Wow & flutter explained
In the world of analog audio, the irregular movement of tape, record or film causes speed fluctuation, which in turn, causes pitch fluctuation. Relatively slow changes in pitch are called wow, faster changes are called flutter.
Wow may be caused by a variety of reasons: off-center record, deformed rubber rollers, worn-out belts, a sticky cassette. It is more pronounced on compact cassette machines: because of slow tape speed travel, a slightest variation of speed turns into a noticeable change in pitch.
Flutter may be caused by a bent capstan, or by other issues with the mechanism, including gears and the motor.
Excessive pitch fluctuations are unpleasant, so it is important to measure them to evaluate performance of audio equipment.
Before measuring the fluctuation of playback speed, it is necessary to ensure that the speed itself is correct. On a record player you would adjust rotation speed using markings on the platter: when illuminated by a strobe light, the markings should appear stationary. On a tape deck you would use a tape with test signal, recorded on a high-quality machine. Playback speed and pitch are directly related, so one can be easily calculated from another.
For example, suppose you have a cassette with a 3 kHz test tone. When played on your Walkman, the actual center frequency is 2965 Hz. Using the formula for speed deviation (where f is actual playback center frequency, f₀ is expected playback frequency), you can calculate that the tape is being played ((|2965–3000|)/3000)×100% = 1.2% slower than normal, which is within generally accepted tolerance of 2% either up or down the nominal speed. For reference, 5% difference in playback speed causes change in pitch of one semitone.
Wow & flutter defined
To measure wow and flutter, use the same test tape or record. The pitch fluctuations are measured relative to the center frequency established on the previous step.
These fluctuations, formally defined by International Electro-Technical Commission (IEC) as undesirable frequency modulation (FM) components, are also represented as percentage:
where f is the center frequency of the audio being played, Δf is the variation of this frequency observed during the playback.
For example, if there are abrupt bursts of playback tone, say 40 Hz higher and 40 Hz lower relative to the center frequency of 2965 Hz, then the wow & flutter would be expressed as (40/2965)×100% = 1.35%
The above formula is correct only when the fluctuations occur exactly four times a second, or with 4 Hz modulating frequency. This rate has been established experimentally as the most objectionable. Fluctuations occurring at a lower or a higher rate have been deemed less offensive. Based on this research, a weighting characteristic to measure wow and flutter have been developed.
Looking at the weighting response curve one can see that if the rate of the irregularities drops to 0.8 Hz or increases to 20 Hz, the “irritation coefficient” is halved (-6 dB attenuation means halving the original value). Continuing with our example, if the center frequency of 2965 Hz has variation of 40 Hz above and below center frequency, with modulation frequency of 20 Hz, wow and flutter coefficient would be equal to (40/2965)×0.5×100% = 0.67%.
A pitch fluctuation, occurring with the frequency of 200 Hz is even less noticeable, so the number reflects this: 0.07×(40/2965)×100% = 0.09%. (-24 dB attenuation corresponds to 1/16 reduction of the original value; or use a formula to convert gain into factor: -23 dB gain means 0.07 factor).
Fluctuations, happening with high frequency can be perceived as “dirty” sound and may cause listening fatigue, but they are not immediately noticeable.
By the end of 1960s five standards for measuring of wow & flutter were in use internationally: CCIR, IEC, DIN, JIS and NAB, not to mention lesser known national and organizational standards.
The standards are based on almost identical weighting curves, but differ in choosing of the test frequency and, more importantly, in meter indication.
Test frequency
Two test tones have been in use for the purposes of testing average playback speed and playback speed variation: 3 kHz, chosen by CCIR, JIS and NAB, and 3.15 kHz, selected by IEC and DIN.
Weighting curves
The weighting characteristics define not one but four response curves: unweighted wow & flutter, weighted wow, weighted flutter, and weighted wow & flutter combined.
Specifications for playback and recording machines usually provide the number corresponding to the combined weighted wow & flutter. This response curve is skewed towards lower modulation frequency, that is, it is more sensitive to wow than to flutter.
Dynamics of the meters
Frequency fluctuations are measured depending on their intensity.
One method is to use a quasi-peak or weighted-peak detector. The quasi-peak detector gives higher weight to a longer impulse.
The table below shows peak weighting employed in CCIR, IEC and DIN standards. In particular, a square pulse with a duration of 0.1 of the full cycle is given 100% weight. The value gradually drops to 40% by the beginning of the next pulse.
On the picture below, impulses on each graph have the same amplitude and the same frequency of 1 Hz, but the duration is different: impulses shown on the right graph are longer, causing more gradual decay of meter input, which produces higher meter output.
