{"id":9450,"date":"2013-05-13T17:55:53","date_gmt":"2013-05-13T15:55:53","guid":{"rendered":"http:\/\/www.oberton.org\/?page_id=9450&#038;lang=en"},"modified":"2025-07-30T13:48:59","modified_gmt":"2025-07-30T11:48:59","slug":"harmonic-series","status":"publish","type":"page","link":"https:\/\/www.oberton.org\/en\/overtone-singing\/harmonic-series\/","title":{"rendered":"Harmonic Series (Music)"},"content":{"rendered":"\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-1vvt7-146e79ddbd6419a26473d371d5ea2db2\">\n#top .av-special-heading.av-1vvt7-146e79ddbd6419a26473d371d5ea2db2{\npadding-bottom:10px;\n}\nbody .av-special-heading.av-1vvt7-146e79ddbd6419a26473d371d5ea2db2 .av-special-heading-tag .heading-char{\nfont-size:25px;\n}\n.av-special-heading.av-1vvt7-146e79ddbd6419a26473d371d5ea2db2 .av-subheading{\nfont-size:15px;\n}\n<\/style>\n<div  class='av-special-heading av-1vvt7-146e79ddbd6419a26473d371d5ea2db2 av-special-heading-h1 blockquote modern-quote  avia-builder-el-0  el_before_av_one_half  avia-builder-el-first '><h1 class='av-special-heading-tag '  itemprop=\"headline\"  >Harmonic Series (Music)<\/h1><div class='av-subheading av-subheading_below'><p>The scale of nature<\/p>\n<\/div><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div>\n<div  class='flex_column av-k4d0ij-00b586235159ab27b23fe38620e1d60c av_one_half  avia-builder-el-1  el_after_av_heading  el_before_av_one_half  first flex_column_div  '     ><p>\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-k043vv-3997972416da6e9e92bdfe6304d11225\">\n#top .hr.hr-invisible.av-k043vv-3997972416da6e9e92bdfe6304d11225{\nheight:50px;\n}\n<\/style>\n<div  class='hr av-k043vv-3997972416da6e9e92bdfe6304d11225 hr-invisible  avia-builder-el-2  el_before_av_icon_box  avia-builder-el-first '><span class='hr-inner '><span class=\"hr-inner-style\"><\/span><\/span><\/div><br \/>\n<article  class='iconbox iconbox_left av-jt96zv-a00e9631f994fcfef434a312b153bc41  avia-builder-el-3  el_after_av_hr  avia-builder-el-last '  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class=\"iconbox_content\"><header class=\"entry-content-header\" aria-label=\"Icon: Definition\"><div class='iconbox_icon heading-color avia-iconfont avia-font-entypo-fontello' data-av_icon='\ue8c9' data-av_iconfont='entypo-fontello'  ><\/div><h3 class='iconbox_content_title '  itemprop=\"headline\" >Definition<\/h3><\/header><div class='iconbox_content_container '  itemprop=\"text\" ><blockquote>\n<p>The harmonic series is the chord of partials that vibrate simultaneously when a natural tone is played.<\/p>\n<\/blockquote>\n<\/div><\/div><footer class=\"entry-footer\"><\/footer><\/article><\/p><\/div>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-jmlnjf-4063fa40492fa11f83ac76c2d32b5d97\">\n.flex_column.av-jmlnjf-4063fa40492fa11f83ac76c2d32b5d97{\nborder-radius:0px 0px 0px 0px;\npadding:0px 0px 0px 0px;\n}\n<\/style>\n<div  class='flex_column av-jmlnjf-4063fa40492fa11f83ac76c2d32b5d97 av_one_half  avia-builder-el-4  el_after_av_one_half  el_before_av_textblock  flex_column_div av-zero-column-padding  '     ><section  class='av_textblock_section av-jg56pn-bdaec96571238b3d04ea1e7cc7a8c428 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" >\n<\/div><\/section><\/div>\n<section  class='av_textblock_section av-j8wnur-95b474afd6c3dba033788957f709a161 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p>The harmonic series is the foundation of all <a href=\"#harmonic_series_8211_intervals\">musical scales and tuning systems<\/a>, because it is the only natural scale. As soon as a tone sounds, overtones resonate. They all sound at the same time. The overtone series is therefore actually a <a href=\"#chord_of_harmonics\">chord<\/a>. The structure is always the same and corresponds to a mathematical <a href=\"#harmonic_series_8211_frequency_ratios\">harmonic series<\/a>, hence the name series. You don&#8217;t usually hear the overtones. Because they all vibrate as a chord at the same time, they seem to us like a single note.<\/p>\n<p>The term overtone series refers to the harmonic partials (<a href=\"#glossary_of_terms\">comparison of overtone\/partial tone\/harmonic, see below<\/a>). There are also sounds with inharmonic overtones. The more inharmonic overtones there are in a sound, the more it becomes noisy.<\/p>\n<\/div><\/section>\n<section  class='av_textblock_section av-1wksoj-f3403be5bc2e3fb018ed73a950cd0d47 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><div style=\"width: 610px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" src=\"https:\/\/www.oberton.org\/wp-content\/uploads\/obertonreihe-A110Hz_trsp600.png\" alt=\"The harmonics of A (110 Hz)\" width=\"600\" height=\"147\" \/><p class=\"wp-caption-text\">The harmonics of A.<\/p><\/div>\n<\/div><\/section>\n<section  class='av_textblock_section av-iyjw3n-9db7c6ac48d82a55eb2921199a333168 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><audio class=\"wp-audio-shortcode\" id=\"audio-9450-1\" preload=\"none\" style=\"width: 100%;\" controls=\"controls\"><source type=\"audio\/mpeg\" src=\"https:\/\/www.oberton.org\/wp-content\/uploads\/obertonreihe-A110Hz-auf.mp3?_=1\" \/><a href=\"https:\/\/www.oberton.org\/wp-content\/uploads\/obertonreihe-A110Hz-auf.mp3\">https:\/\/www.oberton.org\/wp-content\/uploads\/obertonreihe-A110Hz-auf.mp3<\/a><\/audio>\n<p><em>Harmonic Series of A2 (110 Hz).<\/em><\/p>\n<\/div><\/section>\n<section  class='av_textblock_section av-itk4nf-57b155cbb12990dae9a18b639561cfc9 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p>All sounds consist of overtone chords. Only sine waves have no overtones. One sound differs from the other mainly in the volume of the individual overtones (besides the noise components and temporal sound changes). The overtone series is not only the basis for music. It enables us to speak and sing, recognize people by their voice, locate sounds and distinguish a piano from a flute.<\/p>\n<\/div><\/section>\n<section  class='av_textblock_section av-imv71f-a960b2fc737742c67310905da4c4cdb4 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p>This scale does not come from humans, but originates directly from the laws of vibration of nature. It follows a universal wave principle and we are able to hear and experience it. The tones differ from our usual equal tempered tone system. Nevertheless, the equal tempered system, like all other tuning systems, is derived from the overtone series.<\/p>\n<p>The reason is that we assemble sequences of notes internally into small chords and then compare them unconsciously with the harmonic series. We have invented sound systems based on natural intervals because we love consonances with the harmonic series. However, cultures do not always consider the same intervals to be beautiful. Hence, there exist more than 4000 <span class=\"zp-InText-zp-ID--935790-A3W2PKN2--wp9450 zp-InText-Citation loading\" rel=\"{ 'pages': 'np', 'items': '{935790:A3W2PKN2}', 'format': '(%a%, %d%, %p%)', 'brackets': '', 'etal': '', 'separator': '', 'and': '' }\"><\/span> different sound systems in the world.<\/p>\n<p>Our western system with 12 semitones per octave, for example, is based on an idea from Greek antiquity of using the interval between the second and third harmonics &#8211; a fifth &#8211; as a basis and then layering it twelve times.<\/p>\n<\/div><\/section>\n<div  class='flex_column av-igy957-0ba12e9febba119c4c541b51204e134c av_one_full  avia-builder-el-11  el_after_av_textblock  el_before_av_one_full  first flex_column_div  column-top-margin'     ><p><div  class='av-special-heading av-6w50b-7f1cf0bdc1de05babef41d29893f93a1 av-special-heading-h2 blockquote modern-quote  avia-builder-el-12  el_before_av_textblock  avia-builder-el-first '><h2 class='av-special-heading-tag '  itemprop=\"headline\"  >Harmonic Series &#8211; Sound Sample<\/h2><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><br \/>\n<section  class='av_textblock_section av-i4iyir-2c8712f6bbdf97ddb9a6dbb6d680912e '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p>In the following video you will see and hear the overtone series of A3 (220 Hz). The video was recorded by Bodo Maass with our software <a title=\"Overtone Analyzer Software\" href=\"https:\/\/www.oberton.org\/en\/?post_type=portfolio&amp;p=9236\">Overtone Analyzer<\/a>.<\/p>\n<div class=\"lyte-wrapper\" title=\"Obertonreihe anh&ouml;ren\" style=\"width:1280px;max-width:100%;margin:5px;\">\n<div class=\"lyMe\" id=\"WYL__3W2s9NKNdA\" itemprop=\"video\" itemscope itemtype=\"https:\/\/schema.org\/VideoObject\">\n<div><meta itemprop=\"thumbnailUrl\" content=\"https:\/\/www.oberton.org\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2F_3W2s9NKNdA%2Fhqdefault.jpg\" \/><meta itemprop=\"embedURL\" content=\"https:\/\/www.youtube.com\/embed\/_3W2s9NKNdA\" \/><meta itemprop=\"duration\" content=\"PT53S\" \/><meta itemprop=\"uploadDate\" content=\"2009-07-10T14:49:24Z\" \/><\/div>\n<div id=\"lyte__3W2s9NKNdA\" data-src=\"https:\/\/www.oberton.org\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2F_3W2s9NKNdA%2Fhqdefault.jpg\" class=\"pL\">\n<div class=\"tC\">\n<div class=\"tT\" itemprop=\"name\">Obertonreihe anh\u00f6ren<\/div>\n<\/div>\n<p><button tabindex=\"0\" class=\"play\"><\/button><\/p>\n<div class=\"ctrl\">\n<div class=\"Lctrl\"><\/div>\n<div class=\"Rctrl\"><\/div>\n<\/div>\n<\/div>\n<p><noscript><a href=\"https:\/\/youtu.be\/_3W2s9NKNdA\" rel=\"nofollow\"><img decoding=\"async\" src=\"https:\/\/www.oberton.org\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2F_3W2s9NKNdA%2F0.jpg\" alt=\"Obertonreihe anh&ouml;ren\" width=\"1280\" height=\"700\" \/><br \/>Watch this video on YouTube<\/a><\/noscript><meta itemprop=\"description\" content=\"Obertonreihe des Grundtons a = 220Hz von der 1. bis zur 17. Harmonischen und wieder zur\u00fcck, gespielt mit Overtone Analyzer http:\/\/www.sygyt.com\"><\/div>\n<\/div>\n<div class=\"lL\" style=\"max-width:100%;width:1280px;margin:5px;\"><\/div>\n<\/div><\/section><\/p><\/div>\n<div  class='flex_column av-i0099n-a3ac01f6460e5a7c8d991ce26ddfea70 av_one_full  avia-builder-el-14  el_after_av_one_full  el_before_av_one_full  first flex_column_div  column-top-margin'     ><p><div  class='av-special-heading av-1qrvuj-eca6aeb26b1fcb0fdcb3365ebbd7f400 av-special-heading-h2 blockquote modern-quote  avia-builder-el-15  el_before_av_textblock  avia-builder-el-first '><h2 class='av-special-heading-tag '  itemprop=\"headline\"  >Chord of Harmonics<\/h2><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><br \/>\n<section  class='av_textblock_section av-hn2c4b-ecd08f7cbeb6373d5760354c7c0c5cf7 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p>All partials of the overtone series sound simultaneously when singing and in instruments. Our brain combines these partial tone bundles into a single sound and assigns them to a sound source. The frequency spacing between the partials is perceived as the pitch, the volume distribution of the overtones as the timbre. Most singers are not aware of the fact that they always sing whole chords of harmonics. Our brain has an archaic knowledge of this chord. Obviously, it can identify partial chords as a single sound source even before birth, e. g. the mother voice.<\/p>\n<\/div><\/section><br \/>\n<section  class='av_textblock_section av-hn2c4b-12-2167f61174f41797b97916b1b1d068c5 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p><img decoding=\"async\" class=\"aligncenter size-full wp-image-813\" src=\"https:\/\/www.oberton.org\/wp-content\/uploads\/teiltonakkord-c-130.8hz-mit-spktr-trsp.png\" alt=\"Obertonreihe von c als Akkord, mit Spektrum und Spektrogramm\" width=\"960\" height=\"412\" srcset=\"https:\/\/www.oberton.org\/wp-content\/uploads\/teiltonakkord-c-130.8hz-mit-spktr-trsp.png 960w, https:\/\/www.oberton.org\/wp-content\/uploads\/teiltonakkord-c-130.8hz-mit-spktr-trsp-300x128.png 300w, https:\/\/www.oberton.org\/wp-content\/uploads\/teiltonakkord-c-130.8hz-mit-spktr-trsp-450x193.png 450w, https:\/\/www.oberton.org\/wp-content\/uploads\/teiltonakkord-c-130.8hz-mit-spktr-trsp-600x258.png 600w, https:\/\/www.oberton.org\/wp-content\/uploads\/teiltonakkord-c-130.8hz-mit-spktr-trsp-705x303.png 705w, https:\/\/www.oberton.org\/wp-content\/uploads\/teiltonakkord-c-130.8hz-mit-spktr-trsp-768x330.png 768w\" sizes=\"(max-width: 960px) 100vw, 960px\" \/><\/p>\n<\/div><\/section><br \/>\n<section  class='av_textblock_section av-hn2c4b-11-35fc07e5de04b4c03709107601f9e6ac '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p style=\"text-align: center;\"><em>When singing tone C4, the entire series of overtones sounds as a chord.