Tuning our assessment instruments to harmonize our relationships

“Music is the art of measuring well.”
Augustine of Hippo

With the application of Rasch’s probabilistic models for measurement, we are tuning the instruments of the human, social, and environmental sciences, with the aim of being able to harmonize relationships of all kinds. This is not an empty metaphor: the new measurement scales are equivalent, mathematically, with the well-tempered, and later 12-tone equal temperament, scales that were introduced in response to the technological advances associated with the piano.

The idea that the regular patterns found in music are akin to those found in the world at large and in the human psyche is an ancient one. The Pythagoreans held that

“…music’s concordances [were] the covenants that tones form under heaven’s watchful eye. For the Pythagoreans, though, the importance of these special proportions went well beyond music. They were signs of the natural order, like the laws governing triangles; music’s rules were simply the geometry governing things in motion: not only vibrating strings but also celestial bodies and the human soul” (Isacoff, 2001, p. 38).

I have already elsewhere in this blog elaborated on the progressive expansion of geometrical thinking into natural laws and measurement models; now, let us turn our attention to music as another fertile source of the analogies that have proven so productive over the course of the history of science (also explored elsewhere in this blog).

You see, tuning systems up to the invention of the piano (1709) required instruments to be retuned for performers to play in different keys. Each key had a particular characteristic color to its sound. And not only that, some note pairings in any key (such as every twelfth 5th in the mean tone tuning) were so dissonant that they were said to howl, and were referred to as wolves. Composers went out of their way to avoid putting these notes together, or used them in rare circumstances for especially dramatic effects.

Dozens of tuning systems had been proposed in the 17th century, and the concept of an equal-temperament scale was in general currency at the time of the piano’s invention. Bach is said to have tuned his own keyboards so that he could switch keys fluidly from within a composition. His “Well-Tempered Clavier” (published in 1722) demonstrates how a well temperament allows one to play in all 24 major and minor keys without retuning the instrument. Bach also is said to have deliberately used wolf note pairings to show that they did not howl in the way they did with the mean tone tuning.

Equal temperament is not equal-interval in the Pythagorean sense of same-sized changes in the frequencies of vibrating strings. Rather, those frequencies are scaled using the natural logarithm, and that logarithmic scale is what is divided into equal intervals. This is precisely what is also done in Rasch scaling algorithms applied to test, assessment, and survey data in contemporary measurement models.

Pianos are tuned from middle C out, with each sequential pair of notes to the left and right tuned to be the same distance away from C. As the tuner moves further and further away from C, the unit distance of the notes from middle C is slightly adjusted or stretched, so that the sharps and flats become the same note in the black keys.

What is being done, in effect, is that the natural logarithm of the note frequencies is being taken. In statistics, the natural logarithm is called a two-stretch transformation, because it pulls both ends of the normal distribution’s bell curve away from the center, with the ends being pulled further than the regions under the curve closer to the center. This stretching effect is of huge importance to measurement because it makes it possible for different collections of questions addressing the same thing to measure in the same unit.

That is, the instrument dependency of summed ratings or counts of right answers  or categorical response frequencies is like a key-dependent tuning system. The natural logarithm modulates transitions across musical notes in such a way as to make different keys work in the same scaling system, and it also modulates transitions across different reading tests so that they all measure in a unit that remains the same size with the same meaning.

Now, many people fear that the measurement of human abilities, attitudes, health, etc. must inherently involve a meaningless reduction of richly varied and infinite experience to a number. Many people are violently opposed to any suggestion that this could be done in a meaningful and productive way. However, is not music the most emotionally powerful and subtle art form in existence, and simultaneously also incredibly high-tech and mathematical? Even if you ignore the acoustical science and the studio electronics, the instruments themselves embody some of the oldest and most intensively studied mathematical principles in existence.

And, yes, these principles are used in TV, movies, dentists’ offices and retail stores to help create sympathies and environments conducive to the, sometimes painful and sometimes crass, commercial tasks at hand. But music is also by far the most popular art form, and it is accessible everywhere to everyone any time precisely as a result of the very technologies that many consider anathema in the human and social sciences.

