Harry Partch

Harry Partch Ratio Representation Project

by Brian Harlan and Arun Chidambaram

I. Introduction (Part 1)

Harry Partch(b. Oakland, 1901 d. San Diego, 1974)[Photo by Madeline Tourtelot] Harry Partch is a critical figure in American 20th-century music for the influence of his musical ideas. His musical compositions, however, have never become part of the standard repertory, and are seldom closely studied. Although few serious academic surveys of American music would fail to mention Partchs work, his compositions are rarely given the same analytical attention as his contemporaries. Even in his lifetime Partchs ideas often overshadowed his music; in spite of the fact of his oft repeated statement that he, more than anything else, a composer. The primary reason for the reluctance to study his music is due to the fact that Partch composed for an orchestra of instruments that he designed and constructed himself. The need for new instruments was the direct result of his aesthetics, which required musical tones that do not otherwise exist in Western music. These new instruments, and new tones, in turn, demanded a new system with which to notate his compositions. Partch used a tablature system that was specific to each instrument. Tablature notation gives directions to a performer based on the instrument to be used. Therefore, in order to follow his scores, one must be familiar with each unique instrument. All these factors have created a set of encumbrances that make Partchs music inaccessible to most music students.



I. Introduction (Part 2)The primary reason for the reluctance to study his music is due to the fact that Partch composed for an orchestra of instruments that he designed and constructed himself. The need for new instruments was the direct result of his aesthetics, which required musical tones that do not otherwise exist in Western music. These new instruments, and new tones, in turn, demanded a new system with which to notate his compositions. Partch used a tablature system that was specific to each instrument. Tablature notation gives directions to a performer based on the instrument to be used. Therefore, in order to follow his scores, one must be familiar with each unique instrument. All these factors have created a set of encumbrances that make Partchs music inaccessible to most music students. >>..contd Diamond Marimba Cone Gong and Gourd Tree Spoils of War[For other examples of Partchs instruments, go to the following sites:



I. Introduction (Part 3)The Ratio Representation Project was undertaken as an initial step toward solving two fundamental problems in Partch scholarship. The first problem is the need for a visual representation that reveals the heightened relationships of tones. The excerpt below shows that it is not always possible to follow the contour of melodic lines on Partch's score...contd..>>

"Frabjous Day! (TheJabberwock)" fromTwo Settings from Lewis Carroll(1954)

I. Introduction (Part 4)Since his scores were intended for performersand not for studentsit is understandable why tablature notation was the most effective means to the end he had in mind. The result, however, is that students are precluded from following a score during real-time listening. A program was written in JAVA that allows the listener to visualize melodic relationships while hearing an audio output.The second fundamental problem is that it is only possible to recreate a performance of Partchs music if you have access to his instruments. The instruments are currently in the care of Dean Drummond atMontclair State Universityin New Jersey. Drummond performs Partchs music often, and teaches new generations of students how to play, tune, and maintain Partchs instruments. Nevertheless, for the purposes of study, it is not always possible to find a recording of every composition, and it impossible to unequivocally check your analysis (as is usually possible with a piano). A machine-readable representation for ratio notation would be an asset, and a second program was written in MatLab to begin to address this. It should be understood that both program shave significant limitations in terms of recreating the true force of Partchs music. The sine waves that they generate have almost no bearing on the actual sound and effect of his instruments. The motivation for this project was to develop analytical tools for the purpose of encouraging new scholarship. Partch, himself, was an advocate for phenomenological experiences of music. He made recordings of his music only to document it, and he did not believe that a recording could serve the same purpose as a live performance. Music, for Partch must be experienced with the body, not simply with the earsor worseas a mental abstraction Harry Partch Ratio Representation Project


