Acoustics & Music Theory
why it sounds like that
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The triads each scale builds on its own degrees

Every chord that can be stacked in thirds on each degree of each scale, with its quality worked out from the intervals the scale actually supplies. The quality of the chord on each degree is a consequence of each scale's own step pattern rather than of a convention.
The triads each scale builds on its own degrees. Every chord that can be stacked in thirds on each degree of each scale, with its quality worked out from the intervals the scale actually supplies. The quality of the chord on each degree is a consequence of each scale's own step pattern rather than of a convention.

Drawn above with its standard settings, which is almost never how an essay draws it: an essay states the numbers it is arguing about, so the figure a reader meets there is about that argument rather than about the drawing in general. Every option a placement passes is checked against the ones this function actually reads, because an option it does not read is silently ignored and the figure quietly draws what is above instead.

It makes a noise. 10 of its 10 placements carry sound, built from the same numbers as the drawing, offering these buttons: harmonic minor: the chord on degree 5, major: the chord on degree 5, melodic minor: the chord on degree 5, natural minor: the chord on degree 5.

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the blast radius of changing it

The triads each scale builds on its own degrees. Every chord that can be stacked in thirds on each degree of each scale, with its quality worked out from the intervals the scale actually supplies. The quality of the chord on each degree is a consequence of each scale's own step pattern rather than of a convention.

What a raised seventh is for

The harmonic minor is usually taught as a scale with an odd gap in it. It is better understood as a repair to a single chord — raising the seventh degree turns the dominant triad from minor to major, and everything else about the scale is the bill for that.

scales · Modes The probe-tone profile, major key. How well each of the twelve pitch classes was rated as fitting, after a context establishing the key — Krumhansl and Kessler, 1982. The shading is not part of the measurement: it is the tonic, the rest of the tonic triad, the rest of the scale and the remaining five notes, which are categories this subject had before anybody ran the experiment. The profile separates all four without overlap.

Counting produced the hierarchy

Ask listeners how well each of the twelve notes fits after a passage in C major and the answers are not a smooth gradient. They fall into four groups with no overlap at all: the tonic, then the rest of the tonic triad, then the rest of the scale, then everything else — categories the subject had names for centuries before anybody ran the experiment.

perception · Tonal-expectation Which rotations have a fifth above their own tonic. Each rotation drawn by scale degree, with the degree a perfect fifth above the tonic marked. 1 of the 7 does not have one: Locrian. A tonic without a fifth above it has no triad of its own, which is a stronger disqualification than any preference.

The mode with no fifth

Six of the seven rotations have a perfect fifth above their own first degree and one does not, which is a structural disqualification rather than a preference. And the set's single tritone sits on a different pair of degrees in every rotation — on the fourth and seventh in Ionian, on the tonic itself in two others — which decides most of what each mode can do.

intervals · Modes The rotations of the diatonic set, brought to one tonic. The same rotations started on the same note rather than on their own, ordered by how many of their degrees are raised. Every step lowers exactly one note by a semitone, and the notes it lowers, in order, are F♯, B, E, A, D, G — which is the chain of fifths read backwards. A rotation is a rotation whatever the scale; the chain is a property of a set generated by a single interval, and it disappears the moment the set is not.

Seven rotations that are not seven modes

Rotate harmonic minor and the result is not a family the way the diatonic modes are a family. Four of its six generic intervals come in three specific sizes rather than two, so a fourth might be four, five or six semitones; three of its seven rotations have no fifth above their own tonic; and four have a tonic inside a tritone. The word mode has been doing two different jobs.

scales · Modes

All figures · What can be heard