"Coherence" is one of those words that's used so much in wellness marketing that it's easy to forget it started as a technical term with a precise definition. Here's what Shaffer and Meehan's 2020 paper actually says — and why six numbers are better than one.
The word problem
Open any wellness app that involves breathing and you will see the word "coherence." Usually as a single score from 0 to 100, often in a soothing color, occasionally with a checkmark when you hit a threshold. The implication is that this number measures your current emotional and physiological state, and that higher is better.
That implication is mostly true. "Coherence" in the engineering sense really does describe a specific, measurable property of a signal — specifically, how close the signal is to a pure sine wave. When your heart-rate variability signal looks like a single clean oscillation locked to your breath, your HRV trace is, literally, coherent. When it looks like noise with a bunch of competing frequencies in it, it isn't.
The problem is that compressing "how coherent is this signal?" into one number requires choosing one method of measuring sine-wave-ness over several reasonable alternatives. And the method you pick determines what kinds of sessions will score well and what kinds will score poorly. A session can look great on one coherence metric and mediocre on another, for perfectly valid physiological reasons.
In 2020, Fred Shaffer and Zachary Meehan published a paper arguing that the field should stop pretending that a single coherence number captures everything, and instead report six related measurements that together describe the signal's structure. This is the methodology Heart Resonance uses. Let's walk through each one.
Criterion 1: Peak frequency
What it asks: at what frequency does the HRV signal have the most power?
How it's measured: run a Fourier transform on the R-R interval time series and find the single frequency with the largest power-spectrum value.
Why it matters: during resonance-frequency breathing, this peak should be in the LF band (0.04 – 0.15 Hz) and should match the breathing rate you're pacing to. If you're breathing at 5.5 BPM (= 0.092 Hz) and the peak shows up at 0.08 Hz, the signal is there but offset — maybe you're drifting toward 5 BPM without realizing it. If the peak is at 0.2 Hz (= 12 BPM), you're not at resonance at all; you're just recording normal respiratory sinus arrhythmia.
Failure mode: a high-power peak in the wrong place. The amplitude looks impressive but the rhythm isn't locked to your intended pace. Usually means the breathing discipline slipped during the session.
Criterion 2: Peak power
What it asks: how much absolute power is at the peak frequency?
How it's measured: the power-spectrum value at the peak, in ms² / Hz.
Why it matters: this is the direct amplitude measurement. It tells you how much HRV you're actually generating. Big peak = large heart-rate swings, strong RSA, lots of vagal action. Small peak = small swings, weak RSA, not much happening.
Failure mode: peak is in the right place but small. Two common causes: low baseline vagal tone (maybe you're stressed, sick, or dehydrated today), or you're breathing shallowly. Coherence breathing requires both the right rate and enough tidal volume to actually engage RSA.
Criterion 3: Peak height
What it asks: how tall is the peak relative to the background noise?
How it's measured: peak power divided by the power at some reference point — typically the average spectrum power across a broader band.
Why it matters: this is different from criterion 2. A session can have high peak power but also elevated broad-band noise (lots of random variability on top of the resonance rhythm), which means the peak isn't clean. Peak height normalizes for this. A high peak height means the signal is strongly organized, not just loud.
Failure mode: high peak power with low peak height. You're generating HRV, but not coherently. Often means motion artifacts (you shifted position), ectopic beats (an extra heartbeat thrown in), or distracted breathing (inconsistent pace).
Criterion 4: Peak dominance
What it asks: is the peak the only big thing in the spectrum, or is it competing with other peaks?
How it's measured: the ratio of peak power to the power at the second-largest peak, sometimes expressed as a dominance index.
Why it matters: a truly coherent signal is nearly a pure sine wave, which means it has one dominant frequency and essentially nothing else. A session with one big peak and several competing medium peaks is "peaky" but not coherent — there are multiple rhythms fighting for dominance. This often happens when your breathing is inconsistent in a structured way (e.g. pausing at the top of every third breath).
