{"id":615,"date":"2017-05-23T11:54:19","date_gmt":"2017-05-23T11:54:19","guid":{"rendered":"http:\/\/dantepfer.com\/blog\/?p=615"},"modified":"2019-11-29T20:01:34","modified_gmt":"2019-11-30T01:01:34","slug":"listening-to-planetary-orbits","status":"publish","type":"post","link":"https:\/\/dantepfer.com\/blog\/?p=615","title":{"rendered":"The TRAPPIST-1 System: Listening to Planetary Orbits"},"content":{"rendered":"<h5><em>(Cross-posted from <a href=\"http:\/\/wbgo.org\/post\/dan-tepfer-pianist-and-science-enthusiast-walks-us-through-music-cosmos#stream\/0\">WBGO.org<\/a>. Thanks to Nate Chinen for inviting me to write this.)<\/em><\/h5>\n<p>With most things, I&#8217;ve found, what\u2019s most interesting isn\u2019t the thing in itself, but rather how it relates to other things. In other words, everything is relative, which is why I was so excited to see\u00a0the video below. It shows, using harmony, rhythm and visuals, the relationships between the orbits of the seven planets around TRAPPIST-1, a dwarf star about\u00a040\u00a0light years away from us.<\/p>\n<p><iframe loading=\"lazy\" title=\"TRAPPIST Sounds : TRAPPIST-1 Planetary System Translated Directly Into Music\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/WS5UxLHbUKc?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n<p><!--more-->The video was made by astrophysicist Daniel Tamayo, who worked out the planets&#8217; orbits, and Matt Russo, a fellow scientist who also plays jazz guitar. Musician Andrew Santaguida contributed as well.<\/p>\n<p>What&#8217;s going on here? Why does it sound so good? How, in the first place, were these orbits figured out? It&#8217;s only in the past 25 years that we&#8217;ve been\u00a0able to detect planets in orbit around stars other than our own. This is mainly done indirectly, by \u2014 for example \u2014 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Exoplanet#History_of_detection\">measuring faint dips in a\u00a0star&#8217;s brightness as planets pass in front of it<\/a>. In 2015, using this technique, three exoplanets, as planets outside of our Solar System are called, were discovered orbiting around TRAPPIST-1, a dwarf star about 40 light-years away from us in the Aquarius constellation. In February 2017, four more were discovered. The field of exoplanet detection has gotten so advanced that scientists\u00a0are able to determine not only the size and mass of these planets, but also their orbital periods and \u2014 most amazingly \u2014 chemical composition.\u00a0Three of TRAPPIST-1&#8217;s planets are considered to be within its habitable zone, where life could potentially be sustained, and\u00a0<a href=\"https:\/\/en.wikipedia.org\/wiki\/TRAPPIST-1\">some of the planets may even have liquid water on their surface<\/a>.<\/p>\n<div id=\"attachment_644\" style=\"width: 606px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/dantepfer.com\/blog\/?attachment_id=644\" rel=\"attachment wp-att-637\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-644\" class=\"wp-image-644 \" src=\"http:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/NASA-TRAPPIST-pic.jpg\" alt=\"\" width=\"596\" height=\"184\" srcset=\"https:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/NASA-TRAPPIST-pic.jpg 1000w, https:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/NASA-TRAPPIST-pic-300x93.jpg 300w, https:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/NASA-TRAPPIST-pic-768x237.jpg 768w\" sizes=\"auto, (max-width: 596px) 100vw, 596px\" \/><\/a><p id=\"caption-attachment-644\" class=\"wp-caption-text\">Artist Impression of the TRAPPIST-1 system (NASA\/JPL)<\/p><\/div>\n<p>This is remarkable\u00a0enough already. But what makes the TRAPPIST-1 system even more\u00a0special is the relationships between its planets&#8217; orbits. The farthest\u00a0planet completes one orbit every 18\u00a0Earth days, and the next farthest once every 12. What&#8217;s 18 divided by 12?\u00a0That&#8217;s 1.5, or 3\/2. In other words, in the time it takes the farthest planet to go twice around the star, the next farthest has gone around three times.