<\/em><\/p>\n<\/div><\/section><br \/>\n<section  class='av_textblock_section av-1mg5d7-8b6bf920f534ef93b8fd530b2b749b88 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p>Sound spectra and spectrograms can be used to visualize the relationship. Sound analysis software breaks down the sound into its individual frequencies and displays the volume levels by colours. The <a title=\"Overtone Analyzer\" href=\"https:\/\/www.oberton.org\/?page_id=170\">Overtone Analyzer<\/a>, which was developed by Bodo Maass and myself, specializes in providing musicians with an easy-to-understand overview of sound contexts.<\/p>\n<p><strong>The sound spectrum<\/strong> (frequency spectrum) is one way of visualizing sound. The spectrum shows the volume distribution of the overtones in a sung vowel. Each peak corresponds to an overtone, the further right the peak, the louder the overtone. At the bottom is the fundamental. Upwards the frequency (pitch) increases, to the right the volume increases. (Recorded with Overtone Analyzer).<\/p>\n<p><strong>The spectrogram<\/strong> (also called sonagram) is a second way of displaying sounds. Here the volume is shown in colours, in the example the more red, the louder. Each transverse line corresponds to an overtone. At the bottom is the fundamental. Upwards the frequency (pitch) increases, from left to right runs the time. (Recorded with Overtone Analyzer).<\/p>\n<\/div><\/section><\/p><\/div>\n<div  class='flex_column av-h3qckb-25dcb4cc4e90e4d40bbd2fc029d6cd5f av_one_full  avia-builder-el-20  el_after_av_one_full  el_before_av_one_full  first flex_column_div  column-top-margin'     ><p><div  class='av-special-heading av-1ku66b-f8426a41b48c56cf479a8a5c8c967fcb av-special-heading-h2 blockquote modern-quote  avia-builder-el-21  el_before_av_textblock  avia-builder-el-first '><h2 class='av-special-heading-tag '  itemprop=\"headline\"  >Timbre<\/h2><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><br \/>\n<section  class='av_textblock_section av-grylxn-c35aa8315979596483d7aa8d7d203b62 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p>Such a chord of harmonics sounds like a single note, but it has a timbre. While a tone without overtones is colorless. A tone with overtones is called a sound (German: Klang) in physics. Musicians and physicists might mean different things with this word!<\/p>\n<p>Different timbres are caused by <strong>different volumes of the harmonics<\/strong> (besides the noise components and transient response). The personal voice of a person is thus created by a typical volume distribution of the harmonics. If two people sing the same note, they differ only in the overtone volume. If you filter the overtones one by one, you will no longer recognize the individuals. The volume distribution contains a lot of information: Vowels, identification of the person, physical and mental state, age etc.<\/p>\n<\/div><\/section><br \/>\n<div  class='avia-image-container av-gnsbfv-6b2c15faef321d50de1cab6eabb3c3ec av-styling- avia-align-center  avia-builder-el-23  el_after_av_textblock  el_before_av_textblock '   itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" ><div class=\"avia-image-container-inner\"><div class=\"avia-image-overlay-wrap\"><img decoding=\"async\" width=\"680\" height=\"400\" fetchpriority=\"high\" class='wp-image-7038 avia-img-lazy-loading-not-7038 avia_image ' src=\"https:\/\/www.oberton.org\/wp-content\/uploads\/c-sung-on-vowel-ae_680x400.png\" alt='Spectrum of the singtone C3 on the vowel \u00e6.' title='Spectrum of the singtone C3 on the vowel \u00e6.'   itemprop=\"thumbnailUrl\" srcset=\"https:\/\/www.oberton.org\/wp-content\/uploads\/c-sung-on-vowel-ae_680x400.png 680w, https:\/\/www.oberton.org\/wp-content\/uploads\/c-sung-on-vowel-ae_680x400-300x176.png 300w, https:\/\/www.oberton.org\/wp-content\/uploads\/c-sung-on-vowel-ae_680x400-600x353.png 600w, https:\/\/www.oberton.org\/wp-content\/uploads\/c-sung-on-vowel-ae_680x400-450x264.png 450w\" sizes=\"(max-width: 680px) 100vw, 680px\" \/><\/div><\/div><\/div><br \/>\n<section  class='av_textblock_section av-gehc0z-b19d1cd4e187d1deb6df92d417273d56 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p style=\"text-align: center;\"><em>Spectrum of a sung note C3 with its harmonics and the typical volume distribution for the vowel \u00e6.<\/em><\/p>\n<\/div><\/section><\/p><\/div>\n<div  class='flex_column av-g76dz7-c9c5e8d481d5edb87abc3a2ec7417d15 av_one_full  avia-builder-el-25  el_after_av_one_full  el_before_av_one_half  first flex_column_div  column-top-margin'     ><p><div  class='av-special-heading av-1ewdez-41c29cb2897d94a7d0f5fdd0bfd68e2b av-special-heading-h2 blockquote modern-quote  avia-builder-el-26  el_before_av_textblock  avia-builder-el-first '><h2 class='av-special-heading-tag '  itemprop=\"headline\"  >Harmonic Series &#8211; Intervals<\/h2><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><br \/>\n<section  class='av_textblock_section av-1kzeg3-b10839b323fdbb8895119b9800ad5635 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p><strong>The interval sequence of the harmonic series is always the same<\/strong>. The intervals depend only on the position in the row. For example, the interval from the 2nd to the 3rd harmonic is always a fifth. Regardless of which tone you start with, the series results always in the same melody from the respective keynote. The intervals become increasingly narrower towards the top (while the frequency spacing remains the same, see below). All adjacent intervals are unique and occur only once in the series. Each interval repeats itself, once it has occurred, in the octaves above with new intermediate tones.<\/p>\n<p>The overtone slider (picture) displays the intervals from harmonic to harmonic and from the fundamental to the harmonic. It is the keyboard of overtone singing so to speak. On one singing note, you can only perform intervals that occur in the slider, and usually only a part of them (cf. <a href=\"https:\/\/www.oberton.org\/en\/overtone-singing\/composing-with-overtone-singing-composers-guide\/\">Ambitus of overtone singing<\/a>). The interval to the fundamental tone determines the harmonic perception. For example, the 5th partial tone is perceived as major third. If you want to sing a quart in an overtone melody, you will find it between the 3rd and 4th harmonic and then you choose the fundamental accordingly.<\/p>\n<\/div><\/section><br \/>\n<div  class='avia-image-container av-fkz7wz-381fb3c8c372eca7f3db444a6fd4d0b8 av-styling- avia-align-center  avia-builder-el-28  el_after_av_textblock  el_before_av_textblock '   itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" ><div class=\"avia-image-container-inner\"><div class=\"avia-image-overlay-wrap\"><img decoding=\"async\" class='wp-image-17794 avia-img-lazy-loading-not-17794 avia_image ' src=\"https:\/\/www.oberton.org\/wp-content\/uploads\/Teiltonskala-v6.2-web.png\" alt='Scale of partial tones - intervals of the harmonic series' title='Scale of partial tones - intervals of the harmonic series'  height=\"2807\" width=\"2210\"  itemprop=\"thumbnailUrl\" srcset=\"https:\/\/www.oberton.org\/wp-content\/uploads\/Teiltonskala-v6.2-web.png 2210w, https:\/\/www.oberton.org\/wp-content\/uploads\/Teiltonskala-v6.2-web-236x300.png 236w, https:\/\/www.oberton.org\/wp-content\/uploads\/Teiltonskala-v6.2-web-768x975.png 768w, https:\/\/www.oberton.org\/wp-content\/uploads\/Teiltonskala-v6.2-web-811x1030.png 811w, https:\/\/www.oberton.org\/wp-content\/uploads\/Teiltonskala-v6.2-web-600x762.png 600w, https:\/\/www.oberton.org\/wp-content\/uploads\/Teiltonskala-v6.2-web-1181x1500.png 1181w, https:\/\/www.oberton.org\/wp-content\/uploads\/Teiltonskala-v6.2-web-555x705.png 555w, https:\/\/www.oberton.org\/wp-content\/uploads\/Teiltonskala-v6.2-web-450x572.png 450w\" sizes=\"(max-width: 2210px) 100vw, 2210px\" \/><\/div><\/div><\/div><br \/>\n<section  class='av_textblock_section av-1jksor-a78b57175192722363df8118304968de '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p style=\"text-align: center;\"><em>Intervals of the harmonic series &#8211; the overtone slider.<\/em><\/p>\n<\/div><\/section><\/p><\/div>\n<div  class='flex_column av-1jd8b7-fed6952f063dfb54915c0087dca60f76 av_one_half  avia-builder-el-30  el_after_av_one_full  el_before_av_one_half  first flex_column_div  column-top-margin'     ><div  class='avia-button-wrap av-f7cxgb-286d11dadb373e06702e61db8119b5ee-wrap avia-button-right  avia-builder-el-31  avia-builder-el-no-sibling '><a href='\/wp-content\/uploads\/Teiltonskala-v06.pdf'  class='avia-button av-f7cxgb-286d11dadb373e06702e61db8119b5ee av-link-btn avia-icon_select-yes-left-icon avia-size-small avia-position-right avia-color-green'  target=\"_blank\"  rel=\"noopener noreferrer\"  aria-label=\" Download PDF (German version)\"><span class='avia_button_icon avia_button_icon_left avia-iconfont avia-font-entypo-fontello' data-av_icon='\ue82d' data-av_iconfont='entypo-fontello' ><\/span><span class='avia_iconbox_title' > Download PDF (German version)<\/span><\/a><\/div><\/div>\n<div  class='flex_column av-f0n5qz-ed84275d8746452ee1da5a6e8e189987 av_one_half  avia-builder-el-32  el_after_av_one_half  el_before_av_one_full  flex_column_div av-zero-column-padding  column-top-margin'     ><div  class='avia-button-wrap av-eshy6z-23c545f36e7ab23ff9f212c46f4cc6e0-wrap avia-button-left  avia-builder-el-33  avia-builder-el-no-sibling '><a href='\/wp-content\/uploads\/harmonic-series-6.2.pdf'  class='avia-button av-eshy6z-23c545f36e7ab23ff9f212c46f4cc6e0 av-link-btn avia-icon_select-yes-left-icon avia-size-small avia-position-left avia-color-green'  target=\"_blank\"  rel=\"noopener noreferrer\"  aria-label=\"Download PDF (English version)\"><span class='avia_button_icon avia_button_icon_left avia-iconfont avia-font-entypo-fontello' data-av_icon='\ue82d' data-av_iconfont='entypo-fontello' ><\/span><span class='avia_iconbox_title' >Download PDF (English version)<\/span><\/a><\/div><\/div>\n<div  class='flex_column av-em8g4z-aab4c8446cf72b88df992efd662f5efb av_one_full  avia-builder-el-34  el_after_av_one_half  el_before_av_one_half  first flex_column_div  column-top-margin'     ><p><div  class='av-special-heading av-efuf9v-e82f671403dee5c95da47ff4794f8d17 av-special-heading-h2 blockquote modern-quote  avia-builder-el-35  el_before_av_textblock  avia-builder-el-first '><h2 class='av-special-heading-tag '  itemprop=\"headline\"  >Harmonic Series &#8211; Frequency Ratios<\/h2><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><br \/>\n<section  class='av_textblock_section av-ed43x7-a680e4aae73df48b964aeb2947536074 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p><strong>The frequencies of the harmonics are integer multiples of the fundamental frequency<\/strong>. This mathematical connection is called a &#8220;harmonic series&#8221;.<\/p>\n<p><strong>The frequency difference between two harmonics is always identical to the basic frequency<\/strong>, accordingly.<\/p>\n<p>Calculation of the frequencies is therefore quite easy and clearly structured. Calculating the interval, however, is more complicated. While the frequency of an arbitrary harmonic is quickly calculated in the head, you better learn the intervals by heart (except you can calculate logarithms in your head&#8230;).<\/p>\n<\/div><\/section><\/p><\/div>\n<div  class='flex_column av-dsb46r-440e159769d688493926fdeb74147e07 av_one_half  avia-builder-el-37  el_after_av_one_full  el_before_av_one_half  first flex_column_div av-zero-column-padding  column-top-margin'     ><p><span  class='av_font_icon av-dytcab-e523d31b1de9fe1e4db109cc7795844f avia_animate_when_visible av-icon-style-border avia-icon-pos-left avia-iconfont avia-font-entypo-fontello av-no-color avia-icon-animate'><span class='av-icon-char' data-av_icon='\ue836' data-av_iconfont='entypo-fontello' aria-hidden=\"true\" ><\/span><span class='av_icon_caption av-special-font'>Example 1<\/span><\/span><br \/>\n<section  class='av_textblock_section av-dm7w7n-96b8ec17968abf3dfb33f8687a347707 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><div data-update_with=\"content\">\n<div data-update_with=\"content\">\n<p><strong>Calculate the frequencies of the partials of A2 (110 Hz):<\/strong><\/p>\n<p>1st harmonic &#8211; 1-fold frequency = 110 Hz<br \/>\n2nd harmonic &#8211; 2-fold frequency = 220 Hz,<br \/>\n3rd harmonic &#8211; 3 times the frequency = 330 Hz,<br \/>\n&#8230;<br \/>\n11th harmonic &#8211; 11 times the frequency = 1210 Hz etc.