The same seven, started later

Play the white keys from C to C and the result is a major scale. Play the same white keys from D to D and the result is something else entirely — darker, more ambiguous, and instantly identifiable to anyone who has heard a folk tune.

Not one note has changed. What changed is which note is home.

That figure is the whole subject in one picture, and the ordering in it is computed rather than traditional. The rows are sorted by the sum of their intervals above the tonic — brightest at the top, darkest at the bottom — and the single note that changes between adjacent rows is found by comparison rather than annotated.

What “home” means, mechanically #

The claim that changing the tonic changes everything needs cashing out, because it sounds like a claim about attention rather than about sound.

A mode is defined by the pattern of intervals measured from its tonic. In C major the intervals above the tonic are 0, 2, 4, 5, 7, 9, 11. Start the same notes from D and measure from D: 0, 2, 3, 5, 7, 9, 10. The third is now minor and the seventh is flat.

The pitches are identical. The relationships are not, and relationships are what a listener tracks. Somebody hearing a phrase that keeps returning to D, cadencing on D, and outlining a D minor triad is hearing a minor third above the tonic — which is an interval that exists in the sound, is measurable, and would be there whatever anyone believed.

The two semitones are the landmarks. In Ionian they fall between degrees 3–4 and 7–8. In Aeolian they fall between 2–3 and 5–6. A semitone leading up into the tonic — as in Ionian — creates a strong pull toward it; a whole tone below the tonic, as in Aeolian and Mixolydian, does not, and modal music built on those degrees sounds unresolved to ears trained on major and minor.

Brightness, which is a computed quantity #

The modes are usually presented in the order Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, Locrian, which is the order of their starting degrees. That order tells a reader nothing.

Order them by brightness instead and a structure appears. Sum each mode’s intervals above its tonic and sort:

Lydian, Ionian, Mixolydian, Dorian, Aeolian, Phrygian, Locrian.

Each mode in that list differs from the one before it by exactly one note, and that note is always a semitone lower. Lydian has a raised fourth; drop it and Ionian results. Drop the seventh and Mixolydian results. Drop the third, Dorian. Drop the sixth, Aeolian. Drop the second, Phrygian. Drop the fifth, Locrian.

Seven modes, six single-semitone steps, one continuous gradient from bright to dark. That is not a mnemonic imposed afterwards; it is a consequence of the modes being rotations of a set that is a contiguous run on the circle of fifths, and each step down the brightness order moves the run one position flatward.

Computed, the sums are 39, 38, 37, 36, 35, 34, 33 — seven consecutive whole numbers, which is a stronger statement than one semitone per step and is the same fact seen with no gaps in it. There is no mode of the diatonic set whose brightness is not one of those seven values, and no two share one.

Two of them survived and five did not #

Of the seven, two — Ionian and Aeolian — became major and minor, and the other five went into abeyance for roughly three hundred years.

The reason is functional harmony. A tonal cadence needs a dominant chord containing the tritone between the fourth and seventh degrees, resolving onto the tonic, with the seventh degree rising a semitone into it. Ionian has that. Aeolian does not — its seventh is a whole tone below the tonic — which is why the harmonic minor exists: it is Aeolian with the seventh raised specifically to manufacture a leading note and a major dominant.

The other five modes have no functional dominant and cannot produce that cadence, so a system built entirely on it has no use for them. They persisted in folk music, which never adopted functional harmony, and returned in the twentieth century when composers went looking for tonal centres that were not major or minor.

What a mode costs to establish #

The essay’s next claim is that the difference between D Dorian and C major “lives entirely in where phrases end and which notes get weight”, and that is a quantity rather than a description. Take a flat histogram of the seven pitch classes — every note once, which is the mode as a bare set — and weight only the final more heavily until this collection’s own profile key-finder names it. The weight it needs is what the mode costs to establish.

At a flat histogram every one of the seven is read as C major, which is the notation problem stated as an arithmetic one: a bag of the white notes is the parent key and nothing else.

The two modes that survived are the two cheapest, by a distance. Ionian is free because it is what the profile was fitted to, and Aeolian needs fifteen per cent extra on one note out of seven. Everything else needs half again to more than twice, and Locrian — the one nobody has ever built a repertoire on — needs most of all.

