{"id":1818,"date":"2016-04-28T05:58:17","date_gmt":"2016-04-28T10:58:17","guid":{"rendered":"http:\/\/rosewhitemusic.com\/piano\/?p=1818"},"modified":"2016-04-28T20:42:50","modified_gmt":"2016-04-29T01:42:50","slug":"triadic-memory-4-rhythms-structures","status":"publish","type":"post","link":"https:\/\/rosewhitemusic.com\/piano\/2016\/04\/28\/triadic-memory-4-rhythms-structures\/","title":{"rendered":"Triadic memory 4: Rhythms and structures"},"content":{"rendered":"<p><i><span style=\"font-weight: 400;\">Triadic memories<\/span><\/i><span style=\"font-weight: 400;\">, like all late Feldman, is a series of repeated patterns, musical images that \u00a0are extended in time by repetition. Repetition also functions over a larger scale, working with memory: \u201cOh yes, here that comes again.\u201d In some pieces these repetitions are of larger chunks of music, with a system, set of systems, or even pages of music reappearing, often with permutations.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">I\u2019ve always thought of these larger-scale repetitions in terms of the whole pattern: pitch and rhythm together. Playing through <\/span><i><span style=\"font-weight: 400;\">Triadic memories<\/span><\/i><span style=\"font-weight: 400;\">, I\u2019ve become aware of them rhythmically, repeating even as the pitches are moved around. Here\u2019s an example of two systems of music (nine measures each), that establish a pattern that will reappear over the middle third of the piece.<\/span><\/p>\n<figure id=\"attachment_1819\" aria-describedby=\"caption-attachment-1819\" style=\"width: 750px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1819\" src=\"http:\/\/rosewhitemusic.com\/piano\/wp-content\/uploads\/2016\/04\/TM-Ex1.png\" alt=\"Example 1: meas. 352\u2013369\" width=\"750\" height=\"347\" srcset=\"https:\/\/rosewhitemusic.com\/piano\/wp-content\/uploads\/2016\/04\/TM-Ex1.png 750w, https:\/\/rosewhitemusic.com\/piano\/wp-content\/uploads\/2016\/04\/TM-Ex1-300x139.png 300w\" sizes=\"auto, (max-width: 750px) 100vw, 750px\" \/><figcaption id=\"caption-attachment-1819\" class=\"wp-caption-text\">Example 1: meas. 352\u2013369<\/figcaption><\/figure>\n<audio class=\"wp-audio-shortcode\" id=\"audio-1818-1\" preload=\"none\" style=\"width: 100%;\" controls=\"controls\"><source type=\"audio\/mpeg\" src=\"http:\/\/rosewhitemusic.com\/piano_media\/TM4-Ex1.mp3?_=1\" \/><a href=\"http:\/\/rosewhitemusic.com\/piano_media\/TM4-Ex1.mp3\">http:\/\/rosewhitemusic.com\/piano_media\/TM4-Ex1.mp3<\/a><\/audio>\n<p>&nbsp;<\/p>\n<p><span style=\"font-weight: 400;\">Taken at the measure-by-measure level, there are only a handful of patterns used here: the same half-a-dozen permutations of dotted eighths, eighths, and sixteenths (either regular or within quadruplets) that have dominated the entire piece so far. In the beginning, the arrangement of these, together with the unusual placement of the repeat signs, creates a sort of hemiola effect: the first fifteen attacks occur at regular dotted-eighth quadruplet intervals.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This somewhat complicated way to notate straight dotted eighth notes, while theoretically not having any audible consequences, nevertheless has affects me as a pianist. I\u2019m mentally carrying along the patterns defined by the bar lines, even as the constant dotted-eighth-note rhythm is overlapping the bars. Those rests at the starts of measures 353 and 354 suggest a kind of lift, which weakens the following attacks and makes for subtle differences between them and the attacks that occur on a downbeat.