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mathematics

Swing time

Swing time is a mathematics 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 Swing time rather than just read about it. In short: In music, the term swing has two main uses. Colloquially, it is used to describe the propulsive quality or "feel" of a rhythm, especially when the music prompts a visceral response such as foot-tapping or head-nodding (see pulse).

Swing time — main illustration
Swing time — illustration

Key takeaways

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

Reference excerpt

In music, the term swing has two main uses. Colloquially, it is used to describe the propulsive quality or "feel" of a rhythm, especially when the music prompts a visceral response such as foot-tapping or head-nodding (see pulse). This sense can also be called "groove". The term swing feel, as well as swung note(s) and swung rhythm, is also used more specifically to refer to a technique (most commonly associated with jazz but also used in other genres) that involves alternately lengthening and shortening the first and second consecutive notes in the two part pulse-divisions in a beat.

Overview Like the term "groove", which is used to describe a cohesive rhythmic "feel" in a funk or rock context, the concept of "swing" can be hard to define. Indeed, some dictionaries use the terms as synonyms: "Groovy ... denotes music that really swings." The Jazz in America glossary defines swing as, "when an individual player or ensemble performs in such a rhythmically coordinated way as to command a visceral response from the listener (to cause feet to tap and heads to nod); an irresistible gravitational buoyancy that defies mere verbal definition." When jazz performer Cootie Williams was asked to define it, he joked, "Define it? I'd rather tackle Einstein's theory!" Benny Goodman, the 1930s-era bandleader nicknamed the "King of Swing", called swing "free speech in music", whose most important element is "the liberty a soloist has to stand and play a chorus in the way he feels it". His contemporary Tommy Dorsey gave a more ambiguous definition when he proposed that "Swing is sweet and hot at the same time and broad enough in its creative conception to meet every challenge tomorrow may present." Boogie-woogie pianist Maurice Rocco argues that the definition of swing "is just a matter of personal opinion". When asked for a definition of swing, Fats Waller replied, "Lady, if you gotta ask, you'll never know." Bill Treadwell stated:

What is Swing? Perhaps the best answer, after all, was supplied by the hep-cat who rolled her eyes, stared into the far-off and sighed, "You can feel it, but you just can't explain it. Do you dig me?" Stanley Dance, in The World of Swing, devoted the two first chapters of his work to discussions of the concept of swing with a collection of the musicians who played it. They described a kinetic quality to the music. It was compared to flying; "take off" was a signal to start a solo. The rhythmic pulse continued between the beats, expressed in dynamics, articulation, and inflection. Swing was as much in the music anticipating the beat, like the swing of a jumprope anticipating the jump, as in the beat itself. Swing has been defined in terms of formal rhythmic devices, but according to the Jimmie Lunceford tune, "T'aint whatcha do, it's the way thatcha do it" (say it so it swings). Physicists investigating swing have noted that it coincides with a perceptible difference between the timing of a soloist and the rest of the performers.

Swing as a rhythmic style

In swing rhythm the pulse is divided unequally, such that certain subdivisions (typically either eighth note or sixteenth note subdivisions) alternate between long and short durations. Certain music of the Baroque and Classical era is played using notes inégales, which is analogous to swing. In shuffle rhythm, the first note in a pair may be twice (or more) the duration of the second note. In swing rhythm, the ratio of the first note's duration to the second note's duration can range: The first note of each pair is often understood to be twice as long as the second, implying a triplet feel, but in practice the ratio is less definitive and often much more subtle. In traditional jazz, swing is typically applied to eighth notes. In other genres, such as funk and jazz-rock, swing is often applied to sixteenth notes.

In most jazz music, especially of the big band era and later, the second and fourth beats of a 44 measure are emphasized over the first and third, and the beats are lead-in—main-beat couplets (dah-DUM, dah-DUM....). The "dah" anticipates, or leads into, the "DUM." The "dah" lead-in may or may not be audible. It may be occasionally accented for phrasing or dynamic purposes. The instruments of a swing rhythm section express swing in various ways, which evolved as the music developed. During the early development of swing music, the bass was often played with lead-in—main-note couplets, often with a percussive sound. Later, the lead-in note was dropped but incorporated into the physical rhythm of the bass player to help keep the beat "solid” - the lead-in beats were not audible, but expressed in the player’s motion. Similarly, the rhythm guitar was played with the lead-in beat strummed by the player, but so softly as to be nearly or completely inaudible. The piano was played with a variety of devices for swing: Chord patterns played in the rhythm of a dotted-eighth—sixteenth couplet were characteristic of boogie-woogie playing (sometimes also used in boogie-woogie horn section playing). The "swing bass" left hand, used by James P. Johnson, Fats Waller, and Earl Hines, used a bass note on the first and third beats, followed by a mid-range chord to emphasize the second and fourth beats. As with the bass, lead-in beats were not audible, but expressed in the motion of the left arm.

Swing piano also put the first and third beats in a role anticipatory to the emphasized second and fourth beats in two-beat bass figures. Swing-time songs may have a slower beat and be written in an unusual time signature of twelve beats per measure, i.e. 128 instead of 44 with triplets, a quadruple compound time signature. 128 time may be combined with harmonious doo-wop or be used in a ballad, such as the standard "Unchained Melody" from 1955. Unchained Melody represents one of the most famous songs in history with a swing-time rhythm.

… excerpt ends here. Continue reading the full article.

Illustrations

Swing time illustration
Swing time illustration
Swing time illustration
Swing time illustration
Swing time: Straight (•) versus triplet swing (◦) eighth notes in the metric hierarchy
Straight (•) versus triplet swing (◦) eighth notes in the metric hierarchy

Worked examples

Example 1 — a first encounter with Swing time

Start with the simplest possible case. Write down what Swing time claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, 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 Swing time 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 Swing time 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 Swing time

In research
Swing time appears in mathematics 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 Swing time 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
Swing time is common in secondary-school and first-year university syllabi. It links to neighbouring topics Drum patterns, Jazz techniques, Jazz terminology, so understanding it makes those chapters shorter.
In everyday life
Look for Swing time 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 Swing time in 20 minutes

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

Frequently asked questions

What is Swing time in simple terms?

In music, the term swing has two main uses. Colloquially, it is used to describe the propulsive quality or "feel" of a rhythm, especially when the music prompts a visceral response such as foot-tapping or head-nodding (see pulse).

Why does Swing time matter?

Because it connects several mathematics 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 Swing time?

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 Swing time.

Tags

  • Drum patterns
  • Jazz techniques
  • Jazz terminology
  • Mathematics of music
  • Musical notation
  • Musical techniques
  • Popular music
  • Rhythm and meter
  • Swing music

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