That is a second and independent account of the survival the section above attributes to functional harmony. The usual explanation is about cadences: Ionian has a dominant with a leading note in it and the others do not. This one is about statistics: a listener who identifies keys from how often notes are sounded will find Ionian and Aeolian nearly for free and will need a good deal of insistence before hearing anything else. The two explanations pick the same pair and they are not the same argument, which is the most that can be said for either.

Two things this does not establish, and both are worth stating. The profile model has a major profile and a minor profile and no others, so what it names for Dorian is D minor rather than Dorian — the nearest object it possesses, not a reading. And the cost ordering is not the brightness ordering: Dorian is the second most expensive at 2.00 and Phrygian, three steps darker, is cheaper at 1.65. Whatever makes a mode hard to establish, it is not how far it sits along the bright-to-dark line.

A mode is more than a pitch set #

Everything above treats a mode as a rotation of a set, which is what the figures can draw and is a serious understatement.

A mode in actual practice carries a great deal that a pitch set does not contain. Which degrees are structurally important and which are passing. Characteristic melodic turns. Which note the melody tends to sit on when it is not moving — the reciting tone of a psalm tone, which is often not the final. How the mode is approached in ascent versus descent.

Medieval European modal theory distinguished authentic from plagal modes — Dorian from Hypodorian — which have the same final and the same pitches, and differ only in the range the melody occupies relative to that final. A set-based description cannot express that difference at all, and the theory treated it as fundamental.

The same understatement is far more severe outside Europe. An Indian raga specifies ascending and descending forms that may differ, ornaments attached to particular degrees, a hierarchy among notes, characteristic phrases, and often a time of day. Two ragas can share every pitch and be entirely distinct. A maqam likewise carries a melodic path — the sayr — that a pitch list omits.

Calling a raga a scale is roughly like calling a sonnet a list of fourteen line-lengths.

The white keys are what makes modes easy to demonstrate and easy to misunderstand: playing them from D gives Dorian and from E gives Phrygian, and nothing about the keyboard says which note is home. And written out on a stave with no key signature, a D Dorian scale is correct notation and records nothing about the mode — the notation says which pitches, and the mode is a claim about which one of them the music treats as home.

What notation records and what it does not #

Modal music exposes a specific weakness in staff notation, and it is worth naming because it is not the usual complaint.

The stave records pitch exactly. It has no way of recording which pitch is the tonic. A piece in D Dorian and a piece in C major look identical on the page — same key signature, same notes — and the difference lives entirely in where phrases end and which notes get weight.

Modern practice papers over this by writing D Dorian with a one-flat signature and cancelling the B-flat throughout, which is ugly and at least announces the intention. Medieval sources handled it with a stated mode number, which is a label rather than a notational feature.

The general point holds well beyond modes: notation is a compression, optimised for telling a player which key to press, and things that are structural rather than instrumental fall out of it.

Why a mode needs establishing #

A mode is a rotation, and a rotation is only audible if the listener knows which position is the start. That is not free, and modal music spends real effort on it.

The techniques are consistent across traditions. Return — the melody keeps coming back to the final, so repetition marks it. Drone — a sustained tonic underneath removes the ambiguity entirely, which is why so much modal music from Scotland to Rajasthan has one. Range — the final sits at the bottom or the middle of the melodic range in a way characteristic of the mode. Cadential formula — a stock phrase that ends on the final, recognised by anyone inside the tradition.

None of those is harmonic. All of them are available to a single unaccompanied voice, which is the point: modal identity was established for centuries by monophonic music, before harmony existed to do it.

Functional tonality replaced all four with one mechanism — the dominant-to-tonic cadence — which is more efficient and works for exactly two of the seven modes. That trade is the whole reason the other five fell out of use, and the reason they came back when composers wanted tonal centres that harmony could not supply.

Modal harmony’s actual problem #

Twentieth-century modal writing hit a difficulty that the pitch-set description hides completely.

A mode has no dominant, so it cannot cadence in the tonal way. Use ordinary tonal chord progressions on modal material and the mode collapses: play a V–I in D Dorian and the raised C-sharp needed for the dominant destroys the mode, leaving D minor.

So modal harmony has to avoid the very progressions that make harmony feel directed. The solutions are recognisable as a style: static harmony holding one chord for many bars, chords built on fourths rather than thirds, parallel motion, and bass movement by step rather than by fifth.

