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.

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:Then Angrod spoke bitterly against the sons of Fëanor, telling of the blood at Alqualondë, and the Doom of Mandos, and the burning of the ships at Losgar. And he cried: ‘ Wherefore should we that endured the Grinding Ice bear the name of kinslayers and traitors?’ 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 word can also mean just simply "why", for example Matthew 14:31 "Wherefore didst thou doubt?". See dictionary.com, and as some have pointed out in Juliet's Shakespearean lament. This however is certainly a pretty archaic usage. 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. 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. 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.

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On the next day they bore her towards Ephel Brandir; but when they came to Dimrost, the Rainy Stair, where the tumbling stream of Celebros fell towards Teiglin, a great shuddering came upon her, wherefore afterwards that place was called Nen Girith, the Shuddering Water. 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.

Wherefore stood originally as one of a series of very tightly related word-pairs differing only in whether they began with wh- or they began with th-: 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: 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.After only a brief study of intervals it becomes clear that there are two ways of composing with them: 1) arranging them in a fixed mode, or gamut, & then composing within that structure. This is the Strict Style, & is the vastly predominant world method. However, another way is possible—2) to freely assemble, or compose, with whatever intervals one feels that he needs as he goes along. This is the Free Style… 7 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. 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.’

When composing in 12TET, you never need ask yourself, “which Bb do I want here?” or “am I sure that I want a G# here rather than an Ab?” (and which G# or Ab?). In JI, such questions are meaningful and often critical. Referring to the lattice in Figure 5, you will see that there are three varieties or “flavors” of “Bb” in close proximity to C 1/1. B7b 7/4 is the harmonic seventh of C. Bb– 16/9 is a perfect fifth below F 4/3 and a 9:8 whole tone below C. Bb 9/5 is a minor third above G 3/2 and a smaller 10:9 whole tone below C. Any of these tones could be used melodically in relation to C, though with different effects. Harmonically, their uses are quite distinct. B7b 7/4 can be used to form a consonant dominant-seventh type chord with C, E, and G or a subminor triad with G and D. Bb 9/5 is the minor third of a minor triad on G 3/2. Bb– 16/9 is the root of a triad including D– 10/9 and F 4/3. All of these tones also perform other roles in tonalities more distant from C 1/1. One need not look far on the lattice to see many other pairs of tones near C 1/1 that are represented by a single tone in 12TET, such as D 9/8 and D– 10/9 or A 5/3 and A+ 27/16 or C 1/1 and C7+ 63/32. Recognizing such distinctions and understanding their melodic and harmonic implications is an essential aspect of understanding and working with just intonation. 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. 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. As an example of this, consider Hebrews 12:1 from the King James: "Wherefore seeing we also are compassed about with so great a cloud of witnesses...", here meaning therefore.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. 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. 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.