# Added distortion: where the levels come from

Build your own's "Added distortion" (EQ sheet; `js/added-distortion.js`) adds one
of four kinds of distortion ahead of the amp. Each level matches measured gear.
Researched 2026-10-23; Stereophile pages read through their Wayback copies.
**M** measured, **S** spec or definition, **D** our calculation.

Levels are set at the music's loud peaks (about 12 dB above its average, the
level the Why panel's test tones use). Smooth harmonics then fall with level
as in real gear (2nd: 6 dB per 6 dB; 3rd: 12 dB per 6 dB); the crossover dead
zone is fixed, so it grows relative to quiet passages; clipping starts a set
number of dB below the track's own peak.

## Smooth 2nd harmonic

| Level | Anchor | Source |
|---|---|---|
| 0.04% | Audio Research SP20 (unbalanced): 2nd −67 dB at 1 V, 50 Hz (M) | https://www.stereophile.com/content/audio-research-sp20-preamplifier-measurements |
| 0.2% | PrimaLuna ProLogue Premium line stage: 0.2% at 1 V, "predominantly second-harmonic" (M) | https://www.stereophile.com/content/primaluna-prologue-premium-line-preamplifier-measurements |
| 0.87% | Mastersound 300B SE: 0.874% THD+N at 1 W, "almost pure second-harmonic" (M) | https://www.stereophile.com/content/mastersound-300-b-se-integrated-amplifier-measurements |
| 8.7% | Ten times the 300B (our choice, exaggerated) | — |

Not every single-ended amp is 2nd-dominant: Stereophile found the Sophia
Electric 91-01 300B "predominantly third harmonic".

## Smooth 3rd harmonic

| Level | Anchor | Source |
|---|---|---|
| 0.1% | Analog tape at reference level (320 nWb/m, 15 ips): 3rd harmonic 0.10% (S, typical) | ATR Master Tape, https://www.duplication.com/atr_magnetics/ATR-Master-Tape-Technical-Data-Sheet-Standard.pdf ; RTM SM911, https://www.fullcompass.com/common/files/6763-RMGISM911.pdf |
| 1% | RTM SM911 at 15 ips: 1% 3rd harmonic 9 dB over reference (S, typical) | RTM SM911, p.4 |
| 3% | Maximum operating level, defined as the level giving 3% 3rd harmonic (S) | 3M technical bulletin, https://bh.hallikainen.org/uploads/harold/3M%20Technical%20Bulletin.pdf |

Baxandall (Wireless World, Nov 1977) describes tape distortion as mainly 3rd
harmonic, about 2% at peak recording level.

## Crossover distortion

A dead zone of half-width d (relative to the loud peaks), the form Lee and
Geddes (2003) used. For a sine, THD ≈ 62·d % for small d (D: computed by
FFT, harmonics to the 41st).

| Level | d | Anchor | Source |
|---|---|---|---|
| 0.12% | 0.002 | Dan D'Agostino Progression M550: about 0.12% THD+N at 1 W (graph), spikes at each zero crossing, distortion higher at low power than high (M) | https://www.stereophile.com/content/dan-dagostino-master-audio-systems-progression-m550-monoblock-power-amplifier-measurements |
| 0.7% | 0.012 | Conventional class-B stage: nonlinear up to about 1.2% of peak output on the 20 W scale (diagram reading), read here as the dead zone each side of zero (our reading) | Blomley, Wireless World Feb 1971, p.57, https://keith-snook.info/wireless-world-articles/Wireless-World-1971/New%20Approach%20to%20class-B%20Amplifier%20Design%20by%20P%20Blomley.pdf |
| 3.8% | 0.061 | Zero-bias emitter follower without feedback: 3.8% measured at about 9.9 V peak (M) | Elliott Sound Products, https://sound-au.com/articles/crossover-distortion.htm |

Douglas Self (Electronics World, Dec 1993) notes crossover makes "high order
harmonics with the potential to increase in percentage as signal level falls",
and the 1960s consensus that it caused "transistor sound".

## Clipping

No published study measures how many dB of peaks commercial CDs lose, so the
levels lean on practitioners' figures:

| Level | Anchor | Source |
|---|---|---|
| 1 dB | Lesurf, on clipped CDs: turning down "by a dB or so" would have avoided it (estimate) | https://audiomisc.co.uk/HFN/HealthCheck/CD.html ; measured clip counts at https://audiomisc.co.uk/HFN/ClippingOnCD/clipping.html |
| 2 dB | Katz (1999): engineers "can often raise gain by 2 or more dB" by trusting over counters (practitioner) | https://web.archive.org/web/2015/http://www.tcelectronic.com/media/1018177/katz_1999_secret_mastering.pdf |
| 3 dB | Nielsen & Lund (AES 109th, 2000): +3 dBFS intersample peaks, which consumer CD players' converters clip (THD+N −17 to −21 dB) (M) | https://service-tcgroup.tcelectronic.com/media/Level_paper_AES109.pdf |
| 6 dB | Twice the 3 dB case (our choice, exaggerated) | — |

Nielsen & Lund (AES 23rd Conference, 2003) counted overloads per 10 s in pop
and rock tracks: none on older masters, more than 25 above +1 dBFS on some
2000s releases.