Quasi-peak detector never exceeds actual peak values and can misrepresent the signal: a strong but short spike may be left almost unnoticed.
“Averaging” detectors used in JIS and NAB standards flatten the peaks even further.
The method employed in the JIS standard uses a 5-second measuring cycle time instead of 1-second for CCIR, IEC and DIN, and measures root mean squared (RMS) value instead of quasi-peak value.
The NAB detector is similar to JIS, but instead of using RMS value it represents wow & flutter as arithmetic mean value, which is colloquially known simply as average value.
JIS and NAB values (RMS and mean) are numerically lower compared to CCIR, IEC and DIN values (quasi-peak).
By the end of 1970s the “American” NAB standard fell by the wayside. The IEC, CCIR and DIN standards became more homogeneous. The JIS standard remained in use by Japanese manufacturers. So, the industry effectively converged on two standards: “European” and “Japanese”, the major difference between them being the indication of measured value: quasi-peak or RMS.
In 1980s the DIN and IEC standards have been amended to allow an alternative method of detecting peaks — the 2-σ method. It outputs the maximum value that is exceeded no more than 5% of the time or, to put it differently, it is the second-highest reading of a 20-reading group.
This method has been chosen in the 2012 version of the AES6–2008 standard.
Before continuing, let us review the different methods of detecting the shape of a waveform:
- Peak value: maximum absolute value in a half cycle.
- Peak to peak value: sum of absolute values of the opposite peaks; for a pure sine wave peak to peak value = 2 × peak value.
- Quasi peak (QP) value or weighted peak value: the pulses are weighed depending upon their duration within a relatively short measuring cycle.
- 2-σ peak value: the maximum value that is exceeded no more than 5% of the time within a longer measuring cycle.
- Effective value or root mean squared (RMS) value: for a pure sine wave it comes down to 0.707 × peak value; uses long measuring cycle.
- Average value or mean value: equals to 0.637 × peak value for a pure sine wave.
In the case of measuring wow and flutter, the fluctuations of playback speed and pitch are irregular, not a pure sine wave, so it is not possible to convert values obtained with one system into another system, there is no exact formula. You cannot just multiply DIN value by 0.7 to obtain JIS value. You can only compare the values obtained with the same method.
The most that can be asserted is that the relationship between the magnitude of the values holds: peak ≥ quasi-peak ≥ RMS ≥ mean. In practice, RMS value is usually about one half of peak value.
When it comes to practical usage, here are the common meter indications:
* CCIR, IEC and DIN — weighted peak or quasi-peak (QP)
* IEC and DIN — 2-σ method (optional)
* JIS — root mean squared (RMS)
* NAB — arithmetic mean, also sometimes RMS
* AES6–2008 — quasi-peak
* AES6–2008 (2012) — 2-σ method
Analog meters
Before the digital age, wow and flutter were measured using analog meters, like this Leader LFM-39A.
Its mode buttons are described as follows:
- “W&F” (Wow and flutter) — use this switch when measuring overall Wow & Flutter components contained in the measured signal.
- “WTD” (Weighted) — use this switch when making measurements of weighed characteristics in accordance with JIS, CCIR and DIN specifications.
- “WOW” — use this switch when measuring WOW component up to 6 Hz.
- “FLUTTER” — use this switch when measuring FLUTTER component over 6 Hz.
The above means, that if you want to measure the same parameter that is usually provided in technical specifications of cassette decks and record players, you need to use “WTD”, not “W&F”.
The description of the indication buttons is not very creative and basically says that a corresponding button should be used when making measurements in accordance with JIS, CCIR or DIN specifications. Notice that JIS and CCIR buttons are “linked” with 3 kHz label to remind that both of these standards use 3 kHz test tone. DIN button is marked with 3.15 kHz label.
In practice, because this meter has the measuring limits for input frequency within ±10% from nominal, you can use a 3 kHz tone for DIN measurement as long as the actual center frequency is within 2835–3465 Hz. Theoretically, you should be able to use CCIR mode instead of DIN if you have a 3 kHz test tone, and the result should be the same.
Below is the Kenwood FL-140 wow-flutter meter, and its function and indication buttons look very similar. The meaning of the “UNWTD” button is easier to understand than “W&F” on the Leader meter.
This is the Kikusui 6701 wow & flutter meter, its indication selectors include NAB, and its mode buttons are marked even more clearly than on the Kenwood. In particular, the “WEIGHTED” button must be used for measuring in accordance with JIS, CCIR, DIN and NAB standards, while “LINEAR” button must be used for measuring overall unweighted wow and flutter.
