{"id":6097,"date":"2019-04-09T12:51:11","date_gmt":"2019-04-09T16:51:11","guid":{"rendered":"https:\/\/splice.com\/blog\/?p=6097"},"modified":"2026-02-13T13:16:21","modified_gmt":"2026-02-13T18:16:21","slug":"whats-in-a-wave","status":"publish","type":"post","link":"https:\/\/splice.com\/blog\/whats-in-a-wave\/","title":{"rendered":"What\u2019s in a waveform?"},"content":{"rendered":"<h1>Sawtooth, square, triangle, sine &#8211; if you\u2019ve ever messed around with a synthesizer, you\u2019ve probably seen these words or noticed the shapes that represent them.<\/h1>\n<p>Oscillators are at the heart of a synthesizer &#8211; without activating one, it\u2019s more than likely that you won\u2019t hear any sound at all. They come in different shapes, and these shapes drastically affect what you\u2019ll hear coming out of your virtual or hardware synth. A sawtooth wave will sound appropriately very sharp, a square wave will be a bit less bright and a bit more open, and a triangle wave lies somewhere in between the sharpness of a sawtooth wave and the smooth sound of a sine wave.<\/p>\n<p>So if you\u2019re wondering what gives these waves their signature sound, I\u2019m sorry to say that the underlying reason is&#8230; math. That\u2019s right &#8211; all that trigonometry you studied is finally going to pay off. Remember sine waves? As it turns out, all of the complex waveforms described above can actually be traced back to this humble periodic function. Before we get to constructing one of these, let\u2019s get a few important terms out of the way:<\/p>\n<ul>\n<li><strong>Fundamental frequency:<\/strong> This is the lowest note of our wave, and all the other sine waves will be arranged based on its frequency. To make things easy, let\u2019s set our fundamental sine wave to 100 Hz.<\/li>\n<li><strong>Harmonic frequencies:<\/strong> These sine waves are multiples of the fundamental note. For example, the second harmonic of a 100 Hz sine wave will be 200 Hz, the third harmonic will be 300 Hz, and so on.<\/li>\n<li><strong>Amplitude:<\/strong> By adjusting the amplitude of each of these harmonics, we can create different complex waveforms. In a DAW like Ableton Live, this is measured in decibels or dBFS, while an analog synth uses voltage.<\/li>\n<\/ul>\n<p>Each complex wave described above can be created just by playing a series of sine waves at specific frequencies and amplitude levels! Let\u2019s tackle a square wave in Ableton Live and see this magic at work. The formula for creating a square wave is as follows:<\/p>\n<ul>\n<li>We only want to include the <strong>odd<\/strong> harmonics &#8211; the third, fifth, seventh, etc. So if our square wave\u2019s fundamental frequency is 100 Hz, we\u2019ll also want sine waves at 300 Hz, 500 Hz, 700 Hz, and so on.<\/li>\n<li>The amplitude of these harmonics will <strong>decrease<\/strong> based on where they are in the series. For example, the third harmonic will only have a third of the fundamental frequency&#8217;s amplitude, and the seventh harmonic will have one seventh of the fundamental frequency&#8217;s amplitude.<\/li>\n<\/ul>\n<p>That might sound a bit daunting, but let\u2019s see (and hear) it in action. First, I opened up Live and dropped an empty <strong>Instrument Rack<\/strong> into a MIDI track. I then filled this rack with six separate instances of Ableton\u2019s <strong>Operator<\/strong> synthesizer, and checked the box labled <strong>\u201cFixed,\u201d<\/strong> which lets us control the exact frequency of each sine wave. The final step is to adjust the frequency and amplitude for each of the six sine waves so that they follow the relationships described above.