Failure mode: strong peak at the intended frequency, but another big peak at its harmonic (often 2× the breathing frequency). Usually caused by uneven inhale/exhale duration — if your inhale is much shorter than your exhale, the spectrum "smears" into a series of harmonics.
Criterion 5: LF-to-total power ratio
What it asks: what fraction of the signal's energy is concentrated in the resonance band?
How it's measured: sum of power in the LF band (0.04 – 0.15 Hz) divided by total power across all frequencies.
Why it matters: during a good resonance session, most of your HRV power should be in LF. If a large fraction is in HF (> 0.15 Hz), that means fast breathing-rate variability is competing with the resonance rhythm — probably because you're drifting between your target rate and faster spontaneous breathing. If a large fraction is in VLF (< 0.04 Hz), slow drifts are dominating — maybe you haven't settled into the session yet.
Failure mode: peak is good but a lot of energy is elsewhere in the spectrum. The session is mixing resonance with other oscillations. Often improves with longer or more settled practice.
Criterion 6: Time-domain stability
What it asks: do RMSSD and SDNN stay high and consistent across the session, or do they spike and collapse?
How it's measured: RMSSD and SDNN computed in rolling windows (e.g. every two minutes), evaluated for both absolute level and variance across windows.
Why it matters: the frequency-domain criteria all operate on the full session's spectrum, which is a summary that hides temporal structure. A session where you had one great minute and eleven mediocre ones can still produce a respectable peak if that minute was really impressive. Time-domain stability catches that — a good session should be consistently elevated, not spiky.
Failure mode: excellent peak-frequency and peak-power scores but time domain metrics are variable. Usually means the session was inconsistent — you zoned out for minutes at a time and then tuned back in. Common, fixable.
Why six beats one
Each criterion answers a different question about the signal. "Was the rhythm at the right rate?" (1). "Was it loud?" (2). "Was it clean?" (3). "Was it the only rhythm?" (4). "Was it concentrated?" (5). "Was it stable?" (6).
A single coherence score can only summarize all of this by picking weights. Any weighting choice implicitly decides which kinds of failures are penalized and which aren't. HeartMath's score, for instance, is heavily weighted toward peak-to-total-power ratio and peak height — so it penalizes messy signals strongly, but a session that scored high might have drifted off the intended rate and still look good.
None of this makes single-score coherence bad or unusable. It makes it one perspective on the signal. If you know what that perspective is optimizing for, you can work with it. If you don't — as most users don't, because vendors generally don't publish the formula — you're flying partially blind.
How Heart Resonance uses the six
The app shows a single composite coherence score on the main session view, because most users want one number to watch during a session. That composite is a weighted mean of the six criteria, tuned to prioritize peak-dominance and peak-height for real-time feedback.
At the end of every session, the stats screen breaks out each of the six criteria with its own value, threshold, and pass/fail. This is where the information lives. If your composite score was 62%, you can see specifically which criteria were pulling it down — maybe peak height was great but peak dominance was low (harmonics from uneven breathing). That's actionable. The composite alone isn't.
We also store all six in the CSV export, so if you do your own analysis across sessions you can track each metric independently. If you're doing long-term training, RMSSD stability and LF concentration are typically the first to rise. Peak height rises later, after your breath-control becomes more consistent. Peak power takes longest — it's dominated by vagal tone, which you build slowly.
"Coherence" is a real thing, measured on a real signal, using defensible math. It just isn't a number. It's a six-dimensional description of how your heart and breath are coordinating. Some coordinates will be strong, some weak. Knowing which is which is the difference between "my app said 72%" and "I know what to work on."
Further reading
- Shaffer & Meehan 2020 is the paper — linked in the research bibliography with the rest of the key references
- The science page has the physiological background if you want to back up a level
- The app walkthrough shows how the six criteria appear in a session
- The glossary for anything unfamiliar