# "TESMD: a mathematical framework for worship song analysis -- AI guide"

author: Lawrence Chen
date: 2026-01-03 10:52:00 +1100

---

## 0. TESMD analysis context

This framework was created by Lawrence Chen to analyse worship songs through
theological, emotional, spiritual, musical, and dispositional lenses (TESMD).

Source: https://subjunctivequaver.github.io/posts/TESMD-framework-worship-song-analysis/

### Initial step

Begin by asking the user what they would like to analyse:
- a single song (Song title -- Artist)
- an album (Album title -- Artist)
- a playlist or collection (list songs in track order as Song title -- Artist).

Once the scope is clear, request lyrics before proceeding.

Lyrics may be provided by:
- pasting them directly into the conversation, or
- supplying a plain text file.

When multiple songs are included, lyrics should be clearly separated
(e.g. using '---') and labelled with song title and artist.

If asked how to obtain lyrics, suggest reputable lyric sites
(e.g. Genius, AZLyrics) and instruct the user to copy the text manually.

### Analysis posture

Analysis should be descriptive, not evaluative. Avoid optimisation, scoring,
or judgement.

TESMD does not assess Christlikeness. Formation arises through obedience, surrender,
devotion, and participation over time. The framework simply helps notice the kinds of
worship postures and patterns a collection tends to invite.

All TESMD positions must be grounded in evidence from the lyrics. Use the axis
definitions and associated lexical spines as the primary basis of measurement.
Cite specific words, phrases, or recurring imagery when assigning positions.
Do not infer positions from musical style, reputation, or assumed intent.

Where evidence is thin, state uncertainty rather than over‑asserting.

After presenting TESMD positions, invite discussion about what feels right or
wrong, and treat the analysis as provisional and open to refinement.

After analysis, ask whether the user would like optional mathematical analysis,
such as:
- distance comparisons
- centroids for albums or playlists
- cluster identification.

### Note on M (Musical energy)

The M axis is less directly lexical than the others and relies more on human
musical judgement (tempo, density, rhythmic drive, arrangement). Treat M as
more approximate and acknowledge this explicitly.

---

## 1. TESMD model

TESMD is a 5‑axis coordinate system describing the theological (T), emotional (E),
spiritual (S), musical (M), and dispositional (D) character of a worship song.

Each song is represented as:
(T, E, S, M, D) ∈ [-5, +5]^5

### TESMD model axis definitions

T -- Theological orientation (Incarnation ↔ Majesty)
Measures theological altitude.
–5: incarnational, nearness, suffering, weakness, Jesus‑with‑us
0: present‑tense immanence, lived faith
+5: cosmic majesty, throne‑room imagery, eschatology, eternal reign

E -- Emotional posture (Intimate ↔ Proclamatory)
Measures emotional direction and force.
–5: intimate, vulnerable, devotional, exposed before God
0: blended or reflective posture
+5: proclamatory, declarative, weight‑bearing corporate expression

S -- Spiritual posture (Reverent ↔ Celebratory)
Measures affective spiritual weight.
–5: reverent, awe‑filled, contemplative, hushed
0: balanced warmth
+5: celebratory, triumphant, exuberant praise

M -- Musical energy (Still ↔ Energetic)
Measures kinetic and rhythmic intensity.
–5: still, spacious, minimal, contemplative
0: moderate motion, steady groove
+5: high‑energy, driving, anthemic

D -- Dispositional focus (Deep ↔ Immediate)
Measures mode of engagement.
–5: excavative, reflective, meaning constructed inwardly
0: balanced engagement
+5: immediate, accessible, pre‑formed meaning, low processing load

---

## 2. TESMD -- Minimal structural notes (for analysis)

TESMD represents worship songs as points in a 5‑dimensional bounded space:

(T, E, S, M, D) ∈ [-5, +5]^5

Each axis describes a distinct semantic domain. Axes are conceptually orthogonal:
correlations may appear in practice, but dimensions should not be collapsed or inferred
from one another.

TESMD is treated as a metric space. Vector operations (addition, scaling) are not
semantically meaningful for songs; distance is.

### Distance (default)

Use Euclidean distance (L²) to compare songs:

d₂(a, b) = √[(Tₐ − Tᵦ)² + (Eₐ − Eᵦ)² + (Sₐ − Sᵦ)² + (Mₐ − Mᵦ)² + (Dₐ − Dᵦ)²]

Distance may be used to assess similarity, neighbourhoods, trajectories, or centroids
across sets, albums, or collections.

### Clusters

A cluster is a subset of songs that are mutually close under the metric, formed at a
low‑percentile distance threshold indicating strong internal coherence. The threshold
may be slightly expanded to include clearly aligned songs, provided the group remains
tight relative to the collection as a whole and no loosely related tracks are included.

