Variance Indicators

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Purpose

This page exists for engineers. Variance is defined conceptually as “what changes around the kick.” But engineers need to know what to measure. Without shared indicators, two implementations will analyze different signals, produce different Variance values for the same audio, and artists will get inconsistent results.

The indicators listed here are directional guidance — not an algorithm specification. They describe what to look for in the audio signal, using the kick as the fixed reference point.

The Core Principle

The kick occupies a known position in the frequency spectrum and in time (via the beat grid from Pro DJ Link). Everything else in the signal — synths, hats, noise, effects, pads — is “everything else.” Variance indicators measure aggregate properties of “everything else” and track how those properties change over time.

  Frequency spectrum at a given beat:

  ▓▓▓▓▓                                                    
  ▓▓▓▓▓       ░░░                  ░░          ░░░░░       
  ▓▓▓▓▓    ░░░░░░░░░     ░░░░░░░░░░░░░     ░░░░░░░░░░░    
  ▓▓▓▓▓  ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░  
  ──────┬──────────────────────────────────────────────────
  30 Hz │                    Frequency →              20 kHz
        │
     KICK                EVERYTHING ELSE
     (Foundation)        (feeds Variance)

The system doesn’t need to identify what “everything else” is made of. It just needs to track how its aggregate properties change from bar to bar.

Indicators

1. Spectral Brightness

What it is: The ratio of high-frequency energy to low-frequency energy in the non-kick portions of the signal.

What it signals: When spectral brightness increases, the mix is getting brighter — more hi-hats, more cymbal wash, more open filters, more high-frequency content. This is the most universal tension-building signal in techno. Nearly every build involves brightness increasing.

How it maps to Variance:

  Brightness increasing over bars → Variance direction = RISING
  Brightness decreasing over bars → Variance direction = FALLING
  Brightness stable               → Variance direction = STABLE
  
  Rate of brightness change       → Variance magnitude

Why it matters for techno: The filter sweep — opening a resonant low-pass filter over 16 or 32 bars — is the single most common build technique in techno. It directly maps to spectral brightness increasing. When the filter snaps shut, brightness drops. This indicator alone captures a huge percentage of techno’s energy dynamics.

2. Layer Density

What it is: How many distinct spectral bands above the kick’s frequency range have sustained energy. Not individual source identification — just a count of “how many frequency regions are active.”

What it signals: More active bands = more elements in the mix = more energy. Fewer bands = sparser, more minimal. Layer density rising means the DJ or the arrangement is adding elements. Density falling means stripping back.

How it maps to Variance:

  Density increasing over bars → Variance direction = RISING
  Density decreasing over bars → Variance direction = FALLING
  Density stable               → Variance direction = STABLE
  
  Rate of density change       → Variance magnitude

Why it matters for techno: Techno arrangements are built on layering. A track might start with just kick and bass, then add closed hats, then open hats, then a synth stab, then a pad, then a noise sweep. Each new layer fills a new spectral region. The reverse happens during strip-backs. Layer density captures this structural dynamic without needing to identify what each layer is.

3. Rhythmic Complexity (Onset Density)

What it is: The number of percussive transients per bar in the mid-to-high frequency range. How “busy” the rhythmic pattern is above the kick.

What it signals: More transients = busier pattern = more energy. Fewer transients = sparser pattern = less energy. A 16th-note hi-hat pattern has higher onset density than a quarter-note pattern.

How it maps to Variance:

  Onset density increasing → Variance direction = RISING
  Onset density decreasing → Variance direction = FALLING
  Onset density stable     → Variance direction = STABLE
  
  This indicator operates at the MESO timescale —
  it compares bar-level patterns, not individual beats.

Why it matters for techno: Percussion patterns are a primary tool for energy control in techno. A DJ might transition from a track with a simple hat pattern to one with complex polyrhythmic percussion. The kick stays the same, but the groove feels completely different. Rhythmic complexity captures that shift.

4. Accompanying Kicks / Sub-Hits

What it is: Additional transient events in or near the kick’s frequency range that do not fall on the expected beat grid positions.

What it signals: Off-beat kicks, sub-bass hits between beats, kick doubles, or low-frequency percussion that adds drive and intensity to the foundation. These are not the Foundation kick itself (which is on the beat grid) — they are additional low-frequency rhythmic events.

