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Tutoring abilities

If a singer whispers into a microphone, you hear a whisper — but when they suddenly belt out a high note, how does an audio compressor tame the volume without completely crushing the performance?

Audio engineers visualize this dynamic control using an **input-output transfer characteristic graph**, which maps the incoming signal level directly to the outgoing level.

What does a completely untouched audio signal look like on this grid?

In digital audio, volume is measured in **dBFS** (decibels relative to full scale), where $0\text{ dBFS}$ is the absolute maximum level and all quieter signals are negative numbers like $-20\text{ dBFS}$.

When a processor applies no volume change, the input level equals the output level ($\text{Output} = \text{Input}$) — a state called **unity gain**.

This linear unity gain line (1:1 line) passes through the origin/reference coordinates with a slope of $m = 1$ ($\Delta Output / \Delta Input = 1$), representing an uncompressed state where $Output = Input$.

This linear **1:1 line** passes through the reference coordinates with a slope of $m = 1$ ($\Delta\text{Output} / \Delta\text{Input} = 1$), representing an uncompressed state.

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="1:1">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      width: 100%;
      height: 100%;
      font-family: system-ui, -apple-system, sans-serif;
      background: #f8fafc;
      color: #1e293b;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      padding: 16px;
      user-select: none;
      -webkit-user-select: none;
    }

    .graph-wrap {
      width: 100%;
      max-width: 380px;
      aspect-ratio: 1 / 1;
      position: relative;
    }

    svg {
      width: 100%;
      height: 100%;
      overflow: visible;
      touch-action: none;
    }

    .axis-line { stroke: #94a3b8; stroke-width: 1.5; }
    .grid-line { stroke: #e2e8f0; stroke-width: 1; stroke-dasharray: 3,3; }
    .unity-line { stroke: #2563eb; stroke-width: 3; stroke-linecap: round; }
    .proj-line { stroke: #3b82f6; stroke-width: 1.5; stroke-dasharray: 4,4; }
    
    .label {
      font-size: 11px;
      fill: #64748b;
      font-weight: 500;
      text-anchor: middle;
      dominant-baseline: middle;
    }

    .axis-title {
      font-size: 13px;
      fill: #1e293b;
      font-weight: 600;
      letter-spacing: 0.2px;
    }

    .tag-badge {
      font-size: 11px;
      font-weight: 700;
      fill: #2563eb;
    }

    .control-panel {
      width: 100%;
      max-width: 380px;
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 12px 16px;
      box-shadow: 0 1px 3px rgba(0,0,0,0.05);
      display: flex;
      flex-direction: column;
      gap: 8px;
    }

    .readout-row {
      display: flex;
      justify-content: space-between;
      align-items: center;
      font-size: 13px;
      font-weight: 600;
    }

    .pill {
      background: #eff6ff;
      color: #2563eb;
      padding: 3px 8px;
      border-radius: 6px;
      font-family: monospace;
      font-size: 13px;
    }

    .slider {
      width: 100%;
      height: 6px;
      -webkit-appearance: none;
      appearance: none;
      background: #e2e8f0;
      border-radius: 3px;
      outline: none;
      cursor: pointer;
    }

    .slider::-webkit-slider-thumb {
      -webkit-appearance: none;
      width: 20px;
      height: 20px;
      border-radius: 50%;
      background: #2563eb;
      cursor: pointer;
      box-shadow: 0 2px 4px rgba(37,99,235,0.3);
      border: 2px solid #fff;
    }

    .slider::-moz-range-thumb {
      width: 20px;
      height: 20px;
      border-radius: 50%;
      background: #2563eb;
      cursor: pointer;
      box-shadow: 0 2px 4px rgba(37,99,235,0.3);
      border: 2px solid #fff;
    }
  </style>
</head>
<body>

  <div class="graph-wrap">
    <svg id="svgGraph" viewBox="0 0 340 340">
      
      <g id="grid"></g>

      
      <line x1="60" y1="280" x2="280" y2="60" class="unity-line" />
      
      
      <text x="145" y="135" class="tag-badge" transform="rotate(-45 145 135)">1:1 (m = 1)</text>

      
      <line x1="60" y1="60" x2="60" y2="280" class="axis-line" />
      <line x1="60" y1="280" x2="280" y2="280" class="axis-line" />

      
      <line id="projX" x1="60" y1="170" x2="170" y2="170" class="proj-line" />
      <line id="projY" x1="170" y1="280" x2="170" y2="170" class="proj-line" />

