For manay years I have been encouraging the use of JI tuning for harps, zithers, and other appropriate stringed instruments. The results of many workshops have impressed upon me the need for a simplified tuning procedure for implementing JI on acoustical stringed instruments. Certain recurring mental blocks keep reappearing among musicians, for example, the inability to handle ratios. At the same time, many of the musicians I encounter who have a genuine interest in JI are implementing it solely through electronic media, especially synthesizers. The electronic keyboards have great potential in exploring new tunings and timbres, but re-tuning them is (dare I say it?) almost too easy! The proliferation of tuneable electronic keyboards presents the potential danger that hands-on tuning skills for strings may be lost.
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http://siementerpstra.com/writings/Terpstra-SimplifiedJITuning.pdf
Each pattern defines a Class of Just scales, each Class embodying twelve primary modes (not presented here). Symmetrical structures are centred in the page; whereas, non-symmetrical patterns are paired by complementarity. Historical references are presented where appropriate. The classification progresses from generally “horizontal” tuning to generally “vertical” tunings.
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.
The author explains how tendencies within the structure of the Pythagorean chromatic scale supported the transfer to Just Intonation; however, certain features of Just Intonation necessitated the application of some form of temperament. The meantone temperament formed the best compromise for the musical styles that were being explored. The author aims at a co-relation between tuning paradigm and associated musical style.
The author responds to the article “Just Inton(ot)ation,” written by Paul Rapoport and published in 1/1, Volume 7, Number 1 (September 1991).
The use of Just Intonation (simple ratios) as a musical tuning norm has a very long and illustrious history. However, this history is also rather complex. I cannot hope to give but the barest outline of an overview in the abbreviated format – it deserves a book. Nevertheless, an essay is a valuable exercise in condensed presentation, although it inevitably has its price. My interpretations of the historical data are sometimes based on long strings of circumstantial evidence, since this is all the information available. Consequently, it is only possible to present a fraction of the arguments that support my conclusions within this brief context. The reader should not forget that this is only one person’s version of the most likely story.
The author shows how various essential microtones rule relations between Diatonic and Chromatic harmony.
The author shows a formula that results in very good multiple divisions. An epimoric source ratio generates a specific resolution level of harmony.
The author generates a handsome collection of tetrachords by using an archaic arithmetical procedure. He embeds various historical tetrachords into the group, with special focus on Ptolemy. He provides historical context. He also presents a generalized classification of tetrachord types. Finally he demonstrates the usefulness of the schisma resolution in modelling the fine grain of n-limit Just Intonation.
Starting 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.