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# Mathematics and Music Connected

This is a prezi explaining how music and math two subjects that have existed for quite a long time relate to each other.

by

Tweet## Alena Stifel

on 13 March 2013#### Transcript of Mathematics and Music Connected

Mathematics & Music Connected By: Alena Stifel Fibonacci

Sequence What is the

Fibonacci Sequence? -"a numerical progression in which each term is equal to the sum of the two proceeding terms (Brown 66)." Music

and

Learning Works Cited Beer, Michael. How do Mathematics and Music Relate to Each Other?. East Coast Collage of

English, Brisbane, 07 1998. Web. 5 Dec 2012. <http://www.pages.drexel.edu/~jjn27/mathandmusic.pdf>.

Brown, Dan. The DaVinchi Code. New York: Random House, Inc., 2003. 66. Print.

Cromie, William. "How Your Brain Listens to Music."Harvard University Gazette. (1998): n. page. Web. 10 Sep. 2012. <http://news.harvard.edu/gazette/1997/11.13/HowYourBrainLis.html>.

Guralnik, David. "mathematics, music ." Webster's New World Dictionary of the American Language. New York: 1984.

Heimiller, Joseph. "Where Math meets Music." Aspire Software. Joseph Heimiller, n.d. Web. 13 Jan 2013.

<http://www.musicmasterworks.com/WhereMathMeetsMusic.html>.

Hoffer, Charles R. The Understanding of Music. 1st. Belmont: Wadsworth Publishing Company, Inc., 1967. 35, 39-40, 456,

458. Print.

Keller, Charles. "The Golden Mean." Math Department, Mission College, Santa Clara, California. N.p., 21 Mar 2001. Web. 10

Oct 2012. <http://www.missioncollege.org/depts/math/keller/golden.htm>.

Meisner, Gary. "Music and the Fibonacci Series and Phi." Phi 1.618 The Golden Number. N.p., 04 May 2012. Web. 10 Oct

2012. <http://www.goldennumber.net/music/>.

Mickela, Tony. "Does Music have an Impact on Student Development." Music Educators Online. Children's Music Workshop,

2012. Web. 10 Sep 2012. <http://www.childrensmusicworkshop.com/advocacy/studentdevelopment.html>.

M.U.S.I.C. Foundation, The. "Benefits of Music Education to Math, Reading, Language, and Spatial Intelligance."Support

TMF. The M.U.S.I.C. Foundation, Music Unlocks Success In Children, 2001. Web. 10 Oct 2012.

<http://supporttmf.org/documents/BenefitsofMusic-Web.pdf>.

Rosenthal, Jeffery. "The magical mathematics of music." plus magazine. 35 (May 1, 2005): n. page. Web. 10 Oct. 2012.

<http://plus.maths.org/content/magical-mathematics-music>.

Surmani, Andrew, Karen Farnum Surmani, and Morton Manus. Alfred's Complete Essentials of Music Theory. 1, 2, 3. Van

Nuys: Alfred Publishing Co., Inc., 1998. 10, 16, 17. Print. The

Math

of

Note

Frequency Music Symbols

and Math Importance to Music Golden Ratio Golden Ratio

In Math Where it is found in Music? Thesis Song Composition aids in learning fractional math while musical scales can be better understood by mathematically applying frequency as well as music playing an important part in the educational development of a student in mathematics. "A study of 237 second graders who used piano keyboard training and newly designed math software to demonstrate improvement in math skills scored 27% higher on proportional math and fraction tests then children who only used the math software ( The Music Foundation)." Using music to learn math The Mind "...music involves the use of cognitive, perceptual and motor skills..."

