Frequency and Intensity
Every motif in ACIM Atlas is characterized along two axes: how often it appears and how strongly it registers when it does. These are the frequency and intensity metrics computed in Pass 3, and they are the foundation for the role categories that describe each motif’s character.
The two axes measure different things, and the distinction matters. A motif can appear in nearly every section of the Text but almost always in a supporting role—frequent but not intense. Another motif can appear in only a handful of sections but dominate every one of them—intense but not frequent. These are fundamentally different kinds of motifs, and the two axes make that difference visible.
Frequency
Frequency measures how broadly a motif appears across the corpus. It answers: in how many sections does this motif show up?
The metrics
| Metric | Definition | What it tells you |
|---|---|---|
| units_any | Count of units where salience ≥ 0.10 | How broadly the motif appears, including echoes |
| units_sub | Count of units where salience ≥ 0.25 | How broadly the motif appears in a substantive way |
| freq_any | units_any / total units | Echo-or-higher presence rate as a proportion |
| freq_sub | units_sub / total units | Substantive presence rate as a proportion |
The two thresholds (0.10 and 0.25) correspond to the substantive threshold documented on the Salience Tiers page. freq_any includes every recorded occurrence, even the faintest echoes. freq_sub counts only the occurrences where the motif plays a real role in the section’s teaching.
freq_sub is the metric used for banding and role classification. It is the frequency value that determines whether a motif is ranked as Low, Mid, or High frequency. The rationale is that substantive presence is a better measure of a motif’s real distribution than total presence including echoes. A motif that echoes in many sections but is substantive in only a few has a fundamentally different distribution pattern than a motif that is substantive in many sections.
What appears on the site
The Frequency meter on the Motif Overview profile card displays freq_sub as a percentage, with a three-segment bar indicating whether the motif falls in the Low, Mid, or High band. The Sections donut shows the total count-based distribution at the any-salience level, as a companion to the computed frequency metric.
Intensity
Intensity measures how strongly a motif registers when it does appear. It answers: when this motif shows up, how central is it typically?
Where frequency counts sections, intensity looks at what happens inside them. A motif might appear in many sections but always as a Minor or Supporting presence. Another might appear less often but consistently score at the Primary or Pillar level. Intensity captures this distinction.
The metrics
| Metric | Definition | What it tells you |
|---|---|---|
| i_strength | Mean salience across occurrences where salience ≥ 0.25 | The motif’s average centrality when substantively present |
| i_foreground | occ_top3 / occ_total | How often the motif ranks among the top 3 most salient motifs in its unit |
| i_index | 0.5 × i_strength + 0.5 × i_foreground | A blended intensity score combining strength with foregrounding |
Why two components
Intensity is a blend of two different questions, and each one reveals something the other can miss.
i_strength (average salience) tells you how central the motif tends to be when present. A motif with high i_strength consistently scores at the Pillar or Primary level. But average salience alone can be misleading: a motif that appears in only a handful of sections, all at Primary level, has a very high i_strength—but in those sections, it may still be competing with other equally salient motifs. High average salience does not guarantee foregrounding.
i_foreground (top-3 ranking rate) tells you how often the motif is one of the dominant themes in its section. A motif with high i_foreground is not just present and not just scoring well—it is consistently among the most prominent motifs wherever it appears. But foreground ranking alone can be misleading in the other direction: a motif that ranks top-3 in sections where all motifs have low salience is being foregrounded without being intense.
i_index blends the two at equal weight. A motif needs both high average salience and frequent foregrounding to score high on intensity. This produces a more robust measure than either component alone.
A note on foreground ranking
Within each unit, motifs are ranked by salience in descending order using a dense rank. Ties are allowed at the top-3 boundary. If three motifs share the same salience in a section, all three count as top-3 rather than arbitrarily excluding one. This is a small decision, but it matters for motifs that frequently co-occur at similar salience levels—it prevents a motif from being penalized on i_foreground simply because another motif happens to share its salience.
What appears on the site
The Intensity meter on the Motif Overview profile card displays i_index as a percentage, with a three-segment bar indicating whether the motif falls in the Low, Mid, or High band.
How the two axes work together
Frequency and intensity are independent measurements. A motif’s position on one axis says nothing about its position on the other. This independence is what makes their combination informative—when crossed, they produce six recognizable patterns:
| Pattern | Frequency | Intensity | What it looks like |
|---|---|---|---|
| Everywhere and prominent | High | High | The motif appears in many sections and tends to be central when it does. It is both broadly distributed and consistently foregrounded. |
| Everywhere but quiet | High | Low | The motif appears in many sections but usually plays a supporting or minor role. It is part of the background—present often, rarely dominant. |
| Rare but powerful | Low | High | The motif appears in few sections but dominates when it does. Its appearances are events—concentrated and prominent. |
| Rare and quiet | Low | Low | The motif appears infrequently and does not stand out when it does. It is at the periphery of the thematic landscape. |
| Moderate on both | Mid | Mid | The motif appears reasonably often at a reasonable intensity. It is present without being extreme on either axis. |
| Uneven | Mixed | Mixed | The motif does not fall into a clean pattern—perhaps high frequency but moderate intensity, or low frequency but moderate intensity. |
These patterns are formalized as the six role categories. The table above describes what each combination looks like in the data; the role category page describes what each combination means for study.
Banding
To assign role categories, Pass 3 converts the continuous freq_sub and i_index values into three discrete bands—Low, Mid, High—using a rank-based tercile split.
All motifs are rank-ordered on freq_sub. The ranking is divided into three groups of roughly equal size. The same process is applied independently to i_index. Ties are broken deterministically by motif ID so that every motif lands in exactly one band on each axis.
The bands are relative to this corpus and this motif set. “High frequency” means “in the top third of the motifs as measured across the corpus.” A different analysis with different motifs or a different text would produce different boundaries. The bands describe rank position, not absolute thresholds.
Where these metrics appear
The frequency and intensity meters in the motif Overview header are the primary display, showing the band and the percentage at a glance. The full metric values are also visible in Research mode for readers who want exact numbers, and the role category badge on the motif Overview is the downstream classification that these two axes feed into.
For most readers, the meters in the Overview header are the only place they will encounter these metrics directly. The meters are designed to answer a simple question at a glance: does this motif show up a lot, and is it prominent when it does? The detail on this page is for readers who want to understand exactly what the meters are measuring and how.