II. Musical RatiosMusical ratios are simply another way to denote pitch. In Western music we typically denote pitches by using the letters A, B, C, D, E, F, G. If we need to refer to a pitch in between one of these note names, we can use a sharp (#) or flat (b) symbol based on the context. There are, however, other ways in which to denote pitch. The most objective, and thus the one used most often by acousticians, is frequency. Sound is transmitted in waves, and frequency is a measurement of the number of complete waves (or cycles) that occur in one second. The number of cycles per second determines the pitch of atone. For example, 440 cycles per second (or 440hz) is recognized in the West as the pitch A. It is important to note that his is an arbitrary assignment, and that, although we have used the letters A-G as note names from hundreds of years, A = 440hz was only standardized in the 20thcentury. It was because of the arbitrary status of A-G that prompted Partch to prefer the use musical ratios. In a sense, musical ratios are also arbitrary, as they depend on a referential point that can be changed. Yet, ratios have the advantage of revealing relationships that are otherwise less apparent. In order to help his audience conceptualize musical ratios, Partch used the ancient technique of dividing the string of a monochord (a single-stringed instrument). If the sting on a monochord with a tone of 100hz is stopped in the middle, it will produce a new tone of 200hz. The ratio 200/100 can then represent an octave above the source. To make matters simpler, Partch always reduced his ratios to the lowest common denominator; thus, 200/100 = 2/1. He also recognized the phenomenon of the sameness of pitches separated by an octave. Similar to the idea of a pitch class, Partch denotes 200/100, 600/300, 800/400, and so on, with a single identity: 2/1. If the string is stopped at a third division, and only one third is sounded, it will produce 300hz. The 300hz placed in relationship to the previous division then become 300/200, or 3/2.

It is common practice to build ratiosupwardsby putting the smaller number on the bottom, and Partch adheres to this. Yet, he points out that ratios can also be builtdownwards. If we descend from the source tone (rather than ascend from the sources tone, as in the example above) we obtain a result that is more like a simple division of the string length. In fact, the string length is one of the key factors in the pitches that it generates. If we decide that the 1/1 is the note G, then the 3/2 above G is D. The 2/3 below G is also a D, but an octave below the previous D. The fact the these two ratios represent the same pitch , while at the same time reveal a different relationship to 1/1, is a crucial principle in Partchs theory of Monophony. 1/1 = unison2/1 = octave

3/2 = perfect fifth4/3 = perfect fourth

5/4 = major third8/5 = minor sixth

6/5 = minor third5/3 (10/6) = major sixth

9/8 = whole tone16/9 = minor seventh

16/15 = semitone15/8 (30/16) = major seventh

Another significant aspect of musical ratios is that they represent both a pitch, and an interval. In other words, the 3/2 above 1/1 tells us not only which note we have encountered, but also its relationship to (or the distance from) the source tone (1/1). It was explicitly this dual function of ratios that Partch believed to be more meaningful than letter note names. While a D can indeed be recognized as a perfect fifth, it is only so in relation to G. A 3/2, on the other hand, is always a3/2, regardless of its context. Below are ratios equivalents for intervals within an octave in equal temperament (the Western twelve-tone system that tunes all pitches an equal distance apart, or122/1). In Partchs music the ratios and equal temperament intervals will not sound the same because Partch uses a different tuning system called,just intonation. 1/1 = unison2/1 = octave

3/2 = perfect fifth4/3 = perfect fourth

5/4 = major third8/5 = minor sixth

6/5 = minor third5/3 (10/6) = major sixth

9/8 = whole tone16/9 = minor seventh

16/15 = semitone15/8 (30/16) = major seventh

The system of tuning pure (or just) intervals predates the equal temperament system by thousands of years. Through out Western musical history, many theorists and composersincluding Partchhave preferred just intonation because it is more closely aligned with the natural growth of a tone. When a tone is sounded our hearing is immediately drawn to the fundamental tone, which can be described as the pitch produced by the entire string on the monochord. At successively higher frequencies, however, smaller segments (1/2, 1/3, 1/4,etc.) of the monochords string are also producing their own pitches at the same time. This succession of frequencies is generally referred to as the overtone series (also called the harmonic series, or upper partials). The chart bellow shows that, if a string is vibrating at 110 cycles per second, each 1/2 will also vibrate at 220 cycles per second. In a inter-related play of numbers, successive segments of the string (1/3, 1/4, 1/5 etc.) can be expressed as a successive integers multiplied by the fundamental (110 x 3 = 330, 110 x 4 =440, 110 x 5 = 550), and with each new integer, a new overtone is produced. 1/1110hzA2Unison

