{"id":8324,"date":"2023-09-29T14:38:28","date_gmt":"2023-09-29T14:38:28","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=8324"},"modified":"2024-10-18T21:00:19","modified_gmt":"2024-10-18T21:00:19","slug":"math-in-music-fresh-take","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/math-in-music-fresh-take\/","title":{"raw":"Math in Music: Fresh Take","rendered":"Math in Music: Fresh Take"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Explain the fundamentals of frequency and pitch in the context of sound and music<\/li>\r\n\t<li>Assess musical elements including notes, half-steps, whole steps, and octaves<\/li>\r\n\t<li>Determine octave frequencies and their relevance in music<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Basics of Frequency as It Relates to Sound and Basics of Pitch<\/h2>\r\n<div class=\"textbox shaded\"><strong>The Main Idea<\/strong>\r\n<p><strong>Frequency and Pitch:<\/strong> Every sound is created by vibrations that travel in waves. <strong>Frequency <\/strong>measures the number of these waves completed in a second, and it's measured in Hertz (Hz). <strong>Pitch <\/strong>is the tonal quality of a sound, directly related to its frequency.<\/p>\r\n<p><strong>Sound Levels:<\/strong> The intensity or loudness of a sound is measured in decibels (dB). Different sounds have different dB levels, and this measurement helps us understand the loudness of various sounds in our environment.<\/p>\r\n\r\n\r\nBelow are some quick tips for understanding these topics.\r\n\r\n\r\n<ul>\r\n\t<li><strong>Understanding Frequency:<\/strong> Frequency is the heartbeat of sound. It's like the speedometer for sound waves, telling us how many waves pass by in a second. Measured in Hertz (Hz), it's crucial for determining the pitch of the sound you hear.<\/li>\r\n\t<li><strong>Decibels and You:<\/strong> Think of decibels (dB) as the volume knob on your stereo. The higher the dB, the louder the sound. But remember, sounds below [latex]0[\/latex] dB are extremely quiet, almost inaudible, while sounds like firecrackers can go up to [latex]140[\/latex] dB!<\/li>\r\n\t<li><strong>Pitch Perfect:<\/strong> Pitch is your ear's way of interpreting frequency. High-pitched sounds have high frequencies (like a whistle), while low-pitched sounds have low frequencies (like a drum). It's what makes each note in a song distinct.<\/li>\r\n\t<li><strong>Tech-Savvy Tuning:<\/strong> If you're into music, consider using tech tools like graphing calculators with plug-in accessories to tune your instruments. They measure the frequency of the note you're playing, helping you tune it to perfection.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<p>For more information on frequency and pitch, watch the following videos.<\/p>\r\n<section class=\"textbox watchIt\">&lt;<iframe src=\"\/\/plugin.3playmedia.com\/show?mf=11328618&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=y_ZHE3fyuGE&amp;video_target=tpm-plugin-tysefuwj-y_ZHE3fyuGE\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Principles+of+Marketing+Transcriptions\/The+Relationship+Between+Pitch+and+Frequency.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cThe Relationship Between Pitch and Frequency\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n<section class=\"textbox watchIt\"><iframe src=\"\/\/plugin.3playmedia.com\/show?mf=11328619&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=Bf38N0Y9BMw&amp;video_target=tpm-plugin-szrbgu28-Bf38N0Y9BMw\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Principles+of+Marketing+Transcriptions\/Frequency+and+Pitch.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cFrequency and Pitch\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n<section class=\"textbox watchIt\"><iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/g0CSDL5o-jk?si=0fOmpajIXJvxkJPV\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe>\r\n<p>You can view the <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Pitch+and+Frequency.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cPitch and Frequency\u201d here (opens in new window).