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The placement of rests at what would otherwise be the strong part of a bar is a phenomenon that occurs extensively in <\/span><i><span style=\"font-weight: 400;\">Triadic memories<\/span><\/i><span style=\"font-weight: 400;\"> and in Feldman\u2019s music in general. In the last part of the example above, when the rhythm turns to regular dotted eighths (not quadruplet ones), The rhythm extends to an entire measure between attacks in measures 365\u201368, but with the attack coming on the second half of the bar. Besides softening the attack, it also creates the lovely rhythmic effect at the repeat sign of shifting unexpectedly back to attacks every half-measure, thus concealing the repeat.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Elsewhere in the piece this principle of weakening attacks by placing them in weak rhythmic locations occurs at the scale of the entire measure. How can I explain the psychological difference between this, a two-bar phrase consisting of a pattern and a measure of rest:<\/span><\/p>\n<figure id=\"attachment_1820\" aria-describedby=\"caption-attachment-1820\" style=\"width: 360px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1820\" src=\"http:\/\/rosewhitemusic.com\/piano\/wp-content\/uploads\/2016\/04\/TM-Ex2a.png\" alt=\"Example 2a: meas. 271\u201372\" width=\"360\" height=\"278\" srcset=\"https:\/\/rosewhitemusic.com\/piano\/wp-content\/uploads\/2016\/04\/TM-Ex2a.png 360w, https:\/\/rosewhitemusic.com\/piano\/wp-content\/uploads\/2016\/04\/TM-Ex2a-300x232.png 300w\" sizes=\"auto, (max-width: 360px) 100vw, 360px\" \/><figcaption id=\"caption-attachment-1820\" class=\"wp-caption-text\">Example 2a: meas. 271\u201372<\/figcaption><\/figure>\n<p><span style=\"font-weight: 400;\">And this, a two-bar phrase consisting of a measure of rest and the same pattern:<\/span><\/p>\n<figure id=\"attachment_1821\" aria-describedby=\"caption-attachment-1821\" style=\"width: 360px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1821\" src=\"http:\/\/rosewhitemusic.com\/piano\/wp-content\/uploads\/2016\/04\/TM-Ex2b.png\" alt=\"Example 2b: meas. 289\u2013290\" width=\"360\" height=\"281\" srcset=\"https:\/\/rosewhitemusic.com\/piano\/wp-content\/uploads\/2016\/04\/TM-Ex2b.png 360w, https:\/\/rosewhitemusic.com\/piano\/wp-content\/uploads\/2016\/04\/TM-Ex2b-300x234.png 300w\" sizes=\"auto, (max-width: 360px) 100vw, 360px\" \/><figcaption id=\"caption-attachment-1821\" class=\"wp-caption-text\">Example 2b: meas. 289\u2013290<\/figcaption><\/figure>\n<p><span style=\"font-weight: 400;\">I can\u2019t explain it, really, but I do know that I <\/span><i><span style=\"font-weight: 400;\">think<\/span><\/i><span style=\"font-weight: 400;\"> the pattern differently when I put the measure of rest first. This is the sort of thing that Feldman was referring to, I think, when he wrote about \u201cnotational images\u201d in his work:<\/span><\/p>\n<blockquote><p><span style=\"font-weight: 400;\">Though these patterns exist in rhythmic shapes articulated by instrumental sounds, they are also in part <\/span><i><span style=\"font-weight: 400;\">notational images<\/span><\/i><span style=\"font-weight: 400;\"> that do not make a direct impact on the ear as we listen. A tumbling of sorts happens in midair between their translation from the page and their execution. (\u201cCrippled symmetry\u201d, 1981, reprinted in <\/span><i><span style=\"font-weight: 400;\">Give my regards to Eighth Street<\/span><\/i><span style=\"font-weight: 400;\">, p. 143)<\/span><\/p><\/blockquote>\n<p><span style=\"font-weight: 400;\">I feel this \u201ctumbling\u201d as the playing out of a particular kind of engagement between Feldman as a composer and me as a performer. The energy of this engagement is the life-breath of playing <\/span><i><span style=\"font-weight: 400;\">Triadic memories<\/span><\/i><span style=\"font-weight: 400;\">.