2/1220hzA3P8 (1stovertone)

3/2330hzE4P5 (2ndovertone)

4/3440hzA4P4 (3rdovertone)

5/4550hzC#5M3 (4thovertone)

6/5660hzE5m3 (5thovertone)

In just intonation the intervals above are tuned as they naturally occur. Equal temperament tunings, in contrast, must squeeze intervals slightly in order to make them synthetically equal. Although the octave and perfect fifth are nearly as pure as they are in just, on average all the other intervals in equal temperament are slight smaller than nature intended. What Partch also found intriguing about tuning in just intonation is that, if one continues with successive integer as in the method above, intervalsand thus pitchesbegin to appear that do not exist in equal temperament. A 7/6, for instance, produces a tone slightly smaller than a minor third, and an 8/7produces a tone slightly larger than a major second. One can theoretically continue in this way to produce an infinite number of new pitches. Partch decided to stop with the number eleven, but he continued to create new microtonal resources by adding ratios together. His music is decidedly focused on forty-three tones to an octave, but its important to understand that this was his decision as a composer, not the theoretical limit of his system.



III. Partch's theory of "Monophony"Partchs use of the term monophony to describe his aesthetic stance has often resulted in confusion and misunderstanding on the part of students. Partchs Theory of Monophony, and his monophonic resources (namely his forty-three tones), are related to the standard definition of monophony, but must be distinguished with qualifications. When Partch wrote of monophony, he had in mind the Renaissance and Baroque monodies by composers such as Caccini and Monteverdi, which developed in part form ideas that came from a 16th-centuyCamerata . Cameratas were small gatherings of scholars in Italy. A well known camerata led by Giovanni Bardi in Florence that included musicians such as Giulio Caccini, Jacopo Peri, and Vincenzo Galilei (father of Galileo) encouraged a new style of music in reaction to the preponderance of polyphonic music at the time. The style they helped create was intended to be in emulation of ancient Greek drama, and relied heavily on solo voice with accompaniment. There have been many moments in Western history that reveal to a return of interest in Classical thought. So much so that one might metaphorically portray ancient Greece as the 1/1 of Western culture. Yet, there were very significant civilizations prior to ancient Greece as well. Partch was not only interested in returning to the ideas of ancient Greece, he was also interested in returning to the ideas of ancient Egypt and China. He was equally influenced by contemporaneous non-Western musics, which he felt were more visceral and alive. In his essays, Partch depicts Western concert music as abstract and disconnected from natureand specifically, in a state of denial regarding the human body. In other words, ancient and non-Western musics, according to Partch, resonated more with the body, they were more dramatic, and more individualistic expressions that spoke directly to humanity. The formalistic music of the Western concert halls, in contrast, which did not refer to anything outside itself (literally art for the sake of art), resonated only in the mind, and had therefore lost the magic potential that is the basis of these other musics.In his manifestGenesis of a Music: An Account of a Creative Work, its Roots and Its Fulfillment, Partch explains his Monophony as an organization of pitches based on the overtone series, and the human capability to perceive this series in relationship to its source. All the pitches that grow out of the1/1 (2/1, 3/2, 4/3, and so on) are inherently related back to the 1/1. All that music, furthermore, is a play of these perceived relationships. Partch used his concept of Monophony to create what he deemed Corporeal music that taped our ancestral spirit and renewed the ritual power of Western music.



