{"id":566,"date":"2014-06-04T14:27:05","date_gmt":"2014-06-04T13:27:05","guid":{"rendered":"http:\/\/www.jasonalder.com\/blog\/?p=566"},"modified":"2019-01-24T03:27:30","modified_gmt":"2019-01-24T02:27:30","slug":"the-sixth-note-dealing-with-irrational-time-signatures","status":"publish","type":"post","link":"https:\/\/www.jasonalder.com\/blog\/2014\/06\/04\/the-sixth-note-dealing-with-irrational-time-signatures\/","title":{"rendered":"The sixth-note: Dealing with irrational time signatures"},"content":{"rendered":"

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Recently a friend posted a photo on Facebook of a bar of music she encountered and wasn’t sure how to count it. It was a bar of 4\/6, and later in the discussion she posted another one of 5\/6. This thread took a lot of directions, such as why the composer would write this, is there a better way to write it, what performance implications and psychological effects notation has, and how to actually count the bars in question. While all points are very valid and interesting discussions, I want to focus on the last one. How does one actually count a 4\/6 or 5\/6 bar? The problem is that in Western music, we’re subject to thinking of everything in duples of four- 4\/4, 2\/2, 6\/8- but never (at least not until the later 20th century) in “irrational” time signatures. So this post will discuss how to deal with this.<\/p>\n

Back to basics\u2026<\/h2>\n

What does a 4\/4 bar mean? Simply put, it means the quarter note gets the pulse (the bottom number), and there’s four of them in the bar (the top number), just as in a 3\/4 bar the quarter note is still the pulse, but we only have three in the bar. But why is a quarter note called such? What is it a quarter of? And likewise for a half note, eighth note, sixteenth note? What are all of these subdivisions fractions of? A whole note, naturally. This is our reference for time signatures in Western music. We divide the whole note into fractions, and then determine how many of these subdivisions are in each bar.<\/p>\n

So what does having a 6 in the bottom mean? Logically, the whole note is subdivided into 6 parts. To determine what the length of a sixth note is, the value of the whole note remains constant, and therefore 4\/4 = 6\/6. We have to play 6 sixth notes in the same space of time that we would play 4 quarter notes. This creates a 6:4 ratio, or 2 x 3:2. So a bar of 4\/6 would be 3 notes in the space of 2 quarter notes (quarter-note triplets), plus one more note of the triplet, and a bar of 5\/6 would be 3:2 plus 2 more of the triplet.<\/p>\n

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4\/4 = 6\/6. Top line = quarter notes in 4\/4. Middle line = quarter-notes subdivided into sextuplets in 4\/4, grouped in 4s. Bottom line = the beats of a 6\/6 bar fall at the beginning of each grouping of 4 of the sextuplets.<\/figcaption><\/figure>\n

In theory this seems fairly straight forward, but the practical application is problematic. Feeling three against two isn’t very difficult, as this is something Western musicians more regularly do, but it’s the extra notes that cause the problems.<\/p>\n

The way to approach the correct timing is to subdivide the quarter-note of 4\/4 into sextuplets and accent groups of four. This creates six accents within the bar, thus giving a bar of 6\/6. So for a bar of 4\/6, you should take the first four of these, and where the fifth would land is the downbeat of the following measure.<\/p>\n

In this recording I demonstrate how this works. First I begin with sextuplets of a 4\/4 bar- phrased as TA-ka-di-mi-ta-ka<\/em>. Then keeping the same speed of the sextuplet, I phrase it in groups of four as TA-ka-di-mi<\/em>, keeping the quarter-note pulse of a 4\/4 bar for reference. There are six of these TA-ka-di-mi<\/em>‘s per four clicks, so where each of the TA<\/em>‘s fall are the six beats of a 6\/6 bar. I then demonstrate a 4\/6 and 5\/6 bar, alternating between with- and without the subdivisions.<\/p>\n

\nhttps:\/\/www.jasonalder.com\/blog\/wp-content\/uploads\/2014\/05\/tisra2j43.mp3<\/a><\/audio>
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In case it helps to visualize how this relationship works, I’ve made this video to accompany it:<\/p>\n