Golden Music

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Information about Golden Music
Education

Published on August 1, 2009

Author: rubiz

Source: slideshare.net

Description

This is a research done by a group of high school students concerning Golden Ratio found in different categories of Music. Please refer to the 'notes' for our script. If you want to download the presentation, you are welcome to contact me: krubiz[at]gmail[dot]com. Do comment on our work. Thank you!

 

 

 

 

 

 

 

 

 

 

 

 

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,….

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,…. 0+1 = 1 1+1 = 2 1+2 = 3 2+3 = 5 3+5 = 8 5+8 = 13 …

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,…. 0+1 = 1 1+1 = 2 1+2 = 3 2+3 = 5 3+5 = 8 5+8 = 13 … 1÷1 = 1 2÷1 = 2 3÷2 = 1.5 5÷3 = 1.667… … 89÷55 = 1.618… …

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,…. 0+1 = 1 1+1 = 2 1+2 = 3 2+3 = 5 3+5 = 8 5+8 = 13 …

 

C A B

C A B 1-x x 1

C A B 1-x x 1 BC AB = AB AC

C A B 1-x x 1 BC AB = AB AC 1 x = x 1-x

C A B 1-x x 1 BC AB = AB AC 1 x = x 1-x x 2 = 1-x

C A B 1-x x 1 BC AB = AB AC 1 x = x 1-x x 2 = 1-x x 2 + x - 1 = 0

C A B 1-x x 1 x 2 + x - 1 = 0

C A B 1-x x 1 x 2 + x - 1 = 0 Solve by using quadratic formula a = 1, b = 1, and c = -1

C A B 1-x x 1 x 2 + x - 1 = 0 Solve by using quadratic formula a = 1, b = 1, and c = -1 -b ± √ (b 2 – 4ac) 2a x =

C A B 1-x x 1 x 2 + x - 1 = 0 Solve by using quadratic formula a = 1, b = 1, and c = -1 -b ± √ (b 2 – 4ac) 2a x = -(1) ± √ ((1) 2 – 4(1)(-1)) 2(1) =

C A B 1-x x 1 x = -(1) ± √ ((1) 2 – 4(1)(-1)) 2(1)

C A B 1-x x 1 x = -(1) ± √ ((1) 2 – 4(1)(-1)) 2(1) -1 + √5 2 = 0.6180339887 x =

C A B 1-x x 1 x = -(1) ± √ ((1) 2 – 4(1)(-1)) 2(1) -1 + √5 2 = 0.6180339887 Or x = -1 - √5 2 = -1.6180339887 x =

C A B 1-x x 1 x = -(1) ± √ ((1) 2 – 4(1)(-1)) 2(1) -1 + √5 2 = 0.6180339887 Or x = -1 - √5 2 = -1.6180339887 (rejected) x =

C A B 1-x x 1 -1 + √5 2 = 0.6180339887 x =

C A B 1-x x 1 -1 + √5 2 = 0.6180339887 x = ‘’’’’’’’’’’ 1’’’’’’’’’’’ 0.6180339887 = 1.618033989

C A B 1-x x 1 -1 + √5 2 = 0.6180339887 x = ‘’’’’’’’’’’ 1’’’’’’’’’’’ 0.6180339887 = 1.618033989 Φ =  1.61803398874989484820458683436 …

C A B 1 : 1.618…

 

 

A B C D E F G H I

A B C D E F G H I

A B C D E F G H I 1.618 1

“ Mona Lisa”

“ Mona Lisa”

Parthenon

Parthenon

 

 

 

 

 

 

 

 

 

 

 

1 2 3 It rocks!!

 

 

 

 

 

 

 

 

 

 

 

 

 

 

13 notes

8 white keys

5 black keys

3

2

2 3 5 8 13?

2 3 5 8 13?

 

 

 

 

 

 

 

 

Bela Bartok (1881-1945) Music for Strings , Percussion and Celesta

Bela Bartok (1881-1945) Music for Strings , Percussion and Celesta Obey to Φ

Obey to Φ

Bela Bartok (1881-1945) Music for Strings , Percussion and Celesta Xylophone ( 木琴 ) progression occurs at intervals 1:2:3:5:8:5:3:2:1

Xylophone ( 木琴 ) progression occurs at intervals 1:2:3:5:8:5:3:2:1

Bela Bartok (1881-1945) Music for Strings , Percussion and Celesta Divided 89 bars of the movement in 2 part

Divided 89 bars of the movement in 2 part

Bela Bartok (1881-1945) Music for Strings , Percussion and Celesta

Bela Bartok (1881-1945) Sonata for Two Pianos and Percussion

 

Did Mozart use Φ in his piano sonatas?

Sonata No. 1 in C Major

Sonata No. 1 in C Major 2 distinct sections

Sonata No. 1 in C Major Exposition (E)

Sonata No. 1 in C Major Development & Recapitulation (DR)

Sonata No. 1 in C Major DR: 62 bars

Sonata No. 1 in C Major E: 38 bars

Sonata No. 1 in C Major 62÷38 = 1.63... ≈ Φ

Did Mozart use Φ in his piano sonatas?

Soundtracks of video games

In conclude… 1.61803398874989…

 

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