IV. ImplementationThe Implementation of this Project was done in JAVA and MATLAB. We have three versions of this ProjectVersion 1. Polyphonic Visualization of Partch's works developed in JAVAA program was written in JAVA that allows the listener to visualize polyphonic notes from Partch's works. It takes polyphonic notes as input with any number of notes per line on a notepad file .The output is a figure which shows the polyphonic ratios being plotted on it corresponding to the ratiosVersion 2 .Monophonic Visualization and Listening of Partch's work in JAVA (needs internet to run) A program was written in JAVA that allows the listener to visualize melodic relationships while hearing an audio output. It takes monophonic input with one note per line on a notepad file .The output is a figure which shows the monophonic ratios being plotted on it and at the same time sound plays through the speaker corresponding to the note.Version 3 Polyphonic Sound creation of Partch's works developed in MATLABAsecond program was written in MatLab to create a machine-readable representation for ratio notation .This program creates sound according to Partch's ratios and saves as a wav file on the Desktop for future analysisDownload Source Code -JAVA-version1,version 2,MATLAB,Image file(needed to run the program)Creating Input files:For Version 1-Takes polyphonic inputs1.) Open a notepad file2.) Type in the ratios -line by line Example 1/1 32/21 4/3 2/3 4/73.)Save the file as ratios.txtExample for Version 1-InputFor Version 2-1.) Open a notepad file-Takes only monophonic inputs2.) Type in the ratios -line by line Example 1/1 32/21 2/3 4/73.)Save the file as ratios.txtExample for Version2-InputFor Version 3-1.) Open the musmat1.m file in notepad2.) Type in the ratios in vector task Example for 1/1-type a0101, for 16/11 type-a1611, for 160/81 -a16081, for 11/6-a1106 2/1 -a02023.) Ratios can be added for complex sounds Example a1611+a01013.)Save the file as ratios.txtExample for version 3-InputHow to Run-Java1.) Install Java on your machine2.) Go to command prompt -Press start on Windows .Click run. Type cmd on run and click ok3.) Go to the folders where you have all our source files4.) Set path to Java bin Ex: set path=C:\Documents and Settings\'username'\desktop\Jbuilder\jdk1.4\bin 'username' is your login name on your local machine and Jbuilder is the folder where the java files are stored and link to bin5.) Set class path Ex: set classpath=C:\Documents and Settings\'username'\Desktop\sounds .'username' is your login name on your local machine6.)Type in the ratios and save it in ratios.txt6.)Compile the file Ex: javac prog.java for Polyphonic Visualization of Partch's works javac progsound.java for Monophonic Visualization and Listening of Partch's work7.) Execute the file Ex: java prog two.jpg for Polyphonic Visualization of Partch's works .two.jpg is the output image file java progsound two.jpg for Polyphonic Visualization of Partch's works .two.jpg is the output image file8.) Enjoy the Output.How to run- MatLab1.) Start MatLab2.) open musmat1.m in notepad, type in the desired ratios in the vector task, save the file and close it3.) type musmat in the command line on MatLab and press enter4.)type musmat1 on command line on MatLab and press enter5.) Put on your headphones and Enjoy.



V. ExamplesIn order to visualize the relationships between Partchs Monophonic resources, the ratios inputted are then plotted onto a chart Partch developed called the One-Footed Bride. The chart shows all forty-three tones, as well as the twelve tones of equal temperament. The ratios are presented in two columns opposite their compliment (inversion). The tones ascend from the 1/1 beginning at the bottom of the left column until the first compliment is reached, and then continue to ascend by coming back down the right column to the 2/1. The chart also shows primary and secondary ratios, which indicates whether they were produced by successive integers (and their multiples), or by adding ratios together. Finally, the One-Footed Bride also reveals categories of intervals, and their relative intensities, as perceived by Partch. There are four interval categories: Intervals of Power=1/1, 3/2; 4/3, 2/1 (perfect intervals)Intervals of Suspense= 27/20, 11/8, 7/5; 10/7, 16/11, 40/17 (tritone intervals)Intervals of Emotion= 32/21, 6/5, 11/9, 5/4, 14/11, 9/7, 21/16; 32/21, 14/9, 11/7, 8/5, 18/11, 5/3,12/7 (thirds and sixths)Intervals of Approach= 81/80, 33/32, 21/20, 16/15, 12/11, 11/10, 10/9, 9/8, 8/7; 7/4, 16/9, 9/5,20/11, 11/6, 15/8, 40/21, 64/33, 160/81 (seconds and sevenths)

