Can we map minimal musical patterns, better understand their effects, and explore regions that remain relatively underused?
A personal exploration of recurring musical structures, explained without requiring any knowledge of music theory and connected to a broader question: how can a very simple form contribute to communicating energy, melancholy, joy, tension, or serenity?
1. Forty Years of Listening Before Having Names for Things
I have been listening to heavy metal for about forty years. For much of that time, I knew practically nothing about music theory. I did not know scales, modes, or progressions. I had a guitar and did something much more elementary: inspired by the music I loved, I tried to find sounds on the instrument that I liked.
This had an interesting consequence. I did not think about music in terms of note names, and I still do not usually do so. I thought in terms of positions and distances. One note was here; the next was two frets away; then another two; then it was time to go back.
The first song I remember composing did not exactly follow a uniform sequence of two-position jumps. The complete shape, played on a single guitar string, was:
1–3–5–7–9–10
What is interesting is that the two phrases in the riff activated different regions of that shape:
777 5 | 777 5 | 777 10 9 10
555 3 | 555 3 | 111 333 55
The first phrase uses the subshape {5,7,9,10}; the second, {1,3,5}. I was not consciously choosing a scale and extracting a melody from it. I was finding small shapes and linking them together.
Looking back decades later with the vocabulary of music theory, this was not some “non-existent” collection. The sequence 1–3–5–7–9 is a fragment built from whole tones, while 9–10 breaks that symmetry; the complete set can be incorporated into a known scale.
But the autobiographically interesting point is something else: the shape was already my intuitive unit of composition long before I had words to describe it.
And the shape of that first song was not one of the usual patterns in the music I was listening to.
This contrasted with my general impression of heavy metal: a very large proportion of the repertoire seems to move within a single seven-position diatonic shape — the same pattern of distances that we would obtain by playing only the white keys on a piano, although transposed to any pitch and with different anchors.
There is no measured figure yet. This is one of the hypotheses that would need to be tested.
Over time, I began to recognise a much more specific form in heavy metal. For me, it could be summarised in four numbers:
5–5–1–3.
I heard it again and again in songs by Iron Maiden, Judas Priest, and many other bands, and it also kept appearing in compositions of my own or of bands I played in. It seemed particularly common at moments of intensity: choruses, climaxes, riffs that appeared to open the song up.
For an immediate example of the kind of movement I mean, Iron Maiden’s Aces High is almost a showcase for the device: it repeatedly shifts the 5–1–3 relationship to different pitches.
Judas Priest’s Breaking the Law provides another particularly recognisable example in its riff and ending, with the sequence A–F–G, which can literally be seen as 5–1–3 on the sixth guitar string.
I even imagined forming a band called 5513. The name was partly a tribute and partly a private joke: a way of acknowledging a device within the genre that seemed to work with almost obscene effectiveness and that, precisely for that reason, could be exploited consciously.
That band never came into existence, although others did.
For years, all of this remained simply a practical intuition. Later, when trying to organise these observations, I began encountering concepts from music theory that described different parts of the phenomenon from different perspectives: pitch-class sets, schemata, tetrachords, ostinatos, pedal points, recurring progressions, modes, cadences.
The aim here is not to replace those frameworks, but to test a deliberately simple representation that allows structures from very different musical styles to be compared without requiring the reader to know that vocabulary.
2. Counting Positions Instead of Naming Notes
No knowledge of music is required to follow this article.
If you have a guitar, simply think of fret numbers. If you have a piano, imagine numbering every key consecutively, black and white. A black key counts exactly the same as a white one. Every key is simply one position.
When I write 1–3–5, I mean only this: start at one position, move forward two positions, then move forward another two.
From the perspective that matters here, 1–3–5, 3–5–7, and 5–7–9 are therefore the same shape shifted to different locations.
What initially matters is not the name of the note or the key. It is the relationship between positions.
This notation is deliberately rudimentary. Its advantage is that anyone with a guitar or piano can immediately test what is being described and, above all, compare structures before moving into more complex theoretical explanations.
3. First, the Shape
Suppose we have three positions:
{1,3,5}
That is what I will call the shape.
We have not yet said in what order they should be played. We could play 1–3–5, 5–1–3, 3–5–1, or move freely among them.
The small available universe remains the same.
Music theory already provides formal tools that are very close to this idea. Pitch-class set theory, for example, makes it possible to consider groups of notes independently of the particular order in which they appear and to compare structures under transposition.
Here, however, I will use shape as a more visual and intuitive term.
The shape is not yet a song or a melody.
It is the map of positions we have decided to make relevant.
The shape selects the world.
