{"id":8428,"date":"2023-09-29T14:54:57","date_gmt":"2023-09-29T14:54:57","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=8428"},"modified":"2024-10-18T21:00:16","modified_gmt":"2024-10-18T21:00:16","slug":"math-in-arts-common-scenarios-cheat-sheet","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/math-in-arts-common-scenarios-cheat-sheet\/","title":{"raw":"Math in Arts - Common Scenarios: Cheat Sheet","rendered":"Math in Arts &#8211; Common Scenarios: Cheat Sheet"},"content":{"raw":"<p style=\"text-align: right;\"><a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Cheat+Sheets\/Math+in+Arts+-+Common+Scenarios_+Cheat+Sheet.pdf\" target=\"_blank\" rel=\"noopener\"><span style=\"font-size: 14pt;\">Download a PDF of this page here.<\/span><\/a><\/p>\r\n<p style=\"text-align: right;\"><a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Cheat+Sheets\/Spanish+-+QR+Math+in+Arts+Common+Scenarios+Cheat+Sheet.pdf\" target=\"_blank\" rel=\"noopener\"><span style=\"font-size: 14pt;\">Download the Spanish version here.<\/span><\/a><\/p>\r\n<h2>Essential Concepts<\/h2>\r\n<ul>\r\n\t<li>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.<\/li>\r\n\t<li>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.<\/li>\r\n\t<li>Decibels (dB) measure the intensity or loudness of a sound, with higher decibel levels indicating louder sounds.<\/li>\r\n\t<li>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.<\/li>\r\n\t<li>Instruments like guitars and pianos produce sound through the vibration of strings, with the frequency related to the length and thickness of the string.<\/li>\r\n\t<li>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.<\/li>\r\n\t<li>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.<\/li>\r\n\t<li>Chords are combinations of notes played simultaneously, with their structure and harmony governed by mathematical principles.<\/li>\r\n\t<li>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.<\/li>\r\n\t<li>Mathematical concepts in music extend to the construction of instruments, where dimensions and materials are carefully chosen to produce specific sounds and tones.<\/li>\r\n\t<li>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.<\/li>\r\n\t<li>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.<\/li>\r\n\t<li>The frequency of each consecutive higher octave can be found by doubling the frequency of the previous octave.<\/li>\r\n\t<li>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.<\/li>\r\n\t<li>The relationship between math and literature is an example of interdisciplinary studies, which combine multiple academic disciplines to create a comprehensive understanding.<\/li>\r\n\t<li>Mathematical concepts can serve as plot devices, character development tools, or thematic elements in literature.<\/li>\r\n\t<li>The Fibonacci Sequence and the Golden Ratio are mathematical concepts used by authors to structure their narratives, adding depth and complexity to their works.<\/li>\r\n\t<li>The Fibonacci Sequence, where each number is the sum of the two preceding ones, can be used to structure chapters or sections in literature.<\/li>\r\n\t<li>The Golden Ratio, approximately 1.618, is used to divide a story into parts, often marking critical turning points or climaxes in the narrative.<\/li>\r\n\t<li>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.<\/li>\r\n\t<li>Textual analysis in literature has evolved with computational linguistics, employing algorithms to study word frequency and distribution, themes, and sentiments within a text.<\/li>\r\n\t<li>Algorithms range from simple word counts to complex machine learning techniques, offering insights into recurring themes and writing styles.<\/li>\r\n\t<li>Stylometry, the statistical analysis of literary style, uses metrics like lexical richness and sentence length to attribute authorship and analyze writing styles.<\/li>\r\n\t<li>Stylometry has been instrumental in literary studies, helping to identify authors of anonymous or disputed works, such as parts of Shakespeare\u2019s plays or the Federalist Papers.<\/li>\r\n\t<li>Game theory, which models strategic interactions among rational decision-makers, is applied in literature to analyze character dynamics, alliances, and betrayals.<\/li>\r\n\t<li>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.<\/li>\r\n\t<li>Statistical models can predict reader engagement and preferences, influencing the future of literature.<\/li>\r\n<\/ul>\r\n<h2>Glossary<\/h2>\r\n<p><strong>algorithm<\/strong><\/p>\r\n<p>a set of step-by-step procedures or formulas for solving a problem<\/p>\r\n<p><strong>decibels<\/strong><\/p>\r\n<p>measure the intensity or loudness of a sound, with higher decibel levels indicating louder sounds and lower levels indicating softer sounds<\/p>\r\n<p><strong>Fibonacci sequence<\/strong><\/p>\r\n<p>a series of numbers in which each number is the sum of the two preceding ones<\/p>\r\n<p><strong>frequency<\/strong><\/p>\r\n<p>the number of vibrations per second of a sound wave, measured in\u00a0<strong>Hertz<\/strong>\u00a0(Hz), and it determines the pitch of the sound we hear<\/p>\r\n<p><strong>game theory<\/strong><\/p>\r\n<p>the study of mathematical models of strategic interaction among rational decision-makers<\/p>\r\n<p><strong>Golden Ratio<\/strong><\/p>\r\n<p>a mathematical constant approximately equal to [latex]1.618[\/latex]<\/p>\r\n<p><strong>octave<\/strong><\/p>\r\n<p>a foundational unit in music theory, encompassing 12 half-steps and marking the point where the note names repeat but at a higher pitch<\/p>\r\n<p><strong>pitch<\/strong><\/p>\r\n<p>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<\/p>\r\n<p><strong>probability<\/strong><\/p>\r\n<p>the measure of the likelihood that an event will occur<\/p>\r\n<p><strong>statistics<\/strong><\/p>\r\n<p>the study of data: how to collect, summarize, and interpret it<\/p>\r\n<p><strong>stylometry<\/strong><\/p>\r\n<p>the statistical analysis of variations in literary style between one writer or genre and another<\/p>\r\n<h2>\u00a0<\/h2>","rendered":"<p style=\"text-align: right;\"><a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Cheat+Sheets\/Math+in+Arts+-+Common+Scenarios_+Cheat+Sheet.pdf\" target=\"_blank\" rel=\"noopener\"><span style=\"font-size: 14pt;\">Download a PDF of this page here.