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">There is a larger structure of rhythmic patterns here as well. Each of the two systems is a self-contained unit of nine measures (this is an example where <a href=\"http:\/\/rosewhitemusic.com\/piano\/2015\/09\/26\/hand-made-music-feldmans-scores\/\">the manuscript score is essential to understanding <\/a><\/span><a href=\"http:\/\/rosewhitemusic.com\/piano\/2015\/09\/26\/hand-made-music-feldmans-scores\/\"><i><span style=\"font-weight: 400;\">Triadic memories<\/span><\/i><\/a><span style=\"font-weight: 400;\">, like all of Feldman\u2019s late works). Immediately following this, at the top of the next page, the rhythms of these two systems repeat exactly, even though the pitches are slightly different. This second time around, Feldman interpolated a system that forms a third rhythmic block in between the two we\u2019ve already heard:<\/span><\/p>\n<figure id=\"attachment_1822\" aria-describedby=\"caption-attachment-1822\" style=\"width: 750px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1822\" src=\"http:\/\/rosewhitemusic.com\/piano\/wp-content\/uploads\/2016\/04\/TM-Ex3.png\" alt=\"Example 3: meas. 370\u2013396\" width=\"750\" height=\"540\" srcset=\"https:\/\/rosewhitemusic.com\/piano\/wp-content\/uploads\/2016\/04\/TM-Ex3.png 750w, https:\/\/rosewhitemusic.com\/piano\/wp-content\/uploads\/2016\/04\/TM-Ex3-300x216.png 300w\" sizes=\"auto, (max-width: 750px) 100vw, 750px\" \/><figcaption id=\"caption-attachment-1822\" class=\"wp-caption-text\">Example 3: meas. 370\u2013396<\/figcaption><\/figure>\n<audio class=\"wp-audio-shortcode\" id=\"audio-1818-2\" preload=\"none\" style=\"width: 100%;\" controls=\"controls\"><source type=\"audio\/mpeg\" src=\"http:\/\/rosewhitemusic.com\/piano_media\/TM4-Ex3.mp3?_=2\" \/><a href=\"http:\/\/rosewhitemusic.com\/piano_media\/TM4-Ex3.mp3\">http:\/\/rosewhitemusic.com\/piano_media\/TM4-Ex3.mp3<\/a><\/audio>\n<p>&nbsp;<\/p>\n<p><span style=\"font-weight: 400;\">As an additional modification, the repeat signs are omitted from the first system.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Two pages later, after a few other images have arisen and disbanded, the three systems of this passage resurface. Feldman rearranged the blocks this time: he swapped the first two systems (putting the repeats back into the first one) and reversed the third one:<\/span><\/p>\n<figure id=\"attachment_1823\" aria-describedby=\"caption-attachment-1823\" style=\"width: 750px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1823\" src=\"http:\/\/rosewhitemusic.com\/piano\/wp-content\/uploads\/2016\/04\/TM-Ex4.png\" alt=\"Example 4: meas. 460\u2013486\" width=\"750\" height=\"531\" srcset=\"https:\/\/rosewhitemusic.com\/piano\/wp-content\/uploads\/2016\/04\/TM-Ex4.png 750w, https:\/\/rosewhitemusic.com\/piano\/wp-content\/uploads\/2016\/04\/TM-Ex4-300x212.png 300w\" sizes=\"auto, (max-width: 750px) 100vw, 750px\" \/><figcaption id=\"caption-attachment-1823\" class=\"wp-caption-text\">Example 4: meas. 460\u2013486<\/figcaption><\/figure>\n<audio class=\"wp-audio-shortcode\" id=\"audio-1818-3\" preload=\"none\" style=\"width: 100%;\" controls=\"controls\"><source type=\"audio\/mpeg\" src=\"http:\/\/rosewhitemusic.com\/piano_media\/TM4-Ex4.mp3?