      
      <circle id="point" cx="170" cy="170" r="7" fill="#2563eb" stroke="#ffffff" stroke-width="2.5" style="filter: drop-shadow(0 2px 4px rgba(37,99,235,0.35));" />

      
      <text x="170" y="320" text-anchor="middle" class="axis-title">Input (dB)</text>
      <text x="20" y="170" text-anchor="middle" transform="rotate(-90 20 170)" class="axis-title">Output (dB)</text>
    </svg>
  </div>

  <div class="control-panel">
    <div class="readout-row">
      <span>Input: <span class="pill" id="valIn">-20 dB</span></span>
      <span>Output: <span class="pill" id="valOut">-20 dB</span></span>
    </div>
    <input type="range" id="levelSlider" class="slider" min="-40" max="0" value="-20" step="1">
  </div>

  <script>
    const minVal = -40;
    const maxVal = 0;
    const originX = 60;
    const originY = 280;
    const graphSpan = 220; // 280 - 60

    const gridGroup = document.getElementById('grid');
    const dbSteps = [-40, -30, -20, -10, 0];

    // Build Grid & Ticks
    dbSteps.forEach(db => {
      const norm = (db - minVal) / (maxVal - minVal);
      const x = originX + norm * graphSpan;
      const y = originY - norm * graphSpan;

      // Vertical grid & X tick
      if (db > minVal) {
        const vLine = document.createElementNS('http://www.w3.org/2000/svg', 'line');
        vLine.setAttribute('x1', x);
        vLine.setAttribute('y1', 60);
        vLine.setAttribute('x2', x);
        vLine.setAttribute('y2', originY);
        vLine.setAttribute('class', 'grid-line');
        gridGroup.appendChild(vLine);
      }
      const xLabel = document.createElementNS('http://www.w3.org/2000/svg', 'text');
      xLabel.setAttribute('x', x);
      xLabel.setAttribute('y', originY + 16);
      xLabel.setAttribute('class', 'label');
      xLabel.textContent = db;
      gridGroup.appendChild(xLabel);

      // Horizontal grid & Y tick
      if (db > minVal) {
        const hLine = document.createElementNS('http://www.w3.org/2000/svg', 'line');
        hLine.setAttribute('x1', originX);
        hLine.setAttribute('y1', y);
        hLine.setAttribute('x2', originX + graphSpan);
        hLine.setAttribute('y2', y);
        hLine.setAttribute('class', 'grid-line');
        gridGroup.appendChild(hLine);
      }
      const yLabel = document.createElementNS('http://www.w3.org/2000/svg', 'text');
      yLabel.setAttribute('x', originX - 14);
      yLabel.setAttribute('y', y);
      yLabel.setAttribute('class', 'label');
      yLabel.textContent = db;
      gridGroup.appendChild(yLabel);
    });

    const point = document.getElementById('point');
    const projX = document.getElementById('projX');
    const projY = document.getElementById('projY');
    const slider = document.getElementById('levelSlider');
    const valIn = document.getElementById('valIn');
    const valOut = document.getElementById('valOut');

    function update(db) {
      const norm = (db - minVal) / (maxVal - minVal);
      const x = originX + norm * graphSpan;
      const y = originY - norm * graphSpan;

      point.setAttribute('cx', x);
      point.setAttribute('cy', y);

      projX.setAttribute('x1', originX);
      projX.setAttribute('y1', y);
      projX.setAttribute('x2', x);
      projX.setAttribute('y2', y);

      projY.setAttribute('x1', x);
      projY.setAttribute('y1', originY);
      projY.setAttribute('x2', x);
      projY.setAttribute('y2', y);

      valIn.textContent = `${db} dB`;
      valOut.textContent = `${db} dB`;
    }

    slider.addEventListener('input', (e) => {
      update(Number(e.target.value));
    });

    // Touch/drag on graph directly
    const svg = document.getElementById('svgGraph');
    function handlePointer(e) {
      const rect = svg.getBoundingClientRect();
      const clientX = e.touches ? e.touches[0].clientX : e.clientX;
      const relX = (clientX - rect.left) / rect.width * 340;
      const clampedX = Math.max(originX, Math.min(originX + graphSpan, relX));
      const norm = (clampedX - originX) / graphSpan;
      const db = Math.round(minVal + norm * (maxVal - minVal));
      slider.value = db;
      update(db);
    }

    let isDragging = false;
    svg.addEventListener('pointerdown', (e) => {
      isDragging = true;
      handlePointer(e);
    });
    window.addEventListener('pointermove', (e) => {
      if (isDragging) handlePointer(e);
    });
    window.addEventListener('pointerup', () => { isDragging = false; });

    update(-20);
  </script>
</body>
</html>

So how do we show the exact moment a compressor steps in to reduce the level?

