Revisiting the GedLee Metric: A More Reliable Gm Test in VIRTINS Multi-Instrument
Revisiting the GedLee Metric: A More Reliable Gm Test in VIRTINS Multi-Instrument
How a frequency-adaptive FFT test plan, conventional harmonic measurements and harmonic phase are being combined into a standardized format for future electronics and loudspeaker reviews
Scope of this article
This is an academic measurement project concerned with improving the repeatability and usefulness of GedLee Metric measurements. It does not propose that Gm should replace conventional distortion measurements, nor that any single number can predict the perceived quality of an audio product. The purpose is to develop a better test method, understand what the Gm result is responding to, and establish a consistent measurement format for future Joseph Crowe electronics and loudspeaker reviews.
Abstract. Several years ago, I began experimenting with the GedLee distortion metric in VIRTINS Multi-Instrument. At that time my experience with the software was limited, and my original Device Test Plan was supplied directly by VIRTINS. It gave me a valuable starting point, but I remained uncertain about some of the results—particularly at low frequencies. With the assistance of ChatGPT, I recently revisited the complete measurement process. The investigation showed that a fixed FFT length was not equally suitable across a sweep from 20 Hz to 50 kHz. The revised plan now uses progressively longer FFT records as frequency decreases. A second diagnostic layer records THD and the individual H2, H3 and H4 products relative to the fundamental. VIRTINS can also report the relative phase of each harmonic, which is especially relevant because phase is part of the Gm calculation. Together, these measurements provide a much more useful framework for studying how different nonlinear mechanisms produce different Gm results.
VIRTINS Multi-Instrument: an unusually flexible measurement platform
VIRTINS Technology was established in Singapore in 2004, and the first version of Multi-Instrument was released in November of that year. Its original premise was both practical and ambitious: use the sound card already present in a personal computer as the input and output hardware for a collection of virtual laboratory instruments. Over time the software expanded far beyond a basic oscilloscope and spectrum analyzer. It now supports ASIO audio interfaces, dedicated data-acquisition hardware, signal generation, FFT and octave analysis, transfer-function measurements, data logging and automated Device Test Plans. [1][2]
The interface can feel more like a configurable laboratory framework than a conventional consumer-audio application. That flexibility creates a considerable learning curve, but it is also what makes this project possible. A Device Test Plan can load different panel configurations, generate a sequence of static tones, wait for the measurement to settle, collect derived data and plot the results automatically.
Of particular interest here, VIRTINS added harmonic-amplitude and harmonic-phase arrays, together with the GedLee Metric, in Multi-Instrument 3.8 Build 2 in May 2018. At the time of writing, it is the only commercially available audio measurement package I have found that calculates Gm directly. Other programs can perform excellent THD and harmonic analysis—Room EQ Wizard can also display harmonic phase—but they do not calculate Gm. VIRTINS therefore offers the important practical advantage of measuring Gm, THD, individual harmonic magnitude and harmonic phase within one software environment. [2][3]
Why revisit Gm?
Conventional total harmonic distortion is useful, but deliberately incomplete. THD combines the energy of the harmonics into one root-sum-square value. In doing so, it discards the identity and phase of the individual products. A spectrum dominated by H2 can therefore have a larger THD number than another spectrum containing a long sequence of higher-order odd harmonics, even though the two nonlinear behaviours are fundamentally different.
This limitation was illustrated clearly in my previous article, “Beyond THD+N: Exposing Low-Level Crossover Distortion in Audio Power Amplifiers.” In that comparison, a Type 45 triode amplifier produced more total harmonic distortion because its spectrum was dominated by second harmonic. A Class A/B amplifier produced a lower total number but retained a broad comb of higher-order odd harmonics associated with crossover nonlinearity. The headline THD values alone did not adequately describe that distinction.
The GedLee Metric, proposed by Earl Geddes and Lidia Lee, approaches nonlinear distortion differently. Rather than treating every distortion component only according to its energy, Gm is derived from the nonlinear transfer behaviour and applies perceptually motivated emphasis to nonlinearities occurring near the low-level region of the waveform. It also incorporates the relative phase of the harmonics. Consequently, two devices with similar THD—or even identical harmonic amplitudes—can produce different Gm values if their harmonic phases combine to form different transfer characteristics. [4]
This makes Gm particularly interesting for studying mechanisms such as the handoff region of bipolar output transistors in a Class A/B amplifier or asymmetry and position-dependent force in a loudspeaker motor. It does not make Gm a universal sound-quality score. It gives us another way to examine nonlinear behaviour that conventional THD may obscure.