<\/p>\n<p>We hear sound when the air around us vibrates and those vibrations reach our ears. Vibrations are a bit like orbits \u2014 they repeat at a certain frequency (the note A in the middle of a\u00a0piano, for example, vibrates 440 times per second). What does it sound like when sounds vibrate in that same 3\/2 ratio, one sound vibrating twice\u00a0in the time it takes the other\u00a0to vibrate three times? As <a href=\"https:\/\/en.wikipedia.org\/wiki\/Pythagorean_tuning\">Pythagoras discovered long ago<\/a>, it sounds lovely. The musical interval which results, the so-called perfect fifth, is one of the fundamental building blocks of harmony \u2014 and not only Western harmony. It turns up in traditional music from all around the world, in every possible key. It sounds like this:<\/p>\n\t<audio id=\"wp_mep_1\"      controls=\"controls\" preload=\"none\"  >\r\n\t\t\r\n\t\t<source src=\"http:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/3_to_2.mp3\" type=\"audio\/mp3\" \/>\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t<\/audio>\r\n<script type=\"text\/javascript\">\r\njQuery(document).ready(function($) {\r\n\t$('#wp_mep_1').mediaelementplayer({\r\n\t\tm:1\r\n\t\t\r\n\t\t,features: ['playpause','current','progress','duration','volume','tracks','fullscreen']\r\n\t\t,audioWidth:400,audioHeight:30\r\n\t});\r\n});\r\n<\/script>\r\n\n<p>&nbsp;<\/p>\n<p>Now let&#8217;s look at the closest planet to TRAPPIST-1. It orbits the star in only 1.5 Earth days (these orbital periods are short because the system is very compact \u2014\u00a0all seven\u00a0planets orbit the star much closer than\u00a0Mercury orbits the Sun, and the star itself is only about the size of Jupiter). The next closest goes around\u00a0once every 2.4 days, which gives their orbits a relationship of about\u00a08\/5. Now, if one sound vibrates eight times in the time it takes another to vibrate five, we get\u00a0the interval of a minor sixth, which sounds like this:<\/p>\n\t<audio id=\"wp_mep_2\"      controls=\"controls\" preload=\"none\"  >\r\n\t\t\r\n\t\t<source src=\"http:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/8-to-5.mp3\" type=\"audio\/mp3\" \/>\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t<\/audio>\r\n<script type=\"text\/javascript\">\r\njQuery(document).ready(function($) {\r\n\t$('#wp_mep_2').mediaelementplayer({\r\n\t\tm:1\r\n\t\t\r\n\t\t,features: ['playpause','current','progress','duration','volume','tracks','fullscreen']\r\n\t\t,audioWidth:400,audioHeight:30\r\n\t});\r\n});\r\n<\/script>\r\n\n<p>&nbsp;<\/p>\n<p>This is a less basic interval than the perfect fifth, but\u00a0it&#8217;s still part of the fundamental\u00a0material of music. Like the perfect fifth, it&#8217;s a\u00a0<em>consonant<\/em> interval, meaning its sounds seem to belong together; the relationship sounds\u00a0harmonious to our ears. Let&#8217;s pause here for a moment to consider what we&#8217;re talking about: that some planets orbiting a star unfathomably far away from us are doing so in a way that\u00a0<em>sounds good<\/em> to us. Isn&#8217;t that something?<\/p>\n<p>What&#8217;s more, we&#8217;re capable of hearing\u00a0relationships like 3\/2 and 8\/5 in other ways than through harmony. <a href=\"http:\/\/dantepfer.com\/blog\/?p=277\">As I&#8217;ve written about before<\/a>, pitch and rhythm are the same thing, expressed at different time scales. We can hear 8\/5 as an interval between two pitches, and we can also hear it as a rhythm in which one sound\u00a0is played\u00a0eight times in the time the other is played five:<\/p>\n<div id=\"attachment_657\" style=\"width: 435px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/dantepfer.com\/blog\/?attachment_id=657\" rel=\"attachment wp-att-643\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-657\" class=\"wp-image-657 \" src=\"http:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/8-to-5-in-musical-notation-1.png\" alt=\"\" width=\"425\" height=\"119\" srcset=\"https:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/8-to-5-in-musical-notation-1.png 1546w, https:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/8-to-5-in-musical-notation-1-300x84.png 300w, https:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/8-to-5-in-musical-notation-1-768x215.png 768w, https:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/8-to-5-in-musical-notation-1-1024x287.png 1024w\" sizes=\"auto, (max-width: 425px) 100vw, 425px\" \/><\/a><p id=\"caption-attachment-657\" class=\"wp-caption-text\">8 \/ 5 in musical notation<\/p><\/div>\n<p>What does this rhythm sound like?