Measuring and comparing values from different methods
Here are the instructions from the Model 1035 wow & flutter meter by Dynascan corporation. Besides measuring, they also describe how to create your own test tape.
Below are three measurements of the Nakamichi Dragon, performed by Artur Kwiatkowski.
Unweighted wow & flutter using DIN method. Meter indication: quasi-peak value. Nominal playback frequency 3150 Hz. It is the highest value of the three, ±0.12%. It gives equal weight both to low-frequency and higher-frequency pitch fluctuations. Notice the “±” sign, which means that the playback frequency wanders up to 0.12% above and up to 0.12% below the center frequency.
Weighted wow & flutter using DIN method. Meter indication: quasi-peak value. Nominal playback frequency 3150 Hz. It is much lower at ±0.04%, heavily skewed towards the wow portion of the weighting curve and omitting higher-frequency flutter component. This measurement is used for reporting “DIN” wow & flutter in equipment specifications.
Weighted wow & flutter using JIS method. Meter indication: root mean squared or RMS. Nominal playback frequency 3000 Hz. It is the lowest of the three, 0.02%. This measurement is used for reporting combined wow & flutter in equipment specifications. It is often indicated as “W.RMS” or “WRMS” to emphasize that it is a weighted measurement.
These are exceptionally good numbers. How do I know, without listening to this machine? One criterion is the DIN standard, which specifies limits for different kinds of sound recording and playback machines. In particular, hi-fi cassette decks should exhibit weighted wow & flutter no higher than ±0.2%; non-hi-fi cassette machines should stay within ±0.4%. The Dragon shows ±0.04%, an order of magnitude lower!
Another unlikely source of truth is the Soviet state standard GOST 24863–87, which has been fully aligned with IEC standard. It specifies different wow & flutter limits for different classes of tape machines.
In particular, five classes have been defined for cassette machines:
- Highest class (a.k.a. “hi-end”): ±0.08%
- First class (a.k.a. “hi-fi”): ±0.12%
- Second class (“hi-fi” and portables): ±0.2%
- Third class (usually portables): ±0.35%
- Fourth class (personal stereo and dictation machines): ±0.4%
Soviet component decks usually met either the first or the second class specifications, mirroring the DIN requirement.
Having great standards did not transmogrify into products to match them. The Mayak-010 was the only highest class cassette deck ever produced in the Soviet Union, costing as much as ten average monthly salaries.
Nowadays, everyone who owns a computer can measure wow & flutter of their Walkman, cassette deck or record player. The first step is to obtain a test tape or record one using a test tone.
Insert the test tape in your cassette deck or walkman and connect its output to the audio input of your Windows computer. Download WFGUI, developed by Alex Freed. It is a free wow and flutter meter. Its user interface is just a single window, there are few controls, but some options may be confusing.
First, select the test frequency: 3000 Hz or 3150 Hz, depending on the test tape you have. If you remember, IEC and DIN use 3150 Hz tone, while NAB and JIS use 3000 test tone, but the difference in test frequency makes negligible effect on measurements, so you can use either.
Unlike the hardware wow & flutter meters mentioned above, WFGUI does not have “Indication” switches, because it displays measurement results in accordance to DIN and JIS standards, and it does it simultaneously, so there is no need for switching between them.
On the other hand, WFGUI does have an equivalent to “Mode” or “Function” selector similar to hardware meters. It is implemented as an unassuming dropdown box right above the peak meter. You can select one of the four standard weighting curves: “Unweighted”, “Wow”, “Flutter”, and, confusingly, “DIN”. Um, what? Yes, the last option should be called “Weighted wow & flutter”, you should choose it if you want to compare your measurements to the numbers provided in most equipment specifications.
Play the test tape. Make sure that the signal is strong enough, so that the level meter shows the segments somewhere in the middle of the bar.
With “DIN” selected from the dropdown, the Peak display styled as an analog needle instrument shows wow & flutter in accordance to DIN standard, using quasi-peak detector. The RMS box above it shows values according to JIS standard. Both measurements are weighted. Sometimes they are reported in literature as “W.Peak” (or “Q.Peak”) and “W.RMS” (or “WRMS”), respectively. The JIS value is averaged over a longer period of time, so you need to perform at least half a minute worth of measurements; the operation manual for WFGUI recommends discarding the numbers obtained during the first 20 seconds.
The maximum value box shows maximum peak (which is, in fact, quasi-peak) and maximum RMS value (which is weighted if you chose anything but “Unweighted” from the mode dropdown) in the last 10 seconds. If you like pretty graphs, you can turn on the “Save log” option, and then load the resulting log data into a spreadsheet.