The **threshold** is the set input level where compression begins; any signal below it passes through unchanged along the 1:1 line.

Above the threshold, the curve flattens according to the **compression ratio** ($R:1$), which determines how many decibels of input increase are required to produce a $1\text{ dB}$ increase in output.

Above the threshold ($\text{Input} > T$), the slope of the compression curve is the reciprocal of the ratio, $m = \frac{1}{R}$, where an $R:1$ ratio yields $\Delta\text{Output} = \frac{\Delta\text{Input}}{R}$.

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="1:1">
  <title>Compressor Transfer Characteristic</title>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, sans-serif;
      background: #ffffff;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      padding: 10px 12px;
      user-select: none;
    }
    .controls {
      display: flex;
      flex-wrap: wrap;
      gap: 10px;
      width: 100%;
      max-width: 440px;
      justify-content: space-between;
      align-items: center;
      margin-bottom: 8px;
    }
    .ctrl-group {
      display: flex;
      align-items: center;
      gap: 6px;
      font-size: 13px;
      font-weight: 600;
    }
    .ratio-btn {
      padding: 3px 8px;
      border: 1px solid #cbd5e1;
      background: #f8fafc;
      border-radius: 6px;
      font-size: 12px;
      font-weight: 700;
      color: #475569;
      cursor: pointer;
    }
    .ratio-btn.active {
      background: #2563eb;
      color: #ffffff;
      border-color: #2563eb;
    }
    input[type="range"] {
      width: 90px;
      accent-color: #2563eb;
      cursor: pointer;
    }
    .graph-container {
      width: 100%;
      max-width: 440px;
      position: relative;
    }
    svg {
      width: 100%;
      height: auto;
      display: block;
      overflow: visible;
    }
    .formula-bar {
      display: flex;
      flex-wrap: wrap;
      justify-content: center;
      align-items: center;
      gap: 8px 14px;
      width: 100%;
      max-width: 440px;
      margin-top: 6px;
      padding: 6px 10px;
      background: #f8fafc;
      border-radius: 8px;
      font-size: 13px;
      font-weight: 600;
      border: 1px solid #e2e8f0;
    }
    .val-tag {
      display: inline-flex;
      align-items: center;
      gap: 4px;
    }
    .badge {
      padding: 1px 6px;
      border-radius: 4px;
      font-weight: 700;
      font-size: 12px;
    }
    .badge-in { background: #dbeafe; color: #1d4ed8; }
    .badge-out { background: #dcfce7; color: #15803d; }
    .badge-gr { background: #fee2e2; color: #b91c1c; }
  </style>
</head>
<body>

  <div class="controls">
    <div class="ctrl-group">
      <span>Ratio:</span>
      <button class="ratio-btn" data-r="1">1:1</button>
      <button class="ratio-btn" data-r="2">2:1</button>
      <button class="ratio-btn active" data-r="4">4:1</button>
      <button class="ratio-btn" data-r="8">8:1</button>
      <button class="ratio-btn" data-r="999">∞</button>
    </div>
    <div class="ctrl-group">
      <span>Input:</span>
      <input type="range" id="inputSlider" min="-40" max="0" value="-8" step="1">
      <span id="inLabel" style="min-width: 38px; text-align: right;">-8 dB</span>
    </div>
  </div>

  <div class="graph-container">
    <svg viewBox="0 0 360 270" id="graph">
      
      <g stroke="#e2e8f0" stroke-width="1" stroke-dasharray="2,2">
        <line x1="45" y1="20" x2="335" y2="20" />
        <line x1="45" y1="75" x2="335" y2="75" />
        <line x1="45" y1="130" x2="335" y2="130" />
        <line x1="45" y1="185" x2="335" y2="185" />
        <line x1="45" y1="240" x2="335" y2="240" />

        <line x1="45" y1="20" x2="45" y2="240" />
        <line x1="117.5" y1="20" x2="117.5" y2="240" />
        <line x1="190" y1="20" x2="190" y2="240" />
        <line x1="262.5" y1="20" x2="262.5" y2="240" />
        <line x1="335" y1="20" x2="335" y2="240" />
      </g>

