Sight, Sound and Beyond

Posts tagged ‘music theory’

My Love Affair with Math

pythagoras-theoremI was chatting with two of my girlfriends at Starbucks last night, one of which is finishing up her master’s in education.  She is doing her student teaching now and was talking about the math lesson she prepared for a second grade class.  Of course I was all ears.  Math was my strongest subject in school.  I learned how to add and subtract before learning to read and at age 9, I solved my first algebraic equation.  None of my friends liked math.  I was the only who could get excited over a good math problem.  I had plans to major in mathematics in college but once I completed calculus I, my passion began to fade.  I think the math department was slightly disappointed when they learned that I had not pursued a mathematics major, but Our Lord had other plans.  Music, unexpectedly pulled me in and the interesting part is that I was probably a stronger mathematician than I was a musician.

But as I began my studies of music analysis, the glories of mathematics remained with me.  When I was a sophomore in college, I completed a math project using Microsoft Excel in which I calculated the frequencies of all 88 notes played on the piano.

The lowest note on the piano is A, which has a frequency of 27.5 Hertz.  That means the string vibrates 27.5 times per second.  To find the frequency of the note A# (A-sharp), which is one half step above, you multiply 27.5 by the 12th root of 2.  The 12th root of 2 refers to some number multiplied by itself 12 times that will give you something close to 2.  Why are we talking about the 12th root of 2?  Because the octave consists of 12 half steps.

The 12th root of 2 in computer lingo or on a graphic calculator is expressed as 27.5 * ^ 1/12.  The 12th root of 2 expressed as a decimal is about 1.0594631 (rounded).  That means if you take that decimal and multiply it by itself 12 times, you will get close to the number 2.  The 12th root of 2 is an irrational number just like PI

Oh and here is a little side note, the asterisk (*) stands for multiplication because if you use the traditional multiplication sign, it might get confused with a variable X that you find in algebra.  The caret sign (^) is used to indicate an exponent.  So if you want to say 2 squared, you write 2 ^ 2.  To express a square root of a number like the square root of 4 you write 4 ^ 1/2.  Note that you express the exponent as a fraction for square roots, cube roots, fourth etc).  So if you want to say the cube root of 8 you would say 8 ^ 1/3.   The cube root of 8 is 2 because 2 * 2 * 2 = 8.

Now on excel you can use one formula to solve all the frequencies so you don’t have to do it 87 times.  The formula that I came up with is:

Y = 27.5 * 2 ^ (x/12)

Y (the frequency of a note) = 27.5 (the given frequency of the lowest note on piano) * (multiplied by) 2 ^ (X/12).  Okay, I know the factional exponent looks strange with the X and all.  The best way is to show you.

The X stands for the number of half steps away from the given note, A.  For A#, we substitute X with 1 because A# is one half step above A.

Substitute 1 for X and we get

Y = 27.5 * 2 ^ (1/12)

Y = 29.16 (roughly)

Now if I wanted to find the frequency of the next note B, substitute X with 2 (two half steps away from the given note A).  How does this work?  What you are really doing is 27.5 * 2^1/2 * 2^1/2.  Since you are multiplying 2^1/2 by itself you are really doing 27.5 * 2^2/12.  Meaning you are taking the 12th root of 2 and then squaring it.  the Denominator equals the root so in this case, the 12th root of 2 and then squaring it.  The numerator refers to the power (in this case the 2 on top means to square it).

Below are my findings for all 88 frequencies.

88-frequencies2_page_188-frequencies2_page_2

Here is a line graph of all the frequencies.  Notice the shape of the graph.  The higher you go, the larger the gap between each of the frequencies.  Frequencies always double at the octave.  Therefore, if you play A above middle C on the piano, the frequency is 440.  The next A above that would have a frequency of 880.

88-frequencies2_page_3

Music and math go hand and hand.  In math we have substitution where you substitute numbers or expressions in place of letters.  In music we do have chord substitution.  Don’t get me getting on that discussion.  I love secondary functions in both math and music!

If you found this whole thing confusing don’t worry about it.  I must confess that I posted this help preserve the memory.  I was quite proud of myself after I completed this.  I never considered myself a genius, but that was a very high moment in my life because it was my own individual project.

I believe that all things, both living and non living, are a reflection of the Holy Trinity, separate entities that are all connected as one.  I always believed in a common oneness in everything since everything that is comes from God.

Ode to Joyce

Mary Ann Joyce-Walter

On Sunday, February 26, I participated in a Manhattanville College chamber music concert celebrating the compositions of Dr. Mary Ann Joyce-Walter.  The concert was held to honor her retirement from the college this June.  The performers consisted of faulty, students and alumni like myself.  I felt very privileged to be included.   It isn’t everyday that I get asked to perform, but I felt very honored to perform music by my very first teacher of composition.

