Sight, Sound and Beyond

Posts tagged ‘pitch’

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.

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!

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