      
      <g fill="#94a3b8" font-size="11" text-anchor="end" font-weight="600">
        <text x="38" y="24" dominant-baseline="middle">0</text>
        <text x="38" y="79" dominant-baseline="middle">-10</text>
        <text x="38" y="134" dominant-baseline="middle">-20</text>
        <text x="38" y="189" dominant-baseline="middle">-30</text>
        <text x="38" y="244" dominant-baseline="middle">-40</text>
      </g>
      <g fill="#94a3b8" font-size="11" text-anchor="middle" font-weight="600">
        <text x="45" y="258">-40</text>
        <text x="117.5" y="258">-30</text>
        <text x="190" y="258">-20</text>
        <text x="262.5" y="258">-10</text>
        <text x="335" y="258">0</text>
      </g>

      
      <text x="190" y="270" fill="#64748b" font-size="11" font-weight="700" text-anchor="middle">Input (dBFS)</text>
      <text x="14" y="130" fill="#64748b" font-size="11" font-weight="700" text-anchor="middle" transform="rotate(-90 14 130)">Output (dBFS)</text>

      
      <line x1="45" y1="240" x2="335" y2="20" stroke="#cbd5e1" stroke-width="1.5" stroke-dasharray="4,4" />
      <text x="305" y="45" fill="#94a3b8" font-size="10" font-weight="600">1:1 (Linear)</text>

      
      <polygon id="slopeTriangle" points="" fill="rgba(37,99,235,0.08)" stroke="#93c5fd" stroke-width="1" stroke-dasharray="2,2" />
      <text id="deltaXLabel" fill="#2563eb" font-size="10" font-weight="700" text-anchor="middle"></text>
      <text id="deltaYLabel" fill="#16a34a" font-size="10" font-weight="700" text-anchor="start"></text>
      <text id="slopeFormula" fill="#475569" font-size="10" font-weight="700" text-anchor="middle"></text>

      
      <path id="curveLinear" d="" stroke="#2563eb" stroke-width="3" stroke-linecap="round" fill="none" />
      <path id="curveCompressed" d="" stroke="#2563eb" stroke-width="3" stroke-linecap="round" fill="none" />

      
      <circle id="threshPoint" cx="190" cy="130" r="4.5" fill="#ffffff" stroke="#2563eb" stroke-width="2.5" />
      <text id="threshLabel" x="190" y="120" fill="#1e2945" font-size="11" font-weight="700" text-anchor="middle">T = -20 dB</text>

      
      <line id="probeInLine" x1="0" y1="240" x2="0" y2="0" stroke="#94a3b8" stroke-width="1" stroke-dasharray="2,2" />
      <line id="probeOutLine" x1="45" y1="0" x2="0" y2="0" stroke="#94a3b8" stroke-width="1" stroke-dasharray="2,2" />
      <circle id="probePoint" cx="0" cy="0" r="5.5" fill="#16a34a" stroke="#ffffff" stroke-width="2" />
    </svg>
  </div>

  <div class="formula-bar">
    <div class="val-tag">ΔIn = <span class="badge badge-in" id="dInVal">12 dB</span></div>
    <div class="val-tag">ΔOut = <span class="badge badge-out" id="dOutVal">3 dB</span></div>
    <div class="val-tag">Output = <span class="badge badge-out" id="outVal">-17 dBFS</span></div>
    <div class="val-tag">GR = <span class="badge badge-gr" id="grVal">-9 dB</span></div>
  </div>

  <script>
    const T = -20; // Fixed threshold at -20 dBFS
    let ratio = 4;
    let inputVal = -8;

    const xMin = 45, xMax = 335, yMin = 20, yMax = 240;

    function dbToX(db) {
      return xMin + ((db - (-40)) / 40) * (xMax - xMin);
    }
    function dbToY(db) {
      return yMax - ((db - (-40)) / 40) * (yMax - yMin);
    }

    function calcOutput(inp, r) {
      if (inp <= T) return inp;
      if (r >= 999) return T;
      return T + (inp - T) / r;
    }

    function update() {
      const outVal = calcOutput(inputVal, ratio);
      const gr = inputVal - outVal;
      const dIn = Math.max(0, inputVal - T);
      const dOut = Math.max(0, outVal - T);

      const xT = dbToX(T);
      const yT = dbToY(T);
      const x0 = dbToX(0);
      const y0 = dbToY(calcOutput(0, ratio));

