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The Why and the Wherefore of the European War: Bible Study (Classic Reprint)

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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. Tolkien also uses wherefore three times in the posthumously published poetry collected in The Lays of Beleriand, some of which is also written in an intentionally archaic style, even more so than the quotes above. There you will find it resting comfortably at home amongst such relics as ere, rede, methought, forwandered, thou dost, and spake — all examples of more Early Modern English such as found in Shakespeare or the King James Version of the Bible. 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.’

First of all "wherefore" is a pretty archaic usage, it is marked so in many dictionaries (though some special usages are not archaic.) The other posters are drawing a strong distinction between wherefore and therefore, but the fact is that some dictionaries list "therefore" as a meaning of "wherefore". For example Merriam Webster and wiktionary. 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. 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. 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.

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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.

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:

whys and wherefores, the

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 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. 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.

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. Hooker Eccl. Pol. v. lxiii. §1 ― The true reason wherfore Christ doth loue belieuers is because their belief is the gift of God. So far, we have been talking about the properties of musical intervals in isolation. This is much like talking about the properties of paint squeezed from a tube onto a palette. Musical intervals or painter’s colors are not without aesthetic affect when encountered in isolation like this, but it requires the work of a skilled painter or composer to use these materials in a way that reveals their true significance. 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?’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: 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. Originally published in 1985, SIPRI's study suggests some answers to these questions. The book examines the situation in a number of countries of key importance for non-proliferation: the two nuclear-weapon states which have declined to join the 1968 Non-Proliferation Treaty (China and France); a group of nuclear ‘threshold’ states also remaining outside the Treaty (Argentina, Brazil, India, Israel, Pakistan, South Africa and Spain); and a group of states, both developed and developing, which for various reasons have joined the Treaty (Canada, Egypt, South Korea, Sweden, Switzerland and Taiwan).

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