I met Joyce when I was a sophomore in high school.  At that time, my older sister, Elizabeth, was attending Manhattanville and wanted to introduce me to faculty of the music department.  One of the first things that things Joyce said to me was: “You are very pretty.”  She went on to tell me about the music program and the available concentrations.  Little did I know that wouldn’t be the last time I would be seeing her.   At that time, I didn’t even know if I wanted to continue my studies of music at the college level.

Anyway, I began taking Joyce’s classes during my first semester of my second year of college.  She was my music theory teacher, and I immediately grew to like her right from the very first day of class.  “I hear you are a very strong music theory student,” she said.  Not only was she my music professor but she was also my academic adviser as well.  At the end of my first semester with her, she gave me one of her CD recordings that featured her music:.An Evening with Gerard Manley Hopkins.  It was then  that I became interested in composing music.  Of course, I didn’t think I had it in me to even write music.  My only composition was a very short piece I wrote for my freshman music seminar class.  It was a rhythmic piece for four tin cans called Reduce, Reuse, Recycle.

During the second semester of my sophomore year, Joyce began incorporating composition into her class assignments.  Once we began studying 18th century counterpoint, we were to write the first section of a two-part invention.  Being one of her faithful disciples, I wrote a two part invention in its entirety and played it in the Student Composer’s Concert.  We were both quite happy with how the piece turned out.  Even though it was written in an older style, she had told me that I had done well.   During the summer we kept contact and theory and composition continued on.  I wanted to wright another piano piece but was unsure about to organize the piece.  She had gave me some pieces to study and analyze so I could see examples ternary, binary and rondo form.  Many of the pieces we studied were from one of the books we used in class called Anthology for Musical Analysis by Charles Burkhart.  Using the pieces as a model for form, I composed From a Dream.

Besides introducing me to composing, Joyce introduced me to the wonderful world of birds.  She had kept cocketiels for much of her life and always told me again and again about Joe, the marvelous bird who could whistle the theme from the first movement of Beethoven’s 5th symphony.  However, besides birds, she introduced me to the music organization, New York Women Composers, for which I now currently serve as Secretary/PR Coordinator.  In addition, through her, I met and found Flora Kuan, one of my piano instructors, who did wonders in developing my technique.

Till this day, Joyce and I continue to stay in touch and whenever I have any composition-related question, she is the first person I ask.  Also, she is one of Sunny and Nikki’s biggest fans.  One of my favorite memories is when I took the girls to see her at the college for the first time.  She just fell in love with them and her feelings toward them didn’t change one bit after they both pooped on her desk.  “Oh it is just transformed seed, ” she said with a chuckle.

It truly is amazing that we have already known each other for nearly 11 years now.  Manhattanville will surely not be the same without her.  She was the best music professor I had, and she certainly gave her students much encouragement and praise for their hard work.  I felt proud to hear her music performed that day, and if I ever turn out to be a really great composer someday, I will always remember that the composition journey started with her.        .

My First Experiment with Synesthesia

Abstract Symphony in Blue and Green by Vicky Brago Mitchell

When I was a sophomore in college, I made my first attempt at painting music.  I don’t know if I was very successful, but the experiment went like this.  In my theory class, we had to write an example of a tonal modulation.  We had to begin in the key of E minor and modulate to one of the other 5 related keys: G major, C major, D, major, A minor or B minor.  I ended my example in D major by using an E minor chord as a common chord.  The example was about two measure and was written in four voices, like you would find in a Bach four-part chorale.

I showed my musical example to my freshman academic adviser, Randy.  He is an art professor, but I had him for the freshman seminar which all incoming freshman were required to take.  I asked Randy if he would help me make my two measure example into a painting.  He agreed and we began our experiment.

Creating my visual masterpiece took a few attempts, but here is what I ended up finally doing.  I took a large piece of water color paper and painted 2 thirds of it blue to represent E minor and painted the remainder of the paper green to represent D major.   These visual representations were based on my own personal perceptions of these two keys.

Now how did I represent the notes in the chorale and their durations?  Randy gave me a book that consisted of color samples.  He told me to cut the colors out that best represented the notes in the example.  Shorter notes were cut closer to the shape of a square while longer note values were cut more in the shape of a rectangle.  It was not an easy task to do as matching up the colors to my own perceptions was very challenging.  Therefore, I had to chose the ones that were as close to the original as possible.

I arranged the “notes” on the panted paper in the same manner as it appeared on the staff.  The example moved from left to write and the voices were arranged in their conventional order: bass, tenor, alto soprano.  Once the notes were glued in their respectful places, the work was finished.  It turned out to be pretty cool and I titled it From E Minor to D Major.

Once I finished the work, I gave it to Joyce, the professor of the theory class in which I had done the initial assignment.  I had given it to her as a Christmas gift.  Joyce became my academic adviser in my Sophomore year.  It was that same year that I became interested in composing music and began studying composition with her as well.  Even after all these years, I still have close ties to both Randy and Joyce.  I don’t know if Joyce still has the painting, but I am glad we still have our friendship.  That’s more important.

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