Auditory motion: what research says, and starting values for A³

What a listener on a dance floor can and cannot hear of a moving sound, and the values A³ starts from because of it. Written 2026-10-08 as the research base for A³ Motion’s flight (the “ships”), its clips, and the 3D band filter (FREQ/Q); the MJ playbook and the movement lab build on it.

Part A is sources, part B is derived values, part C is a one-evening listening test. Every claim in part A has a source. Strength tags: [solid] means peer-reviewed and replicated, or a standard textbook. [single] means one peer-reviewed study. [practice] means practitioner or press reports, so anecdotal.

Arithmetic used throughout. One bar is 4 beats, so deg/s = 360 × laps_per_bar × BPM / 240 = 1.5 × BPM × laps_per_bar. That is 180 °/s per lap-per-bar at 120 BPM and 195 °/s at 130 BPM.

How A³ moves a sound (the context for part B):

In stereo mode the 3D control pulls a filtered band (an Airwindows Isolator3 band, chosen by FREQ and Q) out of the channel and sends it into the room; the rest stays put as the steady bed. So the band moves and the rest does not. With stems, a whole stem moves instead.
FREQ and Q arrive as 0…1 and are mapped linearly onto the Isolator’s parameter range. How that parameter relates to Hz and octaves had not been measured when this was written (see C0), so part B talks in Hz and octaves, not in A³ control values.
Encoding and decoding are IEM plug-ins (3rd-order Ambisonics). Motion steers azimuth and elevation only; there is no distance.

A. What the research says

A1. Motion perception limits

Finding	Numbers	Source	Strength
The minimum audible movement angle (MAMA) grows with speed	8.3° at 90 °/s up to 21.2° at 360 °/s	Perrott & Musicant 1977, JASA 62(6) 1463 (summary)	solid
MAMA is U-shaped over speed; the best resolution is at slow speeds	horizontal 1.7° at 1.8 °/s, about 10° at 320 °/s; optimum about 2 °/s horizontally and 7–11 °/s vertically; vertical MAMAs are larger at every speed (often > 8°)	Saberi & Perrott 1990, JASA 88(6) 2639 (pdf)	solid
MAMA depends on where the source is	about 5° straight ahead, > 30° at ±90° (500 Hz tones)	Grantham 1986, JASA 79(6) 1939	solid
The ear integrates over time	minimum integration time about 336 ms (500 Hz); MAMA rises steeply below 100–150 ms duration	Chandler & Grantham 1992, JASA 91(3) 1624 (via)	solid
Upper limit of rotation (UL): above it, listeners cannot tell CW from CCW	white noise about 2.5 rot/s (900 °/s); band-limited noise equals white noise in an anechoic room; harmonic tones fall lower as f0 rises	Féron, Frissen, Boissinot, Guastavino 2010, JASA 128(6) 3703	single+ (replicated by the next row)
The UL depends on spectrum and comes from front/back confusion	UL rises with centre frequency and bandwidth; 250 Hz bands fall below 0.5 rot/s (cannot be measured, ITD only); 4 kHz at ½–1 oct is clearly below white noise; 4 kHz at 4 oct is about the same as white noise. Above the UL, people hear “left-right alternation”, “half circles, figure eights, jumps”. 24-speaker ring, r = 1.8 m.	Roggerone, Vacher, Tarlao, Guastavino 2019, Sci Rep 9:16437 (open)	single, strong
Speed discrimination is coarse	20–70 % speed difference needed (Weber fraction roughly constant); a sudden speed-up during motion needs about 3× more than a slow-down; the velocity integration window is about 1 s; listeners have a “slow prior”	Carlile & Best 2002, JASA 111(2) 1026; Locke, Leung, Carlile 2016, Sci Rep 6:27725 (open)	solid
Overview of all the above	the “snapshot” theory: motion is largely successive localisations	Carlile & Leung 2016, Trends in Hearing 20 (open)	review
Static acuity also varies with frequency	MAA about 1° in front below 1 kHz, worst around 1.5–2 kHz (the ITD/ILD hand-over)	Mills 1958, JASA 30(4) 237	solid

Ambisonics, listener position, and a crowd:

The sweet area grows with order. Zotter & Frank define it as the region with localisation uncertainty < 30°. At 1st order it reaches halfway to the speakers; at 3rd order it covers almost the whole array. Ambisonics with max-rE keeps width and loudness constant while panning. VBAP does not: its width changes as the source passes a speaker. Source: Zotter & Frank 2019, Ambisonics, Springer, open access (book). [solid]
Off centre, the precedence effect pulls transients towards the nearest speaker more than steady noise. The source direction depends on signal type. Source: Stitt, Bertet, van Walstijn 2017, JAES 65(3) 188 (abstract). [single] For a club this means a moving hi-hat band is heard by most of the crowd as “which speaker near me gets louder”, not as an angle.
In a hall, how well listeners identify trajectories depends on seat, trajectory and scene complexity. A visible, synchronous performer gesture partly offsets the off-centre loss. Source: Marentakis et al., ICAD 2008 (record). [single]