<\/a><\/p>\r\n \r\n<\/section>\r\n<h2>Note Values, Half-Steps, Whole Steps, and Octaves<\/h2>\r\n<div class=\"textbox shaded\"><strong>The Main Idea<\/strong>\r\n<p>Music and math are deeply intertwined, and nowhere is this more evident than in the structure of musical scales. The keyboard serves as a mathematical playground where each key, whether black or white, represents a distinct note. The distance between these notes is measured in <strong>half-steps<\/strong> and <strong>whole steps<\/strong>, which are the building blocks of musical scales. A <strong>sharp<\/strong> ([latex]\\#[\/latex]) or a <strong>flat <\/strong>([latex]\u266d[\/latex]) alters a note by a half-step, either raising or lowering its pitch. When you span [latex]12[\/latex] half-steps, you've completed an <strong>octave<\/strong>, where the musical alphabet restarts but at a different pitch level.<\/p>\r\n<p><strong>Half-Step:<\/strong> Think of a half-step as a single \"jump\" from one key to the next on a keyboard. It's the smallest interval in Western music.<\/p>\r\n<p><strong>Sharp and Flat:<\/strong> Sharps and flats are like the \"plus or minus one\" in math. They slightly alter the pitch of a note, either raising ([latex]\\#[\/latex]) or lowering ([latex]\u266d[\/latex]) it by a half-step.<\/p>\r\n<p><strong>Whole Step:<\/strong> A whole step is like a \"double jump\" on the keyboard, skipping one key in between. It's two half-steps combined.<\/p>\r\n<p><strong>Octave:<\/strong> An octave is a full cycle of 12 half-steps, or a \"musical lap,\" where the note names start over but at a different pitch level.<\/p>\r\n\r\n\r\nBelow are some quick tips for understanding these topics.\r\n\r\n\r\n<ul>\r\n\t<li><strong>Finding Half-Steps:<\/strong> Using a keyboard, if you're on a white key, the adjacent black key is usually a half-step away. If you're on a black key, both adjacent white keys are half-steps away.<\/li>\r\n\t<li><strong>Understanding Sharps and Flats:<\/strong> A sharp is not always a black key; it's simply the next key to the right. Similarly, a flat is the next key to the left.<\/li>\r\n\t<li><strong>Octaves and Pitch: <\/strong>The same note in different octaves will have the same letter name but will sound higher or lower.<\/li>\r\n\t<li><strong>Whole Steps and Scales:<\/strong> Whole steps are crucial in forming scales. For example, the major scale pattern is \"Whole, Whole, Half, Whole, Whole, Whole, Half.\"<\/li>\r\n<\/ul>\r\n<\/div>\r\n<section class=\"textbox example\">\r\n<p>Name which keys are one half-step up and one half-step down from the following:<\/p>\r\n<ol style=\"list-style-type: decimal;\">\r\n\t<li>[latex]F^\\#[\/latex]<\/li>\r\n\t<li>[latex]B[\/latex]<\/li>\r\n\t<li>[latex]G^\u266d[\/latex]<\/li>\r\n<\/ol>\r\n\r\n\r\n[reveal-answer q=\"4331\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"4331\"]\r\n\r\n\r\n<ol style=\"list-style-type: decimal;\">\r\n\t<li>up [latex]G[\/latex], down [latex]F[\/latex]<\/li>\r\n\t<li>up [latex]C[\/latex], down [latex]B^\u266d[\/latex]<\/li>\r\n\t<li>up [latex]G[\/latex], down [latex]F[\/latex]<\/li>\r\n<\/ol>\r\n\r\n\r\n[\/hidden-answer]<\/section>\r\n<section class=\"textbox example\">\r\n<p>Name which keys are one whole step up and one whole step down from the following:<\/p>\r\n<ol style=\"list-style-type: decimal;\">\r\n\t<li>[latex]D^\u266d[\/latex]<\/li>\r\n\t<li>[latex]C^\\#[\/latex]<\/li>\r\n\t<li>[latex]E[\/latex]<\/li>\r\n<\/ol>\r\n\r\n\r\n[reveal-answer q=\"4332\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"4332\"]\r\n\r\n\r\n<ol style=\"list-style-type: decimal;\">\r\n\t<li>up [latex]E^\u266d[\/latex], down [latex]B[\/latex]<\/li>\r\n\t<li>up [latex]D^\\#[\/latex], down [latex]B[\/latex]<\/li>\r\n\t<li>up [latex]F^\\#[\/latex], down [latex]D[\/latex]<\/li>\r\n<\/ol>\r\n\r\n\r\n[\/hidden-answer]<\/section>\r\n<p>For more information on whole steps and half-steps, watch the following video.<\/p>\r\n<section class=\"textbox watchIt\"><iframe src=\"\/\/plugin.3playmedia.com\/show?mf=11328621&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=6BP6KNmihV0&amp;video_target=tpm-plugin-96txlvpp-6BP6KNmihV0\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Principles+of+Marketing+Transcriptions\/Cracking+the+Code+of+Major+Scales+Whole+%26+Half+Steps.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cCracking the Code of Major Scales: Whole &amp; Half Steps\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n<p>For more information on octaves, watch the following video.<\/p>\r\n<section class=\"textbox watchIt\"><iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/a2jsupw4Bfg?si=hBGcAB-YIz5pjm7Z&amp;start=20\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Principles+of+Marketing+Transcriptions\/Music+Theory+-+01+-+What+is+an+OCTAVE.