<A>
variable efficients: *
coefficients in use: the coefficient of thermal expansion describes how the size of an object changes with a change in temperature. It measures the fractional change in size per degree change in temperature at a constant pressure. Different materials have different coefficients. Different coefficients have been developed for expansion by: volume, area, or linear.
Example
Linear expansion means change in one dimension (length) as opposed to change in volume (volumetric expansion). The coefficient is the fractional change in length per degree of temperature change. We can find the coefficient with the following calculation
The coefficient of thermal expansion is represented by the symbol α (alpha) for solids.
L is a particular length measurement and dL over dT is the rate of change of that linear dimension per unit change in temperature.
Having calculated α we can use it to determine (in most cases) the change in linear dimensions:
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Baroque music (thematic not melodic): *
Rather then developing new & singular melodies, elaboration on a single melody was their focus. Bach for instance used simply melody in his monumental Art of the Fugue. The entire work is based on a theme which consists of the 2 building blocks of tonal music: the 3 notes of a D minor chord & a scale.
This simple theme undergoes many permutations throughout the 14 fugues and 4 canons which constitute this work. Thus in the 3rd fugue he turns it upside down, that is, where the original melody descends it now ascends and vice versa.
In the 5th fugue, we hear it with some intervals filled in with rather jazzy, dotted rhythms.
Later still, it is syncopated and in triple time. Starting with the 8th fugue, new themes are introduced, but they are all in fact derived from this original theme.
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Baroque music (imitative tone-picture):
An example of imitative music is provided by Andrea Gabrieli (1532-85). He was an Italian composer and organist of the late Renaissance, a contemporary of Titian. The uncle of the more famous Giovanni Gabrieli, he was the first internationally renowned member of the Venetian School of composers, & was extremely influential in spreading the Venetian style in Italy as well as in Germany.
<D>
Wagner (leitmotiv): *
leitmotif for Siegfried from Siegfried, Act 2 (3rd Ring opera by Wagner)
<E>
Holderlin (his last poems): *
Locked in his tower in Tübingen an insane Hölderlin wrote strange poems under several pseudonyms, including that of Scardanelli. He would give implausible dates to these writings as well. The ultimate experience Hölderlin’s poetry describes a voyage beyond time and invisibility. Below is the opening verses of a longer poem, a prose version was first published by a university student, Wilhelm Waiblinger. Waiblinger made regular visits to the poet between 1822-26 & claims he transcribed it from Hölderlin's scattered writings. He believed that "In Lovely Blue" was a stark reflection of the poet's insanity.
excerpt from In Lovely Blue by Friedrich Hölderlin
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Like the stamen inside a flower
The steeple stands in lovely blue
And the day unfolds around its needle;
The flock of swallows that circles the steeple
Flies there each day through the same blue air
That carries their cries from me to you;
We know how high the sun is now
As long as the roof of the steeple glows,
The roof that’s covered with sheets of tin;
Up there in the wind, where the wind is not
Turning the vane of the weathercock,
The weathercock silently crows in the wind.