_=3\" \/><a href=\"http:\/\/rosewhitemusic.com\/piano_media\/TM4-Ex4.mp3\">http:\/\/rosewhitemusic.com\/piano_media\/TM4-Ex4.mp3<\/a><\/audio>\n<p>&nbsp;<\/p>\n<p><span style=\"font-weight: 400;\">Here the pitches do not change between the two appearances, but the rearrangement of the blocks confuses my memory of how this all went together before.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The musical patterns of this passage have other descendants that appear in these same pages of <\/span><i><span style=\"font-weight: 400;\">Triadic memories<\/span><\/i><span style=\"font-weight: 400;\">. Some of these use the same pitches in similar, but slightly different patterns. Others maintain only a vague resemblance to the motion and rhythms of measures 352\u2013369. The last appearance of a part of this specific pattern occurs a good deal later in the piece, when that reversed variant of measures 388\u2013396 shows up again, this time embellished by high grace notes:<\/span><\/p>\n<figure id=\"attachment_1824\" aria-describedby=\"caption-attachment-1824\" style=\"width: 750px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1824\" src=\"http:\/\/rosewhitemusic.com\/piano\/wp-content\/uploads\/2016\/04\/TM-Ex5.png\" alt=\"Example 5: meas. 649\u2013657\" width=\"750\" height=\"151\" srcset=\"https:\/\/rosewhitemusic.com\/piano\/wp-content\/uploads\/2016\/04\/TM-Ex5.png 750w, https:\/\/rosewhitemusic.com\/piano\/wp-content\/uploads\/2016\/04\/TM-Ex5-300x60.png 300w\" sizes=\"auto, (max-width: 750px) 100vw, 750px\" \/><figcaption id=\"caption-attachment-1824\" class=\"wp-caption-text\">Example 5: meas. 649\u2013657<\/figcaption><\/figure>\n<audio class=\"wp-audio-shortcode\" id=\"audio-1818-4\" preload=\"none\" style=\"width: 100%;\" controls=\"controls\"><source type=\"audio\/mpeg\" src=\"http:\/\/rosewhitemusic.com\/piano_media\/TM4-Ex5.mp3?_=4\" \/><a href=\"http:\/\/rosewhitemusic.com\/piano_media\/TM4-Ex5.mp3\">http:\/\/rosewhitemusic.com\/piano_media\/TM4-Ex5.mp3<\/a><\/audio>\n<p>&nbsp;<\/p>\n<p><span style=\"font-weight: 400;\">The grace-notes and dotted-eighth rhythm spin off into a new pattern after this, ultimately bringing in <a href=\"http:\/\/rosewhitemusic.com\/piano\/2016\/04\/18\/triadic-memory-figure-memory\/\">the grace-note chord image whose history I have discussed elsewhere<\/a>.<\/span><\/p>\n<p><strong>Note:\u00a0<\/strong>Audio examples are taken from <a href=\"https:\/\/www.discogs.com\/Morton-Feldman-Aki-Takahashi-Triadic-Memories\/release\/1450387\" target=\"_blank\">Aki Takahashi&#8217;s recording of\u00a0<\/a><a href=\"https:\/\/www.discogs.com\/Morton-Feldman-Aki-Takahashi-Triadic-Memories\/release\/1450387\" target=\"_blank\"><em>Triadic memories<\/em><\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Triadic memories, like all late Feldman, is a series of repeated patterns, musical images that  are extended in time by repetition. In some pieces these repetitions are of larger chunks of music, with a system, set of systems, or even pages of music reappearing, often with permutations. I\u2019ve always thought of these larger-scale repetitions in terms of the whole pattern: pitch and rhythm together. Playing through Triadic memories, I\u2019ve become aware of them rhythmically, repeating even as the pitches are moved around. <\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[23],"tags":[113],"class_list":["post-1818","post","type-post","status-publish","format-standard","hentry","category-feldman2","tag-triadic-memories"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - 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