      // Update transfer curve
      document.getElementById('curveLinear').setAttribute('d', `M ${dbToX(-40)} ${dbToY(-40)} L ${xT} ${yT}`);
      document.getElementById('curveCompressed').setAttribute('d', `M ${xT} ${yT} L ${x0} ${y0}`);

      // Probe positions
      const xProbe = dbToX(inputVal);
      const yProbe = dbToY(outVal);

      const pPoint = document.getElementById('probePoint');
      pPoint.setAttribute('cx', xProbe);
      pPoint.setAttribute('cy', yProbe);

      const pInLine = document.getElementById('probeInLine');
      pInLine.setAttribute('x1', xProbe);
      pInLine.setAttribute('x2', xProbe);
      pInLine.setAttribute('y1', yMax);
      pInLine.setAttribute('y2', yProbe);

      const pOutLine = document.getElementById('probeOutLine');
      pOutLine.setAttribute('x1', xMin);
      pOutLine.setAttribute('x2', xProbe);
      pOutLine.setAttribute('y1', yProbe);
      pOutLine.setAttribute('y2', yProbe);

      // Delta slope triangle
      const tri = document.getElementById('slopeTriangle');
      const dXText = document.getElementById('deltaXLabel');
      const dYText = document.getElementById('deltaYLabel');
      const slopeText = document.getElementById('slopeFormula');

      if (inputVal > T + 1) {
        tri.setAttribute('points', `${xT},${yT} ${xProbe},${yT} ${xProbe},${yProbe}`);
        tri.style.display = 'block';

        dXText.textContent = `ΔIn: +${dIn.toFixed(0)} dB`;
        dXText.setAttribute('x', (xT + xProbe) / 2);
        dXText.setAttribute('y', yT + 12);
        dXText.style.display = 'block';

        dYText.textContent = `ΔOut: +${dOut.toFixed(1)} dB`;
        dYText.setAttribute('x', xProbe + 6);
        dYText.setAttribute('y', (yT + yProbe) / 2 + 3);
        dYText.style.display = 'block';

        slopeText.textContent = ratio >= 999 ? 'Slope m = 0' : `Slope m = 1/${ratio}`;
        slopeText.setAttribute('x', (xT + xProbe) / 2);
        slopeText.setAttribute('y', (yT + yProbe) / 2 - 8);
        slopeText.style.display = 'block';
      } else {
        tri.style.display = 'none';
        dXText.style.display = 'none';
        dYText.style.display = 'none';
        slopeText.style.display = 'none';
      }

      // Live bar values
      document.getElementById('inLabel').textContent = `${inputVal} dB`;
      document.getElementById('dInVal').textContent = `+${dIn.toFixed(1)} dB`;
      document.getElementById('dOutVal').textContent = `+${dOut.toFixed(1)} dB`;
      document.getElementById('outVal').textContent = `${outVal.toFixed(1)} dBFS`;
      document.getElementById('grVal').textContent = gr > 0.05 ? `-${gr.toFixed(1)} dB` : '0 dB';
    }

    // Ratio buttons
    document.querySelectorAll('.ratio-btn').forEach(btn => {
      btn.addEventListener('click', () => {
        document.querySelectorAll('.ratio-btn').forEach(b => b.classList.remove('active'));
        btn.classList.add('active');
        ratio = parseFloat(btn.dataset.r);
        update();
      });
    });

    // Input slider
    const inSlider = document.getElementById('inputSlider');
    inSlider.addEventListener('input', (e) => {
      inputVal = parseFloat(e.target.value);
      update();
    });

    update();
  </script>
</body>
</html>

How do you calculate the exact output level for an exam question without guessing by eye?

To find the output level for any signal above the threshold, calculate how many decibels exceed the threshold, divide by the ratio, and add that change back to the threshold value:

$$\text{Output (dB)} = \text{Threshold} + \frac{\text{Input} - \text{Threshold}}{R}$$

Let's work through an example: suppose a compressor has a threshold of $-24\text{ dBFS}$ and a ratio of $4:1$. What is the output level when a loud snare drum hits at $-8\text{ dBFS}$?

First, find the excess level above the threshold: $-8 - (-24) = +16\text{ dB}$.

Next, apply the $4:1$ ratio: $\frac{16\text{ dB}}{4} = +4\text{ dB}$.

Finally, add this compressed gain to the threshold: $-24\text{ dBFS} + 4\text{ dB} = -20\text{ dBFS}$.