Ex. 1**Monophonic Resources*43 Tones within the OctaveListen1/181/8033/3221/2016/1512/1111/1010/99/88/77/632/276/511/95/414/119/721/164/327/2011/87/510/716/1140/273/232/2114/911/78/518/115/327/1612/77/416/99/520/1111/615/840/2164/33160/812/1##[NOTE: In examples 2-4, 1/1is added at the beginning of the file in order to provide a reference point. 1/1 is an interval of Power.]Ex. 2*Intervals of EmotionListen1/11/17/632/276/511/95/414/119/721/1632/2114/911/78/518/115/327/1612/7##Ex. 3*Intervals of SuspenseListen1/11/127/2011/87/510/716/1140/27##Ex. 4*Intervals of ApproachListen1/11/181/8033/3221/2016/1512/1111/1010/99/88/77/416/99/520/1111/615/840/2164/33160/81##Ex. 5*Intervals of PowerListen1/11/14/33/22/1##Examples 6-9 present primary tonalities as they are revealed in Partchs Tonality Diamond. Otonalities (major tonalities) are read from 1/1-7/4, 16/9-14/9, 8/5-7/5,etc.; Utonalities (minor tonalities) are read from 8/7-1/1, 9/7-9/8, 10/7-5/4,etc. Tonalities are determined by the numerary nexus of ratios. For example, all intervals with an under number of 7 (8/7, 9/7, 10/7, etc.) create a distinct tonality.

