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: 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. 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.

Frodo gazed at the ring with awe; for suddenly it seemed to him that he understood. ‘Yes,’ she said, divining his thought, ‘it is not permitted to speak of it, and Elrond could not do so. But it cannot be hidden from the Ring-bearer, and one who has seen the Eye. Verily it is in the land of Lórien upon the finger of Galadriel that one of the Three remains. This is Nenya, the Ring of Adamant, and I am its keeper. He suspects, but he does not know — not yet. Do you not see now wherefore your coming is to us as the footstep of Doom? For if you fail, then we are laid bare to the Enemy. Yet if you succeed, then our power is diminished, and Lothlurien will fade, and the tides of Time will sweep it away. We must depart into the West, or dwindle to a rustic folk of dell and cave, slowly to forget and to be forgotten.’ 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 For uses of therefore that will not tolerate being replaced with wherefore, consider the sense of therefore that is usually spelled therefor without a final -e:Here are a few more examples of wherefore from some of Tolkien’s more commonly read works. He uses it a total of eight times in the the posthumously published Silmarillion assembled by his son but only just once in The Lord of the Rings; he does not use it at all in The Hobbit. 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. You should probably get used to this if you’re reading Tolkien, especially The Silmarillion. One thing you should keep in mind is that your two quotations are respectively from the first two sections of the book you are reading, and these even more than the parts which follow Tolkien intentionally cast into language that would remind the reader of the King James Version of the Bible, because it was telling its own story of creation. Notice the archaic pronoun ye used in your first quote. The focus of the book is on motivations for and against nuclear proliferation. An analysis of these motivations leads the editor to make detailed recommendations aimed at halting the spread of nuclear weapons. The aspect of relationships between simultaneously sounded complex tones that has attracted the most attention among theorists is the coincidence of certain harmonics when pairs of complex tones are tuned in simple-ratio intervals, or conversely, the presence of beats resulting from the non-coincidence of these same partials when pairs of complex tones deviate from these simple intervals.

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. 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.The phrase is an interesting instance of the way English speakers can turn one part of speech into another without breaking stride. Conventional grammar would say that why is an adverb, but here it lurks in the guise of a noun, meaning “reason or explanation”. Likewise wherefore. 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. 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: F. T. Bullen Log Sea-waif 149 ― The ill-used crew promptly refused to do any more in her, and were, of course, clapped in jail therefor.

As you see, those are all location or direction words, with the wh- ones alone useable as the start of a question. Wherefore connects to the past and therefore to the future. Wherefore therefore means “why” or “which is why”; sometimes it means “and so”. 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.

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Hooker Eccl. Pol. v. lxiii. §1 ― The true reason wherfore Christ doth loue belieuers is because their belief is the gift of God. 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.

I would add that there is a “middle way” (with apologies to Buddhists): begin with a fixed scale or mode and then add pitches as required for harmony, counterpoint, transposition, modulation, and so on. This is the approach I use in much of my work. Additionally, pieces composed within a sufficiently large gamut, such as Partch’s 43-tone scale or Ben Johnston’s hyperchromatic scales, may be indistinguishable from “free style” compositions.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