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Harmony Explained: Progress Towards A Scientific Theory of Music. The Major Scale, The Standard Chord Dictionary, and The Difference of Feeling Between The Major and Minor Triads Explained from the First Principles of Physics and Computation; The Theory of Helmholtz Shown To Be Incomplete and The Theory of Terhardt and Some Others Considered Daniel Shawcross Wilkerson Begun 23 September 2006; this version 19 February 2012. Abstract and Introduction Most music theory books are like medieval medical textbooks: they contain unjustified superstition, non-reasoning, and funny symbols glorified by Latin phrases. How does music, in particular harmony, actually work, presented as a real, scientific theory of music?

In particular we derive from first principles of Physics and Computation the following three fundamental phenomena of music: the Major Scale, the Standard Chord Dictionary, and the difference in feeling between the Major and Minor Triads. Table of Contents People push different keys on a piano; some combinations and patterns sound good; others do not. A guide to Luciano Berio's music. What are the limits of a musical instrument? And what are the boundaries of a piece of music? Is an instrument bounded by the reality of the individual piece someone happens to be playing on it, so that all exists when you hear a violinist play, say, a solo Bach partita is that single piece, that single player, and that single instrument?

And is a musical work like an island, cut off from the rest of music history by a sea of difference so that the perimeter of one piece never impinges on the coast of another? A place to start with Berio? Try Laborintus II for voices, instruments and tape, a piece in which not just a musical past but a whole labyrinth of meanings, memories, and histories are conjured by the voices, in the interplay between Edoardo Sanguineti's richly resonant text and Berio's vertiginously surreal collage of references and allusions, to musical pasts of madrigals and polyphony. Folk Songs Sequenza VI Sinfonia Coro Sequenza XII. A guide to Witold Lutosławski's music. Now, we're perilously close to the boundaries of our self-imposed criteria for this whole series with the Polish composer Witold Lutosławski, since his centenary is celebrated next week (on the 25th, to be precise), but unlike that other prospective centennial this year, one Britten, B (who won't be in this series for reasons of sufficient exposure here and elsewhere).

Lutosławski's output is, I think, neither well-known nor well understood enough. It will be, of course, by the end of this 'ere exposition! Or at least, you will have found, I hope, some ear-opening avenues into the work of a composer whose output is among the most complete and coherent of the 20th century. So let's start, obviously, at the end. Listen to this: Lutosławski's Fourth Symphony, his last major work before his death in 1994, and a piece that symbolises and cements the achievement of his musical language. But this wasn't a serene progress to musical maturity carried out in an artistic vacuum.

Third Symphony. What pop music owes to the classical masters. Mozart pleases his public The years 1650 to 1750 were a period of feverish invention and technical ingenuity in music that reached an apotheosis in Handel's sublime oratorios and Bach's cantatas and Passions. Bach was probably the cleverest composer who ever lived; the mind-boggling complexity of much of his late music, in particular, has yet to be matched by any composer. But, as often happens in musical history, the generation after Bach stripped away much of the older composers' harmonic complexity, writing instead with a dramatically simpler palette of harmonies. The likes of Gluck, Mozart and Haydn created a whole new style based on, essentially, four major chords. Mozart – unlike most composers before him – was able to make a living independent of an institution or a single aristocratic patron, but he lived or died by what the public wanted to hear.

Mozart was a melodic genius. Schubert invents the three-minute pop song Schubert was a remarkable talent. As told to Imogen Tilden. Howard Goodall's top 10 music books. Notes on music ... A handwritten composition by Johann Sebastian Bach being displayed in Weimar, Germany. Photograph: Martin Schutt/EPA Music is both a universal joy (it's a cliché because it's true) and a seething map of tribal frontiers across which we stray at our peril. Virtually any paragraph written about its theory, its history, its analysis, its ethics or its science will be met with a hailstorm of contradiction and outrage, so I am nervous suggesting any books about music since such a list would undoubtedly infuriate as much as intrigue.

The music itself can be enough, without comment, of course. But how boring life would be without the debate. The 10 books I've chosen here are simply ones that I have enjoyed reading about the subject I adore; they do not cover the subject comprehensively or even fairly, they are just ways of looking through the kaleidoscope at different angles. Protective armour and helmet not included. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Steve Reich on Schoenberg, Coltrane and Radiohead. There is something oddly reassuring about the fact that Steve Reich lives in precisely the kind of house you might expect Steve Reich to live in. The cab journey to Pound Ridge, the tiny town on the New York-Connecticut border that the composer has called home since 2006, passes a lot of rather grand homes built in various classic styles, from colonial to arts and crafts.

Reich, by contrast, lives in what appears to be one of the area's few examples of modernism. Inside, the rooms are huge and white. There is beautiful mid-20th-century furniture. It is clearly the home of someone of refined taste. On one of the walls, there is a framed score of Clapping Music, Reich's 1972 attempt to apply his phasing technique – in which two instruments playing the same part gradually shift out of unison – to music that "needed no instruments beyond the human body". "Well, I take the Chuck Berry approach," he smiles. Reading this on mobile? Reading this on mobile?