<\/span><\/a><\/p>\n<p style=\"text-align: right;\"><a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Cheat+Sheets\/Spanish+-+QR+Math+in+Arts+Common+Scenarios+Cheat+Sheet.pdf\" target=\"_blank\" rel=\"noopener\"><span style=\"font-size: 14pt;\">Download the Spanish version here.<\/span><\/a><\/p>\n<h2>Essential Concepts<\/h2>\n<ul>\n<li>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.<\/li>\n<li>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.<\/li>\n<li>Decibels (dB) measure the intensity or loudness of a sound, with higher decibel levels indicating louder sounds.<\/li>\n<li>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.<\/li>\n<li>Instruments like guitars and pianos produce sound through the vibration of strings, with the frequency related to the length and thickness of the string.<\/li>\n<li>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.<\/li>\n<li>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.<\/li>\n<li>Chords are combinations of notes played simultaneously, with their structure and harmony governed by mathematical principles.<\/li>\n<li>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.<\/li>\n<li>Mathematical concepts in music extend to the construction of instruments, where dimensions and materials are carefully chosen to produce specific sounds and tones.<\/li>\n<li>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.<\/li>\n<li>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.<\/li>\n<li>The frequency of each consecutive higher octave can be found by doubling the frequency of the previous octave.<\/li>\n<li>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.<\/li>\n<li>The relationship between math and literature is an example of interdisciplinary studies, which combine multiple academic disciplines to create a comprehensive understanding.<\/li>\n<li>Mathematical concepts can serve as plot devices, character development tools, or thematic elements in literature.<\/li>\n<li>The Fibonacci Sequence and the Golden Ratio are mathematical concepts used by authors to structure their narratives, adding depth and complexity to their works.<\/li>\n<li>The Fibonacci Sequence, where each number is the sum of the two preceding ones, can be used to structure chapters or sections in literature.<\/li>\n<li>The Golden Ratio, approximately 1.618, is used to divide a story into parts, often marking critical turning points or climaxes in the narrative.<\/li>\n<li>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.<\/li>\n<li>Textual analysis in literature has evolved with computational linguistics, employing algorithms to study word frequency and distribution, themes, and sentiments within a text.<\/li>\n<li>Algorithms range from simple word counts to complex machine learning techniques, offering insights into recurring themes and writing styles.<\/li>\n<li>Stylometry, the statistical analysis of literary style, uses metrics like lexical richness and sentence length to attribute authorship and analyze writing styles.<\/li>\n<li>Stylometry has been instrumental in literary studies, helping to identify authors of anonymous or disputed works, such as parts of Shakespeare\u2019s plays or the Federalist Papers.<\/li>\n<li>Game theory, which models strategic interactions among rational decision-makers, is applied in literature to analyze character dynamics, alliances, and betrayals.<\/li>\n<li>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.<\/li>\n<li>Statistical models can predict reader engagement and preferences, influencing the future of literature.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<p><strong>algorithm<\/strong><\/p>\n<p>a set of step-by-step procedures or formulas for solving a problem<\/p>\n<p><strong>decibels<\/strong><\/p>\n<p>measure the intensity or loudness of a sound, with higher decibel levels indicating louder sounds and lower levels indicating softer sounds<\/p>\n<p><strong>Fibonacci sequence<\/strong><\/p>\n<p>a series of numbers in which each number is the sum of the two preceding ones<\/p>\n<p><strong>frequency<\/strong><\/p>\n<p>the number of vibrations per second of a sound wave, measured in\u00a0<strong>Hertz<\/strong>\u00a0(Hz), and it determines the pitch of the sound we hear<\/p>\n<p><strong>game theory<\/strong><\/p>\n<p>the study of mathematical models of strategic interaction among rational decision-makers<\/p>\n<p><strong>Golden Ratio<\/strong><\/p>\n<p>a mathematical constant approximately equal to [latex]1.618[\/latex]<\/p>\n<p><strong>octave<\/strong><\/p>\n<p>a foundational unit in music theory, encompassing 12 half-steps and marking the point where the note names repeat but at a higher pitch<\/p>\n<p><strong>pitch<\/strong><\/p>\n<p>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<\/p>\n<p><strong>probability<\/strong><\/p>\n<p>the measure of the likelihood that an event will occur<\/p>\n<p><strong>statistics<\/strong><\/p>\n<p>the study of data: how to collect, summarize, and interpret it<\/p>\n<p><strong>stylometry<\/strong><\/p>\n<p>the statistical analysis of variations in literary style between one writer or genre and another<\/p>\n<h2>\u00a0<\/h2>\n","protected":false},"author":15,"menu_order":1,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":8095,"module-header":"cheat_sheet","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8428"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":5,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8428\/revisions"}],"predecessor-version":[{"id":14348,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8428\/revisions\/14348"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/parts\/8095"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8428\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=8428"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=8428"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=8428"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=8428"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}