{"id":97,"date":"2019-01-05T17:00:40","date_gmt":"2019-01-05T17:00:40","guid":{"rendered":"http:\/\/wordpress.davidlouiepiano.com\/?page_id=97"},"modified":"2023-07-04T10:15:52","modified_gmt":"2023-07-04T14:15:52","slug":"bach-louie-temperament","status":"publish","type":"page","link":"https:\/\/davidlouiepiano.com\/index.php\/bach-louie-temperament\/","title":{"rendered":"Bach&#8217;s Squiggle"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#691a1a\">Bach-Louie Temperament<\/h2>\n\n\n\n<h5 class=\"wp-block-heading has-text-align-center\">&#8220;Decoding Bach&#8217;s Temperament&#8221;<\/h5>\n\n\n\n<figure class=\"wp-block-image alignwide is-style-rounded\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"227\" src=\"https:\/\/davidlouiepiano.com\/wp-content\/uploads\/2019\/01\/Bachs-Squiggle2-1024x227.jpg\" alt=\"\" class=\"wp-image-557\" srcset=\"https:\/\/davidlouiepiano.com\/wp-content\/uploads\/2019\/01\/Bachs-Squiggle2-1024x227.jpg 1024w, https:\/\/davidlouiepiano.com\/wp-content\/uploads\/2019\/01\/Bachs-Squiggle2-150x33.jpg 150w, https:\/\/davidlouiepiano.com\/wp-content\/uploads\/2019\/01\/Bachs-Squiggle2-300x66.jpg 300w, https:\/\/davidlouiepiano.com\/wp-content\/uploads\/2019\/01\/Bachs-Squiggle2-768x170.jpg 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">The &#8220;squiggle&#8221; above the words &#8220;Das Wohltemperierte Clavier&#8221; in Bach&#8217;s handwriting<\/figcaption><\/figure>\n\n\n\n<p class=\"has-drop-cap has-white-color has-text-color has-background\" style=\"background-color:#56686e\">The following tuning method produces a keyboard temperament based upon Bach&#8217;s &#8220;squiggle&#8221; on the autograph title page of the Well-Tempered Clavier, Book I.<br><br>The derivation of this tuning method from the &#8220;squiggle&#8221; is explained fully in the essay &#8220;<strong>Decoding Bach&#8217;s Temperament<\/strong>&#8221; by David Louie. Available as a <strong>free<\/strong> PDF download at the <strong><a href=\"https:\/\/davidlouiepiano.com\/index.php\/shop\/\"><mark style=\"background-color:rgba(0, 0, 0, 0.36)\" class=\"has-inline-color\">Shop<\/mark><\/a><\/strong><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center\">The Method<\/h4>\n\n\n\n<p class=\"has-drop-cap has-gray-background-color has-background\">The \u201c<strong>slightly-tempered<\/strong>\u201d and \u201c<strong>normally-tempered<\/strong>\u201d intervals, represented by corresponding loops in Bach&#8217;s squiggle, are <strong>always<\/strong> tempered as wide fourths and correspondingly narrow fifths. It is helpful to perform checks of the major thirds along the way, as described below.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>start from <strong>F <\/strong>(set pitch as necessary using a tuning fork or an electronic device)\u2026<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>tune <strong>B-flat<\/strong> as a pure interval (no beats) from F\u2026<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>tune <strong>E-flat\/D-sharp<\/strong> as a pure interval (no beats) from B-flat\u2026<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>tune <strong>A-flat\/G-sharp<\/strong> as a pure interval (no beats) from E-flat\/D-sharp\u2026<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>tune <strong>C-sharp<\/strong> as a \u201cslightly-tempered\u201d interval, approximately one-eighteenth Pythagorean comma, from A-flat\/G-sharp. Check the C-sharp to E-sharp (ie. F) third, which beats quickly, but tolerably\u2026<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>tune <strong>F-sharp<\/strong> as a \u201cslightly-tempered\u201d interval from C-sharp. Check the F-sharp to A-sharp (ie. B-flat) third, which beats quickly\u2026<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>tune <strong>B<\/strong> as a \u201cslightly-tempered\u201d interval from F-sharp. Check the B to D-sharp third, which beats fairly quickly\u2026<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>tune <strong>E<\/strong> as a \u201cnormally-tempered\u201d interval, approximately one-sixth Pythagorean comma, from B. Check the E to G-sharp third, which beats moderately quickly\u2026<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>tune <strong>A<\/strong> as a \u201cnormally-tempered\u201d interval from E. Compare the F to A third, the A to C-sharp third, and the C-sharp to E-sharp (ie. F) third. The F to A third beats moderately, the A to C-sharp third beats moderately quickly, and the C-sharp to E-sharp third beats quickly\u2026<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>tune <strong>D<\/strong> as a \u201cnormally-tempered\u201d interval from A. Compare the D to F-sharp third, the B-flat to D third, and the F-sharp to A-sharp (ie. B-flat) third. The D to F-sharp third beats moderately, the B-flat to D third beats moderately quickly, and the F-sharp to A-sharp third beats quickly\u2026<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>tune <strong>G<\/strong> as a \u201cnormally-tempered\u201d interval from D. Compare the G to B third, the E-flat to G third, and the B to D-sharp third. The G to B third beats moderately, the E-flat to G third and the B to D-sharp third both beat fairly quickly\u2026<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>tune <strong>C<\/strong> as a \u201cnormally-tempered\u201d interval from G. Compare the C to E third, the E to G-sharp third, and the A-flat to C third. The C to E third beats moderately, the E to G-sharp beats moderately quickly, and the A-flat to C beats quickly, but tolerably\u2026<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>to finish, check the interval from C to F. If everything has been tempered well, this residual interval should end up either pure, or tempered marginally.