The original test plan
When I first explored Gm, I attempted to create a VIRTINS Device Test Plan myself but found the process difficult. VIRTINS kindly supplied a working plan and its associated panel settings at no charge. Because my experience with the software was limited, I leaned heavily on what had been provided and used it as the basis of my original article, “Measuring GedLee Distortion (Gm).”
That early work was useful, but I was never entirely comfortable with every result. The low-frequency portion of the graph sometimes behaved in ways that did not appear consistent with the DUT or with the conventional distortion measurements. Those doubts did not prove that Gm itself was invalid. They suggested that the test configuration might not be giving the Gm algorithm equally good data at every frequency.
This distinction is important. A calculated result can only be as dependable as the spectral amplitude and phase information supplied to it. Gm is particularly demanding because it uses the relative phase of the harmonics as well as their magnitudes.
What ChatGPT changed in the development process
The recent work began as an attempt to verify the old plan rather than replace it. ChatGPT made it practical to inspect the structure of the VIRTINS Device Test Plan and Panel Setting Files, compare revisions, generate controlled test variants and interpret repeated loopback results. It also helped uncover several configuration details that were not obvious from the interface alone.
This was not a case of asking artificial intelligence for a distortion number and accepting it. Each revision was run in VIRTINS, its behaviour was observed, and incorrect assumptions were rejected. Several early attempts failed. Those failures were useful because they isolated the roles of FFT length, measurement settling, derived-data naming and spectrum normalization. The final method emerged through repeated measurement and comparison.
The most consequential finding concerned the number of FFT points used at different parts of the frequency range.
Why one FFT length was not enough
An FFT does not have the same practical relationship to a 20 Hz signal that it has to a 10 kHz signal. At a fixed sample rate, the number of FFT points determines both the duration of the analyzed record and the spacing between frequency bins:
Record duration = FFT points ÷ sample rate
Frequency-bin spacing = sample rate ÷ FFT points
At the 384 kHz sample rate used for this test, a 262,144-point FFT represents approximately 0.683 second of data and has bins spaced about 1.465 Hz apart. At 20 Hz, that record contains fewer than 14 cycles of the fundamental. By comparison, a 1,048,576-point FFT represents approximately 2.731 seconds, contains about 55 cycles at 20 Hz and reduces the bin spacing to about 0.366 Hz.
For an ordinary amplitude spectrum, a short record may still produce a result that looks plausible. Gm is more sensitive because the measurement depends on stable estimates of both harmonic magnitude and relative phase. At the bottom of the sweep, the original fixed-length approach provided much less low-frequency information than it did higher in the audio band. Increasing the FFT length substantially improved the stability and credibility of the low-frequency result.
Using the longest FFT everywhere would solve the record-length problem, but it would make the entire sweep unnecessarily slow and computationally heavy. The revised plan therefore changes FFT length in four bands:
| Test-frequency range | FFT points | Record duration at 384 kHz | Bin spacing |
|---|---|---|---|
| 20–80 Hz | 1,048,576 | 2.731 s | 0.366 Hz |
| 88–320 Hz | 524,288 | 1.365 s | 0.732 Hz |
| 353–1,160 Hz | 262,144 | 0.683 s | 1.465 Hz |
| 1,281 Hz–50 kHz | 131,072 | 0.341 s | 2.930 Hz |
These boundaries should not be interpreted as universal standards. They are the settings adopted for this 384 kHz measurement system after practical validation. A different sample rate, converter, test bandwidth or required harmonic order may justify different choices. The underlying principle is the important part: the FFT record must be long enough for the lowest frequency being measured, while excessively long records are unnecessary at high frequencies.
The adaptive plan uses 80 logarithmically distributed test frequencies from 20 Hz to 50 kHz. It automatically loads the appropriate Panel Setting File when it enters each FFT range, then allows the analyzer enough time to acquire and publish a settled result. This provides much finer frequency detail than the original plan while improving the area that had created the most doubt.
