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A New Geometry of Musical Chords in Interval Representation: Dissonance, Enrichment, Degeneracy and Complementation

Penned By Miguel Gutiérrez
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4.85
61,874 Global Ratings
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A New Geometry of Musical Chords in Interval Representation: Dissonance, Enrichment, Degeneracy and Complementation

Penned By Miguel Gutiérrez
4.85 61,874 Ratings
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Editor's Note:
This monograph covers a fresh and original look at musical chords. The idea emanates from the fact that an intervallic representation of the chord leads naturally to a discrete barycentric condition. This condition itself leads to a convenient geometric representation of the chordal space as a simplicial grid. Chords appear as points in this grid and musical inversions of the chord would generate beautiful polyhedra inscribed in concentric spheres centered at the barycenter. The radii of these spheres would effectively quantify the evenness and thus the consonance of the chord.Internal symmetries would collapse these chordal structures into polar or equatorial displays, creating a platform for a thorough degeneracy study. Appropiate morphisms would allow us to navigate through different chordal cardinalities and ultimately to characterise complementary chords.

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Length N/A Pages
Language Eng
Released July 1, 2010
Identifier (ISBN) 8709895
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Miguel Gutiérrez
The Mind Behind the Work
Miguel Gutiérrez

After spending years working in the corporate world, Miguel Gutiérrez finally decided to pursue a lifelong passion for writing. They currently reside in a quiet suburb where they spend most of their time outlining new stories, reading extensively, and occasionally attempting to bake.

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James Thompson
James Thompson July 22, 2025
"Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading."
Edward Collins
Edward Collins September 29, 2024
"I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre."
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Deborah Thompson
Deborah Thompson March 27, 2025
"A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me."
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Andrew Davis November 19, 2024
"Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece."
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Gary Cruz March 20, 2025
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Joshua Anderson May 10, 2025
"Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars."
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"I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading."
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"Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars."
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"I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading."
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"Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre."
Brian Young
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"I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers."
Margaret Miller
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"Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre."
Karen Hernandez
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"Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem."
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"A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece."
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"Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading."
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"Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre."
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"A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre."
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"Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece."
Margaret Evans
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"Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author."
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"I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers."
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"Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author."
Mark White
Mark White February 01, 2025
"Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem."
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Jessica Turner March 15, 2024
"A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel."
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"Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre."
Melissa Perez
Melissa Perez January 07, 2025
"I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers."
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"I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem."
Barbara King
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"Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre."
Joshua Harris
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"A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars."
Sandra Hill
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"Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading."
Margaret Gomez
Margaret Gomez June 27, 2025
"Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem."
William Young
William Young September 26, 2024
"A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading."
Donald Torres
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"A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars."
Robert  Davis
Robert Davis August 18, 2024
"Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading."
Joshua Mitchell
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"Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars."
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"Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall."
Melissa Martin
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"An acceptable diversion. It verged on repetitive in the second act. A more concise edit would have served it well. Suitable if your reading queue is empty."
Andrew Walker
Andrew Walker February 09, 2024
"Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre."
Edward White
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"Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers."
Margaret White
Margaret White April 29, 2024
"Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading."
Michael Phillips
Michael Phillips April 24, 2025
"A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece."
Nicholas Ramirez
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Edward Adams
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"Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars."
William Carter
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"I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers."
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"A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars."
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"Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars."
Sandra Roberts
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"Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars."
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"I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author."
Michael Diaz
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"Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars."
Jessica Rivera
Jessica Rivera March 08, 2024
"I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author."
Patricia Roberts
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"Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading."
John Hill
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"Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers."
Betty Clark
Betty Clark October 26, 2024
"I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers."
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"A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel."
Sarah Collins
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"Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece."
Steven Anderson
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"I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading."
Carol Garcia
Carol Garcia March 18, 2024
"Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author."
Sandra Harris
Sandra Harris April 24, 2024
"A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel."
Kenneth Thompson
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"Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem."
Christopher Carter
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"Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author."
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"A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel."
Jessica Ramirez
Jessica Ramirez May 02, 2025
"Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre."
Daniel Flores
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"A decent, if standard, experience. Certain acts were fascinating, while others felt like a slight endeavor to complete. Suitable if your reading queue is empty."
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Matthew Perez June 29, 2024
"Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading."
Kimberly Jackson
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"Excellent, though slightly flawed. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend."
Donna Baker
Donna Baker May 05, 2025
"Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars."
Rebecca Hill
Rebecca Hill June 25, 2024
"Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author."
Sharon  Parker
Sharon Parker May 03, 2025
"A decent, if standard, experience. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perhaps more aligned with a different audience's tastes."
Mary Martinez
Mary Martinez May 23, 2024
"Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem."
Eric Jones
Eric Jones May 11, 2024
"It was adequate. It verged on repetitive in the second act. A more concise edit would have served it well. A fair 3 stars."
Cynthia Lopez
Cynthia Lopez June 12, 2025
"A decent, if standard, experience. Certain acts were fascinating, while others felt like a slight endeavor to complete. Perfectly average."
Karen Rodriguez
Karen Rodriguez May 16, 2024
"Not entirely to my refined tastes. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perhaps more aligned with a different audience's tastes."
Patricia Martin
Patricia Martin December 26, 2024
"Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre."
Cynthia Torres
Cynthia Torres June 21, 2025
"Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem."
Michael Diaz
Michael Diaz April 14, 2024
"I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece."
Ryan Anderson
Ryan Anderson March 01, 2024
"I find myself somewhat conflicted. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. A fair 3 stars."
Sharon  Parker
Sharon Parker January 29, 2024
"Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem."
Brian Diaz
Brian Diaz September 01, 2025
"Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading."
Nicholas Cruz
Nicholas Cruz June 22, 2025
"Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers."
John Rivera
John Rivera June 06, 2025
"Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem."
Anthony Gonzalez
Anthony Gonzalez November 06, 2024
"A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece."
Nancy Wright
Nancy Wright November 27, 2024
"An acceptable diversion. It verged on repetitive in the second act. A more concise edit would have served it well. A fair 3 stars."
Amanda Sanchez
Amanda Sanchez June 07, 2025
"Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem."
Sarah Gomez
Sarah Gomez December 05, 2025
"Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece."
Brian Moore
Brian Moore October 13, 2025
"Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem."
John Martinez
John Martinez February 10, 2025
"A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me."
Melissa Martin
Melissa Martin November 05, 2024
"Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre."
Paul Torres
Paul Torres October 27, 2024
"An acceptable diversion. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perhaps more aligned with a different audience's tastes."
Robert  Davis
Robert Davis December 24, 2024
"A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers."
Gary Walker
Gary Walker October 17, 2024
"Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading."
Karen Hernandez
Karen Hernandez January 10, 2025
"Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author."
Rebecca Martin
Rebecca Martin May 18, 2025
"I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall."
Michelle Clark
Michelle Clark June 07, 2025
"Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem."
Margaret Thomas
Margaret Thomas April 22, 2024
"Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem."
Amanda White
Amanda White May 18, 2025
"I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author."
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