Shapes Within Shapes
The example of my first composition suggests an additional distinction.
A piece can have an overall shape while individual phrases activate different subshapes within it. The complete shape was {1,3,5,7,9,10}; one phrase concentrated on {5,7,9,10}, while another concentrated on {1,3,5}.
This makes it possible to create contrast without completely abandoning the same universe of pitches.
In terms of communication, it would be rather like having a general vocabulary and allowing each paragraph to activate only one region of that vocabulary.
4. The Model: Shape, Path, Emphasis, and Anchoring
Starting from the shape, several layers can be distinguished that we normally hear simultaneously.
SHAPE. Which positions exist within the small structural universe.
PATH. The order in which we visit them. The same shape can be traversed in different ways and produce different gestures.
EMPHASIS. Which position we repeat, prolong, or accent. 5–5–1–3 contains no more positions than 5–1–3, but repeating the 5 changes the weight of the figure.
ANCHORING. Which position we experience as home, reference point, or gravitational centre. The same notes can acquire a different meaning if the position from which we interpret them changes.
NARRATIVE FUNCTION. What the structure is doing within the piece: remaining, oscillating, ascending, descending, breaking an expectation, expanding the available world, returning, suspending, or resolving.
EMOTION. What kind of experience this organisation tends to favour in a particular listener: energy, joy, melancholy, power, serenity, tension, nostalgia, mystery.
SURFACE. Everything we normally recognise immediately as “the music”: rhythm, drums, timbre, distortion, voice, chords, lead lines, arrangements, dynamics.
These layers do not form a rigid causal chain. They interact. But separating them allows more precise questions to be asked.
| Layer | Question |
|---|---|
| Shape | Which positions exist? |
| Path | In what order are they visited? |
| Emphasis | What is repeated, prolonged, or accented? |
| Anchoring | Which position functions as home? |
| Narrative function | What gesture does the structure produce? |
| Emotion | What experience does it tend to favour? |
| Surface | How is it musically realised? |
5. One Note: Remaining
The minimal case is a single repeated position:
5–5–5–5–5…
There is no displacement. Almost everything else can change, yet one reference remains.
Some songs make this particularly clear. Judas Priest’s Turbo Lover maintains a very strong insistence on the same pitch throughout long passages.
In other songs, such as Metallica’s Jump in the Fire, the surface shape is broader, but one note repeatedly functions as the centre to which the riff returns.
This requires a distinction between stasis and anchoring.
STASIS: we barely leave a single position.
ANCHORING: we may travel considerably, but one position organises the others and functions as home.
The resulting impressions may have something in common: permanence, insistence, stability, stubbornness, or determination.
But the same invariance, played slowly with a soft timbre, may produce serenity; with distortion and intense percussion, it may sound threatening.
It therefore seems preferable to describe the elementary gesture first — remaining — and only then study which emotions it tends to favour under different conditions.
6. Two Notes: Oscillating and Waiting
The next possible world contains only two positions:
{5,7}
We can spend a long time playing:
5–7–5–7–5–7…
There is now movement, but no progression.
We go back and forth.
The listener quickly learns the local rule.
After several repetitions, something decisive can happen: a 3 appears.
The shape changes from {5,7} to {3,5,7}.
We have not merely changed the order. We have expanded the world of the song.
Precisely because the 3 did not previously exist, it can acquire considerable narrative value. The new element carries information because a sufficiently stable prior structure had already generated an expectation.
This mechanism — establishing a small world and then expanding it — appears to offer a productive way of studying climax and rupture.
7. The 1–3–5 Shape and 5513
The shape {1,3,5} has an elementary geometry:
+2, +2.
5513 adds path and emphasis:
5–5–1–3.
If repeated cyclically,
5–5–1–3 | 5–5–1–3,
we can begin listening from another point and obtain:
1–3–5–5.
It is the same cycle framed differently.
After decades of listening to heavy metal, my impression is that this shape, and paths very close to it, appear extraordinarily frequently at moments of high intensity.
That impression requires a better-designed corpus study than a collection of familiar examples. The criteria would need to be defined in advance, songs selected without knowing the result, and occurrences independently coded.
Two examples help make the idea audible without abstraction.
In Aces High, sequences such as Em–C–D, Am–F–G, and G–E?–F appear repeatedly. The absolute pitch changes, but the same relationship among the three positions remains.
In Breaking the Law, the A–F–G sequence in the riff and ending makes that same relative path particularly visible.
Even before conducting such a study, what is interesting is the abstract gesture contained in a realisation such as:
3–5–7–7.
Move up two, move up another two, then confirm the arrival.
ASCEND ? ARRIVE ? CONFIRM.
