science

Pitch constellation

Pitch constellation is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Pitch constellation rather than just read about it. In short: A pitch constellation is a graphical representation of pitches used to describe musical scales, modes, chords or other groupings of pitches within an octave range. It consists of a circle with markings along the circumference or lines from the center which indicate pitches.

Key takeaways

Pitch constellation belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Pitch constellation to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Pitch constellation from memory before moving on to harder problems.

Reference excerpt

A pitch constellation is a graphical representation of pitches used to describe musical scales, modes, chords or other groupings of pitches within an octave range. It consists of a circle with markings along the circumference or lines from the center which indicate pitches. Most pitch constellations use of a subset of pitches chosen from the twelve pitch chromatic scale. In this case the points on the circle are spaced like the twelve hour markings on an analog clock where each tick mark represents a semitone.

Scales and modes The pitch constellation provides an easy way to identify certain patterns and similarities between harmonic structures. For example.

A major scale consists of a circle with markings at 0 (or 12), 2, 4, 5, 7, 9 and 11 o'clock. A minor scale consists of a circle with markings at 0 (or 12), 2, 3, 5, 7, 8 and 10 o'clock.

The diagrams above show the two scales marked with "scale degrees". It can be observed that the tonic, second, fourth and fifth are shared, while the minor scale flattens the third, sixth and seventh notes relative to the major scale. Another observation is that the minor scale's constellation is the same as the major scale, but rotated +90 degrees. In the following drawing all of the major/minor scales are drawn. Note that the constellation for all the major scales or all the minor scales are identical. The different scales are generated by rotating the note overlay. The notes that need to be sharpened/flattened can be easily identified.

Moreover, if we draw all seven diatonic modes we can see them all as rotations of the Ionian mode. Note also the significance of the 6 o'clock point. This corresponds to a tritone. The modes including pitches a tritone from the tonic (Locrian and Lydian) are least used. The 5 o'clock and 7 o'clock pitches are also important points corresponding to a perfect fourth and perfect fifth respectively. The most used scales/modes - major (Ionian mode), minor (Aeolian mode) and Mixolydian - include these pitches.

Symmetric scales have simple representations in this scheme.

More exotic scales - such as the pentatonic, blues and octatonic - can also be drawn and related to the common scales.

A more complete list of musical scales and modes

Other overlays In previous sections we saw how various overlays (scale degrees, semi-tone numbering, notes) can be used to notate the circumference of the constellation. Various other overlays can be laid around the constellation. For example:

Intervals. Solfège. Pitch ratios (ratios of pitch frequencies).

Note that once a pitch constellation has been determined, any number of overlays (notes, solfège, intervals, etc.) may be placed on top for analysis/comparison. Often generating one harmonic relationship from another is simply a matter of rotating the overlay or constellation or shifting one or two pitch locations.

Chords Similarities between chords can also be observed as well as the significance of augmented/diminished notes. For triads we have the following:

And for seventh chords:

Circle of fifths Beginning with a pitch constellation of a chromatic scale, the notes of a circle of fifths can be easily generated. Starting at C and moving across the circle to the opposite side and then one tick clockwise, a line is drawn with an arrow indicating the direction moved. Continuing from that point (to the opposite side of the circle and one tick clockwise) all points are connected. Moving through this pattern the notes of the circle of fifths can be determined (C, G, D, A ...).

Technical note The ratio of the frequencies between two pitches in the constellation can be determined as follows. Take the length of the arc (measured clockwise) between the two points and divide by the circumference of the circle. The frequency ratio is two raised to this power. For example, for a fifth (P5, which is located at 7 o'clock relative to the tonic T) the frequency ratio is:

f P5 f T = 2 ( 7 / 12 ) ≈ 1.49821 ≈ 3 2 {\displaystyle {{\text{f}}_{\text{P5}} \over {\text{f}}_{\text{T}}}=2^{(7/12)}\approx 1.49821\approx {3 \over 2}}

Notes

References Burns, Edward M. (1999), Intervals, Scales, and Tuning. The Psychology of Music., Academic Press, ISBN 0-12-213564-4 Glaser, Matt (1999), Ear Training for Instrumentalists (Audio CD), Homespun, ISBN 0-634-00385-2 Josephs, Jess L. (1967), The Physics of Musical Sound, Van Nostrand Company Lerdahl, Fred (2001), Tonal Pitch Space, Oxford University Press, ISBN 0-19-505834-8 Slonimsky, Nicolas (1997) [1947], Thesaurus of Scales and Melodic Patterns, Music Sales America, ISBN 0-8256-1449-X Yamaguchi, Masaya (2006), Symmetrical Scales for Jazz Improvisation, Masaya Music, ISBN 0-9676353-2-2

Further reading Olson, Harry F. (1967), Music, Physics and Engineering, Dover Publications, ISBN 0-486-21769-8

External links On-line app illustrating pitch constellations ScaleTapper - IPhone app which utilizes pitch constellations. PDF of musical scales On-line chord/scale builder (with audio)

Illustrations

Worked examples

Example 1 — a first encounter with Pitch constellation

Start with the simplest possible case. Write down what Pitch constellation claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Pitch constellation before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Pitch constellation ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Pitch constellation

In research: Pitch constellation appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Pitch constellation in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Pitch constellation is common in secondary-school and first-year university syllabi. It links to neighbouring topics Pitch space, so understanding it makes those chapters shorter.
In everyday life: Look for Pitch constellation outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Pitch constellation in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Pitch constellation means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Pitch constellation out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Pitch constellation in simple terms?

Why does Pitch constellation matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Pitch constellation?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Pitch constellation.