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-drop-cap has-gray-background-color has-background\">The setting of the temperament is now complete. The architecture of this tuning method allows the immutable pure fourths\/fifths to be tuned first, followed by those that are \u201cslightly-tempered\u201d and ending with those that are \u201cnormally-tempered.\u201d Control is maintained over the final result by checking and comparing the qualities of the major thirds while tempering the fourths and fifths.<\/p>\n\n\n\n<div class=\"wp-block-cover alignfull is-light\"><span aria-hidden=\"true\" class=\"wp-block-cover__background has-background-dim-20 has-background-dim\"><\/span><img loading=\"lazy\" decoding=\"async\" width=\"2268\" height=\"502\" class=\"wp-block-cover__image-background wp-image-557\" alt=\"\" src=\"https:\/\/davidlouiepiano.com\/wp-content\/uploads\/2019\/01\/Bachs-Squiggle2.jpg\" data-object-fit=\"cover\" srcset=\"https:\/\/davidlouiepiano.com\/wp-content\/uploads\/2019\/01\/Bachs-Squiggle2.jpg 2268w, https:\/\/davidlouiepiano.com\/wp-content\/uploads\/2019\/01\/Bachs-Squiggle2-150x33.jpg 150w, https:\/\/davidlouiepiano.com\/wp-content\/uploads\/2019\/01\/Bachs-Squiggle2-300x66.jpg 300w, https:\/\/davidlouiepiano.com\/wp-content\/uploads\/2019\/01\/Bachs-Squiggle2-768x170.jpg 768w, https:\/\/davidlouiepiano.com\/wp-content\/uploads\/2019\/01\/Bachs-Squiggle2-1024x227.jpg 1024w\" sizes=\"auto, (max-width: 2268px) 100vw, 2268px\" \/><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<h3 class=\"wp-block-heading has-text-align-center has-white-color has-text-color\">Essay: Decoding Bach&#8217;s Temperament<\/h3>\n<\/div><\/div>\n\n\n\n<figure class=\"wp-block-image alignfull\"><img loading=\"lazy\" decoding=\"async\" width=\"638\" height=\"825\" src=\"https:\/\/davidlouiepiano.com\/wp-content\/uploads\/2019\/01\/decosamp1.png\" alt=\"\" class=\"wp-image-1139\" srcset=\"https:\/\/davidlouiepiano.com\/wp-content\/uploads\/2019\/01\/decosamp1.png 638w, https:\/\/davidlouiepiano.com\/wp-content\/uploads\/2019\/01\/decosamp1-232x300.png 232w\" sizes=\"auto, (max-width: 638px) 100vw, 638px\" \/><\/figure>\n\n\n\n<p class=\"has-text-align-center has-white-color has-text-color has-background\" style=\"background-color:#56686e\">The essay &#8220;<strong>Decoding Bach&#8217;s Temperament<\/strong>&#8221; by David Louie is available as a <strong>free<\/strong> PDF download at the <strong><a href=\"https:\/\/davidlouiepiano.com\/index.php\/shop\/\"><mark style=\"background-color:rgba(0, 0, 0, 0.36)\" class=\"has-inline-color\">Shop<\/mark><\/a><\/strong><\/p>\n\n\n\n<p class=\"has-gray-background-color has-background\">For useful information on various keyboard temperaments, and comparisons between Bach-Louie and other interpretations of Bach&#8217;s &#8220;squiggle,&#8221; visit Carey Beebe&#8217;s <a aria-label=\"website (opens in a new tab)\" href=\"http:\/\/hpschd.nu\/tech\/tmp\/louie.html\" target=\"_blank\" rel=\"noreferrer noopener\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0.36)\" class=\"has-inline-color\">CBH<\/mark><\/strong><\/a> website.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bach-Louie Temperament &#8220;Decoding Bach&#8217;s Temperament&#8221; The following tuning method produces a keyboard temperament based upon &hellip; <span class=\"more-button\"><a href=\"https:\/\/davidlouiepiano.com\/index.php\/bach-louie-temperament\/\" class=\"more-link\">Continue Reading<span class=\"screen-reader-text\">Bach&#8217;s Squiggle<\/span><\/a><\/span><\/p>\n","protected":false},"author":1,"featured_media":1604,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-97","page","type-page","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/davidlouiepiano.com\/index.php\/wp-json\/wp\/v2\/pages\/97","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/davidlouiepiano.com\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/davidlouiepiano.com\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/davidlouiepiano.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/davidlouiepiano.com\/index.php\/wp-json\/wp\/v2\/comments?post=97"}],"version-history":[{"count":111,"href":"https:\/\/davidlouiepiano.com\/index.php\/wp-json\/wp\/v2\/pages\/97\/revisions"}],"predecessor-version":[{"id":3948,"href":"https:\/\/davidlouiepiano.com\/index.php\/wp-json\/wp\/v2\/pages\/97\/revisions\/3948"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/davidlouiepiano.com\/index.php\/wp-json\/wp\/v2\/media\/1604"}],"wp:attachment":[{"href":"https:\/\/davidlouiepiano.com\/index.php\/wp-json\/wp\/v2\/media?parent=97"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}