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Three is the Magic Number

The Rule of Three in Mathematics

rule-of-three-calculator-150x150The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions. By having three numbers: a, b, c, such that, ( a / b = c / x), (i.e., a: b :: c: x ) you can calculate the unknown number. The Rule of Three Calculator uses the Rule of Three method to calculate the unknown value immediately based on the proportion between two numbers and the third number.

The working of the Rule of Three Calculator can be expressed as follows:

Rule of Three Calculator

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Rhetorical Devices — Rule of Three

The rule of three describes triads of all types — any collection of three related elements. Two more specific triad variants are hendiatris and tricolon.

Hendiatris

A hendiatris is a figure of speech where three successive words are used to express a central idea.

Examples of hendiatris include:

  • Veni, vidi, vici.” [Julius Caesar]
  • Liberté, Égalité, Fraternité [French motto]
  • Citius, Altius, Fortius” [Olympic motto]
  • Wine, women, and song” [Anonymous]

Tricolon

tricolon is a series of three parallel elements (words or phrases). In a strict tricolon, the elements have the same length but this condition is often put aside.

Examples of tricola include:

  • “Veni, vidi, vici.” [Julius Caesar]
  • Be sincere, be brief, be seated.” [Advice for speakers from Franklin D. Roosevelt]
  • Tonight, we gather to affirm the greatness of our nation – not because of [1] the height of our skyscrapers, or [2] the power of our military, or [3] the size of our economy.” [Barack Obama, Keynote speech to Democratic National Convention, July 2004]
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General MacArthur’s Thayer Award Speech — Duty, Honor, Country (1962)

General Douglas MacArthur
General Douglas MacArthur

The address by General of the Army Douglas MacArthur to the cadets of the U.S. Military Academy in accepting the Sylvanus Thayer Award on 12 May 1962 is a memorable tribute to the ideals that inspired that great American soldier. For as long as other Americans serve their country as courageously and honorably as he did, General MacArthur’s words will live on.

General MacArthur’s service to his country spanned the years from 1903, when he was graduated from the Military Academy, to 5 April 1964 , when he died in Washington, D.C., at the age of 84. He was recognized early in his career as a brilliant officer and was advanced to brigadier general in 1918. Twelve years later he was named Chief of Staff of the Army, and in 1937 he retired. 

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Claude Debussy’s use of the tritone 

Introduction to Debussy’s Pianistic Language

Claude Debussy
Claude Debussy

This is the tritone scale.

Built by pairing two major triads a tritone apart, and then placing those notes in scale order, the tritone scale brings a nice level of tension to your lines that you can use to build energy when soloing over 7th chords in a jazz or fusion context.

Art music in the twentieth century encompasses a wide range of expression, forms, and media. The development of mass communication and easy travel throughout the twentieth-century has linked the world into a global community that allows the collection and blending of many sources. One result of this is that diverse musical sources including folk music, Classical Indian Scales, American jazz elements, and the musical forms of Asia among others, have been assimilated into the Western Musical Tradition.

Debussy-Prelude to a Fawn-Leonard Bernstein

Folk music assimilation began before the end of the nineteenth century as Western thinkers explored previously remote lands and cultures.  An important result of this travel was the use of folk modes, pentatonic scales, and whole tone scales derived from native music in works by composers such as Bartók, Stravinsky, and Debussy.  Non-diatonic scales based on modes and seemingly abstract intervals such as the half step and whole step proved tantalizing to composers during the last part of the nineteenth, and early part of the twentieth century.

See an analysis of Prelude to a Fawn by Leonard Bernstein next.

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