Mathematical analysis of music

1. Mathematical analysis of music Mitsukifujii

2. Abstract Ihave heard that music has a part of the field of math once. However, math and music’s basic theory is the same around the world, music has a differences depending on country and culture. So I decided to study about the relationship between math and music!

3. Purpose and plan I compared Japanese Children’s song with Mother Goose because I want to know that music has differentia by country and culture.

4. RESEARCH METHOD Japanese children’s song Mother goose

5. USED TUNES JAPANESE CHILDREN’A SONG MOTHER GOOSE ・SAKURA SAKURA ・CHATSUMI ・URASHIMATARO ・YUKI ・FUJINOYAMA ・TORYANNSE ・WAREHAUMINOKO • OLD MACDONALD HAD A FARM • EENCYWEENCY SPIDER • OLD MOTHER HUBBARD • THE GRAND OLD DUKE OF YORK • IN A CABIN IN THE WOOD • POP! GOES THE WEASEL • POLLY PUT THE KETTLE ON • THE THREE LITTLE KITTENS

6. ＊how to visualize＊ (C=do, D=re, E=mi, F=fa, G=so, A=la, B=ti) ① ③ ② ① A→B ② C→A ③ A→A

7. EX)SAKURA SAKURA

8. A E G C B D F A B C -2 degree 3 degree 4 degree -3 degree

9. CONSEQUENCE AND CONSIDERATION ⑴VISUALIZE(NUMBER IS PERCENTAGE%) JAPANESE CHILDREN’S SONGS MOTHER GOOSE If X=1, C in Mother Goose also continue but E and D in Japanese Children’s Songs continue.

10. Actually, X gather at 1 and ±2. Especially, Japanese Children’s Songs’ X often ±2. Gradual rise and fall of pitch is more than steep one. Mother Goose’s X is often 1. The same sounds often repoat themselves.

11. ⑵THE SUM OF SOUNDS LENGTH ※PERCENTAGE OF THE SOUNDS OCCUPY LENGTH IN MUSIC. C,E,G are often used in Japanese Children’s Songs. They are cold chord of the 1 degree of the C major, but Mother Goose especially has C,E,D. Only the main chord of the 5 degree have D. The chord of the 5 degree is G,B,D. However, Mother Goose has the little number of G,B. Mother Goose has sense of fun and joy!

12. Table about notes Both of them have many quarter notes and eighth notes. Two kinds of music are made up of these two notes. Both of them have more long notes than short ones. Especially, Mother Goose has more long notes. The sum of these two notes ins one! Mother Goose is rhythmical. Japanese Children’s Songs have the same number of eighth notes have dot and six teen notes because set of the two notes used in Japanese Children’s Songs.

13. Problem of in the future ・Ototama http://ototama.com/・Susumu Sakurai・Hiroki Sakaguchi 『Crossing of Music and Math』 Ootsuki ・『Let’s sing！Mother Goose』Aruku

14. Thank you for listening!