The band your graphic equalizer labels 500 Hz actually sits at 501.187233 Hz, and ISO 266 says so in plain text. The standard calls the rounding a practical consideration. It then quantifies the damage, noting that the largest single gap between a printed frequency and the calculated one is 0.94 percent.
That worst case is not tucked away in some corner nobody visits. It lands on 160 Hz, 1600 Hz, and 16 kHz, three of the most-grabbed faders on any 31-band unit. Each of those bands centers about one percent low, at roughly 158.5 Hz, 1584.9 Hz, and 15,848.9 Hz.
Nothing is broken. But if you have ever set a fader to 1600 and found your analyzer putting the dip somewhere else, this is part of the answer.
Those preferred numbers predate audio entirely. Colonel Charles Renard, a French army engineer working on captive balloon equipment, proposed the scheme around 1877, and ISO adopted it in 1949. The goal was to cut the number of sizes a manufacturer had to stock.
R10 splits each decade into ten geometric steps and rounds every one of them to something a person can print and read at a glance. That yields 1.00, 1.25, 1.60, 2.00, 2.50, 3.15, 4.00, 5.00, 6.30 and 8.00, repeated in every decade. Multiply through, and you have every number on your equalizer.
The rounded preferred numbers printed across the front panel are therefore an industrial convention about legibility, picked up by acousticians much later because a shared vocabulary was worth more than exactness.
The base-two definition treats it as literally one third of an octave, a ratio of the cube root of two, which comes to 400 cents. The base-ten definition, used by IEC 61260-1 and ANSI S1.6, treats it as one tenth of a decade instead. That ratio is the tenth root of ten, about 398.631 cents, and the proper name for it is a decade.
Under one and a half cents of difference per step. Compound that across thirty steps and it stops being academic. The top band on a 31-fader row lands at 19,952.6 Hz under base ten and 20,158.7 Hz under base two, roughly 206 Hz apart.
Audio equipment almost always takes the base-ten path, because ANSI S1.11-2004 puts the center of band k at 1000 times G raised to the power of k minus thirty, over three, with G fixed at ten to the power 0.3. Underwater acousticians work from ISO 18405 and get the base-two answer. Same words, different frequencies.
You will not hear it. A boost at the fader marked 1600 does what a boost at 1584.9 does, because the filter is far too wide for fifteen hertz to move the result.
Where it bites is on paper. Room measurement reports, analyzer captures, and acoustic treatment calculations all reference third-octave bands, and when one tool prints rounded labels while another prints calculated centers, your columns stop lining up even though the filters agree.
It also gives you something useful to ask of a spec sheet. When a plugin promising true ISO centers turns up, the question worth asking is which base it followed, and whether its lowest and highest bands sit where a hardware unit's would.
That span is not a design choice at all. Thirty steps at a tenth of a decade each is exactly three decades, so any 31-fader row has to run from some frequency to a thousand times that frequency. Anchor the bottom at the 20 Hz label and the top is forced to 20 kHz, which is why that pairing shows up on nearly every unit ever made, and why dropping even one band costs you an end of the audible range.
That worst case is not tucked away in some corner nobody visits. It lands on 160 Hz, 1600 Hz, and 16 kHz, three of the most-grabbed faders on any 31-band unit. Each of those bands centers about one percent low, at roughly 158.5 Hz, 1584.9 Hz, and 15,848.9 Hz.
Nothing is broken. But if you have ever set a fader to 1600 and found your analyzer putting the dip somewhere else, this is part of the answer.
The labels come from balloon cable, not from acoustics
ISO 266 does not derive its frequencies from hearing research. It borrows them from the R10 series of preferred numbers in ISO 3, anchored to 1000 Hz, with each step being ten raised to the power of one tenth.Those preferred numbers predate audio entirely. Colonel Charles Renard, a French army engineer working on captive balloon equipment, proposed the scheme around 1877, and ISO adopted it in 1949. The goal was to cut the number of sizes a manufacturer had to stock.
R10 splits each decade into ten geometric steps and rounds every one of them to something a person can print and read at a glance. That yields 1.00, 1.25, 1.60, 2.00, 2.50, 3.15, 4.00, 5.00, 6.30 and 8.00, repeated in every decade. Multiply through, and you have every number on your equalizer.
The rounded preferred numbers printed across the front panel are therefore an industrial convention about legibility, picked up by acousticians much later because a shared vocabulary was worth more than exactness.
Two definitions disagree, and the gap widens as you climb
There is a second wrinkle, and it runs deeper than rounding. The standards do not agree on how wide a third of an octave is.The base-two definition treats it as literally one third of an octave, a ratio of the cube root of two, which comes to 400 cents. The base-ten definition, used by IEC 61260-1 and ANSI S1.6, treats it as one tenth of a decade instead. That ratio is the tenth root of ten, about 398.631 cents, and the proper name for it is a decade.
Under one and a half cents of difference per step. Compound that across thirty steps and it stops being academic. The top band on a 31-fader row lands at 19,952.6 Hz under base ten and 20,158.7 Hz under base two, roughly 206 Hz apart.
Audio equipment almost always takes the base-ten path, because ANSI S1.11-2004 puts the center of band k at 1000 times G raised to the power of k minus thirty, over three, with G fixed at ten to the power 0.3. Underwater acousticians work from ISO 18405 and get the base-two answer. Same words, different frequencies.
The rounding is far smaller than the filter it names
Before you rebuild your workflow around any of this, check the scale. A third-octave filter centered near 1585 Hz spans roughly 370 Hz between its half-power points. A 15 Hz labeling error is about four percent of that width.You will not hear it. A boost at the fader marked 1600 does what a boost at 1584.9 does, because the filter is far too wide for fifteen hertz to move the result.
Where it bites is on paper. Room measurement reports, analyzer captures, and acoustic treatment calculations all reference third-octave bands, and when one tool prints rounded labels while another prints calculated centers, your columns stop lining up even though the filters agree.
It also gives you something useful to ask of a spec sheet. When a plugin promising true ISO centers turns up, the question worth asking is which base it followed, and whether its lowest and highest bands sit where a hardware unit's would.
That span is not a design choice at all. Thirty steps at a tenth of a decade each is exactly three decades, so any 31-fader row has to run from some frequency to a thousand times that frequency. Anchor the bottom at the 20 Hz label and the top is forced to 20 kHz, which is why that pairing shows up on nearly every unit ever made, and why dropping even one band costs you an end of the audible range.