<\/p>\n\t<audio id=\"wp_mep_3\"      controls=\"controls\" preload=\"none\"  >\r\n\t\t\r\n\t\t<source src=\"http:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/8-to-5-rhythm.mp3\" type=\"audio\/mp3\" \/>\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t<\/audio>\r\n<script type=\"text\/javascript\">\r\njQuery(document).ready(function($) {\r\n\t$('#wp_mep_3').mediaelementplayer({\r\n\t\tm:1\r\n\t\t\r\n\t\t,features: ['playpause','current','progress','duration','volume','tracks','fullscreen']\r\n\t\t,audioWidth:400,audioHeight:30\r\n\t});\r\n});\r\n<\/script>\r\n\n<p>&nbsp;<\/p>\n<p>Pretty catchy, I would say! What&#8217;s important to appreciate is that this is exactly the same as hearing a minor sixth as harmony, only about 200 times slower. Pitch and rhythm are simply two different ways for us to\u00a0perceive frequency\u00a0relationships.\u00a0It&#8217;s even <a href=\"http:\/\/dantepfer.com\/blog\/?p=277\">possible to experience one turning into\u00a0the other<\/a>, and back again:<\/p>\n\t<audio id=\"wp_mep_4\"      controls=\"controls\" preload=\"none\"  >\r\n\t\t\r\n\t\t<source src=\"http:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/8-to-5-rhythm-to-pitch.mp3\" type=\"audio\/mp3\" \/>\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t<\/audio>\r\n<script type=\"text\/javascript\">\r\njQuery(document).ready(function($) {\r\n\t$('#wp_mep_4').mediaelementplayer({\r\n\t\tm:1\r\n\t\t\r\n\t\t,features: ['playpause','current','progress','duration','volume','tracks','fullscreen']\r\n\t\t,audioWidth:400,audioHeight:30\r\n\t});\r\n});\r\n<\/script>\r\n\n<p>&nbsp;<\/p>\n<p>With the TRAPPIST-1 system, it&#8217;s not only the inner and outer two planets that orbit in a resonant harmonic relationships. All seven, surprisingly, do \u2014 the only planetary system discovered so far with such consistently resonant\u00a0orbits. Their relationships, from inner to outer, are very nearly as follows:\u00a08\/5, 5\/3, 3\/2, 3\/2, 4\/3, and 3\/2. This works out to a combined 2 \/ 3 \/ 4 \/ 6 \/ 9 \/ 15 \/ 24.\u00a0Let&#8217;s hear all of these together, built up from the outermost planet to the innermost, in music:<\/p>\n\t<audio id=\"wp_mep_5\"      controls=\"controls\" preload=\"none\"  >\r\n\t\t\r\n\t\t<source src=\"http:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/whole-trappist-system-with-whole-ratios.mp3\" type=\"audio\/mp3\" \/>\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t<\/audio>\r\n<script type=\"text\/javascript\">\r\njQuery(document).ready(function($) {\r\n\t$('#wp_mep_5').mediaelementplayer({\r\n\t\tm:1\r\n\t\t\r\n\t\t,features: ['playpause','current','progress','duration','volume','tracks','fullscreen']\r\n\t\t,audioWidth:400,audioHeight:30\r\n\t});\r\n});\r\n<\/script>\r\n\n<p>&nbsp;<\/p>\n<p>Pretty, right? Now\u00a0let&#8217;s hear these same relationships\u00a0as rhythm, but instead of playing each note\u00a0with a percussive sound as we did before with the minor sixth, let&#8217;s express\u00a0each\u00a0with the pitch\u00a0that results from the orbital relationships. For fun, here it is in musical notation:<\/p>\n<div id=\"attachment_668\" style=\"width: 631px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/dantepfer.com\/blog\/?attachment_id=668\" rel=\"attachment wp-att-647\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-668\" class=\"wp-image-668 \" src=\"http:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/Screen-Shot-2017-05-31-at-4.01.59-PM-1024x457.png\" alt=\"\" width=\"621\" height=\"277\" srcset=\"https:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/Screen-Shot-2017-05-31-at-4.01.59-PM-1024x457.png 1024w, https:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/Screen-Shot-2017-05-31-at-4.01.59-PM-300x134.png 300w, https:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/Screen-Shot-2017-05-31-at-4.01.59-PM-768x343.png 768w, https:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/Screen-Shot-2017-05-31-at-4.01.59-PM.png 2004w\" sizes=\"auto, (max-width: 621px) 100vw, 621px\" \/><\/a><p id=\"caption-attachment-668\" class=\"wp-caption-text\">The TRAPPIST-1 system (2 \/ 3 \/ 4 \/ 6 \/ 9 \/ 15 \/ 24) in musical notation<\/p><\/div>\n<p>And in\u00a0sound:<\/p>\n\t<audio id=\"wp_mep_6\"      controls=\"controls\" preload=\"none\"  >\r\n\t\t\r\n\t\t<source src=\"http:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/whole-trappist-system-with-whole-ratios-and-rhythm-3.mp3\" type=\"audio\/mp3\" \/>\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t<\/audio>\r\n<script type=\"text\/javascript\">\r\njQuery(document).ready(function($) {\r\n\t$('#wp_mep_6').mediaelementplayer({\r\n\t\tm:1\r\n\t\t\r\n\t\t,features: ['playpause','current','progress','duration','volume','tracks','fullscreen']\r\n\t\t,audioWidth:400,audioHeight:30\r\n\t});\r\n});\r\n<\/script>\r\n\n<p>&nbsp;<\/p>\n<p>We&#8217;re now hearing the TRAPPIST-1 system as pitch and rhythmic relationships, simultaneously. We&#8217;re experiencing the same thing in two different ways at once. As a friend of mine pointed out, it&#8217;s a bit\u00a0like tasting\u00a0roasted cauliflower next to a cauliflower gratin on a bed of <a href=\"http:\/\/www.thekitchn.com\/how-to-make-cauliflower-rice-couscous-cooking-lessons-from-the-kitchn-203344\">cauliflower couscous<\/a>.<a href=\"http:\/\/dantepfer.com\/blog\/?attachment_id=650\" rel=\"attachment wp-att-650\"><br \/>\n<\/a><\/p>\n<div id=\"attachment_649\" style=\"width: 475px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/dantepfer.com\/blog\/?attachment_id=649\" rel=\"attachment wp-att-649\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-649\" class=\"wp-image-649 \" src=\"http:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/Cauliflower-gratin-goat-cheese-superJumbo-1024x683.jpg\" alt=\"\" width=\"465\" height=\"310\" srcset=\"https:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/Cauliflower-gratin-goat-cheese-superJumbo-1024x683.jpg 1024w, https:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/Cauliflower-gratin-goat-cheese-superJumbo-300x200.jpg 300w, https:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/Cauliflower-gratin-goat-cheese-superJumbo-768x512.jpg 768w, https:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/Cauliflower-gratin-goat-cheese-superJumbo.jpg 2048w\" sizes=\"auto, (max-width: 465px) 100vw, 465px\" \/><\/a><p id=\"caption-attachment-649\" class=\"wp-caption-text\">Cauliflower gratin<\/p><\/div>\n<p>But wait, something&#8217;s off \u2014 if you&#8217;re listening closely, you may have noticed that this\u00a0is quite a bit more in tune and in time than the sounds and rhythms played in the video at top. This is because, although the TRAPPIST-1 system has relationships that are very close to\u00a0whole numbers, they&#8217;re actually a little off. Nature is funny that way.\u00a0<a href=\"https:\/\/en.wikipedia.org\/wiki\/TRAPPIST-1\">The outermost planet doesn&#8217;t orbit in exactly 18 days but rather 18.766<\/a>. The second farthest\u00a0planet goes around\u00a0in 12.353 days rather than 12. So their relationship isn&#8217;t quite 1.5, but rather 1.51918. We&#8217;ve been listening to an idealized version of the system so far. Let&#8217;s see what the real thing sounds like, with the most precise orbital periods plugged in, first as pitch, then as pitch and rhythm:<\/p>\n\t<audio id=\"wp_mep_7\"      controls=\"controls\" preload=\"none\"  >\r\n\t\t\r\n\t\t<source