<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-6099 lazyload\" data-src=\"https:\/\/splice.com\/blog\/wp-content\/uploads\/2019\/04\/whats-in-a-wave-in-post-02.png\" alt=\"whats-in-a-wave-in-post-02\" width=\"2000\" height=\"782\" data-srcset=\"https:\/\/splice.com\/blog\/wp-content\/uploads\/2019\/04\/whats-in-a-wave-in-post-02.png 2000w, https:\/\/splice.com\/blog\/wp-content\/uploads\/2019\/04\/whats-in-a-wave-in-post-02-400x156.png 400w, https:\/\/splice.com\/blog\/wp-content\/uploads\/2019\/04\/whats-in-a-wave-in-post-02-1024x400.png 1024w, https:\/\/splice.com\/blog\/wp-content\/uploads\/2019\/04\/whats-in-a-wave-in-post-02-355x139.png 355w, https:\/\/splice.com\/blog\/wp-content\/uploads\/2019\/04\/whats-in-a-wave-in-post-02-768x300.png 768w, https:\/\/splice.com\/blog\/wp-content\/uploads\/2019\/04\/whats-in-a-wave-in-post-02-1536x601.png 1536w\" data-sizes=\"(max-width: 2000px) 100vw, 2000px\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 2000px; --smush-placeholder-aspect-ratio: 2000\/782;\" \/><\/p>\n<p>Here\u2019s what it sounds like (and looks like) when you add these six sine waves on top of one another, one by one:<\/p>\n<div id=\"mp3jWrap_0\" class=\"mjp-s-wrapper s-graphic unsel-mjp \" style=\"font-size:18px;\"><span id=\"playpause_wrap_mp3j_0\" class=\"wrap_inline_mp3j\" style=\"font-weight:700;\"><span class=\"gfxbutton_mp3j play-mjp\" id=\"playpause_mp3j_0\" style=\"font-size:18px;\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/span>&nbsp;<span class=\"group_wrap\"><span class=\"bars_mp3j\"><span class=\"loadB_mp3j\" id=\"load_mp3j_0\"><\/span><span class=\"posbarB_mp3j\" id=\"posbar_mp3j_0\"><\/span><\/span><span class=\"T_mp3j\" id=\"T_mp3j_0\" style=\"font-size:18px;\"><\/span><span class=\"indi_mp3j\" style=\"font-size:12.6px;\" id=\"statusMI_0\"><\/span><\/span><\/span><\/div><span class=\"s-nosolution\" id=\"mp3j_nosolution_0\" style=\"display:none;\"><\/span><script>\nMP3jPLAYLISTS.inline_0 = [\n\t{ name: \"\", formats: [\"mp3\"], mp3: \"aHR0cHM6Ly9zcGxpY2UuY29tL2Jsb2cvd3AtY29udGVudC91cGxvYWRzLzIwMTkvMDQvc2luZS10by1zcXVhcmUubXAz\", counterpart:\"\", artist: \"\", image: \"\", imgurl: \"\" }\n];\n<\/script>\n\n<script>MP3jPLAYERS[0] = { list: MP3jPLAYLISTS.inline_0, tr:0, type:'single', lstate:'', loop:false, play_txt:'&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;', pause_txt:'&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;', pp_title:'', autoplay:false, download:false, vol:100, height:'' };<\/script>\n<h6 style=\"text-align: center;\"><img decoding=\"async\" class=\"alignnone size-full wp-image-6098 lazyload\" data-src=\"https:\/\/splice.com\/blog\/wp-content\/uploads\/2019\/04\/whats-in-a-wave-in-post-3.png\" alt=\"whats-in-a-wave-in-post-3\" width=\"2000\" height=\"560\" data-srcset=\"https:\/\/splice.com\/blog\/wp-content\/uploads\/2019\/04\/whats-in-a-wave-in-post-3.png 2000w, https:\/\/splice.com\/blog\/wp-content\/uploads\/2019\/04\/whats-in-a-wave-in-post-3-400x112.png 400w, https:\/\/splice.com\/blog\/wp-content\/uploads\/2019\/04\/whats-in-a-wave-in-post-3-1024x287.png 1024w, https:\/\/splice.com\/blog\/wp-content\/uploads\/2019\/04\/whats-in-a-wave-in-post-3-355x99.png 355w, https:\/\/splice.com\/blog\/wp-content\/uploads\/2019\/04\/whats-in-a-wave-in-post-3-768x215.png 768w, https:\/\/splice.com\/blog\/wp-content\/uploads\/2019\/04\/whats-in-a-wave-in-post-3-1536x430.png 1536w\" data-sizes=\"(max-width: 