A2. Frequency: what moves well

Band	Cue	What it means for motion	Source
< about 150 Hz	in-room, mode-dominated; subs usually shared	does not localise or move in a club; practice keeps it static or distributed	[practice]: 4DSOUND keeps bass a “steady pulse” (review); Rex Club L-ISA with distributed subs (PSW)
about 150 Hz – 1 kHz	ITD	azimuth is fine, front/back ambiguous, so rotation direction is lost early (250 Hz UL < 0.5 rot/s)	Roggerone 2019; Yost & Zhong 2014
about 1.5–3 kHz	ITD/ILD gap	worst static acuity for narrow signals	Mills 1958; Yost & Zhong 2014
4–16 kHz	ILD + pinna	up/down cues 6–12 kHz, front/back 8–16 kHz; needed for elevation and for unambiguous circles	Langendijk & Bronkhorst 2002, JASA 112(4) 1583 (summary) [solid]

Bandwidth matters more than centre frequency. Noise wider than 1 octave localises best (about 6–7° rms) and does not depend on CF. Narrower bands are worse, especially at 1–4 kHz. Source: Yost & Zhong 2014, JASA, “Sound source localization identification accuracy: bandwidth dependencies” (summary). [solid] The UL work above shows the same for motion.
Narrow bands have their own elevation. For 1/6-octave noise, perceived elevation and front/back follow the centre frequency, not the source position: Blauert’s “directional bands”. Source: Middlebrooks 1992, JASA 92(5) 2607; Blauert, Spatial Hearing (context). [solid] A narrow, high band moving in elevation will sit at “its” height whatever Core sends.
Pitch-height effect: higher bands are heard higher, and phantom images from wide speaker pairs rise (500 Hz and 8 kHz the most). Source: Lee, ICSA 2015 (pdf). [single]
Moving a filtered band instead of full band: there is no listening study of “extract one band and move it” on a dance floor. The closest practice is timbre or spectral spatialisation, where 4–16 bandpass bands are spread and moved separately. Sources: Normandeau 2009, Organised Sound 14(3) (CUP) [practice/aesthetic]; Kim-Boyle 2008, ICMC, “Spectral spatialization – an overview” [practice]. The psychophysical consequence follows directly from Roggerone 2019 and Yost & Zhong 2014: the moving band must be wide, about 2 octaves or more, and contain energy above 2–4 kHz, or direction and front/back collapse at moderate speeds.

A3. Trajectory shape and timing in practice

Rotation speeds in practice:
- Stockhausen’s rotation table (Kontakte 1958–60, manual) and the electric version for Sirius went up to 25 rot/s. Far above the UL, that becomes a timbre or “flutter”, not a path (Wikipedia, Kontakte; eContact). [practice]
- Leslie speaker: slow at 40–50 rpm (about 0.7–0.8 rot/s), fast at 340–400 rpm (about 6–7 rot/s), which is heard as tremolo or vibrato. This matches the UL (Wikipedia). [practice]
Chowning 1971 simulated moving sources with angle + direct/reverb ratio (distance) + Doppler (speed) and argued that motion reads as motion only when distance and speed cues come with it. Source: JAES 19(1) 2 (CCRMA). [practice/classic]
Listeners find spatial gesture meaningful, but at the level of schemata such as “approach”, “encircle” and “fly-over”, not exact geometry. Source: Kendall 2010, Organised Sound 15(3) (QUB). [review/theory]
BEAST, the large diffusion orchestra, uses n-channel stems and diffusion as performance. Source: Wilson & Harrison 2010, Organised Sound 15(3) 239 (BEAST). [practice]
Club practice from 4DSOUND’s “Techno is Space”:
- hi-hats and kicks “hitting you at different heights and angles” worked;
- few moving elements: “less becomes far more”;
- spatial complexity asks for attention a club does not always give;
- stereo habits produced a “3D-ised version of what we know”.
[practice] (review)
L-ISA at the Rex Club (Molécule): a snare circling, ping-pong between virtual walls, random throws that stop and fade (PSW). [practice]
DJ spatialisation with REAPER and IEM on 7.1.4: the MSc thesis reports that stability and real-time feasibility dominated. It has no speed data. Source: Costa 2025, P.Porto (record). [practice]
Disorientation: a rotating sound field can induce illusory self-rotation (auditory vection), especially with several sources turning together. It is weaker than visual vection. Source: Väljamäe 2009, Brain Res. Rev. 61(2) 240 (Chalmers). [review] There is no published threshold for “tiring” on a dance floor. The practitioner consensus is “few elements, not all moving”.