How composers from Mozart to Bach made their music add up. What's the next number in this sequence? 5, 10, 20, 30, 36 … ? And the next in this? 640, 231, 100, 91 … ? If you know your Mozart then you'll identify 43 as the number that comes after 36 in the first sequence. The second sequence continues with 1,003, the number of Don Giovanni's female conquests in Spain. Mozart loved numbers. As an adult Mozart's obsession with numbers didn't wane. The curious string of numbers 1095060437082 appears in a letter to his wife Constanze. Mozart isn't the only composer to be fascinated by music, numbers and codes. Schumann too was an inveterate user of musical cryptograms. But it's probably Mozart's final opera, The Magic Flute, that is the work most laden with symbolism and numerical imagery.

Beyond the three-note rhythm sequence the number three is threaded through the opera in numerous ways. The opera is also full of pairs. For Mozart The Magic Flute is also a statement of his belief in a changing order, not just politically but also musically. The Rite of Spring – a rude awakening | Stage. At the first performance of The Rite of Spring in May 1913, even well-informed members of the audience had no idea what they were experiencing.

Afterwards, the critic of the French periodical Gil Blas recorded a conversation about the beginning of Stravinsky's prelude to the ballet: "'What instrument produces these sounds? ' I say, 'It's an oboe.' My right-hand neighbour, who is a great composer, insists that it is a muted trumpet. My left-hand neighbour, who is no less of a musical scholar, declares, 'I should have thought it was a clarinet.' In the interval we ask the conductor himself, and we are told that it was a bassoon that gave us such heart-searchings. " We have it on Stravinsky's own authority that the only person in Paris who understood, completely and immediately, The Rite of Spring was the composer Maurice Ravel. Many of the accounts of that famous first night focus on the conditions of near-riot that met the performance.

Is it losing its force? The rest is power: classical music in the age of the dictatorship. In his preface to The Rest Is Noise, Alex Ross writes: "In the classical field it has long been fashionable to fence music off from society, to declare it a self-sufficient language. " He goes on to contend that while in the "hyper-political 20th century, that barrier crumbles again and again", the "vague, mutable and deeply personal nature of musical meaning" makes the establishment of clear connections – let alone correspondences – between music and the outer world "devilishly difficult".

This is in fact a special form of pleading that rests on artificial parameters: implicit in The Rest Is Noise, for all its formal disavowals, there remains an assumed sharp dichotomy between high and low art, and a privileging of the discourse of the former. This is not to claim that Ross pays no attention to the impact of technological modernity on 20th-century classical music – he most certainly does. Hitler loved music because many humans – including evil ones – love music. How Stravinsky's Rite of Spring has shaped 100 years of music. The Rite of Spring was a revolutionary work for a revolutionary time. Its first performance in Paris, exactly 100 years ago on Wednesday, was a key moment in cultural history – a tumultuous scandal. Written on the eve of the first world war and the Russian revolution, the piece is the emblem of an era of great scientific, artistic and intellectual ferment.

No composer since can avoid the shadow of this great icon of the 20th century, and score after score by modern masters would be unthinkable without its model. The Rite of Spring has survived many trials in its first 100 years, not excluding the notorious premiere, during which Nijinsky's provocative choreography elicited such a volume of abuse that the music itself was frequently inaudible. And this score did intend to shock. Stravinsky's greatest weapon in this assault was a fundamental musical resource, low on the list of priorities for most post-Wagnerian composers: rhythm. • Click here for more on Stravinsky. Formalized Music: Thought and Mathematics in Composition - Iannis Xenakis. Scales and emotions. See also a post about making chords from scales. So maybe you want to write a song or an instrumental in a particular mood or style, and you’re feeling overwhelmed by all the scales.

Here’s a handy guide to the commonly used scales in Western pop, rock, jazz, blues and so on. Click each image to play the scale right in your browser with the aQWERTYon. These scales have a major third (E in the key of C), which makes them feel happy or bright. Major scale Happy; can be majestic or sentimental when slow. Mixolydian mode Bluesy, rock; can also be exotic/modal. Lydian mode Ethereal, dreamy, futuristic. Lydian dominant mode Also known as the overtone scale or acoustic scale, because it is close to the first seven pitches in the natural overtone series. Phrygian dominant mode Exotic, Middle Eastern, Jewish. Harmonic major scale Majestic, mysterious.

These scales have a flat third (E-flat in the key of C), which gives them a darker and more tragic feel. Natural minor scale (Aeolian mode) Dorian mode. MusicalMind.org Ear Training Online. Rhinegold Publishing: Music, the Arts & Education. Silence: Lectures and Writings - John Cage. The Music of the Spheres: Music, Science, and the Natural Order of the Universe - Jamie James. Websites - bocpages - the unofficial boards of canada wiki.