(Cromie) "In 2001, students who participated in music education scored 41 points higher on the Math portion of the SATs then those without music participation (The Music Foundation)" Later in Life According to Tony Mickela, "instrumental practice enhances coordination, concentration and memory while also refining the development of the brain and the entire neurological system." What does music do? Time Signature Time signature: -Two numbers -One over the other

-NOT a fraction Time Signatures vs. Fractions Music Notes -Eighth note: 1/2 beat

-Quarter note: 1 beat

-Half note: 2 beats

-Whole note: 4 beats Scales Math "Mathematics is the group of sciences dealing with quantities, magnitudes, and forms, and their relationship and attributes by the use of numbers and symbols (Guralnik)." vs. "Music is the art and science of combining vocal or instrumental sounds or tones in varying melody, harmony, rhythm, and timbre so as to form structurally complete and emotionally expressive compositions (Guralnick)" Music The Notes & Octaves Middle C - 261Hz C-522Hz C- 130Hz -A musical interval is the difference in pitch between two tones and is then named by the number of tones it includes counting the lower and higher tones (Hoffer). -Octaves frequency ratio 1:2 Intervals -Thirds, Fourths, Fifths -The frequencies of notes in a perfect fifth have a ration of three to two 261Hz 392Hz Consonance Dissonance -Two notes that sound pleasing to the ear it is considered consonant (Hoffar 39-40) The frequency of the notes can also be found mathematically by the equation: Hertz = 6.875 x 2^(3+MIDI_Pitch)/12 (Heimiller). -"Disagreeable or harsh sounds are considered dissonant." (Hoffer) Ex: Middle C and B natural,

C and F sharp "There are thirteen notes in a span of any note through its octave and the scale is composed of eight notes of which the fifth and third notes create the basic foundation of chords and based on whole tone which is two steps from the root tone which is the first note in the scale." (Meisner) 13 C and F# Consonant vs Dissonant B flat scale 8/13=0.615

21/34=0.6176

89/144=0.618 AB/AG "A division of a line into two unequal parts is called golden if the relation of the length of the whole line to the bigger part is the same as the relation of the length of the bigger part to the length of the smaller part." (Beer) "Hallelujah" in Handel's Messiah TO CONCLUDE... After much research it seems evident that music and mathematics are interwoven.

Chose this project because these two are my favorite subjects

Now have a better grasp of both and can help others view them in new light.

Learned about frequencies, consonance and dissonance, and cognative learning.

Music and Math aid each other and it seems to me after all this research that they could be used to help struggling students. Thank

You

Full transcriptSequence What is the

Fibonacci Sequence? -"a numerical progression in which each term is equal to the sum of the two proceeding terms (Brown 66)." Music

and

Learning Works Cited Beer, Michael. How do Mathematics and Music Relate to Each Other?. East Coast Collage of

English, Brisbane, 07 1998. Web. 5 Dec 2012. <http://www.pages.drexel.edu/~jjn27/mathandmusic.pdf>.

Brown, Dan. The DaVinchi Code. New York: Random House, Inc., 2003. 66. Print.

Cromie, William. "How Your Brain Listens to Music."Harvard University Gazette. (1998): n. page. Web. 10 Sep. 2012. <http://news.harvard.edu/gazette/1997/11.13/HowYourBrainLis.html>.

Guralnik, David. "mathematics, music ." Webster's New World Dictionary of the American Language. New York: 1984.

Heimiller, Joseph. "Where Math meets Music." Aspire Software. Joseph Heimiller, n.d. Web. 13 Jan 2013.

<http://www.musicmasterworks.com/WhereMathMeetsMusic.html>.

Hoffer, Charles R. The Understanding of Music. 1st. Belmont: Wadsworth Publishing Company, Inc., 1967. 35, 39-40, 456,

458. Print.

Keller, Charles. "The Golden Mean." Math Department, Mission College, Santa Clara, California. N.p., 21 Mar 2001. Web. 10

Oct 2012. <http://www.missioncollege.org/depts/math/keller/golden.htm>.

Meisner, Gary. "Music and the Fibonacci Series and Phi." Phi 1.618 The Golden Number. N.p., 04 May 2012. Web. 10 Oct

2012. <http://www.goldennumber.net/music/>.