Figure 1. The adaptive FFT strategy used for the revised Gm sweep. Longer records improve low-frequency resolution, while shorter records keep the upper-frequency portion of the test efficient. These ranges were validated for this 384 kHz measurement system and are not proposed as universal settings.
Adding THD and the individual harmonics
Once the Gm sweep had been improved, the next question was how to understand what was causing a particular Gm value. A Gm graph by itself tells us that the weighted nonlinear behaviour has changed, but it does not immediately show whether the change is associated primarily with H2, H3, H4 or a more complicated harmonic pattern.
The revised diagnostic plan therefore records conventional THD together with H2, H3 and H4. These harmonics provide a familiar bridge between Gm and the conventional measurements used throughout high-end audio. H2 can help reveal asymmetry; H3 can be associated with a more symmetrical curvature; and a series of odd harmonics can help expose abrupt nonlinear behaviour such as crossover distortion. These are clues rather than automatic diagnoses, but they make the Gm result much easier to investigate.
Measuring the harmonics correctly required one additional discovery. VIRTINS could return the RMS level of each harmonic, but those values initially appeared as absolute analyzer levels. They were therefore not directly comparable with THD, which was already referenced to the fundamental. The solution was to use the Spectrum Analyzer’s tone-peak normalization and set the reference to the exact fundamental at each test frequency.
Because the normalization frequency is stored inside a VIRTINS Panel Setting File, each frequency in the diagnostic sweep requires its own PSF. The Device Test Plan loads the matching PSF before generating each tone. H1 then becomes the 0 dB reference, and H2, H3 and H4 are reported directly in dBc below the fundamental. This makes a simple but essential comparison possible: if H2 is the dominant distortion product, its level should be reasonably consistent with the total THD result.
Figure 2. Tone-peak normalization places H1 at the 0 dB reference so H2, H3 and H4 can be read directly in dBc and compared meaningfully with THD. The levels shown are illustrative rather than measurements from a particular DUT.
Why harmonic phase matters
Harmonic magnitude is only part of the story. VIRTINS can also produce a report containing the frequency, RMS magnitude and relative phase of each harmonic. This is especially insightful in the context of Gm because relative harmonic phase is used in the calculation.
Consider two nonlinear systems that generate the same H2, H3 and H4 amplitudes. Their conventional THD values will be the same. If the relative phases of those harmonics differ, however, the products will combine into different time-domain waveforms and imply different nonlinear transfer behaviour. VIRTINS’ own Gm documentation illustrates this principle with two examples having the same harmonic magnitudes and the same 6.48% THD, but different harmonic polarities. The resulting Gm values are 2.22 and 0.92. [4]
Harmonic phase is not exclusive to VIRTINS; Room EQ Wizard can also display the phase of individual harmonics. The advantage of VIRTINS for this project is integration. REW does not calculate Gm. Within VIRTINS, Gm, THD, harmonic magnitude and harmonic phase can all be examined under the same analyzer configuration and signal conditions. That reduces ambiguity when trying to understand why the perceptually weighted result differs from the conventional one.
Figure 3. A genuine VIRTINS harmonic report showing order, frequency, RMS magnitude, percentage and relative phase. The phase column provides information discarded by conventional THD and used internally by the Gm calculation.
Two complementary test plans
The finished workflow uses two related plans rather than forcing every purpose into one very long test:
| Plan | Primary purpose | Results |
|---|---|---|
| Adaptive 80-point sweep | High-resolution verification of Gm across 20 Hz–50 kHz using four FFT lengths | Gm and THD |
| Normalized 20-point diagnostic sweep | Direct comparison of Gm with conventional harmonic structure | Gm, THD, H2, H3 and H4 |
The reader does not need to reproduce the full development process or manually build hundreds of instructions. The downloadable packages contain the Device Test Plans and their required PSFs. Users will still need to confirm their own audio interface, sampling format, input range, output level and signal routing before running a DUT. A direct loopback test should always be performed first.
Download the adaptive 80-point Gm/THD package:
Download the VIRTINS adaptive-FFT test files
Download the normalized 20-point Gm/THD/H2/H3/H4 package:
Download the VIRTINS comprehensive diagnostic test files
The files were developed using VIRTINS Multi-Instrument Pro 3.9.17.2 with a 384 kHz, 32-bit measurement path. They should be treated as a starting configuration rather than a substitute for validating the complete measurement chain.
