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In accordance with the foregoing investigations on mathematical principles, let bronze vessels be made, proportionate to the size of the theatre, and let them be so fashioned that, when touched, they may produce with one another the notes of the fourth, the fifth, and so on up the double octave.
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Chapter V, Sec. 1

 

Vitruvius

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In theatres... there are the bronze vessels in which are placed in niches under the seats in accordance with the musical intervals on mathematical principles. These vessels are arranged with a view to musical concords or harmony, and apportioned in the compass of the fourth, the fifth, and the octave, and so on up to the double octave, in such a way that when the voice of an actor falls in unison with any of them its power is increased, and it reaches the ears of the audience with greater clearness and sweetness. Water organs too, and the other instruments which resemble them cannot be made by one who is without the principles of music.

 

Vitruvius

 

I didn't want to repeat the same notes in the second verse that I used in the first, so I wrote out all the notes of the song and all the notes that were missing in the scale, given that there are twelve notes from octave to octave. All those notes that weren't in the scale were the ones I wanted in for the next verse. The listener isn't aware that they are new notes, but the sound is pleasing to the ear. I change the key, and somehow it's fresh because you haven't heard those notes before.

 

Paul Simon

 

The utter childishness of our provincial public's verdict upon any art-manifestation that may chance to make its first appearance in their own theatre — for they are only accustomed to witness performances of works already judged and accredited by the greater world outside — brought me to the decision, at no price to produce for the first time a largish work at a minor theatre. When, therefore, I felt again the instinctive need of undertaking a major work, I renounced all idea of obtaining a speedy representation of it in my immediate neighbourhood: I fixed my mind upon some theatre of first rank, that would some day produce it, and troubled myself but little as to where and when that theatre would be found.

 

Richard Wagner

 

I consider the Fourth a patriotic holday more than a nationalist one. We are celebrating the signing of a text, the establishment of a set of laws and principles on the Fourth of July. The Fourth is about political liberty and national independence. It is, for all its pomp and circumstance, a fairly secular and rational holiday. Meanwhile, Thanksgiving plays upon the mystic chords of memory and is prior to and independent of many of things we celebrate on the Fourth. Anyway, I agree its a fair criticism and probably just highlights different perspectives. And, yes, the food on the Fourth of July is really, really good. I am all about hotdogs, beer and barbecue. ()

 

Jonah Goldberg

 

Whereas the conception of space and time as a four-dimensional manifold has been very fruitful for mathematical physicists, its effect in the field of epistemology has been only to confuse the issue. Calling time the fourth dimension gives it an air of mystery. One might think that time can now be conceived as a kind of space and try in vain to add visually a fourth dimension to the three dimensions of space. It is essential to guard against such a misunderstanding of mathematical concepts. If we add time to space as a fourth dimension it does not lose any of its peculiar character as time. ...Musical tones can be ordered according to volume and pitch and are thus brought into a two dimensional manifold. Similarly colors can be determined by the three basic colors red, green and blue... Such an ordering does not change either tones or colors; it is merely a mathematical expression of something that we have known and visualized for a long time. Our schematization of time as a fourth dimension therefore does not imply any changes in the conception of time. ...the space of visualization is only one of many possible forms that add content to the conceptual frame. We would therefore not call the representation of the tone manifold by a plane the visual representation of the two dimensional tone manifold.

 

Hans Reichenbach