Native American Music and Mathematics

    mu·sic (myoo’zik) n. 1.  Vocal or instrumental sounds possessing a degree of melody, harmony, or rhythm.
                                      2.  The art of arranging sounds in time so as to produce a continuous, unified, and
                                            evocative composition, as through melody, rhythm, and timbre.
 

    Music and math go hand in hand.  Both relate numbers with time in an attempt to quantitatively understand a subject that gives many positive qualitative and pleasant human responses.  Both may be simple and conversely may be difficult.  Math and music are a hierarchy of building blocks for which one must be conquered in order to move onto the next.  Perhaps no music is truer to the fundamentals of music as that of the Native American tribes such as the Menomonee, Iroquois, Winnebago, Cherokee, Sioux, and Navajo.

    Native American music is commonly heard at events called pow-wow’s.  These events are commonly open to the public, but are sometimes restricted just to the tribe.  At these events, a stage is set for which each participant in the pow-wow can be easily seen.  Singers, dancers, and drummers of both sexes actively participate in the event.  The word “drum,” as used in the Omaha tribe not only describes the instrument for which a person percusses, but it also names the people surrounding it.  This is a good example for which one word encompasses a whole instead of a sum of many divisions.  In our society we might refer to such a scene as a drum surrounded by five or six drummers.

    The drum is a focal instrument in many tribes.  This instrument goes back many hundreds of years when Native American tribes would use the skin of a recent kill to produce a tightly stretched surface for which percussion could be easily made.  Even today drummers refer to the striking surface as a skin, such as a snare skin.  Modern percussionists use their hands as well as highly manufactured sticks, where as Native American Indian tribes used sticks off trees as well as their palms.  In the modern recordings the Peyote Church, or the Native American Church, use special rattles called horn rattles and water-drums are used.  Stomping on the floor is also another percussive technique used by many tribes.

    The drum is a highly mathematical instrument for which many components must be considered.  First there is tempo.  Tempo is the relative speed at which music is or ought to be played.  Written music tells any musician what the tempo is at the top of the music sheet.  This is denoted with a simple equation involving a note and a number.  The note is usually a quarter note and the number refers to how many beats that note gets in one minute.  So an equation with a quarter note set equal to 60 would get one beat per second, which is a relatively slow tempo.

    Next there is time signature.  This is written on the staff as two numbers, one on top of the other.  When the time signature is written by itself, without a staff, it is written as a fraction, like a/b, although there is actually no division taking place here.  Time signatures tell you how many and what kind of notes per measure there are.  The number on top is the number of notes per measure, and the bottom number is what kind of note.  Let us take for example the most common time signature, 4/4, also denoted as c, for common time.  This means that there are four beats per measure, and the quarter note gets the beat.  Of all the Native American music I have listened to, all have been in 4/4 time.  The time signature, ¾ for example, is the time signature of the waltz.  This would be counted, “1, 2, 3, 1, 2, 3….” with the accent on the one.  In the time signature, the top number, a, can be any positive integer (not 0), 1, 2, 3…etc.   The bottom number in the time signature can be any number b, such that b=2^x|x is contained in the set of all non-negative integers.  However, for the bottom number to be anything higher than 64 would be musically ridiculous.

    Sometimes less is more.  In our narrow-minded society of today, we [ignorant, “educated,” and uncultured people] constantly demand more.  This is true with music as well.  Sometimes the most complicated musical composition can portray less feeling and movement than a piece that consists of the bare minimum.  Let me give you an example.  Two of my truly beloved idols, B.B. King and Stevie Ray Vaughn (SRV) once performed in front of a live, critical audience. During the middle of the song, the two performed a duet.  While Stevie went on a wild rampage of a solo, perfectly hitting hundreds of right notes at the right time, B.B. laid down on one mid-range note with his signature vibrato for the entirety of Stevie’s solo.  Afterwards, most considered B.B.’s solo to blow away his highly ranked competition simply because it had more feeling, meaning, and timbre.  Or, to make a long story short, less is more.

    This is where the tribal music of Native Americans comes into play.  Healing songs, which are now available to the public, were once unlikely to find among the recordings of the Peyote Church.  These songs can be heard today on Healing and Peyote Songs in Sioux and Navajo (Canyon Records CR–16302).  These healing songs contain no key changes (or modulation), no time signature changes, and rarely any harmony, yet they are able to invoke tremendous healing power.  In simple 4/4 time, prayer is often performed in song within the tipi on top of a crescent shaped altar.  Cacti are periodically present which produces a sense of well-being for anyone in attendance.  Often, portions of other peyote plants are passed to the celebrants and eaten as a sacrament.

    Amidst the dancers, percussionists, and singers, background music is also prominent.  Woodwind instruments such as the flute are beautiful instruments.  The Lakota tribe, for example, possess their legend of the flute, or as they call it, the siyotanka.  The siyotanka was an instrument used only by the men of the tribe to play only one type of song, love songs.  The Indians of this tribe were shy and often desolated themselves in order to practice these songs.  Once they mustered up enough courage, the male Indian would approach his winchinchala, a girl he was in love with, and perform this song for her.  Because the flute did all the talking, the music was the major player in the getting of the girl.  Little did the Indian know that it would be physics and math that would ultimately get the girl.

    Sound needs a medium in which to travel through, that’s why there is no audible sound in space.  Through air, sound travels roughly at a speed of 340 meters/second.  And according to the laws of physics, the speed at which a wave travels is the product of its frequency (pitch) and its wavelength (?).  A frequency of 440 Hz, or 440 cycles/second is defined in music as an “A.”  Musical keys are defined as a tonal system consisting of seven tones in fixed relationship to a tonic.  In layman’s terms, this means a set of specific frequencies.  The most pleasing tonality to the human ear is the major scale (in any key).  For example, the frequencies corresponding to A, B, C#, D, E, F#, G#, A octave would be the most pleasing tonality in the key of A, and would probably get the winchinchala.  The most probabilistic event that would occur in the pursuit of a female Indian would be an a Cappella (unaccompanied) performance in 4/4 time.  After all, that is the basis for a lot of love songs today.

    Although mathematics and music are definitely intertwined, one is not necessary to perform the other.  However they do serve as compliments to each other.  There is evidence to support that people with mathematical capability also have musical capability, and vice-versa.  After all, both tasks are performed using the same hemisphere of the brain.  Although Native American Tribes were not drastically educated in music or math, they possess within them the ability to create esthetically pleasing music using accurate pitch, consistent tempo, and well-kept time, all while unknowingly following laws of math and physics.
 
 

Web Site
    http://aboriginalcollections.ic.gc.ca/language/index.html

Web Site
    http://memory.loc.gov/ammem/omhhtml/

Web Site
    http://www.gspyo.com/education/html/timesig.html

Web Site
    Mathematics and Music
    http://www.math.niu.edu/~rusin/papers/uses-math/music/ite

Web Site
    http://www.angelfire.com/co/MedicineWolf/

CD Recording
    Walk In Beauty Healing songs of the Native American Church.  1995.  Canyon Records Productions. Primeaux
    & Mike.

Tape Recording
     Taku Wakan: Lakota Sundance Songs. 1993. Red Road Recordings.

Tape Recording
     Ceremonial Songs and Dances of the Cherokee. 1989. Indian Sounds.

Tape Recording
     Songs of the Sioux.  Canyon Records

Tape Recording
     Traditional Navajo Songs.  1969.  Canyon Records.

Dictionary
     The American Heritage College Dictionary. 1993.  Houghton Mifflin Co. 3rd Ed.