src=\"http:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/trappist-real-ratios-held-and-rhythm-1.mp3\" type=\"audio\/mp3\" \/>\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t<\/audio>\r\n<script type=\"text\/javascript\">\r\njQuery(document).ready(function($) {\r\n\t$('#wp_mep_7').mediaelementplayer({\r\n\t\tm:1\r\n\t\t\r\n\t\t,features: ['playpause','current','progress','duration','volume','tracks','fullscreen']\r\n\t\t,audioWidth:400,audioHeight:30\r\n\t});\r\n});\r\n<\/script>\r\n\n<p>&nbsp;<\/p>\n<p>It still sounds quite harmonious, if a little sour\u00a0(it&#8217;s worth comparing to the two previous recordings above). The discrepancies are particularly\u00a0noticeable in the rhythm, which doesn&#8217;t line up quite as neatly as before. The intervals making up the harmonies aren&#8217;t as clean, either, but they still &#8220;work&#8221; \u2014 we still hear a clear, quite consonant chord (the history of tuning systems tells us that\u00a0<a href=\"https:\/\/en.wikipedia.org\/wiki\/Equal_temperament#Comparison_to_just_intonation\">there is always a little lee-way with tuning<\/a>). One result of\u00a0recreating this rendering\u00a0for myself was to notice\u00a0that there is a wobble, or vibrato, in the piano-like sound that the TRAPPIST-1 physicists used\u00a0in their video. To my ears, this causes the harmonies to sound a little further out of tune than they actually are. I&#8217;m using simpler, more stable sounds in my own rendering.<\/p>\n<p>So \u2014 TRAPPIST-1 is remarkable. Without interfering with its orbits in any way, by just presenting the data scaled up to our range of hearing, we hear what we readily identify as harmonious music. But how special is it? To compare, I wanted\u00a0to listen to our own <a href=\"https:\/\/en.wikipedia.org\/wiki\/Solar_System\">Solar System<\/a>. From Mercury&#8217;s 88-day orbit to Neptune&#8217;s 165-year one, our home planets take a lot longer to orbit the Sun than TRAPPIST-1&#8217;s do. But their relationships \u2014 Earth to Mars relate by\u00a0about 17\/9, for example \u2014 can be rendered in\u00a0music just as well.<\/p>\n<div id=\"attachment_645\" style=\"width: 604px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/dantepfer.com\/blog\/?attachment_id=645\" rel=\"attachment wp-att-645\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-645\" class=\"wp-image-645 \" src=\"http:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/solar-system.jpg\" alt=\"\" width=\"594\" height=\"170\" srcset=\"https:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/solar-system.jpg 1400w, https:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/solar-system-300x86.jpg 300w, https:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/solar-system-768x219.jpg 768w, https:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/solar-system-1024x293.jpg 1024w\" sizes=\"auto, (max-width: 594px) 100vw, 594px\" \/><\/a><p id=\"caption-attachment-645\" class=\"wp-caption-text\">The Solar System (distances not to scale \u2014 WP)<\/p><\/div>\n<p>The Solar System is so spread out that it helps to break it up. Let&#8217;s begin with the four inner planets, Mercury, Venus, Earth and Mars. Heard on their own, they\u00a0spell out\u00a0an eerie kind of Major 7th chord:<\/p>\n\t<audio id=\"wp_mep_8\"      controls=\"controls\" preload=\"none\"  >\r\n\t\t\r\n\t\t<source src=\"http:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/inner-solar-system.mp3\" type=\"audio\/mp3\" \/>\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t<\/audio>\r\n<script type=\"text\/javascript\">\r\njQuery(document).ready(function($) {\r\n\t$('#wp_mep_8').mediaelementplayer({\r\n\t\tm:1\r\n\t\t\r\n\t\t,features: ['playpause','current','progress','duration','volume','tracks','fullscreen']\r\n\t\t,audioWidth:400,audioHeight:30\r\n\t});\r\n});\r\n<\/script>\r\n\n<p>&nbsp;<\/p>\n<p>Meanwhile the outer planets Jupiter, Saturn, Uranus and Neptune together have something of a half-diminished color:<\/p>\n\t<audio id=\"wp_mep_9\"      controls=\"controls\" preload=\"none\"  >\r\n\t\t\r\n\t\t<source