# Synth FM Ratio Calculator AI Agent Connect

> A deterministic FM synthesis engine for calculating harmonic ratios and sideband spectra.

## Overview
- **Category:** mathematics
- **Price:** Free
- **Endpoint:** https://edge.vinkius.com/vk_preview_3lT9doQZYsHYQNnPPw2yzyA6nsyEDhKIlA8ORgqw/ai-agent-connect
- **Tags:** fm-synthesis, audio-engine, harmonic-analysis, sidebands, bessel-function

## Description

This MCP server provides a deterministic Frequency Modulation (FM) synthesis engine. It allows AI agents to calculate the mathematical relationship between carrier and modulator frequencies, classify spectra as harmonic or inharmonic, and generate detailed sideband distributions. Use `analyze_fm_ratio` to find the C:M ratio, `calculate_sideband_spectrum` to map frequency/amplitude distributions, and `identify_audible_frequencies` to filter sidebands based on a specific amplitude threshold.

## Tools

### analyze_fm_ratio
Determines the mathematical relationship between the carrier and modulator to classify the resulting sound type

### calculate_sideband_spectrum
Generates a detailed list of the frequencies and relative amplitudes of the sidebands produced by the modulation

### identify_audible_frequencies
Filters a spectrum to identify only those sidebands that possess sufficient amplitude to be perceived

## Prompt Examples

**Prompt:** 
```
What is the C:M ratio for a carrier of 440Hz and a modulator of 220Hz?
```

**Response:** 
```
The C:M ratio is 2:1, and the resulting spectrum is harmonic.
```

**Prompt:** 
```
Calculate the sideband spectrum for a 440Hz carrier, 110Hz modulator, and 2.0 modulation index.
```

**Response:** 
```
The sidebands include the carrier at 440Hz, and sidebands at 330Hz, 550Hz, 220Hz, 660Hz, 110Hz, and 770Hz with their respective calculated amplitudes.
```

**Prompt:** 
```
Which frequencies are audible if the threshold is 0.1 for a 440Hz carrier and 220Hz modulator with index 1.5?
```

**Response:** 
```
The audible frequencies above the 0.1 threshold are 440Hz, 220Hz, and 660Hz.
```

## Frequently Asked Questions

**What is the difference between harmonic and inharmonic spectra?**
Harmonic spectra occur when the C:M ratio consists of simple integer relationships, resulting in musical tones. Inharmonic spectra occur when the ratio is complex or irrational, creating bell-like or metallic sounds.

**How are sideband amplitudes calculated?**
Sideband amplitudes are determined by approximating Bessel functions of the first kind based on the provided modulation index.

**Can I filter out quiet sidebands?**
Yes, you can use the `identify_audible_frequencies` tool to filter the spectrum for sidebands that exceed a specific amplitude threshold.