The Notes Your Room Rings

Three numbers decide where the bass piles up

The Modes

Every resonance below 300 Hz, axial stems tallest

Axial, tallest: one pair of walls Tangential: four walls Oblique, shortest: all six Hatched: above the Schroeder frequency Bars: modes per third-octave band; a notched bar holds fewer than the band before it

Worst pile-up
Bonello
Widest gap
Schroeder

The Room

The Floor

Walk the room while it plays and listen

VanishesBoomsDashed lines: where it vanishes

Mode

Not Here
Here

One mode at a time. A seat on one mode's quiet line can sit on another's peak: step through the low modes before moving the sofa.

Volume

A sine at the picked mode. It starts only on this click, its loudest is a quarter of full scale, and it stops by itself after 60 s. Small speakers may not play the lowest modes at all: a silent tone is the speaker, not the room.

The Ratios

Published proportions, your room plotted among them

A ratio is a reference point, not a verdict. Each button keeps your room's volume and reshapes it to that ratio, height the shortest side.

Every Mode

Every mode below 300 Hz, as a table

Frequency	Type	Half-waves	Band

The Method

Every formula, its source and its worst error

The modes

A rigid rectangular room of length L, width W and height H rings at every frequency

f = (c/2)·√((n_x/L)² + (n_y/W)² + (n_z/H)²)

with n_x, n_y, n_z whole numbers of half-waves, not all zero (Rayleigh; Kuttruff, Room Acoustics). One index above zero is an axial mode, between one pair of walls; two make a tangential mode; three an oblique one. The pressure of a mode at a point is

p ∝ cos(n_xπx/L)·cos(n_yπy/W)·cos(n_zπz/H)

so every mode is loudest in the corners, and each index draws that many quiet lines across its side. The plan shows |p| at the ear height.

The speed of sound in dry air is c = 331.3·√(1 + T/273.15) m/s, T in °C: 343.2 m/s at 20 °C (Wikipedia, “Speed of sound”).

The checks

Bonello (1981). Count every mode in each third-octave band, from the band of the first mode to the band of the 48th. The count should never fall from one band to the next. Coincident axial modes are flagged. Bonello's paper was not read for this page; it follows three secondary descriptions, quoted:

“non-decreasing density of modes within increasing third-octave-bands” (akutek.info, “Ratios of small rooms”, 2012)
“analyzes the first 48 room modes and plots the number of modes in each one-third of an octave … each one-third of an octave must have more modes than the preceding one” (Wikipedia, “Room acoustics”, after Ballou, Handbook for Sound Engineers, p. 56)
“no third-octave band should contain two or more axial modes that are within 5 Hz of each other” (acoustic.samesound.ru)

The first two disagree on a band that equals the one below; the page fails a band only when it falls, and reports the equal bands too. Bands are IEC 61260-1 base ten, labelled with ISO 266 nominal frequencies.

Schroeder frequency. f_s ≈ 2000·√(T₆₀/V) Hz, V in m³ (Schroeder 1996). Above it, modes overlap and a room stops ringing at separate notes. The reverberation time is an assumption, 0.4 s unless you change it: this page cannot measure your room.

Mode count. Kuttruff's estimate N(f) ≈ (4π/3)V(f/c)³ + (π/4)S(f/c)² + (L/8)(f/c), S the wall area and L the total edge length, is the check on the listing: the count below 200 Hz must land within 10 % of it.

The ratios

Height : width : length, as reported by M. Meissner (Archives of Acoustics 43(2), 2018): Bolt (1946) 1 : 1.25 : 1.6; Sepmeyer (1965) 1 : 1.14 : 1.39, 1 : 1.28 : 1.54 and 1 : 1.6 : 2.33; Louden (1971) 1 : 1.4 : 1.9, from a paper titled for “eigentones”. The IEC 60268-13 listening-room rule, W/H ≤ L/H ≤ 4.5·W/H − 4 with both under 3, is quoted from acoustic.ua; the standard itself was not read.

Receipts

Checked	Against	Worst error	Tolerance
Speed of sound, 0 °C and 20 °C	Wikipedia: 331.3 m/s, 343.2 m/s, 1126.0 ft/s	0.032 ft/s	0.05
18 axial modes of a 5 × 4 × 2.5 m room	Hand arithmetic to 0.001 Hz	0.00048 Hz, the rounding of the written digits	0.0005 Hz
Modes below 200 Hz, three rooms	Kuttruff's N(f)	4.2 %	10 %
Third-octave mid-bands	ISO 266 nominal labels	0.94 %	2 %
Every mode below 300 Hz, five rooms	A brute-force count	0 missing	0
Pressure in all eight corners	±1 for every mode	below 10⁻¹²	10⁻¹²

Limits

Rigid rectangular box only: no L-shapes, no doors, windows or openings, no furniture, no absorption. The modes are where problems can be, not a measurement of what you hear.
No damping, so every mode is drawn as a line. A real mode has a width, and in a damped room its peaks and nulls are shallower than the plan shows.
No source: the plan shows where a mode can be heard, not how hard a speaker in one spot drives it.
Bonello's criterion and the IEC rule come through secondary sources, quoted above.
Dry air. Humidity moves the speed of sound by a fraction of a percent, ignored here.