Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx agentmods add skills/kunitoki/sonic-skills/audio-math-explainernpx skills add kunitoki/sonic-skills --skill audio-math-explainergit clone --depth 1 https://github.com/kunitoki/sonic-skillsWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/kunitoki/sonic-skills/audio-math-explainer)<a href="https://agentmods.dev/skills/kunitoki/sonic-skills/audio-math-explainer"><img src="https://agentmods.dev/badge/skills/kunitoki/sonic-skills/audio-math-explainer.svg" alt="Measured on agentmods" height="20"></a>What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5 | $0.00121 | $0.00789 |
| Opus 5 | $0.00060 | $0.00394 |
| Sonnet 5 | $0.00024 | $0.00158 |
| Haiku 4.5 | $0.00012 | $0.00079 |
Grade A, and why
audio-math-explainer scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 3d ago.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
How it starts
The opening of the file, as written. The whole thing — 75 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Audio Math Explainer
The rule: DSP math is small and composable — each concept builds directly on the last. Start with what the user needs, then connect it to code they're writing.
Step 1 — Identify the concept
| Topic | Core idea | Common "why" |
|---|---|---|
| Fourier transform / DFT / FFT | Decompose signal into frequency components | "Why does my FFT output look wrong?" |
| Convolution | Weighted moving average; LTI system response | "How does an IR reverb work?" |
| Z-transform | Frequency-domain analysis of discrete systems | "How do filter poles/zeros work?" |
| Biquad / IIR filters | Recursive difference equation with feedback | "Why does my filter ring / go unstable?" |
| FIR filters | Non-recursive weighted sum | "How do I design a linear-phase filter?" |
| Windowing | Reduce spectral leakage in DFT | "Why are FFT edges smeared?" |
| Sample rate / Nyquist | Highest representable frequency = sr/2 | "What causes aliasing?" |
| Decibels | Log scale for amplitude/power ratios | "How do I convert gain to dB?" |
If the user's question maps to multiple rows, start with the most fundamental one and build up.
Step 2 — Explain with three anchors
For each concept, give exactly these three things in order:
- Intuition — one sentence a musician could understand
- Math — the key formula (inline, no walls of derivation)
- Code — one-line pseudocode or a real function call from common audio libraries
Keep each anchor to 1–3 lines. Cut anything that doesn't directly answer the question.
Step 3 — Connect to the user's code
After the three anchors:
- Locate where the math appears in their implementation (coefficient calculation, loop structure, buffer size choice, etc.)
- Name the exact variable or line where theory becomes code
- If a value looks wrong, explain which part of the math it violates
Quick connection table
| Math concept | Where it shows up in code |
|---|---|
| DFT basis frequencies | bin_index * sr / N — each FFT bin |
| Convolution sum | FIR tap loop: y[n] = sum(h[k] * x[n-k]) |
| Z-plane pole radius | IIR feedback coefficients a1, a2 |
| Nyquist limit | if (freq > sampleRate / 2) clamp(...) |
| Window function | Multiply x[n] *= window[n] before FFT |
| dB conversion | gain_db = 20 * log10(amplitude) |
What ships with it
1 file beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- 3d ago First seen · 75 lines · 121 tokens per session scan A 4bcbb483b352
audio-math-explainer is a skill published in the GitHub repository kunitoki/sonic-skills (18 stars, last pushed 3mo ago), licensed Unlicense. It adds 121 tokens to every session and 789 once invoked, about $0.0006 per session on Opus 5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-08-30.
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