## Sight, Sound and Beyond

### My Love Affair with Math

I 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.

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.

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.

### Can Music Be a Form of Prayer?

excerpt of  “In the Beginning” from Images

A year or so ago, I was riding in the car with one of my friends who has the same first name as I do.  I don’t remember the exact sequence of the conversation, but I went from talking about God to talking about one of my music composition projects.  “Gee Jen, ” she said, “I am surprised you don’t write religious music.”

I always wondered that myself.  Honestly, I never wrote anything that would be considered religious.  I never wrote a Mass or anything like that.  Many of the great composers have already written such wonderful works, so I never felt the need to write any sacred music myself.  I was always trying to find my own voice and do something different.  The fact that I had not written or was even considering writing any sacred music seemed quite bizarre to me.  After all, I am active in my church’s music ministry.

The topic of music and God, also came up in a discussion I had with my spiritual director some time ago.  She mentioned how music can be a form of prayer and worship and used King David as an example.  While The Ark of the Covenant was being brought to Jerusalem, he danced before the Lord .

“As the ark of the Lord came into the city of David, Michal the daughter of Saul looked out of the window, and saw King David leaping and dancing before the Lord;”2 Samuel 6:16

“Oh, but I don’t compose religious music,” I told her, “and much of the music I play would be considered secular.”  She had told me that my performance and compositions didn’t have to be of a religious nature to be considered a form of prayer.  It seemed really strange to view my own music as a form of prayer or praise to God.  I have studied music written for The Church, is considered sacred since it was clearly directed to our Lord.  However, when I began to think more about the process of composing and the art of performance being forms of prayer, the more it seemed possible.

God is the source of all creation and I believe all things come from God as well.  For example, I just finished recording a CD of original piano music that will be coming out next month.  If at least one of the compositions would be called “good,” I couldn’t take all the credit.  The closest sacred work that I have composed that is included on the disc is Images, a collection of seven piano pieces inspired by my pilgrimage to the Holy Land.  Each piece was inspired by either a specific place, moment or feeing during my visit.   It isn’t written for the Mass or anything like that, but I would consider it sacred because it was inspired holy places and spiritual experiences.  It is a trip that transformed me in many ways.  The scriptures came alive and I felt it brought me closer with the Lord.

excerpt from Revelation

For me, the art of composing and performing is a spiritual collaboration between man and God.  Sometimes the two can be completely in sync with one another where the music just flows freely and effortlessly.  This rarely happens to me, but when it does, the experience is awesome.  An examples of this happened to me in 2011 when I was writing a piece for the North/South Chamber Orchestra called Revelations.  The ideas for this composition seemed to pour out into my head and I simply followed where the music led me.  There seriously had to be strong Divine Intervention for that work.  I called it Revelations because it literally was revealed to me.  Was it revealed to me by God?  I would like to think so!

As for performance, the mind is truly in the present moment and only when the mind is in the present moment can one be in the presence of God.  I can recall many performances in which I felt very well connected with the piano and truly in the moment where I was able to connect with the audience and other musicians who were performing with me.  This is what I love about playing chamber music, there is more of a sense of community, a kind of joining together in group prayer.  In my best performances, all sense of time is lost because I am completely immersed in this heavenly world.

Much of my music comes from my own personal experiences, and even though I have free will, God is still the author of my life since He created me and knows everything about me.  Much of my music is inspired by my two avian companions, Sunny and Nikki, and who created them?  I think our Lord smiled when He imagined those two!  He seems to work His hand in everything.  Man may have built the first piano, but who created man and gave him the ability to imagine such ideas?  Our ability to create comes from the Creator.  After all, we are made in His image.  Therefore, when anyone creates a something that would be considered beautiful, powerful or a masterpiece, it is not simply just a human effort, but a collaboration between God and man.  Where there is collaboration there must be a dialogue of some kind, and when one engages with a dialogue with the Lord, that is called prayer.

As I write this, I recall a gift my mother gave me one Christmas.  I was a pillow that read the following: “Music, a Celebration of the Soul”  I couldn’t agree more, for when the soul is in perfect alignment with God, it truly has a reason to celebrate.

### Dancing on the Sea of Galilee

The Sea of Galilee

One of the most memorable experiences I had while visiting Israel was traveling by boat on the Sea of Galilee. On the morning of February 22nd, we left our hotel in Tiberius and went by boat to Ginosar to visit the Mount of the Beatitudes.