<\/p>\n<p>All harmonics of A2 have the same frequency spacing of 110 Hz.<\/p>\n<\/div>\n<\/div>\n<\/div><\/section><br \/>\n<div  class='hr av-djbbjv-60120467741bec8c6000aa50299e16ef hr-default  avia-builder-el-40  el_after_av_textblock  el_before_av_font_icon '><span class='hr-inner '><span class=\"hr-inner-style\"><\/span><\/span><\/div><br \/>\n<span  class='av_font_icon av-d1tfmj-2ba3865aac4609849eae4521e1e688b0 avia_animate_when_visible av-icon-style-border avia-icon-pos-left avia-iconfont avia-font-entypo-fontello av-no-color avia-icon-animate'><span class='av-icon-char' data-av_icon='\ue836' data-av_iconfont='entypo-fontello' aria-hidden=\"true\" ><\/span><span class='av_icon_caption av-special-font'>Example 2<\/span><\/span><br \/>\n<section  class='av_textblock_section av-db9u97-8a8fa3ea7f54f516a41fdf991290128b '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p>The spacing of the partials of the fundamental note c (130.8 Hz) would then be &#8211; as you might have guessed &#8211; 130.8 Hz, i. e. always identical to the basic frequency.<\/p>\n<\/div><\/section><br \/>\n<section  class='av_textblock_section av-co5asz-8b6bfbabee5b38cc6fc5e9775c599898 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><div data-update_with=\"content\">\n<p><strong>Calculating frequencies of the partials of C3 (130.8 Hz):<\/strong><\/p>\n<p>1st harmonic &#8211; 1-fold the frequency = 130.8 Hz<br \/>\n2nd harmonic &#8211; 2 times the frequency = 261.6 Hz<br \/>\n3rd harmonic &#8211; 3 times the frequency = 392.4 Hz<br \/>\n&#8230;<br \/>\n11th harmonic &#8211; 11 times the frequency = 1,439 Hz etc.<\/p>\n<p>All harmonics of C3 therefore have the same frequency spacing of 130.8 Hz.<\/p>\n<\/div>\n<\/div><\/section><br \/>\n<div  class='hr av-djbbjv-9-dbb0871a6326ff93670ee2920e8ec1c4 hr-default  avia-builder-el-44  el_after_av_textblock  avia-builder-el-last '><span class='hr-inner '><span class=\"hr-inner-style\"><\/span><\/span><\/div><\/p><\/div><div  class='flex_column av-dsb46r-10-7f81b8dd687cf871315608cb77ccb4c3 av_one_half  avia-builder-el-45  el_after_av_one_half  el_before_av_one_full  flex_column_div  column-top-margin'     ><section  class='av_textblock_section av-co5asz-8-f553e3d5c2da2997fe0fc4820d6fa90e '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><div data-update_with=\"content\">\n<p style=\"padding-left: 30px;\"><style>@media (max-width:480px){#cp_calculatedfieldsf_pform_1{min-height:3969px;}}@media (max-width:768px){#cp_calculatedfieldsf_pform_1{min-height:3050px;}}@media (max-width:1024px){#cp_calculatedfieldsf_pform_1{min-height:3974px;}}@media (min-width:1024px){#cp_calculatedfieldsf_pform_1{min-height:3723px;}}<\/style><form name=\"cp_calculatedfieldsf_pform_1\" id=\"cp_calculatedfieldsf_pform_1\" action=\"https:\/\/www.oberton.org\/en\/overtone-singing\/harmonic-series\/\" method=\"post\" enctype=\"multipart\/form-data\" onsubmit=\"return fbuilderjQuery.fbuilder.doValidate(this);\" class=\"cff-form no-prefetch  cff-form-6\"  data-nonce=\"fa0b41d748\">\n<input type=\"hidden\" name=\"cp_calculatedfieldsf_pform_psequence\" value=\"_1\" \/>\n<input type=\"hidden\" name=\"cp_calculatedfieldsf_id\" value=\"6\" \/>\n<input type=\"hidden\" name=\"cp_ref_page\" value=\"https:\/\/www.oberton.org\/en\" \/>\n<pre style=\"display:none !important;\"><script data-category=\"functional\" type=\"text\/javascript\">form_structure_1=[[{\"form_identifier\":\"\",\"name\":\"fieldname2\",\"shortlabel\":\"\",\"index\":0,\"ftype\":\"fnumber\",\"userhelp\":\"\",\"userhelpTooltip\":true,\"tooltipIcon\":false,\"csslayout\":\"\",\"title\":\"1. 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Harmonic\",\"predefined\":\"\",\"required\":false,\"exclude\":false,\"size\":\"medium\",\"eq\":\"PREC(fieldname2*19,1)\",\"suffix\":\" Hz\",\"prefix\":\"\",\"decimalsymbol\":\".\",\"groupingsymbol\":\"\",\"readonly\":true,\"noEvalIfManual\":true,\"formatDynamically\":false,\"hidefield\":false,\"fBuild\":{},\"parent\":\"\"},{\"dependencies\":[{\"rule\":\"\",\"complex\":false,\"fields\":[\"\"]}],\"form_identifier\":\"\",\"name\":\"fieldname27\",\"shortlabel\":\"\",\"index\":20,\"ftype\":\"fCalculated\",\"userhelp\":\"\",\"userhelpTooltip\":false,\"tooltipIcon\":false,\"csslayout\":\"\",\"title\":\"20. Harmonic\",\"predefined\":\"\",\"required\":false,\"exclude\":false,\"size\":\"medium\",\"eq\":\"PREC(fieldname2*20,1)\",\"suffix\":\" Hz\",\"prefix\":\"\",\"decimalsymbol\":\".\",\"groupingsymbol\":\"\",\"readonly\":true,\"noEvalIfManual\":true,\"formatDynamically\":false,\"hidefield\":false,\"fBuild\":{},\"parent\":\"\"},{\"dependencies\":[{\"rule\":\"\",\"complex\":false,\"fields\":[\"\"]}],\"form_identifier\":\"\",\"name\":\"fieldname26\",\"shortlabel\":\"\",\"index\":21,\"ftype\":\"fCalculated\",\"userhelp\":\"\",\"userhelpTooltip\":false,\"tooltipIcon\":false,\"csslayout\":\"\",\"title\":\"21. Harmonic\",\"predefined\":\"\",\"required\":false,\"exclude\":false,\"size\":\"medium\",\"eq\":\"PREC(fieldname2*21,1)\",\"suffix\":\" Hz\",\"prefix\":\"\",\"decimalsymbol\":\".\",\"groupingsymbol\":\"\",\"readonly\":true,\"noEvalIfManual\":true,\"formatDynamically\":false,\"hidefield\":false,\"fBuild\":{},\"parent\":\"\"},{\"dependencies\":[{\"rule\":\"\",\"complex\":false,\"fields\":[\"\"]}],\"form_identifier\":\"\",\"name\":\"fieldname29\",\"shortlabel\":\"\",\"index\":22,\"ftype\":\"fCalculated\",\"userhelp\":\"\",\"userhelpTooltip\":false,\"tooltipIcon\":false,\"csslayout\":\"\",\"title\":\"22. Harmonic\",\"predefined\":\"\",\"required\":false,\"exclude\":false,\"size\":\"medium\",\"eq\":\"PREC(fieldname2*22,1)\",\"suffix\":\" Hz\",\"prefix\":\"\",\"decimalsymbol\":\".\",\"groupingsymbol\":\"\",\"readonly\":true,\"noEvalIfManual\":true,\"formatDynamically\":false,\"hidefield\":false,\"fBuild\":{},\"parent\":\"\"},{\"dependencies\":[{\"rule\":\"\",\"complex\":false,\"fields\":[\"\"]}],\"form_identifier\":\"\",\"name\":\"fieldname30\",\"shortlabel\":\"\",\"index\":23,\"ftype\":\"fCalculated\",\"userhelp\":\"\",\"userhelpTooltip\":false,\"tooltipIcon\":false,\"csslayout\":\"\",\"title\":\"23. Harmonic\",\"predefined\":\"\",\"required\":false,\"exclude\":false,\"size\":\"medium\",\"eq\":\"PREC(fieldname2*23,1)\",\"suffix\":\" Hz\",\"prefix\":\"\",\"decimalsymbol\":\".\",\"groupingsymbol\":\"\",\"readonly\":true,\"noEvalIfManual\":true,\"formatDynamically\":false,\"hidefield\":false,\"fBuild\":{},\"parent\":\"\"},{\"dependencies\":[{\"rule\":\"\",\"complex\":false,\"fields\":[\"\"]}],\"form_identifier\":\"\",\"name\":\"fieldname31\",\"shortlabel\":\"\",\"index\":24,\"ftype\":\"fCalculated\",\"userhelp\":\"\",\"userhelpTooltip\":false,\"tooltipIcon\":false,\"csslayout\":\"\",\"title\":\"24. Harmonic\",\"predefined\":\"\",\"required\":false,\"exclude\":false,\"size\":\"medium\",\"eq\":\"PREC(fieldname2*24,1)\",\"suffix\":\" Hz\",\"prefix\":\"\",\"decimalsymbol\":\".\",\"groupingsymbol\":\"\",\"readonly\":true,\"noEvalIfManual\":true,\"formatDynamically\":false,\"hidefield\":false,\"fBuild\":{},\"parent\":\"\"}],{\"0\":{\"title\":\"Frequencies of Harmonics Calculator\",\"description\":\"\",\"formlayout\":\"top_aligned\",\"formtemplate\":\"\",\"evalequations\":1,\"evalequationsevent\":2,\"autocomplete\":1,\"persistence\":0,\"customstyles\":\"\"},\"formid\":\"cp_calculatedfieldsf_pform_1\"}];<\/script><\/pre>\n<div id=\"fbuilder\">\n\t\t<div id=\"fbuilder_1\">\n\t\t<div id=\"formheader_1\"><\/div>\n\t\t<div id=\"fieldlist_1\"><\/div>\n\t\t<div class=\"clearer\"><\/div>\n\t<\/div>\n\t<div id=\"cpcaptchalayer_1\" class=\"cpcaptchalayer\" style=\"display:none;\">\n\t\t            <div class=\"fields\">\r\n                <label>Please enter the security code<\/label>\r\n                <div class=\"dfield\">\r\n                    <span id=\"cff_captcha_math_1\" class=\"cff-captcha-math-label\">1 + 5 = <\/span>\r\n                    <input type=\"text\" size=\"8\" name=\"hdcaptcha_cp_calculated_fields_form_post\" id=\"hdcaptcha_cp_calculated_fields_form_post_1\" value=\"\" autocomplete=\"off\" \/>\r\n                    <div class=\"error message\" id=\"hdcaptcha_error_1\" style=\"display:none;\"><\/div>\r\n                <\/div>\r\n                <div class=\"clearer\"><\/div>\r\n            <\/div>\r\n        \t<\/div>\n<\/div>\n\t<div id=\"cp_subbtn_1\" class=\"cp_subbtn\" style=\"display:none;\"><\/div><div class=\"clearer\"><\/div>\n\t<input type=\"hidden\" id=\"_cpcff_public_nonce\" name=\"_cpcff_public_nonce\" value=\"dc9f8db6ea\" \/><input type=\"hidden\" name=\"_wp_http_referer\" value=\"\/en\/wp-json\/wp\/v2\/pages\/9450\" \/><\/form>\n\t<\/p>\n<\/div>\n<\/div><\/section><\/div><\/p>\n<div  class='flex_column av-cuj2er-edc09d7f8e988a7c961dc908d5e9fa35 av_one_full  avia-builder-el-47  el_after_av_one_half  el_before_av_one_full  first flex_column_div av-zero-column-padding  column-top-margin'     ><\/div>\n<div  class='flex_column av-cfcd2z-fabf3c5e9435aec775258bc5b4d4753b av_one_full  avia-builder-el-48  el_after_av_one_full  el_before_av_one_full  first flex_column_div  column-top-margin'     ><p><div  class='av-special-heading av-184lyb-541b21611dc87fcaaa66234ff3757db7 av-special-heading-h2 blockquote modern-quote  avia-builder-el-49  el_before_av_textblock  avia-builder-el-first '><h2 class='av-special-heading-tag '  itemprop=\"headline\"  >Musicians and Physicists<\/h2><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><br \/>\n<section  class='av_textblock_section av-c3ckbv-6fe6d6e9e4df570e5739ea3705bea8aa '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p>You can display the frequencies of the harmonic series linearly or logarithmically. Musicians prefer the logarithmic representation because the interval distances appear as we hear them. Physicists often represent the frequencies linearly. The following graphs illustrate the difference.<\/p>\n<\/div><\/section><\/p><\/div>\n<div  class='flex_column av-c1mjaz-e348ee39ca2ca6856ba060186887aa09 av_one_full  avia-builder-el-51  el_after_av_one_full  el_before_av_one_full  first flex_column_div  column-top-margin'     ><p><section  class='av_textblock_section av-bs3g83-64a081eaacb793fb82c7c8118fb44f18 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p><strong>(1) Logarithmic frequency display for musicians<\/strong>: The intervals are important in the musical display. They are therefore presented as we hear them, namely linearly. Musicians only need frequency information for tuning. Advantages: Musicians understand the visualization intuitively, the intervals correspond to our listening.<\/p>\n<\/div><\/section><br \/>\n<div  class='avia-image-container av-bltwmj-5f2cefacbcec2b80587a010e5f90a4e7 av-styling- avia-align-center  avia-builder-el-53  el_after_av_textblock  avia-builder-el-last '   itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" ><div class=\"avia-image-container-inner\"><div class=\"avia-image-overlay-wrap\"><img decoding=\"async\" width=\"672\" height=\"270\" class='wp-image-7041 avia-img-lazy-loading-not-7041 avia_image ' src=\"https:\/\/www.oberton.org\/wp-content\/uploads\/oa-2013.3.png\" alt='Overtone series from a musical point of view - logarithmic frequencies.' title='Overtone series from a musical point of view - logarithmic frequencies.'   itemprop=\"thumbnailUrl\" srcset=\"https:\/\/www.oberton.org\/wp-content\/uploads\/oa-2013.3.png 672w, https:\/\/www.oberton.org\/wp-content\/uploads\/oa-2013.3-300x120.png 300w, https:\/\/www.oberton.org\/wp-content\/uploads\/oa-2013.3-600x241.png 600w, https:\/\/www.oberton.org\/wp-content\/uploads\/oa-2013.3-450x180.png 450w\" sizes=\"(max-width: 672px) 100vw, 672px\" \/><\/div><\/div><\/div><\/p><\/div>\n<div  class='flex_column av-bk9q8z-00681e289e479031a1d2c43d6866e322 av_one_full  avia-builder-el-54  el_after_av_one_full  el_before_av_one_full  first flex_column_div  column-top-margin'     ><p><section  class='av_textblock_section av-be08yr-f7f804b576f3ceaca57ad6fc54cee671 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p><strong>(2) Linear frequency display for physicists<\/strong>: In the physical representation the frequencies are shown in such a way that frequency distances are immediately visible. Advantage: It is easier to calculate and you can see at a glance that all partials have the same frequency spacing, which is is identical to the basic frequency.