276°
Posted 20 hours ago

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

£9.9£99Clearance
ZTS2023's avatar
Shared by
ZTS2023
Joined in 2023
82
63

About this deal

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 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. 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 have asked for a scenario in which only one of wherefore or therefore will work and they aren’t interchangeable. Here’s a good one:Q From Joseph Flanigan: I was wondering about the origin of whys and wherefores and the correct spelling. 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.

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. 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-:

Navigation menu

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.) 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 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. 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.

Asda Great Deal

Free UK shipping. 15 day free returns.
Community Updates
*So you can easily identify outgoing links on our site, we've marked them with an "*" symbol. Links on our site are monetised, but this never affects which deals get posted. Find more info in our FAQs and About Us page.
New Comment