Modal jazz is the clearest case. So What holds one mode for sixteen bars, which gives it room to be heard as a place, and its harmony is built from stacked fourths precisely because stacked thirds would imply functional relationships the mode cannot support.

Whose music, and when #

The word mode covers at least three different things, and conflating them causes most of the confusion in the literature.

Ancient Greek harmoniai were octave species with names — Dorian, Phrygian, Lydian — and a body of ethical doctrine attached about which produced which state of character. They were not the medieval modes, and the tunings were not the modern ones.

Medieval European church modes took the Greek names and applied them, through a misreading in Boethius and later transmission, to different scales altogether. So the mode called Dorian today has the name of a Greek mode it does not correspond to. The mismatch has been known for centuries and the names have not moved.

Modern modal usage — from Debussy and Vaughan Williams through jazz and film scoring — treats the seven rotations as a palette of colours available for any passage, which is a use neither of the earlier traditions would recognise, and which depends on holding one harmony still. Miles Davis’s Kind of Blue is the canonical statement of it: chords held for many bars so that a mode has room to be heard as a place rather than as a moment.

Three traditions, one vocabulary, and only the third is what a modern musician means.

The minor scales are modes with an alteration #

Aeolian is the natural minor, and almost no music in the minor key uses it unaltered. What is used are two modified versions, and both modifications exist for the same reason.

Harmonic minor raises the seventh degree, producing a leading note a semitone below the tonic and a major dominant chord. That is exactly the machinery Aeolian lacks, imported. The cost is a gap of three semitones between the sixth and seventh degrees — an augmented second, which is awkward to sing and unmistakable in sound, and which became a signifier of exoticism in nineteenth-century European writing for reasons that have nothing to do with where it actually came from.

Melodic minor raises the sixth as well when ascending, closing the awkward gap, and reverts to the natural form descending, because the leading note is only needed on the way up. It is the rare scale that is different in each direction, and it is a straightforwardly practical fix.

The general lesson is that a mode is not a fixed object in practice. Traditions alter degrees to get the functional behaviour they want, and the “scale” that results is a description of a repertoire’s habits rather than a set somebody chose.

Where the model stops #

Rotation is not the only way to build a mode. The figures here derive every mode by rotating the diatonic set. Harmonic and melodic minor generate seven more rotations each, and the modes of the melodic minor are in constant use in jazz without usually being described this way.

Brightness is one ordering among several. Summing intervals above the tonic is a defensible measure and not the only one. Ordering by the position of the run on the circle of fifths gives the same answer; ordering by the number of notes shared with the parallel major does not.

The figures show sets. Everything above about melodic behaviour, hierarchy and characteristic phrases is invisible in a picture of which positions are filled, and that is most of what distinguishes real modal traditions from each other.

Equal temperament is assumed. The necklace’s twelve equal beads are an artefact of one tuning. Modal traditions with continuous pitch place several of these degrees somewhere the picture has no bead for.

What the brightness gradient is really measuring #

The ordering from Lydian to Locrian looks like a scale of mood and is something more concrete than that.

Each step flatward on the gradient moves the seven-note window one position along the chain of fifths. So brightness is a position, and the gradient is a line on the same map that key relationships live on.

That has a neat consequence. The distance between two modes on the brightness gradient is the number of notes they differ by — which is the same measure that separates two keys — so modal contrast and key contrast are the same quantity applied to two different questions. Moving from Ionian to Mixolydian on the same tonic changes one note, exactly as moving from C major to F major does. One is heard as a change of colour and the other as a change of place, and the pitch content changed identically.

Which of the two a listener hears depends entirely on whether the tonic moved. That is a striking amount of perceptual difference resting on a single degree of freedom the pitch content does not contain.

The ladder from here #

Later rungs: the modes of the melodic and harmonic minors. Authentic and plagal, and why range mattered. Modal cadences without a dominant. Modal jazz and the harmonic problem of a static chord. Greek harmoniai and the transmission error. Raga and maqam as melodic systems rather than pitch sets. Modal mixture, and borrowing between parallel modes. The brightness gradient formalised. And the question of whether a mode can be established without harmony, which folk monody answers in the affirmative and theory struggles to explain.

The names are wrong. Dorian is not the Greek Dorian, Lydian is not the Greek Lydian, and the mistake is traceable to a misunderstanding of Ptolemy transmitted through Boethius and fixed in place by the ninth century. Every musician alive uses the wrong names, and the wrong names work fine.