<\/p>\n<\/div><\/section><br \/>\n<div  class='avia-image-container av-b8rc1f-6ab51d2a42cd45385c846aeaaff7a0d2 av-styling- avia-align-center  avia-builder-el-56  el_after_av_textblock  el_before_av_hr '   itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" ><div class=\"avia-image-container-inner\"><div class=\"avia-image-overlay-wrap\"><img decoding=\"async\" width=\"672\" height=\"270\" class='wp-image-7040 avia-img-lazy-loading-not-7040 avia_image ' src=\"https:\/\/www.oberton.org\/wp-content\/uploads\/oa-2013.5.png\" alt='Overtone series from a physical point of view - linear frequencies.' title='Overtone series from a physical point of view - linear frequencies.'   itemprop=\"thumbnailUrl\" srcset=\"https:\/\/www.oberton.org\/wp-content\/uploads\/oa-2013.5.png 672w, https:\/\/www.oberton.org\/wp-content\/uploads\/oa-2013.5-300x120.png 300w, https:\/\/www.oberton.org\/wp-content\/uploads\/oa-2013.5-600x241.png 600w, https:\/\/www.oberton.org\/wp-content\/uploads\/oa-2013.5-450x180.png 450w\" sizes=\"(max-width: 672px) 100vw, 672px\" \/><\/div><\/div><\/div><br \/>\n<div  class='hr av-b1g0vf-dac6db519885c74262b3e917d729a2a1 hr-invisible  avia-builder-el-57  el_after_av_image  avia-builder-el-last '><span class='hr-inner '><span class=\"hr-inner-style\"><\/span><\/span><\/div><\/p><\/div>\n<div  class='flex_column av-as2x2j-ff18fbaf59662cb13f2dbbb6bd16c634 av_one_full  avia-builder-el-58  el_after_av_one_full  el_before_av_one_half  first flex_column_div  column-top-margin'     ><p><div  class='av-special-heading av-lrwtf-d9407c7971ea30072d23acdf3232efc7 av-special-heading-h2 blockquote modern-quote  avia-builder-el-59  el_before_av_textblock  avia-builder-el-first '><h2 class='av-special-heading-tag '  itemprop=\"headline\"  >Converting Frequencies into Pitches<\/h2><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><br \/>\n<section  class='av_textblock_section av-ahjfsz-547ea1031b20d101a7efc7f8e872139b '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p>Our ear hears intervals as frequency ratios. A multiplication with the same number is heard as the same interval.<\/p>\n<p style=\"padding-left: 40px;\"><strong>Example<\/strong>: 100 and 200 Hz have a frequency <em>difference<\/em> of 100 Hz. 200 Hz is double the frequency of 100 Hz, a frequency ratio of 2:1. A doubling (or halving) of a frequency is heard as an octave. Between 200 and 300 Hz there is again a 100 Hz difference. But 300 Hz are 3\/2 times 200 Hz. This 100 Hz distance is heard as a fifth. So we do not hear equal distances, but equal ratios as equal intervals. 2:1 and 1:2 are octaves. 2:3 and 3:2 correspond to the fifth. 4:5, 5:4 are major thirds and so on. The corresponding intervals for the ratios can be found in the section <a href=\"https:\/\/www.oberton.org\/en\/overtone-singing\/harmonic-series\/#harmonic_series_8211_frequency_ratios\"><span id=\"harmonic_series_8211_frequency_ratios\">Harmonic Series \u2013 Frequency Ratios<\/span><\/a>.<\/p>\n<p>The conversion from distance to ratio is done by the logarithm. Here is the formula to convert frequency differences into intervals.<\/p>\n<\/div><\/section><\/p><\/div>\n<div  class='flex_column av-as2x2j-7-184d9b1b181446660f4940cbcd37a3b1 av_one_half  avia-builder-el-61  el_after_av_one_full  el_before_av_one_half  first flex_column_div  column-top-margin'     ><p><section  class='av_textblock_section av-ahjfsz-6-4351e6e1540961d317de0f25f7f45e35 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><\/div><\/section><br \/>\n<section  class='av_textblock_section av-ahjfsz-4-a5df46f11ec6e93a825e557d157b06bb '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p><img decoding=\"async\" class=\"wp-image-12350 size-medium alignnone\" src=\"https:\/\/www.oberton.org\/wp-content\/uploads\/\/cent-formula-300x70.png\" alt=\"Formel zur Umrechnung von Frequenzabstand in Intervall in Cent\" width=\"300\" height=\"70\" srcset=\"https:\/\/www.oberton.org\/wp-content\/uploads\/cent-formula-300x70.png 300w, https:\/\/www.oberton.org\/wp-content\/uploads\/cent-formula-768x180.png 768w, https:\/\/www.oberton.org\/wp-content\/uploads\/cent-formula-600x141.png 600w, https:\/\/www.oberton.org\/wp-content\/uploads\/cent-formula-705x165.png 705w, https:\/\/www.oberton.org\/wp-content\/uploads\/cent-formula-450x105.png 450w, https:\/\/www.oberton.org\/wp-content\/uploads\/cent-formula.png 841w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>a = first frequency<\/p>\n<p>b = second frequency<\/p>\n<\/div><\/section><\/p><\/div>\n<div  class='flex_column av-as2x2j-5-e3d1f2148d954ccd9ea1b7798a0d7591 av_one_half  avia-builder-el-64  el_after_av_one_half  el_before_av_one_full  flex_column_div  column-top-margin'     ><section  class='av_textblock_section av-ahjfsz-3-2c111283f30ec762abe8fbc463771565 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p><span class=\"cff-form-name-shortcode\"><style>@media (max-width:480px){#cp_calculatedfieldsf_pform_2{min-height:960px;}}@media (max-width:768px){#cp_calculatedfieldsf_pform_2{min-height:559px;}}@media (max-width:1024px){#cp_calculatedfieldsf_pform_2{min-height:559px;}}@media (min-width:1024px){#cp_calculatedfieldsf_pform_2{min-height:496px;}}<\/style><form name=\"cp_calculatedfieldsf_pform_2\" id=\"cp_calculatedfieldsf_pform_2\" action=\"https:\/\/www.oberton.org\/en\/overtone-singing\/harmonic-series\/\" method=\"post\" enctype=\"multipart\/form-data\" onsubmit=\"return fbuilderjQuery.fbuilder.doValidate(this);\" class=\"cff-form no-prefetch  cff-form-7\"  data-nonce=\"fa0b41d748\">\n<input type=\"hidden\" name=\"cp_calculatedfieldsf_pform_psequence\" value=\"_2\" \/>\n<input type=\"hidden\" name=\"cp_calculatedfieldsf_id\" value=\"7\" \/>\n<input type=\"hidden\" name=\"cp_ref_page\" value=\"https:\/\/www.oberton.org\/en\" \/>\n<pre style=\"display:none !important;\"><script data-category=\"functional\" type=\"text\/javascript\">form_structure_2=[[{\"form_identifier\":\"\",\"name\":\"fieldname3\",\"shortlabel\":\"\",\"index\":0,\"ftype\":\"fnumber\",\"userhelp\":\"\",\"userhelpTooltip\":false,\"tooltipIcon\":false,\"csslayout\":\"\",\"title\":\"Frequency a  [Hertz]\",\"predefined\":\"\",\"predefinedClick\":false,\"required\":false,\"exclude\":false,\"readonly\":false,\"size\":\"small\",\"thousandSeparator\":\"\",\"decimalSymbol\":\".\",\"min\":\"\",\"max\":\"\",\"formatDynamically\":true,\"dformat\":\"number\",\"formats\":[\"digits\",\"number\",\"percent\"],\"fBuild\":{},\"parent\":\"\"},{\"form_identifier\":\"\",\"name\":\"fieldname4\",\"shortlabel\":\"\",\"index\":1,\"ftype\":\"fnumber\",\"userhelp\":\"\",\"userhelpTooltip\":false,\"tooltipIcon\":false,\"csslayout\":\"\",\"title\":\"Frequency b [Hertz]\",\"predefined\":\"\",\"predefinedClick\":false,\"required\":false,\"exclude\":false,\"readonly\":false,\"size\":\"small\",\"thousandSeparator\":\"\",\"decimalSymbol\":\".\",\"min\":\"\",\"max\":\"\",\"formatDynamically\":true,\"dformat\":\"number\",\"formats\":[\"digits\",\"number\",\"percent\"],\"fBuild\":{},\"parent\":\"\"},{\"dependencies\":[{\"rule\":\"\",\"complex\":false,\"fields\":[\"\"]}],\"form_identifier\":\"\",\"name\":\"fieldname1\",\"shortlabel\":\"\",\"index\":2,\"ftype\":\"fCalculated\",\"userhelp\":\"\",\"userhelpTooltip\":false,\"tooltipIcon\":false,\"csslayout\":\"\",\"title\":\"Cents between the two frequencies\",\"predefined\":\"\",\"required\":false,\"exclude\":false,\"size\":\"medium\",\"eq\":\"(ROUND(1200*(LOG(fieldname3\\\/fieldname4)\\\/LOG(2))))\",\"suffix\":\" cents\",\"prefix\":\"\",\"decimalsymbol\":\".\",\"groupingsymbol\":\"\",\"readonly\":true,\"noEvalIfManual\":true,\"formatDynamically\":false,\"hidefield\":false,\"fBuild\":{},\"parent\":\"\"}],{\"0\":{\"title\":\"Cent Calculator\",\"description\":\"\",\"formlayout\":\"top_aligned\",\"formtemplate\":\"\",\"evalequations\":1,\"evalequationsevent\":2,\"autocomplete\":1,\"persistence\":0,\"customstyles\":\"\"},\"formid\":\"cp_calculatedfieldsf_pform_2\"}];<\/script><\/pre>\n<div id=\"fbuilder\">\n\t\t<div id=\"fbuilder_2\">\n\t\t<div id=\"formheader_2\"><\/div>\n\t\t<div id=\"fieldlist_2\"><\/div>\n\t\t<div class=\"clearer\"><\/div>\n\t<\/div>\n\t<div id=\"cpcaptchalayer_2\" class=\"cpcaptchalayer\" style=\"display:none;\">\n\t\t            <div class=\"fields\">\r\n                <label>Please enter the security code<\/label>\r\n                <div class=\"dfield\">\r\n                    <span id=\"cff_captcha_math_2\" class=\"cff-captcha-math-label\">3 + 9 = <\/span>\r\n                    <input type=\"text\" size=\"8\" name=\"hdcaptcha_cp_calculated_fields_form_post\" id=\"hdcaptcha_cp_calculated_fields_form_post_2\" value=\"\" autocomplete=\"off\" \/>\r\n                    <div class=\"error message\" id=\"hdcaptcha_error_2\" style=\"display:none;\"><\/div>\r\n                <\/div>\r\n                <div class=\"clearer\"><\/div>\r\n            <\/div>\r\n        \t<\/div>\n<\/div>\n\t<div id=\"cp_subbtn_2\" class=\"cp_subbtn\" style=\"display:none;\"><\/div><div class=\"clearer\"><\/div>\n\t<input type=\"hidden\" id=\"_cpcff_public_nonce\" name=\"_cpcff_public_nonce\" value=\"4942878556\" \/><input type=\"hidden\" name=\"_wp_http_referer\" value=\"\/en\/wp-json\/wp\/v2\/pages\/9450\" \/><\/form>\n\t<\/span><\/p>\n<\/div><\/section><\/div>\n<div  class='flex_column av-as2x2j-2-3705d8a66c658684045edfad34166a70 av_one_full  avia-builder-el-66  el_after_av_one_half  el_before_av_one_full  first flex_column_div  column-top-margin'     ><section  class='av_textblock_section av-ahjfsz-1-7a4f09763392370fda8e2a62128e1a1b '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p>The results of this formula are cent values, that is 1\/100 semitones. 100 cent is exactly one (equally tempered) semitone. 1200 cents are 12 semitones, that is one octave. 700 cents are 7 semitones, i.e. one fifth.<\/p>\n<p>If values differ from even 100s, e.g. 702, this means that a tone differs by this cent amount from the standard equal temperament on the piano. 702, the pure fifth from the harmonic series, is thus 2 cents, 2 hundredths of a semitone higher than on the piano. The tones of the harmonic series all deviate from the equal temperament except for the octaves.<\/p>\n<\/div><\/section><\/div>\n<div  class='flex_column av-ae2837-1b93de627ece411bb3585ecededc874c av_one_full  avia-builder-el-68  el_after_av_one_full  el_before_av_one_full  first flex_column_div  column-top-margin'     ><p><div  class='av-special-heading av-10mki3-ddab1fdeece2a06f42975a70507c5ae2 av-special-heading-h2 blockquote modern-quote  avia-builder-el-69  el_before_av_image  avia-builder-el-first '><h2 class='av-special-heading-tag '  itemprop=\"headline\"  >Overtones vs Harmonics<\/h2><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><br \/>\n<div  class='avia-image-container av-9xyqz7-9167901bda8bdede9cbe10c3dbc748ac av-styling- avia-align-center  avia-builder-el-70  el_after_av_heading  el_before_av_textblock '   itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" ><div class=\"avia-image-container-inner\"><div class=\"avia-image-overlay-wrap\"><img decoding=\"async\" width=\"1030\" height=\"546\" class='wp-image-7185 avia-img-lazy-loading-not-7185 avia_image ' src=\"https:\/\/www.oberton.org\/wp-content\/uploads\/Teiltonskala-Oberton-vs-Teilton-1030x546.png\" alt='https:\/\/en.wikipedia.org\/wiki\/Strike_tone' title='Partial tone scale - overtone vs. partial tone'   itemprop=\"thumbnailUrl\" srcset=\"https:\/\/www.oberton.org\/wp-content\/uploads\/Teiltonskala-Oberton-vs-Teilton-1030x546.png 1030w, https:\/\/www.oberton.org\/wp-content\/uploads\/Teiltonskala-Oberton-vs-Teilton-300x159.png 300w, https:\/\/www.oberton.org\/wp-content\/uploads\/Teiltonskala-Oberton-vs-Teilton-768x407.png 768w, https:\/\/www.oberton.org\/wp-content\/uploads\/Teiltonskala-Oberton-vs-Teilton-600x318.png 600w, https:\/\/www.oberton.org\/wp-content\/uploads\/Teiltonskala-Oberton-vs-Teilton-710x375.png 710w, https:\/\/www.oberton.org\/wp-content\/uploads\/Teiltonskala-Oberton-vs-Teilton-705x373.png 705w, https:\/\/www.oberton.org\/wp-content\/uploads\/Teiltonskala-Oberton-vs-Teilton-450x238.png 450w, https:\/\/www.oberton.org\/wp-content\/uploads\/Teiltonskala-Oberton-vs-Teilton.png 1280w\" sizes=\"(max-width: 1030px) 100vw, 1030px\" \/><\/div><\/div><\/div><br \/>\n<section  class='av_textblock_section av-9wzg57-dd2577ac63a3e0aa397155beb579d160 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p>Overtones are numbered in two different ways. This is because some people count the fundamental, others do not. Overtones are actually only the tones above the fundamental. However, since the numbering including the fundamental has advantages, it is better to speak of harmonics (or partials), since the fundamental tone is also considered as a partial tone of the sound.