A4. Stereo DJ effects and their note values

Pioneer DJ DJM-900NXS2 Beat FX (operating instructions): delay and echo at 1/16–16 beats; filter, flanger and phaser cycles at 1/16–64 beats. There is no dedicated auto-pan, but PING PONG and TRANS exist (manuals). [manufacturer]
Generic auto-pan: 0.05–10 Hz free, or note values in sync (Roland SPD-SX PRO). [manufacturer]
No published mapping from stereo DJ effects to 3D was found. What follows in B is derived.

A5. Distance and size (brief)

Distance is cued by level, direct-to-reverberant ratio and spectrum (air absorption). Doppler cues speed. Source: Zahorik, Brungart, Bronkhorst 2005, Acta Acustica 91, 409. [review] Chowning 1971. A³ steers azimuth and elevation only. A velocity-dependent level or HF change (“closer when faster”) would be the cheapest add-on, but it is out of scope.

B. Starting values for A³ (derived, not sourced)

Tags: R = from research (with the A-row it rests on). G = guess, test it.

B1. Speed

laps/bar	lap every	°/s at 120	°/s at 130	Reading	Tag
1/32	32 bars (a slow precession)	5.6	6.1	not heard as motion on its own; “the room drifts”	R (Saberi: optimum resolution, but too slow to notice without a reference) + G
1/8	8 bars	22.5	24	slow, clear for wide bands	R (MAMA about 5° front)
1/4	4 bars (the base orbit)	45	49	clear path, readable in the crowd: keep as the default	R
1/2	2 bars	90	98	energetic; side MAMA > 20°	R
1	1 bar	180	195	direction still clear for wide high bands, ambiguous for low bands	R (Roggerone: 250 Hz UL < 0.5 rot/s = 180 °/s)
2	2 beats	360	390	“swirl”; direction only for broadband or ≥ 2 oct at 4 kHz	R
4	1 beat	720	780	at the UL (2.5 rot/s = 900 °/s): turns into a texture, tremolo-like	R (Féron 2010)

speedMax: 1 lap per 2 beats (≈ 360–400 °/s) for full band or wide bands, and 1 lap per bar for a band with FREQ below about 1 kHz. Faster than that is an effect (Leslie, flutter), not a path. R + G
speedMin for a captured ship: ≥ 1 lap per 2 bars (the escort lap). Its radius is small, though, so check the angular speed seen from the room: a small orbit around a group at the rim sweeps only a few degrees, and that is below the MAMA. G
Speed changes must be ≥ 1.5×, and ≥ 2× when speeding up, to be heard as “faster”. A slingshot that adds 20 % is inaudible as speed. It is only audible as a change of path. R (Carlile & Best; Locke 2016)

B2. Excursion, meaning how far a bend must go

Item	Value	Tag
Smallest deviation from the orbit that counts as “it bent”	≥ 20° azimuth front, ≥ 30° to the sides; use 30° as the design minimum for the crowd	R (Grantham MAMA 5°→30°; sweet-area criterion 30°)
A body’s capture orbit seen from the centre	must subtend ≥ 30°, otherwise ESCORT sounds like “parked”	G (derived from the row above)
Wander per bar	≤ 10° is inaudible, so it is safe as “life”; 20–30° is heard as a wobble	R + G

B3. Elevation

Item	Value	Tag
Use elevation for	bands with energy at 6–12 kHz (hats, air, claps); otherwise it is mostly not heard	R (Langendijk & Bronkhorst)
Smallest elevation step	≥ 15–20° (vertical MAMA > 8° in the lab; worse with a dome and a crowd)	R + G
Vertical speed	slower than azimuth: ≤ 1/2 of the azimuth speed	R (vertical optimum is slower; G for the factor)
Narrow high band (Q > about 1 oct)	elevation will be fixed by its frequency (directional bands), so do not rely on elevation movement there	R (Middlebrooks 1992)

B4. The 3D filter (FREQ, Q)

Hz and octave values. Mapping them onto Isolator3’s 0.05…0.9 needs C0 first.