How it maps to Variance:

  Accompanying hits appearing  → Variance direction = RISING
                                 (groove intensifying)
  Accompanying hits dropping   → Variance direction = FALLING
                                 (groove simplifying)
  
  This is a MESO-level indicator.
  A single off-beat kick is MICRO — it doesn't change the story.
  A sustained pattern of off-beat kicks is MESO — it does.

Why it matters for techno: The off-beat kick or “second kick” is a defining element of many techno subgenres. When a track has a heavy kick on every beat AND a second lower hit on the off-beats, the groove feels more driving, more relentless. The appearance or disappearance of this pattern is a meaningful change in the music’s character — even though the Foundation kick itself hasn’t changed.

Detection note: Because these hits are in the same frequency range as the kick, they can be detected by looking for transient energy at beat grid positions where the Foundation kick is not expected (e.g., off-beats, &-beats). The system knows where the Foundation kicks are (from the beat grid), so anything else in that frequency range is an accompanying hit.

5. Spatial Width

What it is: The stereo spread and reverb energy in the mix. How “wide” or “narrow” the sound field feels.

What it signals: Wider spatial characteristics suggest atmospheric, expansive sections. Narrower suggests focused, intense, intimate sections. Spatial width often changes at the macro timescale — over the course of a section or a track transition.

How it maps to Variance:

  Width increasing → can signal either RISING or FALLING direction
                     depending on context (atmospheric build vs.
                     post-drop expansion)
  
  Width is more of a character modifier than a direction driver.
  It is most useful in combination with other indicators.

Why it matters for techno: Reverb and spatial effects are used extensively in techno to create atmosphere and signal structural changes. A bone-dry mix suddenly opening into a wide reverb tail changes the feel of the room dramatically. This is captured partly by Sustain (which measures kick decay), but spatial width captures the overall mix spatiality, not just the kick.

6. Filter Movement (Spectral Centroid Rate of Change)

What it is: How quickly the spectral center of mass of the non-kick signal is moving. A stable spectral centroid means the tonal balance is steady. A rapidly moving centroid means a filter is sweeping or the spectral balance is shifting.

What it signals: Fast spectral centroid movement = active filter use = tension/energy manipulation. The direction of the movement (centroid moving up vs. down) maps directly to filter opening vs. closing.

How it maps to Variance:

  Centroid moving up   → Variance direction = RISING (filter opening)
  Centroid moving down → Variance direction = FALLING (filter closing)
  Centroid stable      → Variance direction = STABLE
  
  Rate of centroid change → Variance magnitude
  (slow sweep = low magnitude, fast sweep = high magnitude)

Why it matters for techno: This is essentially a direct measurement of the filter knob — the most expressive tool on a DJ mixer for techno. When a DJ sweeps the filter, the spectral centroid moves. When it’s parked, the centroid is stable. This indicator is so directly tied to DJ performance that it’s arguably the single most important Variance signal.

Combining Indicators

These indicators should be combined into a single Variance signal, not exposed individually to artists. The model’s purpose is to abstract away technical details. Artists receive variance.direction and variance.magnitude — not “spectral brightness = 0.7, layer density = 0.4.”

The combination strategy is an engineering decision, but some principles apply:

  1. Agreement amplifies.
     If multiple indicators agree (all rising, or all falling),
     confidence in the direction is high and magnitude should
     be boosted.

  2. Disagreement dampens.
     If some indicators are rising and others are falling,
     the direction is ambiguous and magnitude should be low.
     Direction might be STABLE even though individual signals
     are moving — because the overall picture is unclear.

  3. Filter movement dominates.
     In techno, a filter sweep is such a clear directional
     signal that it should have disproportionate influence
     on the combined Variance output.

  4. Indicators have different timescales.
     Spectral brightness and filter movement change quickly
     (meso). Layer density and spatial width change slowly
     (macro). The combination should respect these timescales —
     a fast indicator shouldn't be averaged away by a slow one.

What These Indicators Cannot Capture

These indicators measure aggregate spectral properties. They cannot capture:

  • Musical key or harmonic content — whether the synth is playing a minor or major chord
  • Emotional intent — whether the DJ is building tension intentionally or accidentally
  • Track boundaries — when one track ends and another begins
  • Sample-level content — what specific sound is playing at any moment

This is by design. The model works with what can be reliably extracted from a summed live signal in real time. It intentionally limits its scope to maintain accuracy.

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