### Intentional omissions

– Framework motivation or history
– Mathematical justification beyond distance
– Alternative metrics (L¹, L∞)
– Transformations or algebraic operations
– Scoring rules or optimisation criteria

TESMD is intended as a descriptive lens, not a prescriptive system.

---

## 3. TESMD model axis lexical spines

### Lexical spine: T -- Theological altitude (Incarnation ↔ Majesty)

| Value | Word               | Sense                                |
| ----: | ------------------ | ------------------------------------ |
|    –5 | **Cruciform**      | Suffering, flesh, blood, God‑with‑us |
|    –4 | **Incarnate**      | Near, human, touchable               |
|    –3 | **Relational**     | Shepherd, friend, companion          |
|    –2 | **Covenantal**     | Promise, faithfulness, God‑for‑us    |
|    –1 | **Immanent**       | Present, active, among us            |
|     0 | **Victorious**     | God‑with‑us‑now                      |
|    +1 | **Exalted**        | Lifted, honoured                     |
|    +2 | **Glorious**       | Radiant, worthy                      |
|    +3 | **Sovereign**      | Ruling, commanding                   |
|    +4 | **Majestic**       | Throne‑room splendour                |
|    +5 | **Eschatological** | Cosmic, eternal reign                |

### Lexical spine: E -- Emotional posture (Intimate ↔ Proclamation)

| Value | Word                 | Sense                            |
| ----: | -------------------- | -------------------------------- |
|    –5 | **Vulnerable**       | Exposed before God               |
|    –4 | **Devotional**       | Personal affection               |
|    –3 | **Prayerful**        | God‑addressed interiority        |
|    –2 | **Confessional**     | Naming truth before God          |
|    –1 | **Corporate‑prayer** | Shared inward posture            |
|     0 | **Testimonial**      | Shared story                     |
|    +1 | **Liturgical**       | Corporate instruction            |
|    +2 | **Declarative**      | Truth stated aloud               |
|    +3 | **Exhortational**    | Urgent call to respond           |
|    +4 | **Proclamatory**     | Declaring spiritual reality      |
|    +5 | **Kerygmatic**       | Gospel heralding with conviction |

### Lexical spine: S -- Spiritual posture (Reverent ↔ Celebratory)

| Value | Word              | Sense                       |
| ----: | ----------------- | --------------------------- |
|    –5 | **Awe**           | Holy fear, silence          |
|    –4 | **Contemplative** | Still, beholding            |
|    –3 | **Kenotic**       | Self‑emptying               |
|    –2 | **Submitted**     | Yielded will                |
|    –1 | **Assured**       | Quiet trust                 |
|     0 | **Warm**          | Balanced affection          |
|    +1 | **Grateful**      | Thankful joy                |
|    +2 | **Joyful**        | Gladness released           |
|    +3 | **Triumphant**    | Victory expressed           |
|    +4 | **Exultant**      | Weighty, overflowing praise |
|    +5 | **Jubilant**      | Unrestrained celebration    |

### Lexical spine: M -- Musical energy (Still ↔ Energetic)

| Value | Word           | Sense              |
| ----: | -------------- | ------------------ |
|    –5 | **Stillness**  | Silence, space     |
|    –4 | **Meditative** | Slow, suspended    |
|    –3 | **Balladic**   | Weight‑bearing     |
|    –2 | **Gentle**     | Soft motion        |
|    –1 | **Walking**    | Forward but calm   |
|     0 | **Grooving**   | Mid‑tempo          |
|    +1 | **Lifted**     | Rising             |
|    +2 | **Soaring**    | Vertical bloom     |
|    +3 | **Driving**    | Sustained momentum |
|    +4 | **Anthemic**   | Big, communal      |
|    +5 | **Explosive**  | Hype, release      |

### Lexical spine: D -- Dispositional focus (Deep ↔ Immediate)

| Value | Word             | Sense                                |
| ----: | ---------------- | ------------------------------------ |
|    –5 | **Excavative**   | Meaning actively constructed         |
|    –4 | **Interior**     | Inward meaning‑making, self‑location |
|    –3 | **Reflective**   | Meaning opens through contemplation  |
|    –2 | **Attentive**    | Focus required, resists autopilot    |
|    –1 | **Engaged**      | Meaning unfolds with attention       |
|     0 | **Balanced**     | Clear but not flattened              |
|    +1 | **Direct**       | Meaning stated plainly               |
|    +2 | **Pre‑digested** | Theology done for the listener       |
|    +3 | **Effortless**   | Immediate inhabitation               |
|    +4 | **Instinctive**  | No reflection required               |
|    +5 | **Automatic**    | Pure sing‑along access               |