Category Archives: Well-Temperament

Irregular Temperaments and the Division of the Ditonic Comma

WellTemperaments titlepageThe author presents an analysis of the structure of irregular temperaments, with special emphasis on well-temperaments or circulating temperaments. Roughly 200 scales are examined, of which about a third are historical and the rest are original to the author. A systematic method is presented for the conversion of various regular temperaments (meantone temperaments) into circulating temperaments. Thus the historical material is embedded within the wider context of scalar architecture. The aim is an overview, leading to the understanding and control of design characteristics.

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-WellTemperament.pdf

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

bonus:
http://www.siementerpstra.com/writings/Terpstra-TwoBestWellTemperaments.pdf

The Laws of Harmonics

LawsofHarmonics titlepageStarting in the middle 1980’s, around the time that I wrote up A Short List of Musical-Cosmological Monochords, I began a patient compilation of diagrams. Most of them consisted of elaborate tables showing numerous just ratios calculated in cents, as well as some speculative monochords and representations of the Harmonic Series. I meant this work to accompany a text that sums up my investigations into Harmonics. Inevitably, it reflected my interests during the seventies and early eighties – just intonation, drone-based music, and monochords. I never got around to writing the text, though I left a couple of pages of notes. After a few years I scrapped the whole project and archived it under the rather imposing heading: The Laws of Harmonics. Recently I dragged it out of its storage to reconsider the project.

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-LawsofHarmonics.pdf

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