Mickela, Tony. "Does Music have an Impact on Student Development." Music Educators Online. Children's Music Workshop,

2012. Web. 10 Sep 2012. <http://www.childrensmusicworkshop.com/advocacy/studentdevelopment.html>.

M.U.S.I.C. Foundation, The. "Benefits of Music Education to Math, Reading, Language, and Spatial Intelligance."Support

TMF. The M.U.S.I.C. Foundation, Music Unlocks Success In Children, 2001. Web. 10 Oct 2012.

<http://supporttmf.org/documents/BenefitsofMusic-Web.pdf>.

Rosenthal, Jeffery. "The magical mathematics of music." plus magazine. 35 (May 1, 2005): n. page. Web. 10 Oct. 2012.

<http://plus.maths.org/content/magical-mathematics-music>.

Surmani, Andrew, Karen Farnum Surmani, and Morton Manus. Alfred's Complete Essentials of Music Theory. 1, 2, 3. Van

Nuys: Alfred Publishing Co., Inc., 1998. 10, 16, 17. Print. The

Math

of

Note

Frequency Music Symbols

and Math Importance to Music Golden Ratio Golden Ratio

In Math Where it is found in Music? Thesis Song Composition aids in learning fractional math while musical scales can be better understood by mathematically applying frequency as well as music playing an important part in the educational development of a student in mathematics. "A study of 237 second graders who used piano keyboard training and newly designed math software to demonstrate improvement in math skills scored 27% higher on proportional math and fraction tests then children who only used the math software ( The Music Foundation)." Using music to learn math The Mind "...music involves the use of cognitive, perceptual and motor skills..."

(Cromie) "In 2001, students who participated in music education scored 41 points higher on the Math portion of the SATs then those without music participation (The Music Foundation)" Later in Life According to Tony Mickela, "instrumental practice enhances coordination, concentration and memory while also refining the development of the brain and the entire neurological system." What does music do? Time Signature Time signature: -Two numbers -One over the other

-NOT a fraction Time Signatures vs. Fractions Music Notes -Eighth note: 1/2 beat

-Quarter note: 1 beat

-Half note: 2 beats

-Whole note: 4 beats Scales Math "Mathematics is the group of sciences dealing with quantities, magnitudes, and forms, and their relationship and attributes by the use of numbers and symbols (Guralnik)." vs. "Music is the art and science of combining vocal or instrumental sounds or tones in varying melody, harmony, rhythm, and timbre so as to form structurally complete and emotionally expressive compositions (Guralnick)" Music The Notes & Octaves Middle C - 261Hz C-522Hz C- 130Hz -A musical interval is the difference in pitch between two tones and is then named by the number of tones it includes counting the lower and higher tones (Hoffer). -Octaves frequency ratio 1:2 Intervals -Thirds, Fourths, Fifths -The frequencies of notes in a perfect fifth have a ration of three to two 261Hz 392Hz Consonance Dissonance -Two notes that sound pleasing to the ear it is considered consonant (Hoffar 39-40) The frequency of the notes can also be found mathematically by the equation: Hertz = 6.875 x 2^(3+MIDI_Pitch)/12 (Heimiller). -"Disagreeable or harsh sounds are considered dissonant." (Hoffer) Ex: Middle C and B natural,

C and F sharp "There are thirteen notes in a span of any note through its octave and the scale is composed of eight notes of which the fifth and third notes create the basic foundation of chords and based on whole tone which is two steps from the root tone which is the first note in the scale." (Meisner) 13 C and F# Consonant vs Dissonant B flat scale 8/13=0.615

21/34=0.6176

89/144=0.618 AB/AG "A division of a line into two unequal parts is called golden if the relation of the length of the whole line to the bigger part is the same as the relation of the length of the bigger part to the length of the smaller part." (Beer) "Hallelujah" in Handel's Messiah TO CONCLUDE... After much research it seems evident that music and mathematics are interwoven.

Chose this project because these two are my favorite subjects

Now have a better grasp of both and can help others view them in new light.

Learned about frequencies, consonance and dissonance, and cognative learning.

Music and Math aid each other and it seems to me after all this research that they could be used to help struggling students. Thank

You