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cMusic Theory - 01 - What is an OCTAVE\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n<h2>Frequencies of Octaves<\/h2>\r\n<div class=\"textbox shaded\"><strong>The Main Idea<\/strong>\r\n<p>Music and math are deeply intertwined, especially when it comes to the concept of frequency and octaves. While you might know octaves for their musical resonance, they also have a mathematical formula that relates them. Notes that are an octave apart have frequencies that are powers of two. For example, if the frequency of [latex]C_4[\/latex] is [latex]262[\/latex] Hz, then [latex]C_5[\/latex] would be [latex]524[\/latex] Hz, and [latex]C_6[\/latex] would be [latex]1,048[\/latex] Hz. This doubling or halving of frequency continues as you move up or down the musical scale.<\/p>\r\n\r\n\r\nBelow are some quick tips for understanding this topic.\r\n\r\n\r\n<ul>\r\n\t<li><strong>Frequency Doubling:<\/strong> When moving to a higher octave, the frequency of the note doubles.<\/li>\r\n\t<li><strong>Frequency Halving:<\/strong> When moving to a lower octave, the frequency of the note is halved.<\/li>\r\n\t<li><strong>Keyboard Labels:<\/strong> Keys on a keyboard are often labeled with numbers for easy identification. For example, [latex]C_4[\/latex] is the middle [latex]C[\/latex] on a standard keyboard.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<p>For more information on frequencies of octaves, watch the following video.<\/p>\r\n<section class=\"textbox watchIt\"><iframe src=\"\/\/plugin.3playmedia.com\/show?mf=11328622&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=yht5HEZw5sU&amp;video_target=tpm-plugin-u122m50l-yht5HEZw5sU\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Principles+of+Marketing+Transcriptions\/The+Octaves+and+Sound+Frequencies+Explained.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cThe Octaves and Sound Frequencies Explained\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Explain the fundamentals of frequency and pitch in the context of sound and music<\/li>\n<li>Assess musical elements including notes, half-steps, whole steps, and octaves<\/li>\n<li>Determine octave frequencies and their relevance in music<\/li>\n<\/ul>\n<\/section>\n<h2>Basics of Frequency as It Relates to Sound and Basics of Pitch<\/h2>\n<div class=\"textbox shaded\"><strong>The Main Idea<\/strong><\/p>\n<p><strong>Frequency and Pitch:<\/strong> Every sound is created by vibrations that travel in waves. <strong>Frequency <\/strong>measures the number of these waves completed in a second, and it&#8217;s measured in Hertz (Hz). <strong>Pitch <\/strong>is the tonal quality of a sound, directly related to its frequency.<\/p>\n<p><strong>Sound Levels:<\/strong> The intensity or loudness of a sound is measured in decibels (dB). Different sounds have different dB levels, and this measurement helps us understand the loudness of various sounds in our environment.<\/p>\n<p>Below are some quick tips for understanding these topics.<\/p>\n<ul>\n<li><strong>Understanding Frequency:<\/strong> Frequency is the heartbeat of sound. It&#8217;s like the speedometer for sound waves, telling us how many waves pass by in a second. Measured in Hertz (Hz), it&#8217;s crucial for determining the pitch of the sound you hear.<\/li>\n<li><strong>Decibels and You:<\/strong> Think of decibels (dB) as the volume knob on your stereo. The higher the dB, the louder the sound. But remember, sounds below [latex]0[\/latex] dB are extremely quiet, almost inaudible, while sounds like firecrackers can go up to [latex]140[\/latex] dB!<\/li>\n<li><strong>Pitch Perfect:<\/strong> Pitch is your ear&#8217;s way of interpreting frequency. High-pitched sounds have high frequencies (like a whistle), while low-pitched sounds have low frequencies (like a drum). It&#8217;s what makes each note in a song distinct.<\/li>\n<li><strong>Tech-Savvy Tuning:<\/strong> If you&#8217;re into music, consider using tech tools like graphing calculators with plug-in accessories to tune your instruments. They measure the frequency of the note you&#8217;re playing, helping you tune it to perfection.<\/li>\n<\/ul>\n<\/div>\n<p>For more information on frequency and pitch, watch the following videos.<\/p>\n<section class=\"textbox watchIt\">&lt;<iframe loading=\"lazy\" src=\"\/\/plugin.3playmedia.com\/show?mf=11328618&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=y_ZHE3fyuGE&amp;video_target=tpm-plugin-tysefuwj-y_ZHE3fyuGE\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Principles+of+Marketing+Transcriptions\/The+Relationship+Between+Pitch+and+Frequency.