<\/p>\n<p>I prefer the numbering of partials (or harmonics, see below), thus including the fundamental.<\/p>\n<ol>\n<li>Partial tone numbering has the advantage that the frequency ratio results directly from the digit. The 14th partial tone has a 14-fold frequency of the fundamental tone, partial tone number 23 has a 23-fold frequency, etc.<\/li>\n<li>The frequency ratios of the intervals are also derived directly from the partial tone numbers. Example: The 3rd partial is the fifth in the 2nd octave. It has three times the basic frequency. The 2nd partial tone is the octave to the fundamental. The two adjacent partials 2 and 3 have a frequency ratio of 2:3 (upwards) or 3:2 (downwards) and sound as a fifth. Their doublings are fifths again. So the partial tone pairs 4\/6, 8\/12 etc. also form fifths with the same frequency ratio (since the fractions can be shortened to 2\/3).<\/li>\n<\/ol>\n<p>The illustration shows that the octaves are always even numbers in the case of partial tone (harmonics) numbering, whereas they are odd in the case of overtone numbering. This can be important for musicians: For example, the clarinet can only produce the odd partials by overblowing, i. e. no octaves. Even textbooks sometimes say that wrong. For overtone singers it has of course special meaning, because their music is <a href=\"https:\/\/www.oberton.org\/en\/overtone-singing\/composing-with-overtone-singing-composers-guide\/\">notated with the partial tone numbers<\/a>.<\/p>\n<\/div><\/section><\/p><\/div>\n<div  class='flex_column av-9o2f1n-5465276d444c2f75c11cf92659052c38 av_one_full  avia-builder-el-72  el_after_av_one_full  el_before_av_one_full  first flex_column_div  column-top-margin'     ><p><div  class='av-special-heading av-9i0iwr-f907764eb3a5dc0c36ef28788c3df27e av-special-heading-h2 blockquote modern-quote  avia-builder-el-73  el_before_av_textblock  avia-builder-el-first '><h2 class='av-special-heading-tag '  itemprop=\"headline\"  >Natural Tone Series vs. Harmonic Series<\/h2><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><br \/>\n<section  class='av_textblock_section av-9cgxq3-ff19884796230874daf69d52cb7e95ee '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p>The natural tone series (series played on brass instruments e. g.) has the same tonal structure as the harmonic series, but it is not the same. While the partials of the overtone series are pure sine waves, the tones of the natural tone series consist of individual harmonics.<\/p>\n<\/div><\/section><br \/>\n<div class='avia-data-table-wrap av-97i8ur-0430052dbbf7cde9e46a1c91eccaecf2 avia_responsive_table avia-table-1'><table  class='avia-table avia-data-table avia_pricing_default  avia-builder-el-75  el_after_av_textblock  avia-builder-el-last '  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/Table\" ><tbody><tr class='avia-heading-row'><th class=''>Natural Tone Series<\/th><th class=''>Harmonic Series<\/th><\/tr><tr class=''><td class=''>Tone sequence that can be produced on wind instruments (tubes) by overblowing or changing the lip frequency.<\/td><td class=''>Partials of a real sound.<\/td><\/tr><tr class=''><td class=''>Natural tones are real tones and have their own overtones.<\/td><td class=''>Partial tones (harmonics) are pure tones and do not have overtones themselves.<\/td><\/tr><\/tbody><\/table><\/div><style type='text\/css'>.avia-table-1 td:nth-of-type(1):before { content: 'Natural Tone Series'; } .avia-table-1 td:nth-of-type(2):before { content: 'Harmonic Series'; } <\/style><\/p><\/div>\n<div  class='flex_column av-7jo5sb-e02076d0a74f1235fbd4279024f09755 av_one_full  avia-builder-el-76  el_after_av_one_full  el_before_av_one_full  first flex_column_div  column-top-margin'     ><p><div  class='av-special-heading av-15nrnf-928318feca571c5c9f55b01406812560 av-special-heading-h2 blockquote modern-quote  avia-builder-el-77  el_before_av_textblock  avia-builder-el-first '><h2 class='av-special-heading-tag '  itemprop=\"headline\"  >Examples: Harmonic series of F and E<\/h2><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><br \/>\n<section  class='av_textblock_section av-75s48r-ddd5056d9e559e9eda2334399c21a1a3 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p>With <a href=\"https:\/\/www.oberton.org\/en\/portfolio-item\/software-overtone-analyzer-vocevista\/\" target=\"_blank\" rel=\"noopener noreferrer\">Overtone Analyzer<\/a> software, you can instantly display overtone series of any tone, including tone name, frequency, and cent deviation from the tempered system, and you can listen to them right away. Download the <a href=\"https:\/\/www.oberton.org\/en\/portfolio-item\/software-overtone-analyzer-vocevista\/\">free trial version<\/a>.<\/p>\n<\/div><\/section><br \/>\n<section  class='av_textblock_section av-705vdn-9e30d669d94caa274d36e179f7a723ed '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p>Download the overtone series (1-24) as a MuseScore file (<a href=\"https:\/\/musescore.org\" target=\"_blank\" rel=\"noopener\">MuseScore<\/a> freeware) and MusicXML file below and transpose and listen to it as needed. The cent deviations always remain the same for each harmonic position in the series. The notes in the files are tuned accordingly.<\/p>\n<\/div><\/section><br \/>\n<div  class='avia-button-wrap av-6tyj97-28e09dbd5d82db1bf2e21f25d2057d0d-wrap avia-button-left  avia-builder-el-80  el_after_av_textblock  el_before_av_heading '><a href='https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe_mit_Centabweichungen.zip'  class='avia-button av-6tyj97-28e09dbd5d82db1bf2e21f25d2057d0d av-link-btn avia-icon_select-yes-left-icon avia-size-small avia-position-left avia-color-green'  target=\"_blank\"  rel=\"noopener noreferrer\"  aria-label=\"Download ZIP\"><span class='avia_button_icon avia_button_icon_left avia-iconfont avia-font-entypo-fontello' data-av_icon='\ue82d' data-av_iconfont='entypo-fontello' ><\/span><span class='avia_iconbox_title' >Download ZIP<\/span><\/a><\/div><br \/>\n<div  class='av-special-heading av-v3whv-96417fd378db288a5509862bfee0a5fd av-special-heading-h3 blockquote modern-quote  avia-builder-el-81  el_after_av_button  el_before_av_image '><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >Harmonic series of E<\/h3><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><br \/>\n<div  class='avia-image-container av-6h0c2r-b21f819ac2bc2be305178298e92b2fcd av-styling- avia-align-center  avia-builder-el-82  el_after_av_heading  el_before_av_image '   itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" ><div class=\"avia-image-container-inner\"><div class=\"avia-image-overlay-wrap\"><img decoding=\"async\" width=\"1280\" height=\"242\" class='wp-image-7288 avia-img-lazy-loading-not-7288 avia_image ' src=\"https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-E-1-24-mit-Centabweichung1.png\" alt='' title='Harmonics 1-24 of E2 with cent deviation'   itemprop=\"thumbnailUrl\" srcset=\"https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-E-1-24-mit-Centabweichung1.png 1280w, https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-E-1-24-mit-Centabweichung1-300x56.png 300w, https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-E-1-24-mit-Centabweichung1-1030x194.png 1030w, https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-E-1-24-mit-Centabweichung1-768x145.png 768w, https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-E-1-24-mit-Centabweichung1-600x113.png 600w, https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-E-1-24-mit-Centabweichung1-705x133.png 705w, https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-E-1-24-mit-Centabweichung1-450x85.png 450w\" sizes=\"(max-width: 1280px) 100vw, 1280px\" \/><\/div><\/div><\/div><br \/>\n<div  class='avia-image-container av-6bmomj-b08202404d9bcfffbf543f2ecc6921b1 av-styling- av-img-linked avia-align-center  avia-builder-el-83  el_after_av_image  el_before_av_heading '   itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" ><div class=\"avia-image-container-inner\"><div class=\"avia-image-overlay-wrap\"><a href=\"https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-E-1-24.png\" data-srcset=\"https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-E-1-24.png 710w, https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-E-1-24-300x152.png 300w, https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-E-1-24-600x304.png 600w, https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-E-1-24-705x357.png 705w, https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-E-1-24-450x228.png 450w\" data-sizes=\"(max-width: 710px) 100vw, 710px\" class='avia_image '  aria-label='Harmonics 1-24 of E2'><img decoding=\"async\" width=\"710\" height=\"360\" class='wp-image-7289 avia-img-lazy-loading-not-7289 avia_image ' src=\"https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-E-1-24.png\" alt='Harmonics 1-24 of E2' title='Harmonics 1-24 of E2'   itemprop=\"thumbnailUrl\" srcset=\"https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-E-1-24.png 710w, https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-E-1-24-300x152.png 300w, https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-E-1-24-600x304.png 600w, https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-E-1-24-705x357.png 705w, https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-E-1-24-450x228.png 450w\" sizes=\"(max-width: 710px) 100vw, 710px\" \/><\/a><\/div><\/div><\/div><br \/>\n<div  class='av-special-heading av-sqif7-48da7a515662241737b2edd4b4ac2b84 av-special-heading-h3 blockquote modern-quote  avia-builder-el-84  el_after_av_image  el_before_av_image '><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >Harmonic series of F<\/h3><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><br \/>\n<div  class='avia-image-container av-lq8mr-aab626ab2dd5ffeea76f0a23358b1c10 av-styling- avia-align-center  avia-builder-el-85  el_after_av_heading  el_before_av_image '   itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" ><div class=\"avia-image-container-inner\"><div class=\"avia-image-overlay-wrap\"><img decoding=\"async\" width=\"1280\" height=\"246\" class='wp-image-7287 avia-img-lazy-loading-not-7287 avia_image ' src=\"https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-F-1-24-mit-Centabweichung-1.png\" alt='Harmonic series from F2' title='Harmonic series from F2'   itemprop=\"thumbnailUrl\" srcset=\"https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-F-1-24-mit-Centabweichung-1.png 1280w, https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-F-1-24-mit-Centabweichung-1-300x57.png 300w, https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-F-1-24-mit-Centabweichung-1-1030x197.png 1030w, https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-F-1-24-mit-Centabweichung-1-768x148.png 768w, https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-F-1-24-mit-Centabweichung-1-600x115.png 600w, https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-F-1-24-mit-Centabweichung-1-705x135.png 705w, https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-F-1-24-mit-Centabweichung-1-450x86.png 450w\" sizes=\"(max-width: 1280px) 100vw, 1280px\" \/><\/div><\/div><\/div><br \/>\n<div  class='avia-image-container av-5xgqln-6dcfa8ce443434c67a5a10301847a36f av-styling- av-img-linked avia-align-center  avia-builder-el-86  el_after_av_image  avia-builder-el-last '   itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" ><div class=\"avia-image-container-inner\"><div class=\"avia-image-overlay-wrap\"><a href=\"https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-F-25.png\" data-srcset=\"https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-F-25.png 720w, https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-F-25-300x150.png 300w, https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-F-25-600x300.png 600w, https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-F-25-705x352.png 705w, https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-F-25-450x225.png 450w\" data-sizes=\"(max-width: 720px) 100vw, 720px\" class='avia_image '  aria-label='Harmonic series from F2'><img decoding=\"async\" width=\"720\" height=\"360\" class='wp-image-7286 avia-img-lazy-loading-not-7286 avia_image ' src=\"https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-F-25.png\" alt='Harmonic series from F2' title='Harmonic series from F2'   itemprop=\"thumbnailUrl\" srcset=\"https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-F-25.png 720w, https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-F-25-300x150.png 300w, https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-F-25-600x300.png 600w, https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-F-25-705x352.png 705w, https:\/\/www.oberton.org\/wp-content\/uploads\/Obertonreihe-auf-F-25-450x225.png 450w\" sizes=\"(max-width: 720px) 100vw, 720px\" \/><\/a><\/div><\/div><\/div><\/p><\/div>\n<div  class='flex_column av-hgda3-227c35f2c884216845a7471d815345a2 av_one_full  avia-builder-el-87  el_after_av_one_full  el_before_av_one_full  first flex_column_div  column-top-margin'     ><p><div  class='av-special-heading av-5m2psr-c10dcc15a6cff9f498fbd6f327f73c6b av-special-heading-h2 blockquote modern-quote  avia-builder-el-88  el_before_av_codeblock  avia-builder-el-first '><h2 class='av-special-heading-tag '  itemprop=\"headline\"  >Calculate Harmonic Series (first 32 partials)<\/h2><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><br \/>\n<br \/>\n<section  class='av_textblock_section av-5dpfcj-80d0cbe895dd213e2a008ac3e76cd2d9 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p>Here you can calculate the first 32 partials of the harmonic series of any tones or frequencies:<\/p>\n<ol>\n<li>Change the concert pitch if desired.