_______ 0. Imperfect Pitch PDF Print E-mail
Written by D. Bond   
Saturday, 31 October 2009 10:21
 

The Harmonic Matrix: 

 

prime materials of harmony & intonation

 

 

Daryn Bond

 

edited: 2009.10.10.

source material composed:  2008.07.25

 

 
1st draft completed: 2008.09.16

discussion document

 

 

For my sister, Jolene.

 

One day we will swim in rooms of jello!

 

 

“With the divine ear element which is purified and surpasses the human, may I hear both kinds of sounds, the divine and the human, those that are far as well as near.”

 

Anguttara Nikaya 3:100 1-10; I 253-56

Translated by Bhikkhu Bodhi. In the Buddha’s Words.

Contents

 

 

0. Imperfect Pitch................................................................................................................ 4

1. It Goes Like This.............................................................................................................. 5

2. Thus Have I Heard........................................................................................................... 7

3.  Oh, the inJustice!......................................................................................................... 12

4. Ring the Bells – a crack in the universe............................................................................ 14

5. Spacing the Spheres – the protractions of scale building................................................. 19

6. The Devil’s Playground - Diablos en Musica.................................................................... 22

    a. the howling wolf.......................................................................................................... 22

    b. pitchforks: tunings and temperaments......................................................................... 23

    c. the unbinding of heaven [fixing the piano].................................................................... 26

    d. in the garden.............................................................................................................. 28

7. The Harmonic Matrix...................................................................................................... 30

8. The Reflecting Mirror: Mysterium Contrapunctus............................................................. 35

10. The Great Work of Counting......................................................................................... 40

11. As Above and Below…................................................................................................ 43

12. The Completion Stage................................................................................................. 47

 

References & Works Cited................................................................................................. 53

0. Imperfect Pitch

 

 

- There is no place for speculation in scientific discourse.

                                    Sir Isaac Newton

 

I don’t have perfect pitch. I have trouble identifying intervals by ear. I am a terrible piano player. I’m an even worse computer programmer. That I should find myself compelled to write this paper at this time, I find quite phenomenal.

 

These failings notwithstanding, I will be presenting a brief discussion on the prime materials of musical harmony and intonation. I use the term ‘prime materials’ alluding perhaps to alchemical prima materia among other things but mostly as an indication of the importance that prime numbers and their interactions have in this theory of harmony.

 

I have tried to be as clear as possible within the limits of my own understanding. Please remember, this is not a text book. I make no claims of mathematical completeness or scientific rigour. I possess no degree of authority with the exception of that insight and knowledge that I have attained through my own studies and work on this subject. All mistakes found within this work are my own. I pledge to correct and clarify to the best of my ability as time passes.

 

Being thus unencumbered by academic constraints, I feel at liberty to include criticism, speculation and metaphors a good editor would likely find superfluous.  I leave this in, in hopes it may provoke further thought, and perhaps entertain a bit too.

 

I would include here the names of those kind few who have helped me remove errors and clarify this paper, but so far there haven’t been any takers.[1] Clearly, more work needs to be done in this regard. This is far from the final version of this paper. Comments and questions most welcome [ This e-mail address is being protected from spambots. You need JavaScript enabled to view it ].

 

Thus:

 

Here begins an exposition of the prime materials of harmony.

 

next 1. It Goes Like This



[1] Until recently: Thank you to Professor Orjan Sandred for reading and listening, and for his instruction in high quality recording techniques. I have failed to edit this paper based on his recommendations, choosing instead to write a fresh summary article, and to work on my sampling technique. This version, as Dr. Sandred rightly pointed out, offers little that is new until page 30, aspiring to the condition of a ‘textbook’.


 

 

Last Updated on Tuesday, 25 May 2010 22:15