But it seems to me that the issue is far more a matter of who controls the technology than it is one of the technology itself. In the current frameworks of the human and social sciences, and of the economic domains of human, social, and natural capital, whoever owns the instrument owns the measurement system and controls the interpretation of the data, since each instrument measures in its own unit. But in the new Rasch technology’s open architecture, anyone willing to master the skills needed can build instruments tuned to the reference standard, ubiquitous and universally available scale. What is more, the demand that all instruments measuring the same thing must harmonize will transfer control of data interpretation to a public sphere in which experimental reproducibility trumps authoritarian dictates.

This open standards system will open the door to creativity and innovation on a par with what musicians take for granted. Common measurement scales will allow people to jam out in an infinite variety of harmonic combinations, instrumental ensembles, choreographed moves, and melodic and rhythmic patterns. Just as music ranges from jazz to symphonic, rock to punk to hiphop to blues to country to techno, or atonal to R & B, so, too, do our relationships. A whole new world of potential innovations opens up in the context of methods for systematically evaluating naturally occurring and deliberately orchestrated variations in organizations, management, HR training methods, supply lines, social spheres, environmental quality, etc.

The current business world’s near-complete lack of comparable information on human, social, and natural capital is oppressive. It puts us in the situation of never knowing what we get for our money in education and healthcare, even as costs in these areas spiral into absolutely stratospheric levels. Having instruments in every area of education, health care, recreation, employment, and commerce tuned to common scales will be liberating, not oppressive. Having clear, reproducible, meaningful, and publicly negotiated measures of educational and clinical care outcomes, of productivity and innovation, and of trust, loyalty, and environmental quality will be a boon.

In conclusion, consider one more thing. About 100 years ago, a great many musicians and composers revolted against what they felt were the onerous and monotonous constraints of the equal-tempered tuning system. Thus we had an explosion of tonal and rhythmic innovations across the entire range of musical artistry. With the global popularity of world music’s blending of traditional forms with current technology and Western forms, the use of alternatives to equal temperament has never been greater. I read once that Joni Mitchell has used something like 32 different tunings in her recordings. Jimi Hendrix and Neil Young are also famous for using unique tunings to define their trademark sounds. What would the analogy of this kind of creativity be in the tuning of tests and surveys? I don’t know, but I’m looking forward to seeing it, experiencing it, and maybe even contributing to it. Les Paul may not be the only innovator in instrument design who figured out not only how to make it easy for others to express themselves in measured tones, but who also knew how to rock out his own yayas!

References and further reading:

Augustine of Hippo. (1947/2002). On music. In Writings of Saint Augustine Volume 2. Immortality of the soul and other works. (L. Schopp, Trans.) (pp. 169-384). New York: Catholic University of America Press.

Barbour, J. M. (2004/1954). Tuning and temperament: A historical survey. Mineola, NY: Dover Publications.

Heelan, P. A. (1979). Music as basic metaphor and deep structure in Plato and in ancient cultures. Journal of Social and Biological Structures, 2, 279-291.

Isacoff, S. M. (2001). Temperament: The idea that solved music’s greatest riddle. New York: Alfred A. Knopf.

Jorgensen, O. (1991). Tuning: Containing the perfection of eighteenth-century temperament, the lost art of nineteenth-century temperament and the science of equal temperament. East Lansing, Michigan: Michigan State University.

Kivy, P. (2002). Introduction to a philosophy of music. Oxford, England: Oxford University Press.

Mathieu, W. A. (1997). Harmonic experience: Tonal harmony from its natural origins to its modern expression. Rochester, Vermont: Inner Traditions International.

McClain, E. (1984/1976). The myth of invariance: The origin of the gods, mathematics and music from the Rg Veda to Plato (P. A. Heelan, Ed.). York Beach, Maine: Nicolas-Hays, Inc.

Russell, G. (2001/1953). Lydian chromatic concept of tonal organization (4th ed.). Brookline, MA: Concept Publishing.

Stone, M. (2002, Autumn). Musical temperament. Rasch Measurement Transactions, 16(2), 873.

Sullivan, A. T. (1985). The seventh dragon: The riddle of equal temperament. Lake Oswego, OR: Metamorphous Press.

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One Response to “Tuning our assessment instruments to harmonize our relationships”

  1. Creatively Expressing How Love Matters for Justice: Setting the Stage and Tuning the Instruments | Livingcapitalmetrics's Blog Says:

    […] applicable to the Socratic midwifery of ideas and to the products of social intercourse. Tuning the instruments of the human, social, and environmental arts and sciences to harmonize and choreograph […]

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