<\/li>\n<li>Select the notation system.<\/li>\n<li>Enter the fundamental tone.\n<ul>\n<li>You can enter any frequency, e.g. 262 Hz,<\/li>\n<li>or a note name, e.g. C4, if you have selected the American notation system,<\/li>\n<li>or e.g. c1 if you have chosen the German notation system. Incidentally, all three example entries would be the same note, with a fundamental tuning of 440 Hz.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<p>The <strong>concert pitch<\/strong> is the frequency selected for the note A4 (a1 in German notation). The usual frequency is 440 Hz. However, some orchestras tune up to 444 Hz. A popular frequency in esoteric contexts is 432 Hz, for example. If you change the fundamental frequency, new frequencies are assigned to all tones. Or the frequencies are renamed, so to speak.<\/p>\n<p>The <strong>American or scientific notation system<\/strong> designates the lowest audible octave as 0. C0 corresponds to 16 Hz, which would just be perceptible as a pitch. The octaves above this are simply numbered consecutively. Simple and logical.<\/p>\n<p>The <strong>German notation system<\/strong> uses an old notation according to Helmholtz. C0 or the frequency 16 Hz is called subcontra C, or C2. The octave above it is called contraoctave C1, the octave above it major octave C, then comes the minor octave c (capitalization is important here, in American notation only capital letters are used), then the single-dashed octave c1 (or c&#8217;), the double-dashed c2 (or c&#8221;) and so on. A little more complicated than the scientific version. In addition, in German the note B is referred to as h, presumably because of an age-old spelling mistake when people still wrote with ink nibs and a stroke was missing at the letter b.<\/p>\n<\/div><\/section><\/p><\/div>\n<div  class='flex_column av-kla3f-8f4cbd773deb4b86032908032ec265b1 av_one_full  avia-builder-el-91  el_after_av_one_full  el_before_av_one_full  first flex_column_div  column-top-margin'     ><p><div  class='av-special-heading av-aubu3-623014cffe34899ab49de6b384abbddd av-special-heading-h2 blockquote modern-quote  avia-builder-el-92  el_before_av_textblock  avia-builder-el-first '><h2 class='av-special-heading-tag '  itemprop=\"headline\"  >Table of Harmonics<\/h2><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><br \/>\n<section  class='av_textblock_section av-7r37f-811cfcd64d8cf304eb023022cbbb577f '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p>Sometimes numbers are useful.<\/p>\n\n<table id=\"tablepress-1\" class=\"tablepress tablepress-id-1\">\n<thead>\n<tr class=\"row-1\">\n\t<th class=\"column-1\">Teilton-Nr.<\/th><th class=\"column-2\">Oberton-Nr.<\/th><th class=\"column-3\">Intervall zum Grundton<\/th><th class=\"column-4\">Cent zum Grundton<\/th><th class=\"column-5\">Intervall zum Teilton darunter<\/th><th class=\"column-6\">Cent zum Teilton darunter<\/th>\n<\/tr>\n<\/thead>\n<tbody class=\"row-striping row-hover\">\n<tr class=\"row-2\">\n\t<td class=\"column-1\">18<\/td><td class=\"column-2\">17<\/td><td class=\"column-3\">4 Oktaven + gr. Sekunde + 4ct<\/td><td class=\"column-4\">5004<\/td><td class=\"column-5\">kl. Sekunde -1ct<\/td><td class=\"column-6\">99<\/td>\n<\/tr>\n<tr class=\"row-3\">\n\t<td class=\"column-1\">17<\/td><td class=\"column-2\">16<\/td><td class=\"column-3\">4 Oktaven + kl. Sekunde +5ct<\/td><td class=\"column-4\">4905<\/td><td class=\"column-5\">kl. Sekunde +5ct<\/td><td class=\"column-6\">105<\/td>\n<\/tr>\n<tr class=\"row-4\">\n\t<td class=\"column-1\">16<\/td><td class=\"column-2\">15<\/td><td class=\"column-3\">4 Oktaven<\/td><td class=\"column-4\">4800<\/td><td class=\"column-5\">kl. Sekunde +12ct<\/td><td class=\"column-6\">112<\/td>\n<\/tr>\n<tr class=\"row-5\">\n\t<td class=\"column-1\">15<\/td><td class=\"column-2\">14<\/td><td class=\"column-3\">3 Oktaven + gr. Septime -12ct<\/td><td class=\"column-4\">4688<\/td><td class=\"column-5\">kl. Sekunde +19ct<\/td><td class=\"column-6\">119<\/td>\n<\/tr>\n<tr class=\"row-6\">\n\t<td class=\"column-1\">14<\/td><td class=\"column-2\">13<\/td><td class=\"column-3\">3 Oktaven + kl. Septime -31ct<\/td><td class=\"column-4\">4569<\/td><td class=\"column-5\">kl. Sekunde +28ct<\/td><td class=\"column-6\">128<\/td>\n<\/tr>\n<tr class=\"row-7\">\n\t<td class=\"column-1\">13<\/td><td class=\"column-2\">12<\/td><td class=\"column-3\">3 Oktaven + kl. Sexte +41ct<\/td><td class=\"column-4\">4441<\/td><td class=\"column-5\">kl. Sekunde +39ct<\/td><td class=\"column-6\">139<\/td>\n<\/tr>\n<tr class=\"row-8\">\n\t<td class=\"column-1\">12<\/td><td class=\"column-2\">11<\/td><td class=\"column-3\">3 Oktaven + Quinte +2ct<\/td><td class=\"column-4\">4302<\/td><td class=\"column-5\">3\/4-Ton<\/td><td class=\"column-6\">151<\/td>\n<\/tr>\n<tr class=\"row-9\">\n\t<td class=\"column-1\">11<\/td><td class=\"column-2\">10<\/td><td class=\"column-3\">3 Oktaven + \u00fcberm. Quarte -49ct<\/td><td class=\"column-4\">4151<\/td><td class=\"column-5\">Gr. Sekunde +35ct<\/td><td class=\"column-6\">165<\/td>\n<\/tr>\n<tr class=\"row-10\">\n\t<td class=\"column-1\">10<\/td><td class=\"column-2\">9<\/td><td class=\"column-3\">3 Oktaven + gr. Terz -14ct<\/td><td class=\"column-4\">3986<\/td><td class=\"column-5\">Gr. Sekunde (Kl. Ganzton) +18ct<\/td><td class=\"column-6\">182<\/td>\n<\/tr>\n<tr class=\"row-11\">\n\t<td class=\"column-1\">9<\/td><td class=\"column-2\">8<\/td><td class=\"column-3\">3 Oktaven + gr. Sekunde +4ct<\/td><td class=\"column-4\">3804<\/td><td class=\"column-5\">Gr. Sekunde (Gr. Ganzton) +4ct<\/td><td class=\"column-6\">204<\/td>\n<\/tr>\n<tr class=\"row-12\">\n\t<td class=\"column-1\">8<\/td><td class=\"column-2\">7<\/td><td class=\"column-3\">3 Oktaven<\/td><td class=\"column-4\">3600<\/td><td class=\"column-5\">Gr. Sekunde +31ct<\/td><td class=\"column-6\">231<\/td>\n<\/tr>\n<tr class=\"row-13\">\n\t<td class=\"column-1\">7<\/td><td class=\"column-2\">6<\/td><td class=\"column-3\">2 Oktaven + kl. Septime -31ct<\/td><td class=\"column-4\">3369<\/td><td class=\"column-5\">5\/4-Ton<\/td><td class=\"column-6\">267<\/td>\n<\/tr>\n<tr class=\"row-14\">\n\t<td class=\"column-1\">6<\/td><td class=\"column-2\">5<\/td><td class=\"column-3\">2 Oktaven + Quinte +2ct<\/td><td class=\"column-4\">3102<\/td><td class=\"column-5\">Kl. Terz +16ct<\/td><td class=\"column-6\">316<\/td>\n<\/tr>\n<tr class=\"row-15\">\n\t<td class=\"column-1\">5<\/td><td class=\"column-2\">4<\/td><td class=\"column-3\">2 Oktaven + gr. Terz -14ct<\/td><td class=\"column-4\">2786<\/td><td class=\"column-5\">Gr. Terz -14ct<\/td><td class=\"column-6\">386<\/td>\n<\/tr>\n<tr class=\"row-16\">\n\t<td class=\"column-1\">4<\/td><td class=\"column-2\">3<\/td><td class=\"column-3\">2 Oktaven<\/td><td class=\"column-4\">2400<\/td><td class=\"column-5\">Quarte -2ct<\/td><td class=\"column-6\">498<\/td>\n<\/tr>\n<tr class=\"row-17\">\n\t<td class=\"column-1\">3<\/td><td class=\"column-2\">2<\/td><td class=\"column-3\">Oktave + Quinte +2ct<\/td><td class=\"column-4\">1902<\/td><td class=\"column-5\">Quinte +2ct<\/td><td class=\"column-6\">702<\/td>\n<\/tr>\n<tr class=\"row-18\">\n\t<td class=\"column-1\">2<\/td><td class=\"column-2\">1<\/td><td class=\"column-3\">Oktave<\/td><td class=\"column-4\">1200<\/td><td class=\"column-5\">Oktave<\/td><td class=\"column-6\">1200<\/td>\n<\/tr>\n<tr class=\"row-19\">\n\t<td class=\"column-1\">1<\/td><td class=\"column-2\">Grundton<\/td><td class=\"column-3\">Prime<\/td><td class=\"column-4\">0<\/td><td class=\"column-5\">Prime<\/td><td class=\"column-6\">0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-1 from cache -->\n<\/div><\/section><br \/>\n<section  class='av_textblock_section av-57z00r-83cee2067a6f19832e6141cb47810915 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><ol>\n<li><em>column: Numbering of partials including fundamental tone. This numbering is the more useful one.<\/em><\/li>\n<li><em>column: Numbering of overtones, the fundamental note is not counted.<\/em><\/li>\n<li><em>column: Interval to the fundamental tone with cents deviation to the nearest equally tempered tone.<\/em><\/li>\n<li><em>column: Interval to the keynote in cents (100-th semitone).<\/em><\/li>\n<li>column: Interval between the partials (to the lower ones) with cents deviation to the equal tempered interval.<\/li>\n<li>column: Interval between the partials in cents (100th semitone).<\/li>\n<\/ol>\n<\/div><\/section><\/p><\/div>\n<div  class='flex_column av-525zbv-1cc69e49b1809a7bd53da61c15c42048 av_one_full  avia-builder-el-95  el_after_av_one_full  el_before_av_one_half  first flex_column_div  column-top-margin'     ><p><div  class='av-special-heading av-4wqakr-4a2166b647acef97bf2bab63de526be6 av-special-heading-h2 blockquote modern-quote  avia-builder-el-96  el_before_av_promobox  avia-builder-el-first '><h2 class='av-special-heading-tag '  itemprop=\"headline\"  >What are Overtones?<\/h2><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><br \/>\n<div  class='av_promobox av-4q1ykj-ba06f7a81167041b041aa9912a25bace avia-button-no  avia-builder-el-97  el_after_av_heading  avia-builder-el-last '><div class='avia-promocontent'><p>\n<span  class='av_font_icon av-4j3seb-47999b82a51cc2a1674c7c467bfc8239 avia_animate_when_visible av-icon-style- avia-icon-pos-left avia-iconfont avia-font-entypo-fontello av-no-color avia-icon-animate'><span class='av-icon-char' data-av_icon='\ue8c9' data-av_iconfont='entypo-fontello' aria-hidden=\"true\" ><\/span><\/span> Overtones are <a href=\"https:\/\/www.oberton.org\/en\/overtone-singing\/faq-glossary\/\">sine tones<\/a> that oscillate above the fundamental frequency of a natural tone and as a chord produce the timbre.