How do you determine the total amount of attenuation applied to the signal?

**Gain Reduction** ($GR$) at any given input level corresponds to the vertical distance between the unity gain (1:1) line and the compressed transfer line:

$$GR = Input - Output = (Input - T)\left(1 - \frac{1}{R}\right)$$

For our snare drum, the total reduction is $-8\text{ dBFS} - (-20\text{ dBFS}) = 12\text{ dB}$ of dynamic attenuation.

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      <div class="metric-card">
        <div class="metric-label">Output</div>
        <div class="metric-val" id="valOut">-20 dBFS</div>
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        <line x1="40" y1="170" x2="280" y2="170" stroke="#edf2f7" stroke-width="1"/>

        
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    // SVG Y: 220px (-40 dBFS) to 20px (0 dBFS) -> height = 200px -> 5px per dB
    
    const threshold = -20; // dBFS
    // For this lesson example: limiting / high ratio resulting in total dynamic attenuation shown
    // Let ratio = Infinity (Limiter) or 4:1? Context: "-8 dBFS - (-20 dBFS) = 12 dB of dynamic attenuation" 
    // This directly matches output = -20 dBFS (limiter, ∞:1 ratio above -20 dBFS).
    const ratio = Infinity;

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      return 220 - (db + 40) * 5;
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      const outVal = getOutput(inVal);
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      const pThreshX = dbToX(threshold), pThreshY = dbToY(threshold);
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      const curveY = dbToY(outVal);

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      ptLinear.setAttribute('cy', linearY);

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      ptCurve.setAttribute('cy', curveY);

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        attenLine.setAttribute('x2', curX);
        attenLine.setAttribute('y2', curveY);

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        const textX = curX > 220 ? curX - 52 : curX + 8;
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        attenText.textContent = `-${Math.round(atten)} dB`;
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        attenLine.style.display = 'none';
        attenText.style.display = 'none';
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      // Update text values
      valIn.textContent = `${inVal} dBFS`;
      valOut.textContent = `${Math.round(outVal)} dBFS`;
      valAtten.textContent = `${Math.round(atten)} dB`;

      // Preset button highlight
      presetBtns.forEach(btn => {
        const pVal = parseInt(btn.getAttribute('onclick').match(/-?\d+/)[0]);
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    }

    function setPreset(val) {
      slider.value = val;
      update();
    }

    slider.addEventListener('input', update);
    update();
  </script>
</body>
</html>

How do we measure how many decibels of volume the compressor is actively cutting?

**Gain Reduction** ($GR$) at any given input level corresponds to the vertical distance between the 1:1 unity gain line and the compressed transfer line.

$$GR = \text{Input} - \text{Output} = (\text{Input} - T)\left(1 - \frac{1}{R}\right)$$

For our snare drum hit at $-8\text{ dBFS}$, the gain reduction is $-8 - (-20) = 12\text{ dB}$ of downward attenuation.

What is the single most common mistake students make on transfer graph exam questions?

Because dBFS uses negative numbers, remember that $-8\text{ dBFS}$ is **louder** (higher up and further right) than $-24\text{ dBFS}$.

Always double-check your arithmetic when subtracting negatives: $\text{Input} - \text{Threshold}$ will always be a positive number when the signal exceeds the threshold.

Next time you look at a compressor graph, find the bend point for the threshold, check the slope for the ratio, and you can instantly predict the output volume.

music-technology

Interpreting Input-Output Transfer Characteristic Graphs. Read and plot decibel values on logarithmic Cartesian grids showing linear unity gain (1:1 line) and compression slopes.

Dynamics Processing Explained: Transfer Curves, Ratios, and Thresholds

A-Level Music Technology: Graphical Analysis of Dynamic Processors (MUSTECH-9.4)

Visual Guide to Audio Compression: Transfer Functions and Input/Output Graphs

To master MUSTECH-9.4, students should be trained using a two-step pedagogical approach: first, connecting algebraic linear equations ($y = mx + c$) to Cartesian dB plots where $m = 1$ below threshold and $m = \frac{1}{R}$ above threshold; second, practicing coordinate extraction on exam-style negative decibel grids ($-60\text{ dBFS}$ to $0\text{ dBFS}$). Emphasize that decibel grids on compressors are linear representations of logarithmic signal power, making slopes directly calculable via simple geometric rise-over-run ratios.

Interpreting Input-Output Transfer Characteristic Graphs

The 1:1 Unity Line

Threshold and Compression Slope