That already resembles a small narrative structure.
8. Flamenco: Down, Down, and Close
Another recurring shape can be expressed as:
{0,1,3,5}.
A characteristic path is:
5–3–1–0.
Its movements are:
-2, -2, -1.
Down two.
Down two.
Finally, down one.
Music theory relates this family to the Phrygian tetrachord and to central resources in flamenco.
There is no need to know those terms in order to hear the shape. It is enough to play it.
The gesture contrasts with the previous one.
Where 3–5–7–7 ascends and reaffirms, 5–3–1–0 descends until it closes.
DESCEND ? DESCEND ? CLOSE.
This does not justify a universal equivalence such as “this pattern means melancholy.”
It does, however, allow us to separate a structural property — the shape of the movement — from the emotional interpretation that subsequently emerges within a particular musical and cultural context.
9. Two Together, a Gap, Two Together: The Geometry of the Shape
Some shapes have a recognisable character even before a particular path has been established.
A clear example can be written as:
{0,1,4,5}.
Visually:
XX··XX.
Two adjacent positions, two positions left empty, then another two adjacent positions.
The internal distances are:
+1, +3, +1.
On an equal-tempered piano or guitar, this shape approximates Jins Hijaz, a basic four-note unit in the Arabic maqam tradition.
The concept of jins is particularly suggestive for this exploration because it describes precisely these kinds of small intervallic blocks with their own identity, centres, and notes of emphasis.
This example introduces another idea: within a shape, what matters is not only how many positions there are, but also how they are distributed.
We can speak of geometry, density, clustering, gaps, and symmetries.
Two four-position shapes may be radically different even though both contain four elements.
10. The Black Keys: Anchoring Changes the World
If you have a piano, play only the black keys.
The five keys form a pentatonic collection.
For many Western listeners, associations with East Asian musical traditions may immediately emerge.
Yet those same five pitches can also be organised as a minor pentatonic scale, one of the fundamental materials of blues and rock.
The shape has not changed.
What has changed, above all, is which of those positions we experience as home, how we move through them, which ones we emphasise, and what musical surface we construct around them.
This is probably one of the clearest examples of why separating the layers is useful.
The shape selects the world.
Anchoring determines where its centre lies.
The path determines what happens within it.
Emphasis indicates which positions acquire greater importance.
11. Two Joyful Patterns That Turned Out to Be the Same Cycle
One of the best-known sequences in modern pop can be expressed in this notation as:
0–7–9–5.
Played alone on the bass, it gives me an immediate impression of joy and a sound strongly reminiscent of pop-punk.
I then remembered another path that I had frequently used in metal to introduce a more cheerful character:
5–1–8–3.
When both are compared under transposition and rotation, an interesting coincidence appears: they are equivalent realisations of the same four-pitch cycle, beginning from different points and transposed to different positions.
This observation does not demonstrate that the shape “causes joy.”
But it suggests an empirical question: if two realisations independently associated with a similar affective impression turn out to be structurally equivalent, how much of that impression survives changes in style, timbre, and surface?
This is precisely the kind of coincidence that a systematic map should make it possible to discover.
12. Same Shape, Different Path
The distinction between shape and path also appears in well-known families of chord progressions.
Modern pop makes extremely frequent use of:
I–V–vi–IV.
The doo-wop tradition made extensive use of:
I–vi–IV–V.
In an abstract representation, they may share the same set of four locations while visiting them in different orders.
Same vocabulary; different syntax.
The experience is not identical.
This reinforces a central idea: knowing which positions belong to the shape is not enough.
Order can change narrative direction, the sense of closure, and the points at which expectations arise.
13. Music and Communication
This architecture offers a useful analogy with human communication.
Not because music and language are the same, but because in both cases the effect depends on more than the elements that are available.
In music, the shape can be compared with vocabulary or the conceptual field; the path with syntax; emphasis with prosody and repetition; anchoring with the frame from which we interpret; narrative function with the organisation of discourse; emotion with the effect on the receiver; and surface with style and rhetoric.
Consider the words:
loss, absence, memory, farewell.
Before constructing a sentence, a particular conceptual world has already been selected.
The words can then be arranged in different ways, one can be repeated, the discourse can begin from another perspective, or it can close with one of them.
Selection matters.
Order matters.
Emphasis matters.
The frame matters.
Something similar may occur in music.