Item	Value	Tag
FREQ default (centre)	about 3 kHz, roughly 1.5–6 kHz at 2 oct: hats, claps and vocal presence, inside the best UL region (4 kHz, ≥ 2 oct)	R (Roggerone, Yost & Zhong) + G (club content)
FREQ useful range	about 250 Hz – 10 kHz. Below about 250 Hz it moves “something”, but the crowd hears no path (ITD only, front/back gone, room modes)	R + practice
FREQ below about 150 Hz	not useful for motion; a test point at most	practice
Q (bandwidth) default	2 octaves	R
Q range	4 oct (wide) to 1 oct (narrow). Narrower than 1 oct is a “colour that wobbles”, and narrower than ½ oct moves almost nothing audible	R (Yost & Zhong: > 1 oct needed; Roggerone: 4 kHz ½–1 oct UL drops sharply)
Coupling	the narrower Q or the lower FREQ, the lower the usable speed (B1 caps)	R
Energy	a 2-oct band at 3 kHz in club music carries roughly −10 to −15 dB relative to full band (genre-dependent). The 3D gain should make it audible against the steady bed, so measure it on the system’s meters	G

FREQ and Q only act in 3D, yet they sit on the motion controller. That is consistent with B4: they choose what moves, which is a motion decision and not a tone control. A label such as “MOVE BAND” with a Hz/oct readout would make that explicit. G (UI suggestion, not decided).

B5. Gravity pulse

Item	Value	Tag
A gravity pulse on the beat	it acts on acceleration. The audible quantity is the positional deviation per beat near a body, and it must reach ≥ 20–30° (B2) to be heard as “pulled on the beat”. It is probably inaudible with small pulse depths (0.3 / 0.6 of the acceleration) unless a ship passes close to a body	R (MAMA) + G (needs a log of the deviation in the unit tests: max angle change per beat at 120 BPM)
Rhythm resolution	a beat at 120 BPM lasts 500 ms, just above the 336 ms integration time, so a per-beat spatial accent is near the limit and a per-1/8 one (250 ms) is below it	R (Chandler & Grantham)
Suggestion	pulse on half bars or bars, not on every beat; keep the downbeat accent	G

B6. Stereo DJ effects translated to 3D (proposals)

Stereo effect	3D translation	Rate (note value)	Tag
Auto-pan L↔R	ping-pong between two opposite points, a step or a fast glide (≤ 1/16 bar)	1/2–2 beats per side	G; a step reads better than a glide, because short glides fall below integration time (R)
Auto-pan circle	rotation	1 lap per 1–4 bars; 1 lap per beat only as “swirl”	R (B1)
Filter sweep	FREQ sweep of the moving band while it orbits: the band “climbs” (pitch-height)	4–16 bars	R (Lee) + G
Echo throw	throw the delay return to a point opposite the source and let it drift back over 1–2 bars	1/4–1 bar delay	G (needs the delay on its own movable path, so out of the current routing)
Riser	elevation sweep from 0° to the top + faster rotation (×2 per 4 bars), high FREQ	8–16 bars	R (elevation needs HF) + G
Drop	snap the band back to front or static on the 1 (contrast)	1 beat	G

C. Listening test: one evening at the system

Safety first: a PA set up for a club is loud. No signal goes to the speakers until the person responsible for the PA says so, and that person sets the level and the amps. Music only (the DJ’s own tracks), no test tones on the PA.

C0. Before the evening (no PA): measure the band filter’s Hz and octaves for the parameters 0.05 / 0.25 / 0.5 / 0.75 / 0.9 (offline, or on the headphone bus) so that FREQ and Q can be talked about in Hz and octaves.

Who and where: 3–5 listeners: whoever runs the system, the DJ, and 1–3 others. Three positions: centre, halfway to the ring, and about 1 m from a speaker. Listeners rotate between blocks, and each listener answers on a sheet.

Method: the DJ plays one loop-friendly track (and a second, darker one). The operator switches the settings in a random order without naming them. Each trial lasts 8 bars. Listeners answer:

direction (CW / CCW / unclear), which is an objective check;
“motion clear” on a 1–5 scale;
“comfortable / musical” on a 1–5 scale.

Block	Compare	Settings	Time
1 Speed	full band vs default band	1 lap per 8 / 4 / 2 / 1 bars, and per 2 beats	20 min
2 FREQ	at Q 2 oct, 1 lap per 4 bars	250 Hz, 1 kHz, 3 kHz, 8 kHz	15 min
3 Q	at the best FREQ	4 / 2 / 1 / ½ oct	15 min
4 Elevation	high band, azimuth fixed	elevation 0↔45° on vs off, A/B	10 min
5 Gravity	one orbiting ship, one heavy group	pulse depth 0 / small / 2× small	15 min
6 Load	1 vs 2 vs 4 ships moving at once	for comfort and vection	10 min

About 90 minutes with changes of position. Decide from the results: the speed caps (B1), the FREQ and Q defaults and range limits (B4), whether elevation is worth a control (B3), the pulse depth (B5), and how many simultaneous movers are pleasant (B6/A3). The measured values then go into Motion’s flight tuning and clip defaults, with a reference to this page.

Status: no record of it having been run as of 2026-10-31. Until it is, every G above is a guess and every R is a reading of the literature, not of this system.