src=\"http:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/outer-solar-system.mp3\" type=\"audio\/mp3\" \/>\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t<\/audio>\r\n<script type=\"text\/javascript\">\r\njQuery(document).ready(function($) {\r\n\t$('#wp_mep_9').mediaelementplayer({\r\n\t\tm:1\r\n\t\t\r\n\t\t,features: ['playpause','current','progress','duration','volume','tracks','fullscreen']\r\n\t\t,audioWidth:400,audioHeight:30\r\n\t});\r\n});\r\n<\/script>\r\n\n<p>&nbsp;<\/p>\n<p>Now let&#8217;s try to hear these together. Because it is so compact, the planetary system of TRAPPIST-1 can fit\u00a0neatly\u00a0into the\u00a0range of frequencies where we comfortably hear harmonies. Not so for the Solar System. TRAPPIST-1&#8217;s innermost planet makes only 12 orbits in the time the outermost makes 1, whereas Mercury makes 684 in the time\u00a0Neptune makes 1, a vastly greater range that stretches our hearing to the limits. If\u00a0I assign\u00a0an extremely low\u00a0note to\u00a0Neptune, a low 23Hz rumble right at the bottom of our audible range, that puts Mercury&#8217;s sound\u00a0right at the top of what we can hear, a mere dog whistle at 15,736Hz \u2014 which younger listeners will have more success hearing than older ones. Even if we&#8217;re able to\u00a0hear this, we just don&#8217;t have the perceptual capacity to hear\u00a0real\u00a0harmonic relationships between tones spread\u00a0that far apart.<\/p>\n<p>For that reason, I&#8217;ve transposed the inner four planets down by 2 octaves, and the outer four up by 1 octave. As you&#8217;ll remember from music theory\u00a0class, if you were there, this doesn&#8217;t alter the resulting harmony (think chord inversions) \u2014 it just allows us to hear it. Here is the sound of our Solar System, from Neptune through Mercury:<\/p>\n\t<audio id=\"wp_mep_10\"      controls=\"controls\" preload=\"none\"  >\r\n\t\t\r\n\t\t<source src=\"http:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/whole-solar-system.mp3\" type=\"audio\/mp3\" \/>\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t<\/audio>\r\n<script type=\"text\/javascript\">\r\njQuery(document).ready(function($) {\r\n\t$('#wp_mep_10').mediaelementplayer({\r\n\t\tm:1\r\n\t\t\r\n\t\t,features: ['playpause','current','progress','duration','volume','tracks','fullscreen']\r\n\t\t,audioWidth:400,audioHeight:30\r\n\t});\r\n});\r\n<\/script>\r\n\n<p>&nbsp;<\/p>\n<p>There&#8217;s no doubt when we hear this that the Solar System isn&#8217;t anywhere as harmonious as TRAPPIST-1. Not even in the same ballpark. I actually\u00a0<em>like<\/em> the sound that results \u2014 it has a mystery that I find enticing \u2014 but it&#8217;s wildly dissonant.\u00a0While there are some near-resonances in the Solar System \u2014 Uranus makes nearly\u00a0two orbits in the time it takes Neptune to make one, for example \u2014 most of them are too far out of tune to qualify as harmonious.<\/p>\n<p>The fact that the TRAPPIST-1 orbits are so obviously\u00a0harmonious in comparison\u00a0tells us something important about the physics of the system.\u00a0The planets are so close together that they\u00a0<a href=\"https:\/\/www.youtube.com\/watch?v=7i8Urhbd6eI\">would collide with each other<\/a> if they hadn&#8217;t settled into these resonant orbital relationships. Meanwhile, the planets of the Solar System are far enough apart that they face\u00a0fewer\u00a0demands on their orbits.<\/p>\n<div id=\"attachment_653\" style=\"width: 488px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/dantepfer.com\/blog\/?attachment_id=653\" rel=\"attachment wp-att-653\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-653\" class=\"wp-image-653 \" src=\"http:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/kepler.png\" alt=\"\" width=\"478\" height=\"155\" srcset=\"https:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/kepler.png 806w, https:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/kepler-300x98.png 300w, https:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/kepler-768x250.png 768w\" sizes=\"auto, (max-width: 478px) 100vw, 478px\" \/><\/a><p