Category Archives: Multiple Divisions

The Modular Keyboard – Novel Tuning Utilities Software for MIDI-Equiped Digital Synthesizers

Back in the middle 1980’s I had an idea for converting a standard keyboard into a keyboard capable of applying 53-equal temperament. It was developed for the Apple 2E computer synthesizer called the Soundchaser. It uses software to change subsets of the wider field of possibilities. This file also includes a printout of the computer program. The project was funded by a Canada Counsel Arts Grant.

Click on the link to see the article in your browser or right-click to save the file to your drive.

http://www.siementerpstra.com/writings/Terpstra-ModularKeyboard.pdf

 

 

The Matrix Model of Musical Harmony

MatrixModel titlepage

A picture is worth a thousand words, and this collection of diagrams is largely self-explanatory. However, a brief introduction to the conceptual framework is in order.

The matrix is an integrated model for the description of cyclical temperaments, that is, temperaments which can be expressed by one or more circle of fifths. As such, they are equal temperaments, using some step interval as a basic building block. Of course, the most familiar of such temperaments is 12-E.T. But a host of others exist, which need to be evaluated according to their interval structure and musical worth.

Click on the link to see the article in your browser or right-click to save the file to your drive.

www.siementerpstra.com/writings/Terpstra-MatrixModel.pdf

the Meantone Series of Cyclical Temperaments

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A cyclical temperament is a tuning system which may be expressed as a closed circle of Fifths. Such tunings have the advantage of unlimited modulation of harmonic pattern, that is, price for this mobility. The drawback lies in the mandatory use of irrational ratios instead of small-integer “Just” ratios. Such tuning systems use controlled “mis-tunings” of the normative simple ratios. Hence they are called Temperaments.

Click on the links to see the articles in your browser or right-click to save the files to your drive.

http://www.siementerpstra.com/writings/Terpstra-MeantoneSeries.pdf

http://www.siementerpstra.com/writings/Terpstra-MeantoneSeriesDiagrams.pdf

Toward a Theory of Meantone (and 31-E.T.) Harmony

MeantoneTheory titlepageThe author develops a syntax for meantone harmony based on the structural characteristics of the temperament. These features include a description of the Regions with their boundary functions, and also the three genera. An abstract topology of triad progression is introduced, as well as an introduction to the organization of functional tables for 31-ET.

Click on the links to see the articles in your browser or right-click to save the files to your drive.

http://www.siementerpstra.com/writings/Terpstra-MeantoneTheory.pdf

http://www.siementerpstra.com/writings/Terpstra-MeantoneTheoryDiagrams.pdf

Notes on an Approach to Musical Composition in 31-E.T.

31Composition titlepageThe purpose of this article is to examine certain aspects of theory which concert practical musical composition in 31-E.T. (or extended meantone). The principles which are put forth may also be used to advantage with other equal divisions, including 12-E.T., 19-E.T., and so on. This article was meant to compliment the other articles which I have written on meantone theory. Those articles are: TOWARD A THEORY OF MEANTONE HARMONY, THE MEANTONE SERIES OF CYCLICAL TEMPERAMENTS, THE MATRIX MODEL OF MUSICAL HARMONY, and THE EXTENDED MEANTONE STYLE OF GESUALDO. These articles form a unified approach with no (I hope!) internal contradictions.

Click on the links to see the articles in your browser or right-click to save the files to your drive.

http://www.siementerpstra.com/writings/Terpstra-31Composition.pdf

http://www.siementerpstra.com/writings/Terpstra-31CompositionDiagrams.pdf

 

An Abbreviated Dictionary of 31-et Harmonies

31etdictionary titlepageThis collection of harmonies is an expansion of the set presented in my paper Notes on Composition. The need for this information arose out of very practical concerns. I have been playing the enharmonic guitar, and I wanted to work out the finger-positions for chords. Consequently I needed a reference of useful 31-et harmonies. Of course, this information could also be applied to keyboards or other instruments capable of chord functions. The collection of harmonies shown in Notes are presented in a most concise but abstract way. My aim here is to present the information in such a manner that it can have practical applications for real music-making.

Click on the link to see the article in your browser or right-click to save the file to your drive.

http://www.siementerpstra.com/writings/Terpstra-31Dictionary.pdf

Technical Drawings of the Geometric Mean

These diagrams show how the Geometric Mean can be used to find the fret positions for various temperaments. There is mention of it in various papers, namely

http://siementerpstra.com/introductionmonochord/
http://siementerpstra.com/aristoxenus/
http://siementerpstra.com/ptolemy/
http://siementerpstra.com/lawsofharmonics/

Terpstra-GeometricMeanGenerating4ETTerpstra-GeometricMeanGenerating5ET Terpstra-GeometricMeanGenerating7ET Terpstra-GeometricMeanGenerating12ET Terpstra-GeometricMeanGenerating19ET Terpstra-GeometricMeanGenerating31ET Terpstra-GeometricMeanGenerating53ET

The Spectrum Keyboard

SpectrumKeyboard titlepageThe Spectrum Keyboard is a redesigned music keyboard intended for digital synthesizers, samplers, and other electronic media applications. It is planned as a ‘musical typewriter’, making the playing of chords and scales much easier than the old black-and-white keyboard. This is the first version (1988) of the keyboard built in New York in 1991 called the Terpstra-keyboard.

Click on the link to see the article in your browser or right-click to save the file to your drive.

http://www.siementerpstra.com/writings/Terpstra-SpectrumKeyboard.pdf

 

The Global Keyboards: design specifications

GlobalKeyboards titlepageThe GLOBAL KEYBOARDS refer to a complimentary pair of generalized musical typewriters for computer-based electronic media. Since the design was formulated in 1986 it has been given several names: the Spectrum Keyboards (after a discarded color scheme), the One-Circle Global Keyboards (after an essential parameter of the design), or just my generalized keyboards. The complimentary relation between the two keyboards has also led me to call them male and female.

Click on the link to see the article in your browser or right-click to save the file to your drive.

http://www.siementerpstra.com/writings/Terpstra-GlobalKeyboards.pdf