The boat ride was not what I expected it to be. I imagined that we would all be sitting in something similar to a row boat, but the boat was a fairly decent size. We were able to walk around on it and at one point we were dancing on it. We all danced to traditional Israeli folk music, and it was a lot of fun. I felt so happy and alive, and I enjoyed learning the Hebrew words to the traditional folk songs. I had always been familiar with the melodies, but never really knew how the words went. There were CDs there for sale, and I purchased the one that featured the folk music.

There is something so wonderful about music and dance. I believe that God expresses Himself through these art forms and that much of the arts are really a conversation between God and us. We speak, He answers, and the dialogue continues. As a musician, I feel fortunate to have this ability. Even if I am not the best of the best, I know the integrity and love is there, and through that, the Lord can work His hand in it.  I attribute my finest works and performances to Him because anything that is good comes from the God.

We are all called to a close relationship with God, and I believe that music is the best way for the Lord and I to communicate and nurture our divine friendship. Music is a language that everyone can understand, and it has the power bring people together. My mother always used to recite a well- known quote. I don’t know who actually said it, but it goes something like this: “Music is the language from heaven, which cannot be spoken in words.” I couldn’t agree more.

### What Does Sound Look Like?

Composition VII by Wassily Kandinsky

There is nothing more pleasing to the eyes than the colors of a symphony.  To put it simply, an orchestra contains lines and blobs.  The bowed strings contribute to the linear designs while the winds contribute the roundish blobs.  That is why the winds add body to the overall orchestral sound.  Unlike the linear design of the strings, the blobs created by wind instruments expand in all directions.

The individual colors of the orchestral instruments are marvelous: The strings are brownish-red and brass sounds consist of varying yellow hues.  However, the trombones are gold and carry a regal appearance to my eye.  The percussion contributes various highlights to the scene with their colorful specks and splashes.  However, the woodwinds are the icing on the cake because of their variety of colors.  Bassoons are yellow ocher, while oboes are a warm chestnut brown, clarinets are metallic dark brown and flutes are a shimmering light blue.

In December 2007, I sang in the Purchase College Choir, which performed Mendelssohn’s choral symphony entitled Lobgesang (“Hymn of Praise”).  Having the earth tone colors of the human voices mixed with an orchestra is something you cannot imagine, and to be on stage, standing in the middle of it all is even more amazing because the colors are all around you.  I stood in the alto section with bass and tenor voices to my left, sopranos to my right and the orchestra in front of me.

Voices appear as blobs just as the wind instruments do.  Bass voices are a sandy color, while tenor voices are brown.  Altos are light green, and sopranos are an ocean blue.  Mix that with your colorful orchestra and the colorful harmonies of Mendelssohn’s symphonic cantata and you really have something to talk about.  The fugal sections of that work are especially fun to watch as they run past you in varying colors and hues

Tonalities have color, instrumental sonorities have colors, and individual pitches have colors, especially when heard on piano.  Human voices have colors even when they are just speaking.  This is very interesting because when a person’s emotions changes so does the hue or shade of color of his voice.  Everything I hear appears as a line, speck or blob with some kind of color.  High sounds have brilliant, shimmering colors while low sounds are more faint and dull.  Images flash, splash, or even flicker (like when a telephone rings) before my eyes.

Animals create colors when they vocalize.  I was surprised and shocked when I heard one of my parrots, a Sun Conure, squawk for the first time.  She is a brightly-colored bird with a predominantly yellow plumage.  I nearly jumped out of my chair when her high pitched squeak produced a speck of dark blue.  Nikki’s call is a little less surprising as it is a greenish brown blob.  It is funny is funny when the two of them squawk back and forth because the color splatter all over the place.  However when they speak the colors appear much lighter.  Sunny has a low, scratchy voice, which is huge contrast to her high pitched call, so her speech is yellow in color while Nikki’s is tan.  Unfortunately, the colors of their voices are not nearly as beautiful as the colors of their feathers.  Oh well, you can’t have everything!