id=\"caption-attachment-653\" class=\"wp-caption-text\">Kepler&#8217;s Harmonices Mundi<\/p><\/div>\n<p>The great astronomer\u00a0Johannes\u00a0Kepler, in addition to contributing enormously to the field \u00a0of astronomy in the 17th century, was also something of an astrologer. He was particularly interested in how a planet&#8217;s speed varied during its orbit, which is what he\u00a0rendered in musical notation in the figure above. He believed that the happiness\u00a0of life\u00a0on Earth\u00a0<a href=\"https:\/\/en.wikipedia.org\/wiki\/Harmonices_Mundi\">depended on how harmoniously the orbits of the planets related to one another<\/a>. He was following in the footsteps of the ancient Greeks, who <a href=\"https:\/\/en.wikipedia.org\/wiki\/Musica_universalis\">advocated for a Harmony of the Spheres<\/a>\u00a0over 2,000\u00a0years ago. It turns out people\u00a0have been trying to listen to planetary orbits for a very long time; it&#8217;s remarkable that we live in a time where we can accurately listen not only to our own, but to planets around other stars as well.<\/p>\n<p>Aristotle and Kepler would have had to believe that life in the\u00a0TRAPPIST-1 system, if indeed there any, is\u00a0pretty dandy. It&#8217;s hard to imagine a system with more harmonious planets. Or is it? I&#8217;ll leave you with a sound rendering I made of the four <a href=\"https:\/\/en.wikipedia.org\/wiki\/Moons_of_Jupiter\">Galilean Moons of Jupiter<\/a>, both in pitch and rhythm. Io, Europa, Ganymede and Callisto have orbits that are perhaps even more harmonious than those of TRAPPIST-1, with a beautiful\u00a0minor key sonority. Three of the moons\u00a0are in quasi-perfect octaves, a 2 to 1 relationship that is the simplest there is. I guess life must be pretty good there, too.<\/p>\n\t<audio id=\"wp_mep_11\"      controls=\"controls\" preload=\"none\"  >\r\n\t\t\r\n\t\t<source src=\"http:\/\/dantepfer.com\/blog\/wp-content\/uploads\/2017\/05\/long-jupiter-orbits.mp3\" type=\"audio\/mp3\" \/>\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t<\/audio>\r\n<script type=\"text\/javascript\">\r\njQuery(document).ready(function($) {\r\n\t$('#wp_mep_11').mediaelementplayer({\r\n\t\tm:1\r\n\t\t\r\n\t\t,features: ['playpause','current','progress','duration','volume','tracks','fullscreen']\r\n\t\t,audioWidth:400,audioHeight:30\r\n\t});\r\n});\r\n<\/script>\r\n\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>(Cross-posted from WBGO.org. Thanks to Nate Chinen for inviting me to write this.) With most things, I&#8217;ve found, what\u2019s most interesting isn\u2019t the thing in itself, but rather how it relates to other things. In other words, everything is relative, &hellip; <a href=\"https:\/\/dantepfer.com\/blog\/?p=615\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5,45],"tags":[],"class_list":["post-615","post","type-post","status-publish","format-standard","hentry","category-music-2","category-science"],"_links":{"self":[{"href":"https:\/\/dantepfer.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/615","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/dantepfer.com\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/dantepfer.com\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/dantepfer.com\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/dantepfer.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=615"}],"version-history":[{"count":31,"href":"https:\/\/dantepfer.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/615\/revisions"}],"predecessor-version":[{"id":742,"href":"https:\/\/dantepfer.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/615\/revisions\/742"}],"wp:attachment":[{"href":"https:\/\/dantepfer.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=615"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dantepfer.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=615"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dantepfer.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=615"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}