2000px) 100vw, 2000px\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 2000px; --smush-placeholder-aspect-ratio: 2000\/560;\" \/><\/h6>\n<p><em>The sine wave slowly nears the shape of a square wave as more waves are added<\/em><\/p>\n<p>Even though each wave was created separately, our brain perceives them as a single tone &#8211; and thus a complex waveform is born. This is the basic foundation behind <strong>additive synthesis<\/strong>, a technique for creating\u00a0interesting sounds by just layering sine waves on top of one another. In the case of our square wave, the more harmonic frequencies you add, the richer the wave will end up sounding. Just compare the <strong>Square 6<\/strong> wave preset in Operator, which should sound exactly like the wave you just heard, with the <strong>Square 64<\/strong> preset, which will sound much more full and bright due to a few dozen more layered harmonics.<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-6100 lazyload\" data-src=\"https:\/\/splice.com\/blog\/wp-content\/uploads\/2019\/04\/whats-in-a-wave-in-post-01.png\" alt=\"what's-in-a-wave-in-post-01\" width=\"2000\" height=\"1407\" data-srcset=\"https:\/\/splice.com\/blog\/wp-content\/uploads\/2019\/04\/whats-in-a-wave-in-post-01.png 2000w, https:\/\/splice.com\/blog\/wp-content\/uploads\/2019\/04\/whats-in-a-wave-in-post-01-400x281.png 400w, https:\/\/splice.com\/blog\/wp-content\/uploads\/2019\/04\/whats-in-a-wave-in-post-01-1024x720.png 1024w, https:\/\/splice.com\/blog\/wp-content\/uploads\/2019\/04\/whats-in-a-wave-in-post-01-355x250.png 355w, https:\/\/splice.com\/blog\/wp-content\/uploads\/2019\/04\/whats-in-a-wave-in-post-01-768x540.png 768w, https:\/\/splice.com\/blog\/wp-content\/uploads\/2019\/04\/whats-in-a-wave-in-post-01-1536x1081.png 1536w\" data-sizes=\"(max-width: 2000px) 100vw, 2000px\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 2000px; --smush-placeholder-aspect-ratio: 2000\/1407;\" \/><\/p>\n<p>If you\u2019d like to learn more about how different waveforms are constructed, make sure to check out the Ableton project below. I\u2019ve included constructed versions of sawtooth, square, and triangle waves for you to mess around with. You can also quickly access an entire selection of pre-constructed waveforms under the <strong>Wave<\/strong> menu in the <strong>Oscillator<\/strong> section of Operator. This feature makes it easy to craft your own unique waveforms too &#8211; just click and drag along the graph to add, remove, and adjust the amplitude of up to 64 individual frequencies. Have fun, and don\u2019t be afraid to get ~wavy~.<\/p>\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"has-text-align-center\">Browse, preview, and license Splice samples directly inside Ableton Live with our new in-DAW integration:<\/p>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-1 wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/splice.com\/plans\/ableton-live\/about\" target=\"_blank\" rel=\"noreferrer noopener\">Learn more<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>In this blog post, let&#8217;s learn about how you can construct complex waveforms using nothing but the humble sine wave.<\/p>\n","protected":false},"author":28,"featured_media":6102,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"categories":[1851,1850,1696,1704],"tags":[1721,1638],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v22.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>What\u2019s in a waveform? 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