<\/p>\n<\/div><\/div><\/p><\/div>\n<div  class='flex_column av-4gan6z-ff4026d6707416def68b6c24c8951b04 av_one_half  avia-builder-el-99  el_after_av_one_full  el_before_av_one_half  first flex_column_div  column-top-margin'     ><div  class='avia-image-container av-481vjv-b8aa54f233b91d2a755b33ac8c456a06 av-styling- avia-align-center  avia-builder-el-100  avia-builder-el-no-sibling '   itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" ><div class=\"avia-image-container-inner\"><div class=\"avia-image-overlay-wrap\"><img decoding=\"async\" width=\"219\" height=\"300\" class='wp-image-7042 avia-img-lazy-loading-not-7042 avia_image ' src=\"https:\/\/www.oberton.org\/wp-content\/uploads\/g8818-219x300.png\" alt='Harmonics of a string' title='Harmonics of a string'   itemprop=\"thumbnailUrl\" srcset=\"https:\/\/www.oberton.org\/wp-content\/uploads\/g8818-219x300.png 219w, https:\/\/www.oberton.org\/wp-content\/uploads\/g8818-220x300.png 220w, https:\/\/www.oberton.org\/wp-content\/uploads\/g8818-755x1030.png 755w, https:\/\/www.oberton.org\/wp-content\/uploads\/g8818-1099x1500.png 1099w, https:\/\/www.oberton.org\/wp-content\/uploads\/g8818-768x1048.png 768w, https:\/\/www.oberton.org\/wp-content\/uploads\/g8818-600x819.png 600w, https:\/\/www.oberton.org\/wp-content\/uploads\/g8818-517x705.png 517w, https:\/\/www.oberton.org\/wp-content\/uploads\/g8818-450x614.png 450w, https:\/\/www.oberton.org\/wp-content\/uploads\/g8818-754x1030.png 754w, https:\/\/www.oberton.org\/wp-content\/uploads\/g8818.png 1501w\" sizes=\"(max-width: 219px) 100vw, 219px\" \/><\/div><\/div><\/div><\/div>\n<div  class='flex_column av-3zzdzn-e8896982400a4a34192b88ac05931d44 av_one_half  avia-builder-el-101  el_after_av_one_half  el_before_av_heading  flex_column_div av-zero-column-padding  column-top-margin'     ><section  class='av_textblock_section av-3u4rff-5b8fdd4d3dc7948f424e291e3f9d9811 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p>All vibrations are accompanied by faster oscillations.This is a universal behaviour of nature, whether it is sound or other vibrations.<\/p>\n<p>Strings vibrate harmoniously. This means that in addition to the basic vibration, the string also vibrates in integral sections, i. e. over half the length, 1\/3, 1\/4, 1\/5, etc. of the string length. These vibrations all occur simultaneously and superimpose each other to the total vibration. The partial oscillations look like the following figure.<\/p>\n<\/div><\/section><\/div>\n<div  class='av-special-heading av-hublf-fb0e33813d4ee87c5b1f95bb8195918a av-special-heading-h3 blockquote modern-quote  avia-builder-el-103  el_after_av_one_half  el_before_av_content_slider '><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >Videos: Wave Formation<\/h3><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div>\n<div  class='avia-content-slider-element-container av-3l9jwz-5d8afdc44424f57801a7de6be24154f6 avia-content-slider-element-slider avia-content-slider avia-smallarrow-slider avia-content-slider-active avia-content-slider-odd  avia-builder-el-104  el_after_av_heading  el_before_av_one_full  av-slideshow-ui av-control-default av-nav-arrows-visible av-nav-dots-visible av-no-slider-navigation av-slideshow-manual av-loop-once av-loop-manual-endless avia-content-slider1' data-slideshow-options=\"{&quot;animation&quot;:&quot;slide&quot;,&quot;autoplay&quot;:false,&quot;loop_autoplay&quot;:&quot;once&quot;,&quot;interval&quot;:5,&quot;loop_manual&quot;:&quot;manual-endless&quot;,&quot;autoplay_stopper&quot;:false,&quot;noNavigation&quot;:false,&quot;bg_slider&quot;:false,&quot;keep_padding&quot;:&quot;&quot;,&quot;hoverpause&quot;:false,&quot;show_slide_delay&quot;:30}\"><div class='avia-smallarrow-slider-heading  no-content-slider-heading '><div class='new-special-heading'>&nbsp;<\/div><div class='avia-slideshow-arrows avia-slideshow-controls' ><a href='#prev' class='prev-slide  avia-svg-icon avia-font-svg_entypo-fontello' data-av_svg_icon='left-open-big' data-av_iconset='svg_entypo-fontello' tabindex='-1' title=\"Previous\"><svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15\" height=\"32\" viewBox=\"0 0 15 32\" preserveAspectRatio=\"xMidYMid meet\" aria-labelledby='av-svg-title-1' aria-describedby='av-svg-desc-1' role=\"graphics-symbol\" aria-hidden=\"true\">\n<title id='av-svg-title-1'>Previous<\/title>\n<desc id='av-svg-desc-1'>Previous<\/desc>\n<path d=\"M14.464 27.84q0.832 0.832 0 1.536-0.832 0.832-1.536 0l-12.544-12.608q-0.768-0.768 0-1.6l12.544-12.608q0.704-0.832 1.536 0 0.832 0.704 0 1.536l-11.456 11.904z\"><\/path>\n<\/svg><span class='avia_hidden_link_text'>Previous<\/span><\/a><a href='#next' class='next-slide  avia-svg-icon avia-font-svg_entypo-fontello' data-av_svg_icon='right-open-big' data-av_iconset='svg_entypo-fontello' tabindex='-1' title=\"Next\"><svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15\" height=\"32\" viewBox=\"0 0 15 32\" preserveAspectRatio=\"xMidYMid meet\" aria-labelledby='av-svg-title-2' aria-describedby='av-svg-desc-2' role=\"graphics-symbol\" aria-hidden=\"true\">\n<title id='av-svg-title-2'>Next<\/title>\n<desc id='av-svg-desc-2'>Next<\/desc>\n<path d=\"M0.416 27.84l11.456-11.84-11.456-11.904q-0.832-0.832 0-1.536 0.832-0.832 1.536 0l12.544 12.608q0.768 0.832 0 1.6l-12.544 12.608q-0.704 0.832-1.536 0-0.832-0.704 0-1.536z\"><\/path>\n<\/svg><span class='avia_hidden_link_text'>Next<\/span><\/a><\/div><\/div><div class=\"avia-content-slider-inner\"><div class=\"slide-entry-wrap\"><section class='slide-entry av-3e77a3-31285780bdc2255893b77360a61ea298 flex_column av_fullwidth post-entry slide-entry-overview slide-loop-1 slide-parity-odd  first'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" ><div class=\"lyte-wrapper\" title=\"Slow motion: rubber string pulled and released\" style=\"width:1280px;max-width:100%;margin:5px;\">\n<div class=\"lyMe\" id=\"WYL_Qr_rxqwc1jE\" itemprop=\"video\" itemscope itemtype=\"https:\/\/schema.org\/VideoObject\">\n<div><meta itemprop=\"thumbnailUrl\" content=\"https:\/\/www.oberton.org\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FQr_rxqwc1jE%2Fhqdefault.jpg\" \/><meta itemprop=\"embedURL\" content=\"https:\/\/www.youtube.com\/embed\/Qr_rxqwc1jE\" \/><meta itemprop=\"duration\" content=\"PT31S\" \/><meta itemprop=\"uploadDate\" content=\"2006-11-24T13:17:15Z\" \/><\/div>\n<div id=\"lyte_Qr_rxqwc1jE\" data-src=\"https:\/\/www.oberton.org\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FQr_rxqwc1jE%2Fhqdefault.jpg\" class=\"pL\">\n<div class=\"tC\">\n<div class=\"tT\" itemprop=\"name\">Slow motion: rubber string pulled and released<\/div>\n<\/div>\n<p><button tabindex=\"0\" class=\"play\"><\/button><\/p>\n<div class=\"ctrl\">\n<div class=\"Lctrl\"><\/div>\n<div class=\"Rctrl\"><\/div>\n<\/div>\n<\/div>\n<p><noscript><a href=\"https:\/\/youtu.be\/Qr_rxqwc1jE\" rel=\"nofollow\"><img decoding=\"async\" src=\"https:\/\/www.oberton.org\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FQr_rxqwc1jE%2F0.jpg\" alt=\"Slow motion: rubber string pulled and released\" width=\"1280\" height=\"700\" \/><br \/>Watch this video on YouTube<\/a><\/noscript><meta itemprop=\"description\" content=\"A rubber string is held with two nails on the ends and pulled from the middle to form the triangular shape, and then suddenly released. We see here the first milliseconds of the unusual oscillating mode (which is later destroyed by further cycles by non-linearity and friction, and decays into a familiar cosinus-like oscillation). Shot by repeated experiment time-lapse photography by a Nikon D200 camera and flash delay circuitry, 50 microseconds per video frame, 30 frames\/second (1.5 milliseconds per second of the video). As a simple theoretical explanation to explain the shape, it can be considered that the symmetric initial conditions should produce a symmetric solution, which should also be a sum of leftward and rightward triangular waves forming the plateau. What is amazing though that it&#039;s not a photoshop simulation, but a real video - and it behaves exactly as we would expect from the wave analysis. On the other hand, it can be also noted that the release event at the top cannot propagate faster than the wave velocity along the string, so the lower parts should remain intact for a while. Additional credits for ideas and the hard work while doing this go to Almog, Yoav, Ariel, Amir, Omer, Eli and Braude College lab staff.\"><\/div>\n<\/div>\n<div class=\"lL\" style=\"max-width:100%;width:1280px;margin:5px;\"><\/div>\n<\/p>\n<p>The propagation of a wave in a string.<\/p>\n<\/div><\/section><\/div><div class=\"slide-entry-wrap\"><section class='slide-entry av-385tnv-a61540d202d5d5dda98237dd1aaf6c1b flex_column av_fullwidth post-entry slide-entry-overview slide-loop-2 slide-parity-odd  first'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" ><div class='avia-iframe-wrap'>\n<div class=\"lyte-wrapper\" title=\"* Stehende Welle durch Wellenreflexion\" style=\"width:1280px;max-width:100%;margin:5px;\">\n<div class=\"lyMe\" id=\"WYL_kJn_a9flKGk\" itemprop=\"video\" itemscope itemtype=\"https:\/\/schema.org\/VideoObject\">\n<div><meta itemprop=\"thumbnailUrl\" content=\"https:\/\/www.oberton.org\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FkJn_a9flKGk%2Fhqdefault.jpg\" \/><meta itemprop=\"embedURL\" content=\"https:\/\/www.youtube.com\/embed\/kJn_a9flKGk\" \/><meta itemprop=\"duration\" content=\"PT1M12S\" \/><meta itemprop=\"uploadDate\" content=\"2011-12-21T09:09:40Z\" \/><\/div>\n<div id=\"lyte_kJn_a9flKGk\" data-src=\"https:\/\/www.oberton.org\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FkJn_a9flKGk%2Fhqdefault.jpg\" class=\"pL\">\n<div class=\"tC\">\n<div class=\"tT\" itemprop=\"name\">* Stehende Welle durch Wellenreflexion<\/div>\n<\/div>\n<p><button tabindex=\"0\" class=\"play\"><\/button><\/p>\n<div class=\"ctrl\">\n<div class=\"Lctrl\"><\/div>\n<div class=\"Rctrl\"><\/div>\n<\/div>\n<\/div>\n<p><noscript><a href=\"https:\/\/youtu.be\/kJn_a9flKGk\" rel=\"nofollow\"><img decoding=\"async\" src=\"https:\/\/www.oberton.org\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FkJn_a9flKGk%2F0.jpg\" alt=\"* Stehende Welle durch Wellenreflexion\" width=\"1280\" height=\"700\" \/><br \/>Watch this video on YouTube<\/a><\/noscript><meta itemprop=\"description\" content=\"An der Wellenmaschine werden Knoten und B\u00e4uche von stehenden Wellen sichtbar gemacht. Teil der Playliste https:\/\/www.youtube.com\/playlist?list=PL8FB961B5A5E3E035 Alle Videos und Skripte: http:\/\/www.phys.ch Niveau der Videos: * Einfach, ** Berufsschule \/ Gymnasium, *** Uni \/ FH\"><\/div>\n<\/div>\n<div class=\"lL\" style=\"max-width:100%;width:1280px;margin:5px;\"><\/div>\n<\/div>\n<p>Stationary waves.<\/p>\n<\/div><\/section><\/div><div class=\"slide-entry-wrap\"><section class='slide-entry av-34rwrv-10d2aefa55420cee7b73135699d4acca flex_column av_fullwidth post-entry slide-entry-overview slide-loop-3 slide-parity-odd  post-entry-last  first'  itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='slide-entry-excerpt entry-content'  itemprop=\"text\" ><div class='avia-iframe-wrap'>\n<div class=\"lyte-wrapper\" title=\"Motion of Plucked String\" style=\"width:1280px;max-width:100%;margin:5px;\">\n<div class=\"lyMe\" id=\"WYL__X72on6CSL0\" itemprop=\"video\" itemscope itemtype=\"https:\/\/schema.org\/VideoObject\">\n<div><meta itemprop=\"thumbnailUrl\" content=\"https:\/\/www.oberton.org\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2F_X72on6CSL0%2Fhqdefault.jpg\" \/><meta itemprop=\"embedURL\" content=\"https:\/\/www.youtube.com\/embed\/_X72on6CSL0\" \/><meta itemprop=\"duration\" content=\"PT1M34S\" \/><meta itemprop=\"uploadDate\" content=\"2011-02-24T22:32:57Z\" \/><\/div>\n<div id=\"lyte__X72on6CSL0\" data-src=\"https:\/\/www.oberton.org\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2F_X72on6CSL0%2Fhqdefault.jpg\" class=\"pL\">\n<div class=\"tC\">\n<div class=\"tT\" itemprop=\"name\">Motion of Plucked String<\/div>\n<\/div>\n<p><button tabindex=\"0\" class=\"play\"><\/button><\/p>\n<div class=\"ctrl\">\n<div class=\"Lctrl\"><\/div>\n<div class=\"Rctrl\"><\/div>\n<\/div>\n<\/div>\n<p><noscript><a href=\"https:\/\/youtu.be\/_X72on6CSL0\" rel=\"nofollow\"><img decoding=\"async\" src=\"https:\/\/www.oberton.org\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2F_X72on6CSL0%2F0.jpg\" alt=\"Motion of Plucked String\" width=\"1280\" height=\"700\" \/><br \/>Watch this video on YouTube<\/a><\/noscript><meta itemprop=\"description\" content=\"What happens to a string when it is plucked?\"><\/div>\n<\/div>\n<div class=\"lL\" style=\"max-width:100%;width:1280px;margin:5px;\"><\/div>\n<\/div>\n<p>The wave is created in a string by the migration of pulses.<\/p>\n<\/div><\/section><\/div><\/div><\/div>\n<div  class='flex_column av-2vypsj-2f47a7a01750e0b7061504e0d10f57ba av_one_full  avia-builder-el-105  el_after_av_content_slider  el_before_av_one_full  first flex_column_div  '     ><p><div  class='av-special-heading av-1d0sr-b0e4871b450d9aa020b8e98d159edf8d av-special-heading-h2 blockquote modern-quote  avia-builder-el-106  el_before_av_image  avia-builder-el-first '><h2 class='av-special-heading-tag '  itemprop=\"headline\"  >Glossary of Terms<\/h2><div class='av-subheading av-subheading_below'><p>Overtones, Partials, Harmonics&#8230;.