The shape selects the world; the path tells what happens within it; emphasis indicates what matters; anchoring establishes the standpoint from which everything else is interpreted.
| Music | Communication |
|---|---|
| Shape | Vocabulary / conceptual field |
| Path | Syntax / order |
| Emphasis | Prosody / repetition / relevance |
| Anchoring | Frame / context |
| Narrative function | Discourse structure |
| Emotion | Effect on the receiver |
| Surface | Style / rhetoric / realisation |
14. From Emotion to Gesture
It would be tempting to construct a simple dictionary:
5513 = energy
5310 = melancholy
Hijaz = mystery
0–7–9–5 = joy
That would probably be an excessive simplification.
The same structure can change radically through tempo, rhythm, register, timbre, distortion, dynamics, accompaniment, and cultural context.
Listeners also learn musical regularities through exposure. Expectation, predictability, and surprise all contribute to the experience of musical pleasure.
It may therefore be more robust to begin with elementary narrative functions rather than specific emotions:
REMAIN.
OSCILLATE.
ASCEND.
DESCEND.
EXPAND THE SHAPE.
BREAK A RULE.
RETURN.
CONFIRM.
SUSPEND.
RESOLVE.
It would then be possible to study which emotional profiles are statistically associated with these gestures under different conditions.
15. An Emotional Map Still Full of Gaps
Research on musical emotion provides taxonomies that are considerably more refined than a simple happy/sad distinction.
The Geneva Emotional Music Scale, for example, distinguishes families such as wonder, transcendence, tenderness, nostalgia, peacefulness, power, joyful activation, tension, and sadness.
These categories can be used as a provisional map, allowing us to ask which shapes, paths, forms of emphasis, and anchors appear associated with each region.
Some cells will have obvious candidates.
Others will remain empty.
The gaps may mean different things: perhaps the search has not yet been extensive enough; perhaps those emotions depend mainly on rhythm, timbre, or dynamics; perhaps there is no characteristic pitch structure; or perhaps some regions of musical space remain relatively underexplored.
The last possibility is the most speculative, but also the most creatively interesting.
| Emotional region | Provisional candidates | Status |
|---|---|---|
| Power / culmination | +2,+2 with 5513-type paths | Priority hypothesis |
| Joy / activation | 0–7–9–5 family and equivalents | Hypothesis |
| Melancholy / tension | 5–3–1–0 descent | Strong candidate |
| Mystery | Hijaz-type geometries +1,+3,+1 | Strong cultural association |
| Determination | Prolonged anchoring on one position | Candidate |
| Expectation | Oscillation between two positions | Candidate |
| Sadness | Descending tetrachords / lament | Historical precedent |
| Nostalgia | Axis, doo-wop, and other cycles | To be tested |
| Serenity | ? | Gap |
| Wonder | ? | Gap |
| Transcendence | ? | Gap |
| Tenderness | ? | Gap |
16. Musical Styles as Processes of Search and Selection
There is no need to imagine that a musical style invents each of its structures from scratch.
Elementary combinations of pitches have appeared in different contexts for centuries.
What a style can do, however, is select a particularly fertile combination of shape, path, emphasis, anchoring, timbre, and narrative function, and exploit it systematically.
A device appears in songs that work; other musicians reuse it; listeners become familiar with it; the pattern acquires associations; new compositions begin from that already established language.
From this perspective, musical styles can be understood, at least partly, as historical processes of exploration and selection within a space of possibilities.
They find fertile regions, exploit them, and turn them into shared vocabulary.
17. How Much Space Remains to Be Explored?
A Western octave contains twelve chromatic positions.
If we consider only shapes consisting of three different positions, there are 220 raw combinations.
If we consider four positions, there are 495.
That gives a total of 715 possible three- or four-position shapes before eliminating equivalences under transposition and other symmetries.
For each shape, multiple paths, rotations, repeated notes, anchors, directions, cycles, ruptures, and expansions can then be studied.
The space is large, but not beyond computational analysis.
This changes the question.
It is no longer only:
Which patterns appear again and again?
It also becomes:
Which regions of the space appear far less often than expected?
18. Deliberately Searching for Underused Patterns
Imagine a research programme with several stages.
First, construct a large corpus of songs from different styles and reduce certain layers to shapes, paths, emphases, and anchors.
A very simple first test would be to measure something that, so far, exists only as an auditory impression: what proportion of classic heavy metal remains, apart from transpositions, within a single seven-position diatonic shape — the structural equivalent of the white keys on a piano?
If a prediction had to be written down before doing the count, I would place it at approximately 70–80%.
That figure is not a result.
Its purpose is precisely to turn an impression into a prediction that can turn out to be right or wrong.
The next stage would be to measure which structures occur extremely frequently and which are rare.
Then shapes and paths could be generated experimentally while holding other variables constant: the same instrument, tempo, rhythm, register, and intensity.
