In addition, one of the main themes contained within the book is where the author explores the mathematical properties associated with good rhythms. He looks at the mathematical property of a sequence and highlights the rhythms that use said property.Furthermore, he takes time to discover the properties associated only with the rhythm he's looking at.
Godfried begins by defining rhythm, looking at what a steady beat is and explores timelines and meter before moving on to specific rhythms and the distance contained within a rhythm. He also looks at classifying rhythms, binary, ternary rhythms, syncopated rhythms, plus topics such as Euclidean rhythms, rhythms o stars, crystallography, radio astronomy and so many other topics including regular and irregular rhythms.
In addition, he provides a notation for the different rhythms he speaks about in the various chapters. In chapter 7 where he discusses six distinguished rhythm timelines, he focuses on 5 onsets (emphasized beat) in a span of 16 pulses or beats from around the world. The Bossa-nova has onsets on 0,3, 6, 10, and 13 while the Rumba is 0, 3, 7, 10, and 12. The two are quite similar with two onsets that are different and three the same.
In chapter 8, the distance geometry of rhythm, he takes the same six rhythms from chapter 7 and creates geometric visualizations of them. Instead of using a flat bar, he creates circles with smaller points labeled 0 to 15 and he colors in the points that match up with the ones in the earlier rhythms before connecting these points together with straight lines to create pentagons. Some of these pentagons have mirror symmetry or are palindromes. Furthermore, many rhythms contain isosceles triangles within the pentagons but not all.
He also creates both full interval and adjacent interval content histograms tot show how these 6 timelines appear in this visualization. Then in chapter 9, he goes through a classification for these rhythms from the earlier two chapters. He created a flow chart beginning with the simple question of if there is a 90 degree angle? From there he moves to the number of isosceles triangles contained in the rhythm and finally asks about an axis of symmetry. In addition, he created a decision tree to classify the same rhythms based on local shape features of the interval histogram or the inter-onset interval distances.
Godfried relies on the circular visualization to show the rhythms of other musical types. As he goes through these, he also include the mathematics to explain things like balanced vs uneven rhythm. It's a fun book but it does require one pay attention to the material as one works slowly through it. The material in here would make a fun lesson here and there to show students who love music the connection between what they play and the mathematics. Let me know what you think I'd love to hear. Have a great day.
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