Download a PDF of this page here.

Download the Spanish version here.

Essential Concepts

• Sound is created by vibrations that travel in waves, with frequency measuring the number of vibrations per second in Hertz (Hz), determining the pitch of the sound.
• Higher frequencies result in higher-pitched sounds, while lower frequencies produce lower-pitched sounds, with the human ear typically hearing sounds in the range of [latex]20[/latex] Hz to [latex]20,000[/latex] Hz.
• Decibels (dB) measure the intensity or loudness of a sound, with higher decibel levels indicating louder sounds.
• Pitch is the tonal quality of a sound, allowing us to perceive it as high or low, and is directly related to the frequency of the sound wave.
• Instruments like guitars and pianos produce sound through the vibration of strings, with the frequency related to the length and thickness of the string.
• The link between math and music is evident in the way musical notes, scales, and chords are structured, with mathematical relationships defining the intervals between notes.
• Musical scales consist of a series of notes in a specific order, with each scale having its own unique pattern of intervals, often described in terms of whole steps and half steps.
• Chords are combinations of notes played simultaneously, with their structure and harmony governed by mathematical principles.
• Rhythm in music involves patterns of beats, with time signatures indicating the number of beats in each measure and the note value that represents one beat.
• Mathematical concepts in music extend to the construction of instruments, where dimensions and materials are carefully chosen to produce specific sounds and tones.
• Notes that are one octave apart have the same name and are related in frequency, with the frequency of a note one octave higher being double that of the lower note. This relationship continues as you move up and down the octaves on a musical instrument, such as a keyboard or guitar.
• For example, if the frequency of middle [latex]C[/latex] ([latex]C4[/latex]) is [latex]262[/latex] Hz, the frequency of the [latex]C[/latex] one octave higher ([latex]C5[/latex]) is [latex]524[/latex] Hz, and so on.
• The frequency of each consecutive higher octave can be found by doubling the frequency of the previous octave.
• Conversely, moving to a lower octave involves halving the frequency of the note in the higher octave. This mathematical relationship is used to find the approximate frequency of any given note in different octaves.
• The relationship between math and literature is an example of interdisciplinary studies, which combine multiple academic disciplines to create a comprehensive understanding.
• Mathematical concepts can serve as plot devices, character development tools, or thematic elements in literature.
• The Fibonacci Sequence and the Golden Ratio are mathematical concepts used by authors to structure their narratives, adding depth and complexity to their works.
• The Fibonacci Sequence, where each number is the sum of the two preceding ones, can be used to structure chapters or sections in literature.
• The Golden Ratio, approximately 1.618, is used to divide a story into parts, often marking critical turning points or climaxes in the narrative.
• Rhythmic and linguistic patterns in literature, such as syllabic patterns in poetry and rhyme schemes, are often mathematically structured, adding musicality and rhythm to the works.
• Textual analysis in literature has evolved with computational linguistics, employing algorithms to study word frequency and distribution, themes, and sentiments within a text.
• Algorithms range from simple word counts to complex machine learning techniques, offering insights into recurring themes and writing styles.
• Stylometry, the statistical analysis of literary style, uses metrics like lexical richness and sentence length to attribute authorship and analyze writing styles.
• Stylometry has been instrumental in literary studies, helping to identify authors of anonymous or disputed works, such as parts of Shakespeare’s plays or the Federalist Papers.
• Game theory, which models strategic interactions among rational decision-makers, is applied in literature to analyze character dynamics, alliances, and betrayals.
• Probability theory is used to create realistic scenarios in literature, such as the likelihood of events in mystery novels or exploring themes of fate and chance.
• Statistical models can predict reader engagement and preferences, influencing the future of literature.

Glossary

algorithm

a set of step-by-step procedures or formulas for solving a problem

decibels

measure the intensity or loudness of a sound, with higher decibel levels indicating louder sounds and lower levels indicating softer sounds

Fibonacci sequence

a series of numbers in which each number is the sum of the two preceding ones

frequency

the number of vibrations per second of a sound wave, measured in Hertz (Hz), and it determines the pitch of the sound we hear

game theory

the study of mathematical models of strategic interaction among rational decision-makers

Golden Ratio

a mathematical constant approximately equal to [latex]1.618[/latex]

octave

a foundational unit in music theory, encompassing 12 half-steps and marking the point where the note names repeat but at a higher pitch

pitch

the tonal quality of a sound that allows us to perceive it as high or low, and it is directly related to the frequency of the sound wave

probability

the measure of the likelihood that an event will occur

statistics

the study of data: how to collect, summarize, and interpret it

stylometry

the statistical analysis of variations in literary style between one writer or genre and another