With the advancements of computer technology, why are we not making more music with unconventional sonorities? A report detailing theoretical and computing tools available to the microtonal composer.

Experiments in microtonal tuning systems and composition have been explored by avant-garde composers throughout the past century. Partch details with great intricacy his Chromelodeon, a 43 note per octave harmonium in which he devised specific tunings for his compositions (Partch, 1974, pp. 207-219). Ivan Wyschnegradsky also composed experimental performances in 24 TET by tuning one piano 50 ¢ below A 440 Hz whilst leaving the other in concert pitch increasing the amount of notes available in his work ‘24 Preludes in Quarter Tone System’ (Keeler, N.D). With the advent of computing technology and software synthesis, there are more efficient tools at the disposal to microtonal composers as opposed to working under the constraints of acoustic law.

The work of Plomp and Levelt (1965) concludes that by plotting the consonances and dissonances of a fundamental sine and overtone series on a graph using the equation in fig. 1 , the maximum consonances can be found across the broadband spectrum at simple integer ratios of the fundamental frequency, correlating with the Harmonic Series (Sethares, 2005, pp. 85-87). Partch understood when designing his ‘One Footed Bride’ that the consequences of acoustic harmonic law would add dissonant property to his music. “Short of a lifetime of laboratory work which the composer cannot undertake, the general is the only practical approach” (Partch, 1974, pg 157). With the creation of microtonal software synthesisers such as XEN FM (Xen Arts, 2014) and .tun code generators such as SCALA, (huygens-fokker, 2017) composers can now design tuning systems and overtone spectra for their synthesisers and it becomes possible to compose music that would not be physically possible in the real world due to acoustic principles.

d(f1,f2,a1,a2)

where:

f1 is the frequency of the lower sine,

f2 is the frequency of the higher sine, and

a1 and a2 are the corresponding amplitudes

fig. 1 (Sethares, 2005, pg. 91)

My research report will look into the possibilities of creating music removed from conventional harmony in an effort to expand the harmonic sonorities composers have at their disposal. The paper will start by addressing tuning theory and how we have arrived at the western standardisation of 12 TET. This is relevant to my research because the canon of tuning theory has to be addressed before it can be systematically manipulated. This is also relevant because as my portfolio project will incorporate both chordophones and electrophones (Hornbostel & Sachs, 1914, pp 553–90 ), I will need to research the implications of the acoustical phenomenon of the Harmonic Series and to what extent it will affect my chosen scales for acoustic instruments in which I cannot specify the spectra. Sethares details methodology for understanding this in his book Tuning, Timbre, Spectrum, Scale (2005). In preparation for incorporating and treating acoustic instruments into microtonal compositions, a study of the harmonic series and its mathematical interval relationships will be undertaken and I will research how to prepare the frets of a sitar to play the Harmonic Series. This process will be adapted from the Monochord/Canon procedure and I will document the process inside my work, explained in a way which can be applied to any string instrument (Partch, 1974, pg. 79). This part of my research will have me reflect critically on academic theoretics of tuning theory and establish the rules in which determine my compositional process.

After my research above is conducted, I can arbitrarily choose four TET scales to research, compare and contrast for my compositions. The scales chosen for this project will include a TET scale that shares a common factor of 12, the Carlos Alpha scale (Benson, 2007, pg. 232), a TET scale divided by a prime factor and the Just Intonation scale. I will begin to make comparisons on said scales by using Ellis’ Cents System (Helmholtz, 1885) and the ratio language of intervals as described by Partch (1974) to categorise each respective tuning system. Erv Wilson’s theories on Moment of Symmetry scales (MOS) (1975) provide sufficient methodology for computing scales using intervals as generators periodically. This allows us to analyse the scale movements in which can be traversed inside tuning systems melodically and harmonically. I will use Wilson’s MOS tool to document these movements within different tuning systems in my research which in turn will influence my compositional process in demonstrating my research. The same techniques used in de-constructing the four arbitrary scales chosen for my compositions will also be applied to 12 TET for the purposes of being able to make qualitative study and comparisons against what is considered standardised western tuning. During my preliminary research, I found that dividing the octave (1200 ¢) by x (the number of equal divisions you want to the octave) gives you the distance of the smallest interval playable from the scale. Whilst comparing 12 TET and 15 TET respectively, I noticed that 400¢ (a major 3 rd in 12 TET) also appears in 15 TET when multiplying the smallest interval of 80¢ by 5. Because the number 400¢ appears in both tuning systems, it becomes possible to navigate through 15 TET with steps of 12 TET major 3rds. This is because both 12 TET and 15 TET both share a common factor of 3 (To see this, draw a line of best fit from the value 400¢ starting at the top of column 3 TET and join all other 400¢ in the table together). Extracting this arms us with a tool to make evident which intervals are present in TET tunings and classify the interval distances present in TET systems. My research into different temperament tunings will expand on this idea of classification and I intend on researching other practitioners and theorists sources to see if there are any other bodies of work in which I can reference.

Next, I can begin to practically research common tools available to the microtonal composer such as XEN FM and SCALA in order to document their effectiveness and efficiency at realising my tuning systems explored above. This part of the research project will act as a product review and explain the technical features in which are necessary to create microtonal music. As there are many ways to achieve the same goal, which in this case is microtonal composition, I can narrate my process of experimentation within alternative tuning systems and this will work as an instructional guide to my process.

Bibliography:

Benson, D. (2007) M usic: A Mathematical Offering . Cambridge University Press, UK.

Helmholtz, H. (1885) O n the Sensation of Tone . 2 nd Ed. Longmans, Green & Co, London.

Hornbostel, H. & Sachs, C. (1914) Zeitschrift . (Internet Source) [Available at: https://archive.org/details/zeitschriftfre46berluoft] [Accessed 02/10/2017].

Huygens-Fokker. (2017) Scala Home Page. (Internet Source) [Available at:

http://www.huygens-fokker.org/scala] [Accessed 02/10/17].

Keeler, J. (N.D) How does Ivan Wyschnegradsky explore microtonality in reference to his 24 preludes for piano? (Internet Source) [Available at: https://www.scribd.com/document/260873334/Wyschnegradsky-Essay] [Accessed 26/10/17].

Partch, H. (1974) G enesis of a Music . 2 nd Ed. Da Capo Press, New York.

Plomp, R. & Levelt W. J. M (1965) T onal Consonance and Critical Bandwidth . (Internet Source) [Available at: http://www.mpi.nl/world/materials/publications/levelt/Plomp_Levelt_Tonal_1965.pdf] [Accessed 12/10/17].

Popular Music (2005) C an we get rid of the ‘popular’ in popular music? A virtual symposium with contributions from the International Advisory Editors of Popular Music . Volume 24/1. Cambridge University Press, United Kingdom.

Sethares, W. (2005) T uning, Timbre, Spectrum, Scale . 2 nd Ed. Springer, London.

Wilson, E. (1975) A Letter Explaining MOS Scales. (Internet Source) [Available at: http://anaphoria.com/mos.pdf] [Accessed 27/09/2017].

Xen-arts. (2014) Xen Arts Home Page. (Internet Source) [Available from: http://xen-arts.net/xen-fmts-2] [Accessed 02/10/17].