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cThe Relationship Between Pitch and Frequency\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" src=\"\/\/plugin.3playmedia.com\/show?mf=11328619&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=Bf38N0Y9BMw&amp;video_target=tpm-plugin-szrbgu28-Bf38N0Y9BMw\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Principles+of+Marketing+Transcriptions\/Frequency+and+Pitch.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cFrequency and Pitch\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/g0CSDL5o-jk?si=0fOmpajIXJvxkJPV\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>You can view the <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Pitch+and+Frequency.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cPitch and Frequency\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<h2>Note Values, Half-Steps, Whole Steps, and Octaves<\/h2>\n<div class=\"textbox shaded\"><strong>The Main Idea<\/strong><\/p>\n<p>Music and math are deeply intertwined, and nowhere is this more evident than in the structure of musical scales. The keyboard serves as a mathematical playground where each key, whether black or white, represents a distinct note. The distance between these notes is measured in <strong>half-steps<\/strong> and <strong>whole steps<\/strong>, which are the building blocks of musical scales. A <strong>sharp<\/strong> ([latex]\\#[\/latex]) or a <strong>flat <\/strong>([latex]\u266d[\/latex]) alters a note by a half-step, either raising or lowering its pitch. When you span [latex]12[\/latex] half-steps, you&#8217;ve completed an <strong>octave<\/strong>, where the musical alphabet restarts but at a different pitch level.<\/p>\n<p><strong>Half-Step:<\/strong> Think of a half-step as a single &#8220;jump&#8221; from one key to the next on a keyboard. It&#8217;s the smallest interval in Western music.<\/p>\n<p><strong>Sharp and Flat:<\/strong> Sharps and flats are like the &#8220;plus or minus one&#8221; in math. They slightly alter the pitch of a note, either raising ([latex]\\#[\/latex]) or lowering ([latex]\u266d[\/latex]) it by a half-step.<\/p>\n<p><strong>Whole Step:<\/strong> A whole step is like a &#8220;double jump&#8221; on the keyboard, skipping one key in between. It&#8217;s two half-steps combined.<\/p>\n<p><strong>Octave:<\/strong> An octave is a full cycle of 12 half-steps, or a &#8220;musical lap,&#8221; where the note names start over but at a different pitch level.<\/p>\n<p>Below are some quick tips for understanding these topics.<\/p>\n<ul>\n<li><strong>Finding Half-Steps:<\/strong> Using a keyboard, if you&#8217;re on a white key, the adjacent black key is usually a half-step away. If you&#8217;re on a black key, both adjacent white keys are half-steps away.<\/li>\n<li><strong>Understanding Sharps and Flats:<\/strong> A sharp is not always a black key; it&#8217;s simply the next key to the right. Similarly, a flat is the next key to the left.<\/li>\n<li><strong>Octaves and Pitch: <\/strong>The same note in different octaves will have the same letter name but will sound higher or lower.<\/li>\n<li><strong>Whole Steps and Scales:<\/strong> Whole steps are crucial in forming scales. For example, the major scale pattern is &#8220;Whole, Whole, Half, Whole, Whole, Whole, Half.&#8221;<\/li>\n<\/ul>\n<\/div>\n<section class=\"textbox example\">\n<p>Name which keys are one half-step up and one half-step down from the following:<\/p>\n<ol style=\"list-style-type: decimal;\">\n<li>[latex]F^\\#[\/latex]<\/li>\n<li>[latex]B[\/latex]<\/li>\n<li>[latex]G^\u266d[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q4331\">Show Solution<\/button><\/p>\n<div id=\"q4331\" class=\"hidden-answer\" style=\"display: none\">\n<ol style=\"list-style-type: decimal;\">\n<li>up [latex]G[\/latex], down [latex]F[\/latex]<\/li>\n<li>up [latex]C[\/latex], down [latex]B^\u266d[\/latex]<\/li>\n<li>up [latex]G[\/latex], down [latex]F[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox example\">\n<p>Name which keys are one whole step up and one whole step down from the following:<\/p>\n<ol style=\"list-style-type: decimal;\">\n<li>[latex]D^\u266d[\/latex]<\/li>\n<li>[latex]C^\\#[\/latex]<\/li>\n<li>[latex]E[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q4332\">Show Solution<\/button><\/p>\n<div id=\"q4332\" class=\"hidden-answer\" style=\"display: none\">\n<ol style=\"list-style-type: decimal;\">\n<li>up [latex]E^\u266d[\/latex], down [latex]B[\/latex]<\/li>\n<li>up [latex]D^\\#[\/latex], down [latex]B[\/latex]<\/li>\n<li>up [latex]F^\\#[\/latex], down [latex]D[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/section>\n<p>For more information on whole steps and half-steps, watch the following video.