Listeners could rate energy, joy, nostalgia, serenity, tension, power, wonder, tenderness, and other dimensions.
Successive experiments could compare:
the same shape with different paths;
the same shape and path with different anchors;
the same structure with different patterns of emphasis.
The aim would be to estimate what each layer contributes and to identify, if they exist, structures with a particularly interesting combination:
HIGH EMOTIONAL RESPONSE + LOW HISTORICAL EXPLOITATION.
That quadrant would represent a zone of creative opportunity.
19. The Really Interesting Test Would Be to Compose
A theory of this kind would become more valuable if it generated predictions.
It should not merely explain retrospectively that a particular band uses a certain device frequently.
It should also be able to suggest something like:
this shape appears rarely, but the map suggests that under certain conditions it might favour a particular experience.
A piece would then have to be composed using that shape deliberately.
If it works, the model would have helped to explore musical space.
If it does not, information would still have been gained: perhaps the correct path was missing, or the right anchoring, rhythm, or timbre; or perhaps that emotional region does not depend on pitch structure in the way predicted.
In either case, the theory becomes falsifiable and useful.
20. What This Approach Might Contribute
The components of this exploration belong to well-studied areas of music: pitch sets, modes, schemata, ostinatos, pedal points, recurring progressions, expectation, and emotion.
When attempting to organise a practical experience that began by counting frets, it is natural to encounter this literature.
The possible usefulness of the approach lies in bringing several distinctions together within an especially simple representation:
SHAPE ? PATH ? EMPHASIS ? ANCHORING ? NARRATIVE FUNCTION ? EMOTION ? SURFACE.
First, it allows musical phenomena to be explained and compared without requiring prior knowledge of music theory.
Second, it prevents us from attributing to “the pattern” effects that may actually arise from order, anchoring, or emphasis.
Third, it turns the representation into a search tool: not merely a way of classifying what is already known, but a means of systematically exploring which combinations are heavily used, which barely appear, and which deserve to be tested.
The final question, therefore, is not simply why four particular notes work.
It is this:
Can we build a map of the space of minimal musical shapes, identify the regions that the history of music has exploited most successfully, and find emotionally powerful regions that remain relatively unexplored?
The answer is not yet known.
But it is striking that the path towards this question began in such an unsophisticated way: listening to a guitar, searching for sounds, and counting frets.
Perhaps part of the research can continue in exactly the same way.
Listen. Compare. Count. Then test.
References
A brief selection intended to situate some of the concepts mentioned above and provide avenues for further exploration. The article deliberately uses its own accessible notation so that the argument can be followed without prior musical training.
[1] Open Music Theory. Pitch-Class Sets, Normal Order and Transformations.
https://viva.pressbooks.pub/openmusictheory/chapter/pc-sets-normal-order-and-transformations/
[2] MaqamWorld. Jins Hijaz.
https://www.maqamworld.com/en/jins/hijaz.php
[3] Open Music Theory. Scales and Scale Collections.
https://openmusictheory.github.io/scales2.html
[4] Richards, M. Axis Progressions in Pop Music. Music Theory Online.
https://mtosmt.org/ojs/index.php/mto/article/view/308
[5] Cheung et al. Uncertainty and Surprise Jointly Predict Musical Pleasure. Nature Human Behaviour / review context.
https://www.nature.com/articles/s41583-019-0245-y
[6] Geneva Emotional Music Scale (GEMS), review and validation literature.
https://pmc.ncbi.nlm.nih.gov/articles/PMC11133078/
[7] Iron Maiden, Aces High. Harmonic transcription consulted.
https://www.guitartabsexplorer.com/iron-maiden/aces-high-chords
[8] Judas Priest, Breaking the Law. Tablature and chords consulted.
https://www.cifraclub.com/judas-priest/breaking-the-law/
[9] Ableton Learning Music. Whole-Tone Scale.
https://learningmusic.ableton.com/advanced-topics/whole-tone.html
[10] Music Theory for the 21st-Century Classroom. Minor Scales and Diatonic Practice.
https://musictheory.pugetsound.edu/mt21c/DiatonicChordsInMinor.html
Methodology
This article was produced using a model of human conceptual leadership and editorial execution delegated to artificial intelligence. The author provided the thesis, examples, objections, revision criteria, and editorial decisions. The AI developed the prose, proposed reorganisations and alternative formulations, searched for and cross-checked references, and maintained the master version of the text—that is, the documentary reference to which successive changes were applied.
The author critically reviewed the successive versions and approved the final version.
Summary of the method: conceptual leadership, human; drafting and master version, AI; reference search and verification, AI; critical review and final approval, human.
1 Comment