<\/p>\n<\/div><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><br \/>\n<div  class='avia-image-container av-2i5kez-c53e5f81fd5d68ed55ef99f1fa0f2ed6 av-styling- avia-align-center  avia-builder-el-107  el_after_av_heading  el_before_av_image '   itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" ><div class=\"avia-image-container-inner\"><div class=\"avia-image-overlay-wrap\"><img decoding=\"async\" width=\"710\" height=\"270\" class='wp-image-7189 avia-img-lazy-loading-not-7189 avia_image ' src=\"https:\/\/www.oberton.org\/wp-content\/uploads\/spt_sin_saegez_stimme_klangsch_rauschen-710x270.jpg\" alt='Spectra of tone, sound, noise' title='Spectra of tone, sound, noise'   itemprop=\"thumbnailUrl\" srcset=\"https:\/\/www.oberton.org\/wp-content\/uploads\/spt_sin_saegez_stimme_klangsch_rauschen-710x270.jpg 710w, https:\/\/www.oberton.org\/wp-content\/uploads\/spt_sin_saegez_stimme_klangsch_rauschen-845x321.jpg 845w\" sizes=\"(max-width: 710px) 100vw, 710px\" \/><\/div><\/div><\/div><br \/>\n<div  class='avia-image-container av-8x3jv-5084987c391035c8ab029bae0b83acab av-styling- avia-align-center  avia-builder-el-108  el_after_av_image  el_before_av_textblock '   itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" ><div class=\"avia-image-container-inner\"><div class=\"avia-image-overlay-wrap\"><img decoding=\"async\" width=\"710\" height=\"270\" class='wp-image-7188 avia-img-lazy-loading-not-7188 avia_image ' src=\"https:\/\/www.oberton.org\/wp-content\/uploads\/spg_sin_saegez_stimme_klangsch_rauschen-710x270.jpg\" alt='Spectrograms of tone, sound, noise' title='Spectrograms of tone, sound, noise'   itemprop=\"thumbnailUrl\" srcset=\"https:\/\/www.oberton.org\/wp-content\/uploads\/spg_sin_saegez_stimme_klangsch_rauschen-710x270.jpg 710w, https:\/\/www.oberton.org\/wp-content\/uploads\/spg_sin_saegez_stimme_klangsch_rauschen-845x321.jpg 845w\" sizes=\"(max-width: 710px) 100vw, 710px\" \/><\/div><\/div><\/div><br \/>\n<section  class='av_textblock_section av-26auj7-4ddbbc44d85dff783b72574feab8df7b '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p><em>Illustrations: Spectra (top) and spectrograms from left: 1) sinus tone, 2) synthetic sound (sawtooth tone), 3) natural sound (voice), 4) unharmonious sound (singing bowl), 5) noise (white noise).<\/em><\/p>\n<\/div><\/section><br \/>\n<section  class='av_textblock_section av-21qe0b-c61153e2aa459a77b921a64825cefc51 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p><strong>Sine tones<\/strong> (Fig. 1. from the left) have no overtones, i. e. they are oscillations with only one frequency. The perceived pitch does not always correspond to that of a natural tone played at the same basic frequency. High sine tones often sound too low to us. Sine tones are a mathematical construct. Completely overtone free sounds are not existent, there is always a sound or noise component.<\/p>\n<p><strong>Sound<\/strong> (fig. 2. and 3. from left) in acoustics means a tone with overtones. In music, the term is usually used in a different way and can refer to the sound color, for example. Every real natural tone is a sound. Sine tones are only found in nature as an approximation.<\/p>\n<p><strong>Noises<\/strong> (fig. 5. from the left) are sound events that have such dense overtones or constantly changing overtone frequencies that we no longer perceive any pitch. But there are seamless transitions to sounds. Depending on the characteristic, one refers to either noises with a sound character or sounds with a noise component.<\/p>\n<p><strong>Partial tones<\/strong> (or simply partials) are the set of (sinusoidal) tones that make up a sound, including the fundamental tone. They are counted from the keynote (the one with the lowest frequency). There can be harmonic and unharmonic partials, even mixed. Harmonic partials oscillate with integer multiples of the basic frequency, inharmonic partials with non-integer ones.<\/p>\n<p><strong>Harmonics<\/strong>. Abbreviation for &#8220;harmonic partials&#8221;. Partial tones with integer multiples of the basic frequency are also called harmonics. For harmonics, the intervals always correspond to the natural overtone series. So harmonics are always also partial tones. Most melody instruments and the human voice have harmonious overtones.<\/p>\n<p><strong>Overtones<\/strong> are all partials above the fundamental. The numbering starts above the keynote, i. e. with the 2nd partial tone. Therefore, the numbering of the overtones is always 1 lower than that of the partials. There can be harmonic and unharmonic overtones, or both.<\/p>\n<p><strong>Unharmonic partials \/ overtones<\/strong> (Fig. 4. from left): Drums, bells, gongs, singing bowls or xylophones are examples of instruments with unharmonic partials \/ overtones. This means that the overtone frequencies are not (all) integer multiples of the lowest frequency. There also exist sounds that contain both harmonic and inharmonic overtones. It is often not possible to speak of a fundamental tone in the case of non-harmonic sounds, because the pitch that is heard is sometimes not that of the lowest frequency, such as the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Strike_tone\" target=\"_blank\" rel=\"noopener\">strike tone of a bell<\/a>.<\/p>\n<\/div><\/section><\/p><\/div>\n<div  class='flex_column av-1utlzn-2dd6050a6ff3f0d164a7124afc477656 av_one_full  avia-builder-el-111  el_after_av_one_full  el_before_av_comments_list  first flex_column_div  column-top-margin'     ><p><div  class='av-special-heading av-1op94b-fae94646f00c1db46bff0f062ecc71cb av-special-heading-h2 blockquote modern-quote  avia-builder-el-112  el_before_av_heading  avia-builder-el-first '><h2 class='av-special-heading-tag '  itemprop=\"headline\"  >Bibliography <span class='special_amp'>&amp;<\/span> Sources<\/h2><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><br \/>\n<div  class='av-special-heading av-1klel7-66fc27b119d2c0c0be95334c800bd07a av-special-heading-h3 blockquote modern-quote  avia-builder-el-113  el_after_av_heading  el_before_av_textblock '><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >Itemizations<\/h3><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><br \/>\n<section  class='av_textblock_section av-1gt4q3-21903e1a044628639fba2194f9e81e22 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" >\n<div id='zp-InTextBib-zotpress-30f4b56e22b5e20b536aceb03df294f3' class='zp-Zotpress zp-Zotpress-InTextBib wp-block-group zp-Post-9450'>\r\n\t\t<span class=\"ZP_ITEM_KEY ZP_ATTR\">{935790:A3W2PKN2}<\/span>\r\n\t\t<span class=\"ZP_STYLE ZP_ATTR\">chicago-author-date-de<\/span>\r\n\t\t<span class=\"ZP_SORTBY ZP_ATTR\">default<\/span>\r\n\t\t<span class=\"ZP_ORDER ZP_ATTR\">asc<\/span>\r\n\t\t<span class=\"ZP_TITLE ZP_ATTR\"><\/span>\r\n\t\t<span class=\"ZP_SHOWIMAGE ZP_ATTR\"><\/span>\r\n\t\t<span class=\"ZP_SHOWTAGS ZP_ATTR\"><\/span>\r\n\t\t<span class=\"ZP_DOWNLOADABLE ZP_ATTR\"><\/span>\r\n\t\t<span class=\"ZP_NOTES ZP_ATTR\"><\/span>\r\n\t\t<span class=\"ZP_ABSTRACT ZP_ATTR\"><\/span>\r\n\t\t<span class=\"ZP_CITEABLE ZP_ATTR\"><\/span>\r\n\t\t<span class=\"ZP_TARGET ZP_ATTR\"><\/span>\r\n\t\t<span class=\"ZP_URLWRAP ZP_ATTR\"><\/span>\r\n\t\t<span class=\"ZP_FORCENUM ZP_ATTR\">0<\/span>\r\n\t\t<span class=\"ZP_HIGHLIGHT ZP_ATTR\"><\/span>\r\n\t\t<span class=\"ZP_POSTID ZP_ATTR\">9450<\/span><div class='zp-List loading'>\n<div class=\"zp-SEO-Content\"><\/div><!-- .zp-zp-SEO-Content -->\n<\/div><!-- .zp-List --><\/div><!--.zp-Zotpress-->\n\n\n<\/div><\/section><br \/>\n<div  class='av-special-heading av-18kvln-dc0ebc559ed53ee8276ecacb87a59b5a av-special-heading-h3 blockquote modern-quote  avia-builder-el-115  el_after_av_textblock  el_before_av_textblock '><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >Literature Section Physics of the Harmonic Series<\/h3><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><br \/>\n<section  class='av_textblock_section av-139xdf-5a36bb0b6c95c3677fd482b8d7375735 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><div id=\"zotpress-25e6def9be25188b134d20711a192fb4\" class=\"zp-Zotpress zp-Zotpress-Bib wp-block-group\">\n\n\t\t<span class=\"ZP_API_USER_ID ZP_ATTR\">935790<\/span>\n\t\t<span class=\"ZP_ITEM_KEY ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_COLLECTION_ID ZP_ATTR\">R3GBX3T6,I3WVWQ5I<\/span>\n\t\t<span class=\"ZP_TAG_ID ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_AUTHOR ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_YEAR ZP_ATTR\"><\/span>\n        <span class=\"ZP_ITEMTYPE ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_INCLUSIVE ZP_ATTR\">1<\/span>\n\t\t<span class=\"ZP_STYLE ZP_ATTR\">chicago-fullnote-bibliography<\/span>\n\t\t<span class=\"ZP_LIMIT ZP_ATTR\">50<\/span>\n\t\t<span class=\"ZP_SORTBY ZP_ATTR\">creator<\/span>\n\t\t<span class=\"ZP_ORDER ZP_ATTR\">asc<\/span>\n\t\t<span class=\"ZP_TITLE ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_SHOWIMAGE ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_SHOWTAGS ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_DOWNLOADABLE ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_NOTES ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_ABSTRACT ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_CITEABLE ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_TARGET ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_URLWRAP ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_FORCENUM ZP_ATTR\"><\/span>\n        <span class=\"ZP_HIGHLIGHT ZP_ATTR\"><\/span>\n        <span class=\"ZP_POSTID ZP_ATTR\">9450<\/span>\n\t\t<span class=\"ZOTPRESS_PLUGIN_URL ZP_ATTR\">https:\/\/www.oberton.org\/wp-content\/plugins\/zotpress\/<\/span>\n\n\t\t<div class=\"zp-List loading\">\n\t\t\t<div class=\"zp-SEO-Content\">\n\n\t\t\t<\/div><!-- .zp-zp-SEO-Content -->\n\t\t<\/div><!-- .zp-List -->\n\t<\/div><!--.zp-Zotpress-->\n\n\n<\/div><\/section><br \/>\n<div  class='av-special-heading av-w8r6b-bf0aa5635f8eeb1a59c8660e2b1f305a av-special-heading-h2 meta-heading  avia-builder-el-117  el_after_av_textblock  el_before_av_textblock '><h2 class='av-special-heading-tag '  itemprop=\"headline\"  >Picture Credits<\/h2><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><br \/>\n<section  class='av_textblock_section av-qhg7n-71ccaca2e11413e4752b2f448dea0782 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p>Harmonic overtones.\u00a0<a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Harmonic_partials_on_strings.svg\" target=\"_blank\" rel=\"noopener\">By Qef [Public domain], via Wikimedia Commons<\/a><\/p>\n<\/div><\/section><\/p><\/div>\n<div  class='av-buildercomment av-l1zy3-1133e0f2fbf811a2a83fa98eaf0533f3  av-blog-meta-html-info-disabled'><\/div>\n<div  class='av-special-heading av-7pkf7-0dfb7bd5ecea8b260c54f4b13539750f av-special-heading-h2  avia-builder-el-120  el_after_av_comments_list  el_before_av_hr '><h2 class='av-special-heading-tag '  itemprop=\"headline\"  >Tell a Friend<\/h2><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div>\n<div  class='hr av-9biub-0b76b5c2b7955a1b0f7400faa61dcaa5 hr-default  avia-builder-el-121  el_after_av_heading  avia-builder-el-last '><span class='hr-inner '><span class=\"hr-inner-style\"><\/span><\/span><\/div>\n<div class=\"shariff shariff-align-left shariff-widget-align-left\" style=\"display:none\"><div class=\"ShariffHeadline\"><h3>Share<\/h3><\/div><ul class=\"shariff-buttons theme-round orientation-horizontal buttonsize-medium\"><li class=\"shariff-button twitter shariff-nocustomcolor\" style=\"background-color:#595959\"><a 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It is the only natural scale and therefore the basis of all pitch spaces and tuning systems. As soon as a note sounds, overtones oscillate simultaneously. So the harmonic series is actually a chord.<\/p>\n","protected":false},"author":2,"featured_media":7001,"parent":7788,"menu_order":2,"comment_status":"open","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":["post-9450","page","type-page","status-publish","has-post-thumbnail","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Harmonic Series - structure, application and background<\/title>\n<meta name=\"description\" content=\"The harmonic series is the sequence of harmonic partials of a sound. It is the only natural scale and therefore the basis of all pitch spaces and tuning systems. As soon as a note sounds, overtones oscillate simultaneously. 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