The Strict Style, in addition to being the “vastly predominant world method,” is the method used in many works by composers including Lou Harrison himself, Terry Riley, La Monte Young, Michael Harrison, and many others. This approach is more or less necessary if one intends to compose for a fixed-pitch instrument, such as a retuned piano or harpsichord or a refretted guitar, or an ensemble such as the Harrison/Colvig American gamelan. (Composing in the free style is a subject for advanced students, and is beyond the scope of this article.) If you have some experience with composition, you already have some idea of what sorts of scales, modes, and harmonic progression interest you and what their expressive properties are. Try mapping different versions of these figures onto a JI lattice like that in Figure 5. (Learn to construct such lattices for yourself; they’re a vital tool for understanding JI.) You will discover that there are many different versions of familiar resources such as pentatonic or diatonic scales. In 12TET, there is only one whole tone and one semitone, which can be arranged in a limited number of ways to construct five- or seven-tone scales. (There are only eleven unique intervals smaller than an octave in 12TET, though they may, in some cases, be called by different names.) In contrast, JI offers a much larger variety of such intervals (see Table 3), which can be used in constructing scales that are at once familiar and novel. Different versions of familiar scales will have different expressive properties and tonal centricities. Once one has chosen a mode or gamut, what then? Take time to familiarize yourself with all of the tones and the intervals that connect them. By this I mean familiar both aurally and computationally. Which intervals feel stable and which are in need of resolution? What melodic or harmonic figures lead to or away from the stable intervals? The simple-ratio intervals upon which JI is based are what the human auditory system recognizes as consonance, if it ever has the opportunity to hear them in a musical context. 1 The significance of whole-number ratios has been recognized by musicians around the world for at least 2,500 years. Beats take place between two simple tones whose frequencies are near unison. These beats—regular variations in loudness—occur at a rate that is the difference in Hz between the two generating frequencies. Beats can be perceived clearly when the difference is less than 20–25Hz, but as the difference increases beyond this point the beats blend together, giving rise to a general sensation of roughness. This roughness gradually decreases as the difference increases, persisting until the difference exceeds an interval called the critical band, which, for most of the audio range, falls between a whole tone and a minor third. There is no simple answer to the question “how do I go about composing in JI?” once you have acquired the basic resources needed to begin. There is no manual or course that will tell you how to do it. It is a question that individual composers must answer for themselves, depending on their musical taste and aesthetic preferences, and on how the music is ultimately to be performed. Lou Harrison, in his Music Primer, made a useful distinction:

If you would like something written in your own lifetime, look no farther than this citation from Steven Brust’s Orca, published in 1996 and hardly a hallmark of archaic speech: There it is used like the conjunction and so; using therefore in that position would have caused a comma-splice error. To have used therefore, a semicolon not a comma would have been required. It was not until about five years later that I had a second and more revelatory encounter with JI. In the summer of 1975, I enrolled in a class called “Intonation in World Music,” presented by Lou Harrison at the Center for World Music in Berkeley, California. In this course, I learned the fundamentals of JI, its relation to various musical cultures, and how to work with musical ratios. Equally important, I had the experience of JI in conjunction with a very different musical aesthetic. At the time, Lou and Bill Colvig were building their first American gamelan, later known as “Old Granddad” (the instruments used in the Suite for Violin and American Gamelan and La Koro Sutro). Students were invited to perform in a concert on these instruments at the end of the term and several also composed for the ensemble (I did not). Old Granddad was tuned in a straightforward just D-major scale, about as different from Partch’s scale as possible in the realm of JI. Several of the pieces presented were in a minimalist/proceduralist style, a compositional practice that interested me at that time. The simple intervals of 5-limit JI, heard in that context, were stunningly beautiful. That experience changed my life. I came away from that class and concert with both the tools necessary to understand JI and the germ of a compositional and instrument-building program that culminated in the creation of Other Music’s American Gamelan in 1977–78. 