### What is Synesthesia?

Broadway Boogie Woogie by Piet Mondrian

I have talked about Synesthesia in many of my posts, but I thought I would take the time to discuss the term in further detail.  Derived from the Greek syn meaning together and aesthesia meaning sensation, synesthesia can simply be defined as senses coming together.  The stimulation in one sense will trigger perception in another.  For example, a person may see colors in response to hearing speach, music and other sounds.  This is one of the most common forms of synesthesia known as Color Hearing Synesthesia or just simply as Color Hearing.

Synesthesia is a completely normal neurological condition.  It is considered to be abnormal because it is statistically rare.  One of the leading authorities on the study of synesthesia is Richard Cytowic.  When I began my research on synesthesia in college, I read many of his articles and even a book of his called The Man Who Tasted Shapes.

Synesthetic experiences usually begin during childhood and consist of what Cytowic refers to as “a parallel arrangement of two gradient series.”  These series may be emotions, tastes, odors, temperature or colors, which are paired with letters, words, numbers, pitches and tonalities.  Imagine what it would be like to taste words.  It may sound bizarre to you, but for someone who has this form of synesthesia, it would be strange for words not to have particular tastes.

Synesthetic perceptions must have certain characteristics in or order to qualify as true synesthetic experiences.  Synesthetic perception is projected rather than experiences in the “mind’s eye”  For example, a person with synesthesia based on tonalities literally perceives the individual tonalities in color in response to hearing them.  These experiences are not imagined and not created at will.  I don’t tell myself to have them, they just happen simultaneously with the sounds.  Synesthetic experiences are also durable.  This means that the cross-sensory perceptions remain the same and never changes over time.  To me, the tonality of A was red, it still is red, and it will continue to be red.  I can’t imagine it being anything else but red.

In addition, synesthetic perceptions are generic meaning they are not elaborate or pictorial.  Let me use Beethoven’s 6th Symphony as an example.  Most people may imagine themselves out in the country when listening to this.  If I tell myself to do so, I can imagine myself walking in a wide open field or something of that sort.  However, whenever I listen to Beethoven’s sixth, the work produces an abstract image to my eyes.  It is a a mixture of different colored blobs and lines that move to the music.   These blobs and lines are based on the instrumental sonorities as well as the underlining harmonies.

Bassoons are yellow ocher and flutes are a shimmering, light blue.  Even individual tones have colors.  The c major scale played one octave would look like this: pink, green blue, lavender, violet, red, yellow, and  pink.  Notes in high registers are shiny and bright while notes in lower registers are more faint and dull.

Besides Color Hearing Synesthesia, I also experience Grapheme Color Synesthesia in which individual letters and numbers are perceived in color.  This is how I learned my alphabet and how to count. The letter A is red and M is pink, for example.  Many of my friends have pink names because many of them have names that begin with the letter M.  As for numbers, if you count from 0 through 9, the numbers would look like this: gray, white, pink, yellow, dark blue, tan, purple, red, light blue, and light green.

Even days of the week and the twelve months of the year have colors.  This is known as Lexeme Color Synesthesia..  I don’t know how or why.  It’s just always been like that.  Tuesdays are red and Fridays are green.  June is a blue month while August is pink.

I could go on and on but perhaps we will save that for another post.  Until then, stay tuned!

### Me, Myself and Synesthesia

Fugue in Red by Paul Klee

While I was a graduate student at Purchase College, I had a meeting with a professor of mine on my final composition project for one of my classes.  For this particular class I was to write a piece for string quartet exhibiting one of the techniques we studied.  My piece was inspired by a painting by Paul Klee entitled “Fugue in Red” which later became part of a set of pieces call Images By Paul Klee.  To put is simply, “Fugue in Red” is a fugue but in a more modern sense.  With regard to the painting, my professor asked me:  “Why do you think this piece is called Fugue in Red?”

“Well,” I began “You can see how the images appear in layers and they look like one another.  This suggests imitative counterpoint, which you find in a standard fugue.  As for the color red, that, to my eye, refers to the tonality.  My fugue is not tonal in the conventional sense, but if you notice, I use the pitch A as a tonal center here at the beginning.”  I pointed to the repeated A’s in the head motive of my fugal subject.  I continued.  “I chose A because A is red.”

I nodded “Yes.”

“Says who?”

Uh oh, I shouldn’t have said that.  I forgot for a moment that my perceptions of music were clearly my own and no one else’s.  My professor obviously didn’t see what I see with regard to tonality or sound in general.  Perhaps she didn’t see tonalities at all.  Though she seemed fascinated by my perceptions I felt a little embarrassed after that particular conversation.  To many “normal” musicians the whole idea of seeing sounds sounded a little crazy.  I moved away from that topic and discussed with her my plans regarding completing the work.  I hadn’t finished it yet.