Ex. 6**Tonality Diamond Hexachords*Otonality of UnityListen1/19/85/411/83/27/4##Ex. 7*Utonality of UnityListen8/74/311/168/516/91/1##Ex. 8*Primary OtonalitiesListen1/19/85/411/83/27/416/99/910/911/94/314/98/59/55/511/106/57/516/1118/1120/1111/1112/1114/114/33/25/311/63/37/68/79/710/711/712/77/7##Ex. 9*Primary UtonalitiesListen8/74/311/168/516/91/19/73/218/119/59/99/810/75/320/115/510/95/411/711/611/1111/1011/911/812/73/312/116/54/33/27/77/614/117/514/97/4##Ex. 10**Ptolemaic Scales [fromHarmonics]*Enharmonic TetrachordListen1/128/2716/154/3##Ex. 11*Chromatic TetrachordListen1/128/2710/94/3##Ex. 12*Diatonic TetrachordListen1/116/156/54/3##Ex. 13*Enharmonic ScaleListen3/214/98/51/19/87/66/53/2##Ex. 14*Chromatic ScaleListen1/116/1510/94/33/28/55/32/1##Ex. 15*Diatonic ScaleListen1/112/116/54/33/218/119/52/1##Ex. 16*Olympos PentatonicListen9/86/53/28/52/19/8##Ex. 17**Non-Western Scales*Chinese sequence [circa300BC]Listen1/18/76/55/44/33/25/32/1##The last example does not produce a visual output. Each ratio (NOTE: 0503 = 5/3, 0403 = 4/3, etc.) occurs for .25 seconds. Therefore, in order to achieve sixty quarter notes per second, a ratio must be inputted four times. Polyphony is possible by adding ratios together.Ex. 18**Score Excerpt*By the Rivers of Babylon [mes. 21-29]Listena0503+a0403 a0503+a0403 a0503+a0403 a0503+a0403 a0503 a0503 a0503 a0503 a0503+a0706 a0503+a0706 a0503+a0706 a0503+a0101 a0503+a2011 a0503 a0503+a0504 a0503 a0504+a0503 a0504+a0503 a0504+a0503 a0504+a0503a0504+a1811+a0101 a0504+a1811+a0101 a0504+a1811+a0101 a0504+a1811+a0101 a0504+a0805+a0101 a0504+a0805+a0101 a0504+a0805+a0101 a0504+a0805+a0101 a0504+a1409+a0101 a0504+a1409+a0101 a0504+a1409+a0101 a0504+a1409+a0101 a0504+a0302+a0905 a0504+a0302+a0905 a0504+a0302+a0905 a0504+a0302+a0905 a0504+a0302+a0101 a0504+a0302+a0101 a0504+a0302+a0101 a0504+a0302+a0101 a0504+a1409+a0101 a0504+a1409+a0101 a0504+a1409+a0101 a0504+a1409+a0101 a0504+a0805+a0101 a0504+a0805+a0101 a0504+a0805+a0101 a0805+a0101 a0504+a0101+a0503 a0504+a0101+a0503 a0504+a0101+a0503 a0504+a0101+a0503 a0504+a6433+a0805 a0504+a6433+a0805 a0504+a6433+a0805 a0504+a6433+a0805 a0504+a1508+a1409 a0504+a1508+a1409 a0504+a1508+a1409 a0504+a1508+a1409 a0504+a1106+a0302 a0504+a1106+a0302 a0504+a1106+a0302 a0504+a1106+a0302 a0504+a0302+a1106 a0504+a0302+a1106 a0504+a0302+a1106 a0504+a0302+a1106 a0504+a1611+a0905 a0504+a1611+a0905 a0504+a1611+a0905 a0504+a1611+a0905 a0504+a1007+a0704 a0504+a1007+a0704 a0504+a1007+a0704 a0504+a1007+a0704 a0504+a0302+a0908 a0504+a0302 a0504+a0302+a0101 a0302 a0504+a1409+a1211 a0504+a1409+a1211 a0504+a1409+a1211 a0504+a1409+a1211 a0504+a1409+a0101 a0504+a1409+a0101 a0504+a1409+a0101 a0504+a1409+a0101 a0504+a0202+a0503 a0504+a0202+a0503 a0504+a0202+a0503 a0504+a0202+a0503 a0504+a0805+a0101 a0504+a0805+a0101 a0504+a0805+a0101 a0504+a0805+a0101 a0504+a1409+a0908 a0504+a1409+a0908 a0504+a1409+a0908 a0504+a1409+a0908 a0504+a0302 a0504+a0302 a0504+a0302 a0504+a0302 a0504+a0302 a0504+a0302 a0504+a0302 a0504+a0302 a0101+a0504+a0908 a0101+a0504+a0302 a0101+a0504+a0101 a0101+a0504+a0302 a0504+a0302+a0908+a0101 a0504+a0302+a0908+a0101 a0504+a0302+a0908+a0101 a0504+a0302+a0908+a0101 a0504+a0302+a0908+a0101 a0504+a0302+a0908+a0101 a0504+a0302+a0908+a0101 a0504+a0302+a0908+a0101 a0504+a0101+a0908+a0302 a0504+a0101+a0908+a0302 a0504+a0101+a0908+a0302 a0504+a0101+a0908+a0302 a0504+a0101+a0908+a0302 a0504+a0101+a0908+a0302 a0504+a0101+a0908+a0302 a0504+a0101+a0908+a0302 a0504+a4021 a0504+a4021 a0504+a4021 a0504+a4021 a0504+a4021 a0504+a4021 a0504+a4021 a0504+a4021 a0504+a0805 a0504+a0805 a0504+a0805 a0504+a0805 a0504+a0805 a0504+a0805 a0504+a0805 a0504+a0805