4 Noun Eschewing cheap shots, McBride favors a careful, winding excavation – reaching into history for the whys and wherefores of his novels’ crowded casts, while delivering whopper stories with electric finales. — Erin Douglass, The Christian Science Monitor, 12 Oct. 2023 Soccer, though, did not waste time wondering about the whys and wherefores. — Ahmed Al Omran, New York Times, 13 July 2023 The political whys and wherefores are important — and might be left to another piece. — Jay Nordlinger, National Review, 14 May 2023 As in most of Tim and Eric’s sketch humor, there are few whys and wherefores. — Austin Considine, New York Times, 26 Mar. 2020 Julian Fellowes, a master writer who understands so well all the peculiarities of time and place, manners and historical significance of the whys and wherefores of his fictional inhabitants, is to be applauded. — Los Angeles Times, 11 Oct. 2019 In addition to gleaning the why and wherefore behind America’s foundational document, teenage listeners will meet up with the Declaration of Independence and a roster of seminal Supreme Court decisions. — Louis Bayard, New York Times, 28 May 2018 The book casts its spell in revealing the whys and wherefores of the killings, as investigated by Burke’s onetime high school classmate, Rob Barrett, a Boston FBI agent whom Burke likes nothing better than to humiliate. — Lloyd Sachs, chicagotribune.com, 21 May 2018 Harris will explain the whys and wherefores of rituals and the choreography of services. — Courant Community, 5 June 2017 See More Now Sauron prepared war against the Eldar and the Men of Westernesse, and the fires of the Mountain were wakened again. Wherefore seeing the smoke of Orodruin from afar, and perceiving that Sauron had returned, the Númenóreans named that mountain anew Amon Amarth, which is Mount Doom.How do the intervals of twelve-tone equal temperament (12TET), the predominant tuning system in the West over the past 250+ years, compare with the simple-ratio intervals I just described? The basic premise of temperament (any temperament) is that the number of pitches required to play in different keys can be reduced by compromising the tuning of certain tones so that they can perform different functions in different keys, whereas in JI a slightly different pitch would be required to perform each function. In other words, temperament compromises the quality of intervals and chords in the interest of simplifying instrument design and construction and playing technique. 12TET takes advantage of the fact that the sum of twelve perfect fifths (312:212) is slightly greater than seven octaves (27:1). The difference is the Pythagorean comma (531,441:524,288, about 23.5 cents). Each fifth in 12TET is flatted (narrowed) by 1/12 of the Pythagorean comma (approximately 1.96 cents) causing the fifths to form a closed circle. To achieve this, the starting frequency is multiplied twelve times in succession by the twelfth root of two (12√2), an irrational number that is approximately 1.05946. This ensures that none of the resulting intervals except the octave will be simple ratios. The problems with 12TET are not limited to its fifths being slightly narrow; chaining fifths, whether perfect or slightly flatted, does not result in good thirds or sixths. And, of course, 12TET, being a closed system, makes no provision for the admission or understanding of any additional intervals. It provides “acceptable” approximations of those intervals that most musicians in Europe c. 1750 considered useful and no more. Attempts by some twentieth-century composers and musicians to expand the resources of 12TET by subdividing it into smaller arbitrary intervals, such as quarter tones, third tones, etc., failed to solve its fundamental psychoacoustic problems.

Just intonation (hereinafter “JI”) is any system of tuning in which all of the intervals can be represented by ratios of whole numbers, with a strongly implied preference for the smallest numbers compatible with a given musical purpose. Unfortunately, this definition, while accurate, doesn't convey much to those who aren't already familiar with the art and science of tuning. The aesthetic experience of just intervals and chords, however, is unmistakable. A You have the spelling right, though I can see why you might feel it looks odd, not least because it’s one of those fixed expressions that one trots out without thinking much about them. And one half of it is archaic, anyway. Wherefore is a word that first arose in Middle English and saw much use in Early Modern English as well, dwindling then across the 18 th and 19 th centuries, and whose use is today mostly limited to literary, poetic, and oratorical registers. You found it in literature, where it still at whiles appears. It is also still found in modern ecclesiastical writings, probably because of how frequently it occurs in the King James Version of the Bible, which is in Early Modern English. You won't encounter this word really very much in modern writing. However, there is one place where it is common, and that is in the idiom "whys and wherefores" or sometimes just "wherefores" as a noun. This means "an intent or a why". (See for example in wiktionary above.) I sat down at the table, closed my eyes, and took my first deep breath in what seemed like a year or so. The old woman looked at me and didn’t ask any questions, wherefore I gave her no answers. I really wished you were here, Kiera, because I felt the need to confess and to have some help sorting out what had just happened.He’s asking out of what earlier reason he was born, not to what future purpose. He’s just asking why; you can’t start a question with therefore.