What the method can—and cannot—tell us
The combined presentation of Gm, THD and individual harmonics is intended to encourage better questions rather than produce a simplistic ranking. If two products have similar THD but different Gm, their harmonic order and phase may help explain the difference. If Gm rises at the same frequency that H3 or H4 rises, that relationship is worth investigating. If Gm changes while the first few harmonic magnitudes appear unchanged, the higher orders or harmonic phase may be contributing.
The measurement still has practical limits. Noise, hum, acoustic background, converter distortion, bandwidth and clipping can all contaminate the result. At a 384 kHz sample rate, the theoretical Nyquist frequency is 192 kHz. H4 from a 50 kHz fundamental would occur at 200 kHz and is therefore not a valid measurement. Acoustic testing introduces further complications because the room, microphone and ambient noise become part of the measurement chain.
Figure 4. The 192 kHz Nyquist boundary determines which harmonics remain physically measurable. At a 50 kHz fundamental, H2 and H3 remain below the theoretical limit, while H4 occurs at 200 kHz and must be excluded.
Most importantly, Gm should not be treated as a final verdict on audibility or musical quality. It is an experimental, perceptually informed nonlinear-distortion metric. Its value here is comparative: it may reveal distinctions that THD alone does not, especially when the associated harmonic magnitude and phase information is available for context.
Standardizing future Joseph Crowe measurements
The practical goal of this work is to establish a repeatable format for future testing. Electronics and loudspeaker reviews can now present Gm and THD on consistent frequency axes, use sufficient FFT length at low frequencies, and add normalized H2–H4 when a closer look at the distortion structure is useful.
This will make comparisons between products more meaningful. A loudspeaker motor, tube amplifier, Class A solid-state amplifier and bipolar Class A/B output stage may arrive at similar THD values through very different nonlinear mechanisms. Viewing Gm beside the individual harmonics—and, where appropriate, their relative phase—provides a more complete record of those differences.
The work is not finished. The next objective is to develop transfer-function and distortion-residual graphs similar to those discussed in the Gedlee literature. Harmonic magnitudes and phases can be used to reconstruct the nonlinear waveform after the fundamental is removed. That may help readers see whether the underlying distortion is smooth and asymmetrical, concentrated near the zero crossing, or associated with another region of the transfer curve.
Such a graph will not identify a physical cause by itself. It could, however, make the measured behaviour much easier to relate to plausible mechanisms—for example, loudspeaker motor nonlinearity, suspension asymmetry, magnetic hysteresis, tube transfer curvature or the handoff between complementary output transistors.
Conclusion
This project began with a simple concern: I had been measuring Gm, but I was not fully convinced that the original low-frequency results were dependable. The solution was not to abandon the metric. It was to improve the measurement supplied to it.
The revised adaptive plan increases FFT length as frequency decreases, giving the analyzer a much longer and more finely resolved record at the bottom of the sweep. Conventional THD and normalized H2, H3 and H4 were then added as diagnostic references. Finally, the ability to inspect the relative phase of each harmonic provides another important link between the measured spectrum, the nonlinear transfer behaviour and the resulting Gm value.
VIRTINS is unusually well suited to this work because it brings all of these measurements together in one environment. The result is not merely a more elaborate graph. It is a standardized and more transparent test format that can be applied to future electronics and loudspeaker measurements, compared across products, and developed further as our understanding of Gm grows.
References
1. VIRTINS Technology — company history
2. VIRTINS Multi-Instrument downloads and version history
3. VIRTINS Multi-Instrument brochure — harmonics, phase, Gm and Device Test Plan functions
4. VIRTINS Multi-Instrument manual — GedLee Metric and harmonic-phase measurement
6. Room EQ Wizard documentation — harmonic magnitude and phase measurement
7. Joseph Crowe — “Measuring GedLee Distortion (Gm)”
8. Joseph Crowe — “Beyond THD+N: Exposing Low-Level Crossover Distortion in Audio Power Amplifiers”
Development note: The Device Test Plans were developed iteratively through loopback testing and comparison of VIRTINS configuration files. The FFT ranges shown here are specific to the 384 kHz test configuration and should be revalidated if the sample rate, acquisition hardware or measurement bandwidth is changed.