As far back as I can remember all sounds have images and colors.  I wish that people could experience the things I see when I hear music, a bird chirping, or even a person speaking.  I was surprised to learn that not many people experience this kind of phenomena called Synesthesia.  As a someone who plays piano, the keyboard has always been my pallet of paints and my fingers are what make the paints come together to create a visual masterpiece.  I conduct all the colors of the keyboard in the manner I feel makes the work most understandable to the audience.  Music looks like an abstract painting: blobs and splashes of colors move across the keyboard as I play.  The colors of music operate on two different levels: instrumental sonority and harmony.  That is how it works.  Generally speaking, the sound of a piano is silver, but the harmonies and pitch sonorities are what make the music come to life in color.  Piano sounds appear as metallic blobs to me and disappear as their sounds decay.

To understand what music truly looks like to me, look at the abstract artwork of Wassily Kandinsky.  There is nothing more sensational then playing piano and watching the music come to life before my eyes.  I had always wished to someday play a piano concerto with an orchestra.  Wouldn’t that be grand to mix the metallic timbres of the piano with the spectral hues of an orchestra?  I certainly think so!

### Introduction

Spectrum V by Ellsworth Kelly

Since this is my very first blog post, I thought it would be best to begin with an introduction.  That’s usually a good place to start.  Anyway, this is not my first blog.  I actually started keeping a blog about 2 years ago when I was an active online member of a parrot forum.  Writing has always been a great outlet of expression for me, so here I am starting it up again.

Allow me to introduce myself.  My name is Jennifer and I love music and birds.  I am a music educator at a community music school and also incorporate music into my work in therapeutic recreation at a children’s home.  I have been playing piano for over 20 years and I have been writing my own music for almost 10 years.  I play the handbells in my church’s handbell choir and absolutely love it.  Some people would call me a professional musician, but I don’t consider myself one, just a great lover of this wonderful art form.

As  much as I love music, I also love birds.  I live with two very special, feathered companions: a sun conure, Sunny, and a quaker parrot, Nikki.  Both are girls and were born in 2004.  They are very dear to my heart and add much color to my life.  They are my girls and anyone who knows me, knows my girls.  They are my biggest musical inspirations.

That brings me to the title of this blog.  Spectrum is a very special title to me because it is the title of one of my favorite artworks that I saw at the Metropolitan Music of Art.  The work is specifically called Spectrum V (as opposed to Spectrum IV) and is by a contemporary artist named Ellsworth Kelly (b. 1923),  The work consists of thirteen large panels, each containing a different color or shade of color. The first panel is yellow and the last is yellow.  To me this work is a visual representation of a chromatic scale played one full octave up the piano keyboard.  Years after my first sighting of Spectrum at the Met, I decided that I wanted to make an audio representation of the seven colors of the rainbow, each represented by a different tonality or pitch center: A being red, B orange, C yellow, D green, E blue, F indigo, and G violet.”

I have played Spectrum many times.  To me it is my signature piece.  Anyone who hears it or for any pianist who plays it hopefully gets a glimpse of what’s going on in my head.

The word Spectrum conjures up both audio and visual memories for me.  I am a great lover of both color and sound and find the senses of both vision and hearing to be very fascinating.  Ironically, when I was born, these two senses were not the sharpest tools in the shed because I was born both hearing and visually impaired.  However since I have never had normal vision and hearing, all seems pretty normal to me.  I am very happy with my aural and visual perceptions.  I can see enough to appreciate all the beautiful colors, and I can hear enough appreciate all the beautiful sounds.

To me, my girls, are the the most beautiful creatures in my life with their beautiful colors and bright eyes, and their unique vocalizations are the most beautiful sounds to my ears (except when they nag for my attention).  There is nothing more beautiful than the sound of their happy chirps.  Of course, other people would disagree with me.  Many find the vocalizations of parrots, even small ones, to be quite annoying.  Oh well, when you love, you do not only become blind but deaf too!

My topics for discussion will range from anything that I feel relates to either sound and/or color as well as vision and/or hearing.  Feel free to leave comments and thank you for visiting!