<\/p>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" src=\"\/\/plugin.3playmedia.com\/show?mf=11328621&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=6BP6KNmihV0&amp;video_target=tpm-plugin-96txlvpp-6BP6KNmihV0\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Principles+of+Marketing+Transcriptions\/Cracking+the+Code+of+Major+Scales+Whole+%26+Half+Steps.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cCracking the Code of Major Scales: Whole &amp; Half Steps\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<p>For more information on octaves, watch the following video.<\/p>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/a2jsupw4Bfg?si=hBGcAB-YIz5pjm7Z&amp;start=20\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Principles+of+Marketing+Transcriptions\/Music+Theory+-+01+-+What+is+an+OCTAVE.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cMusic Theory &#8211; 01 &#8211; What is an OCTAVE\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<h2>Frequencies of Octaves<\/h2>\n<div class=\"textbox shaded\"><strong>The Main Idea<\/strong><\/p>\n<p>Music and math are deeply intertwined, especially when it comes to the concept of frequency and octaves. While you might know octaves for their musical resonance, they also have a mathematical formula that relates them. Notes that are an octave apart have frequencies that are powers of two. For example, if the frequency of [latex]C_4[\/latex] is [latex]262[\/latex] Hz, then [latex]C_5[\/latex] would be [latex]524[\/latex] Hz, and [latex]C_6[\/latex] would be [latex]1,048[\/latex] Hz. This doubling or halving of frequency continues as you move up or down the musical scale.<\/p>\n<p>Below are some quick tips for understanding this topic.<\/p>\n<ul>\n<li><strong>Frequency Doubling:<\/strong> When moving to a higher octave, the frequency of the note doubles.<\/li>\n<li><strong>Frequency Halving:<\/strong> When moving to a lower octave, the frequency of the note is halved.<\/li>\n<li><strong>Keyboard Labels:<\/strong> Keys on a keyboard are often labeled with numbers for easy identification. For example, [latex]C_4[\/latex] is the middle [latex]C[\/latex] on a standard keyboard.<\/li>\n<\/ul>\n<\/div>\n<p>For more information on frequencies of octaves, watch the following video.<\/p>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" src=\"\/\/plugin.3playmedia.com\/show?mf=11328622&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=yht5HEZw5sU&amp;video_target=tpm-plugin-u122m50l-yht5HEZw5sU\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Principles+of+Marketing+Transcriptions\/The+Octaves+and+Sound+Frequencies+Explained.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cThe Octaves and Sound Frequencies Explained\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n","protected":false},"author":15,"menu_order":9,"template":"","meta":{"_candela_citation":"[{\"type\":\"copyrighted_video\",\"description\":\"The Relationship Between Pitch and Frequency\",\"author\":\" CK-12 Foundation\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/y_ZHE3fyuGE\",\"project\":\"\",\"license\":\"arr\",\"license_terms\":\"\"},{\"type\":\"copyrighted_video\",\"description\":\"Frequency and Pitch\",\"author\":\"Aze Linguistics\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/Bf38N0Y9BMw\",\"project\":\"\",\"license\":\"arr\",\"license_terms\":\"\"},{\"type\":\"copyrighted_video\",\"description\":\"Pitch and Frequency\",\"author\":\"TeachEngineering\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/g0CSDL5o-jk\",\"project\":\"\",\"license\":\"arr\",\"license_terms\":\"\"},{\"type\":\"copyrighted_video\",\"description\":\"Cracking the Code of Major Scales: Whole & Half Steps\",\"author\":\"Soundfly\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/6BP6KNmihV0\",\"project\":\"\",\"license\":\"arr\",\"license_terms\":\"\"},{\"type\":\"copyrighted_video\",\"description\":\"Music Theory - 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