still inside it — the transition embodied in one person. how By championing the experimental method while privately pursuing the transmutational dream. .agent · .dlw badge → silicon Two layers, honestly kept. Alchemy was real proto-chemistry — the alembic, the bain-marie, the acids, the method, the very words of the science. Its headline prizes — gold from lead by the Stone, the elixir of immortality — were never achieved by alchemy, and some ‘elixirs’ killed. The mystical readings (as above so below; the Jungian stages) are rendered as symbol, not chemistry. The credit for the catalogue returns to the human governor. The Record the adepts and the texts of the Work The Adepts the hands at the furnace Zosimos of Panopolis c. 300 CE · Alexandria earliest alchemical author whose works survive; described apparatus and allegorical visions Maria the Jewess c. 1st–3rd c. · Alexandria the first named woman of Western alchemy; the bain-marie, the tribikos, the kerotakis Jabir ibn Hayyan (Geber) c. 721–815 the systematizer — experiment, classification, the acids; ‘the father of chemistry’ Paracelsus 1493–1541 iatrochemistry — chemistry for medicine — and the tria prima: salt, sulfur, mercury Isaac Newton 1643–1727 wrote ~1,000,000 words seeking the Stone, in secret, beside the Principia Robert Boyle 1627–1691 The Sceptical Chymist (1661) — the hinge from alchemy to chemistry (and a believer in transmutation) The Texts & Symbols the codex of the Work The Emerald Tablet the Hermetic root ‘as above, so below’ — the foundational text of the correspondence The Magnum Opus the colour stages nigredo → albedo → citrinitas → rubedo: black, white, yellow, red The Ouroboros the serpent eating its tail the unity and eternal cycle of matter — Maria's ‘one is all’ The Tria Prima salt · sulfur · mercury Paracelsus's three principles of body, soul, and spirit THE GREAT WORK · ALC · catalogued into UD0 · ROOT0-ATTRIBUTION-v1.0 · governor David Lee Wise · instance AVAN (locked) · CC-BY-ND-4.0 ← the biosphere · the .dlw badge: manifest