{"id":7900,"date":"2023-11-16T20:13:44","date_gmt":"2023-11-16T18:13:44","guid":{"rendered":"http:\/\/www.tonmeister.ca\/wordpress\/?p=7900"},"modified":"2023-11-16T20:21:42","modified_gmt":"2023-11-16T18:21:42","slug":"dynamic-styli-correlator-v","status":"publish","type":"post","link":"http:\/\/www.tonmeister.ca\/wordpress\/2023\/11\/16\/dynamic-styli-correlator-v\/","title":{"rendered":"Dynamic Styli Correlator Pt. 5"},"content":{"rendered":"\n<p>In the last posting, I showed a scale drawing of a 15 \u00b5m radius needle on a 1 kHz sine tone with a modulation velocity of 50 mm\/s (peak) on the inside groove of a record. Looking at this, we could see that the maximum angular rotation of the contact point was about 13\u00ba away from vertical, so the total range of angular rotation of that point would be about 27\u00ba.<\/p>\n\n\n\n<p>I also mentioned that, because vinyl is mastered so that the signal on the groove wall has a constant velocity from about 1 kHz and upwards, then that range will not change for that frequency band. Below 1 kHz, because the mastering is typically ensuring a constant amplitude on the groove wall, then the range decreases with frequency.<\/p>\n\n\n\n<p>We can do the math to find out exactly what the angular rotation the contact point is for a given modulation velocity and groove speed.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1450\" height=\"262\" src=\"http:\/\/www.tonmeister.ca\/wordpress\/wp-content\/uploads\/rotation_maxima-1.png\" alt=\"\" class=\"wp-image-7903\" srcset=\"http:\/\/www.tonmeister.ca\/wordpress\/wp-content\/uploads\/rotation_maxima-1.png 1450w, http:\/\/www.tonmeister.ca\/wordpress\/wp-content\/uploads\/rotation_maxima-1-300x54.png 300w, http:\/\/www.tonmeister.ca\/wordpress\/wp-content\/uploads\/rotation_maxima-1-1024x185.png 1024w, http:\/\/www.tonmeister.ca\/wordpress\/wp-content\/uploads\/rotation_maxima-1-768x139.png 768w\" sizes=\"auto, (max-width: 1450px) 100vw, 1450px\" \/><figcaption class=\"wp-element-caption\">Figure 1: A scale drawing of a 15 \u00b5m radius needle on a 1 kHz sine tone with a modulation velocity of 50 mm\/s (peak) on the inside groove of a record. These two points are the two extremes of the angular rotation of the contact point.<\/figcaption><\/figure>\n<\/div>\n\n\n<p>Looking at Figure 1, the rotation is \u00b113.4\u00ba away from vertical on the maximum; so the total range is 26.8\u00ba. We convert this to a time modulation by converting that angular range to a distance, and dividing by the groove speed at the location of the needle on the record.<\/p>\n\n\n\n<p>If we repeat that procedure for a range of needle radii from 0 \u00b5m to 75 \u00b5m for the best-case (the outside groove) and the worst-case (the inside groove), we get the results shown in Figure 2.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"768\" src=\"http:\/\/www.tonmeister.ca\/wordpress\/wp-content\/uploads\/jitter_vs_radius-1024x768.png\" alt=\"\" class=\"wp-image-7904\" srcset=\"http:\/\/www.tonmeister.ca\/wordpress\/wp-content\/uploads\/jitter_vs_radius-1024x768.png 1024w, http:\/\/www.tonmeister.ca\/wordpress\/wp-content\/uploads\/jitter_vs_radius-300x225.png 300w, http:\/\/www.tonmeister.ca\/wordpress\/wp-content\/uploads\/jitter_vs_radius-768x576.png 768w, http:\/\/www.tonmeister.ca\/wordpress\/wp-content\/uploads\/jitter_vs_radius.png 1120w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Figure 2. The peak-to-peak equivalent &#8220;jitter&#8221; values of the inside and outside grooves for a range of needle radii.<\/figcaption><\/figure>\n<\/div>\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In the last posting, I showed a scale drawing of a 15 \u00b5m radius needle on a 1 kHz sine tone with a modulation velocity of 50 mm\/s (peak) on the inside groove of a record. Looking at this, we could see that the maximum angular rotation of the contact point was about 13\u00ba away [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[66,63,4,60,72],"tags":[],"class_list":["post-7900","post","type-post","status-publish","format-standard","hentry","category-analogue","category-analysis","category-audio","category-jitter","category-vinyl"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p48hIM-23q","_links":{"self":[{"href":"http:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/posts\/7900","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/comments?post=7900"}],"version-history":[{"count":7,"href":"http:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/posts\/7900\/revisions"}],"predecessor-version":[{"id":7918,"href":"http:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/posts\/7900\/revisions\/7918"}],"wp:attachment":[{"href":"http:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/media?parent=7900"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/categories?post=7900"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/tags?post=7900"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}