The above graph shows the WRMS value numerically being about a half of Peak value. This relationship can be tracked through specifications for different machines.
Some comments to the above specs are in order:
Onkyo TA-207 is a high-quality 3-head cassette deck from early 1990s with the numbers well within the requirements for a hi-fi machine. JIS WRMS value is 2/3 of the DIN Peak value.
The 1993 Technics RS-TR333 double-cassette deck manages to stay within hi-fi specs, if only barely. Areas other than the U.S. and Canada have better JIS specs while having the same DIN value, I wonder how this is possible.
The inexpensive JVC TD-W118 double cassette deck was produced in late 1990s. The specs are similar to the Technics machine. The same value is reported for DIN and IEC, while JIS WRMS value being just one half of it.
The 3-head Sony TC-K615S has some interesting numbers. WRMS is reported for NAB instead of average value. Also, the IEC number is twice lower than the DIN number. This flies in the face of the assumption that DIN and IEC tests should produce the same numbers. Or should DIN and CCIR produce the same numbers, and IEC is different?
The TEAC Z-6000, a gorgeous early 1980s machine, has unweighted wow & flutter of 0.15% JIS RMS, and weighted wow & flutter 0.03% JIS RMS (or WRMS for short), every bit as good as the Nakamichi Dragon.
The TEAC W-1200, one of the very few cassette decks that you can buy new in 2021, is spec’d to have no more than 0.25% WRMS. Knowing that DIN (Peak) is always higher than JIS WRMS, this number is significantly higher than ±0.2% DIN Quasi-Peak. This deck would not be considered a hi-fi machine back in 1980s. This would be a poor showing even for a cheap portable player, but for a component deck that is priced around $500 it is a disaster.
What is your magic number
So, what is the highest value of wow & flutter that you are willing to tolerate? For myself, I decided that for playing back pre-recorded tapes, 0.15% WRMS is good enough for most kinds of music, and anything above 0.2% WRMS is unacceptable.
To record my own tape I need the number twice lower to account for the fluctuations introduced during recording, so it comes down to about 0.08% WRMS, which, incidentally, is what I measured on my Technics deck. All in all, my “black plastic crap” deck is good enough for me.
It is interesting to compare modern perception of acceptable wow & flutter with the early days of magnetic recording and long play records. In this 1954 booklet Ampex is boasting about high quality of its tape recorders and magnetic tape, quoting wow & flutter numbers “under 0.25% RMS” for their cheapest model, noting that the irritating effects of wow and flutter “would become noticeable to even the non-critical listener at a level of about 0.5% RMS”.
I don’t know what to say except, WOW! I don’t think that human hearing and tolerance to pitch fluctuation changed so much in half a century. I suppose the “noticeable 0.5% RMS” is an unweighted number. It can be seen from the specifications posted above, that unweighted measurements can be easily several times higher than weighted ones.
Maybe TEAC designers were guided by these numbers when they came up with 0.25% WRMS for their W-1200 cassette deck? As good as a 1954 Ampex.
That is all, folks! Below is additional reading if you are inclined to learn about calculating of average and root mean squared values.
Math: average value
The American NAB standard represented wow & flutter as an average value, which is a colloquial name for arithmetic mean value.
Arithmetic mean is calculated by adding up the values of a set and dividing by the number of elements in the set.
The average value of a symmetrical alternating quantity like voltage represented by a sine wave is measured over one half of a cycle, since the average value over a complete cycle is zero.
It can be found by integrating the sinusoidal quantity over half a cycle and dividing by half the period.
The practical takeaway is that the average value for a pure sinusoidal waveform can be calculated as:
Average value = 0.637 × maximum or peak value
Math: root mean square value
The JIS standard calculates wow and flutter using root mean squared value also known in electrical engineering as effective value.
To find the root mean squared value of a set of numbers, all the numbers in the set are squared, then arithmetic mean of the squares is calculated, and the square root is taken of the result.
In electrical engineering, RMS value has a physical meaning, indicating the voltage of a DC circuit that supplies the same electrical power to a given load as an AC circuit. In particular, RMS value is used to calculate heating effect of AC circuits. It does not have any special meaning for measuring wow and flutter, though.
This allows calculating RMS value from peak value for a pure sinusoidal waveform:
Root mean squared value = 0.707 × maximum or peak value
Math: 2-σ method
Yet another method to account both for the duration and amplitude of the fluctuations is the statistical weighting on the basis of the normalized 2-σ frequency of the Gaussian distribution curve over a defined test period.
2-σ method gives the maximum value that is exceeded no more than 5% of the time or, to put it differently, it is the second-highest reading of a 20-reading group.
