scholarly journals II. On just intonation in music; with a description of a new instrument for the easy control of all systems of tuning other than the ordinary equal temperament

1873 ◽  
Vol 21 (139-147) ◽  
pp. 131-132
Keyword(s):  
Theory And Practice ◽  
Just Intonation ◽  
New Instrument ◽  
Equal Temperament

The object of this communication is to place the improved systems of tuning within the reach of ordinary musicians; for this purpose the theory and practice are reduced to their simplest forms. A notation is described, adapted to use with ordinary written music by which the notes to be performed are clearly distinguished.

scholarly journals The theory of the division of the octave, and the practic treatment of the musical systems thus obtained. Revise version of a paper entitled 'on just intonation in music with a description of a new instrument for the easy control systems of tuning other than the equal temperament of 1 divisions in the octave

1875 ◽  
Vol 23 (156-163) ◽  
pp. 390-408
Keyword(s):  
Control Systems ◽  
Royal Society ◽  
Just Intonation ◽  
New Instrument ◽  
Equal Temperament ◽  
Musical Systems ◽  
Revise Version

The mode of expressing Intervals . In the original paper presented by the writer to the Royal Society logarithms were employed as the measure of intervals, as they have been commonly employed by others. Great advantages have been found, however, to result from the adoption of the equal temperament (E. T.) mitone, which is 1/12 of an octave, as the unit of interval. It is the unit most familiar to musicians, and has been found to admit of the expression of the theory of cyclical systems by means of formulæ of the simplest character. The writer therefore devised the following rules for the transformation of ratios into E. T. semitones and vice versâ , and subsequently found that De Morgan had given rules for the same purpose which are substantially the same (Camb. Phil. Trans, vol. x. p. 129). The rules obviously depend on the form of log 2. The form of the first e affords a little more accuracy than De Morgan’s.

EPISTEMOLOGY OF TONE: AN OBITUARY FOR JULIEN JALÂL ED-DINE WEISS

Tempo ◽  
2017 ◽  
Vol 71 (281) ◽  
pp. 71-79
Author(s):  
Stefan Pohlit
Keyword(s):  
Twentieth Century ◽  
Cross Cultural ◽  
Theory And Practice ◽  
Just Intonation ◽  
Modal System ◽  
Helpful Tool ◽  
Near Eastern ◽  
Avant Garde ◽  
History Of ◽  
Major Discrepancy

AbstractDuring the 1980s, Julien Jalâl Ed-Dine Weiss, founder of the Al-Kindi ensemble of Aleppo, invented a qānūn in just intonation with which he attempted to solve a major discrepancy between the theory and practice of maqām-scales. Weiss objected to the introduction of Western standards, observing that they distort the significance of interval ratios and prevent a comparative understanding of the modal system as a transnational phenomenon. In the twentieth century, the implementation of equal-semitone temperament emerged simultaneously with a notable invasion of sociological criteria into musical inquiry. The polarity observed between westernisation and tradition can be seen most visibly in the present search for identity amongst Middle- and Near-Eastern musicians, but this schismogenic process can also be observed in the history of the Western avant-garde, where microtonal explorations have been halted in favour of extra-musical conceptuality. While cross-cultural musicians are faced with a new climate of distrust, it seems most likely that the principles that draw us apart may originate in the very patterns of thought in which our notion of culture operates. Weiss's tuning system may serve as a helpful tool to foster a new and universal epistemology of tone, bridging and transcending the apparent contradictions between the two spheres.

A Computer-Based Training Program for Developing Harmonic Intonation Discrimination Skill

1992 ◽  
Vol 40 (2) ◽  
pp. 139-152 ◽  
Author(s):  
Bruce F. Dalby
Keyword(s):  
Training Program ◽  
Matched Control ◽  
Control Group ◽  
Music Majors ◽  
Just Intonation ◽  
Computer Based Training ◽  
Equal Temperament ◽  
Computer Based ◽  
Experimental Subjects ◽  
Experimental Group

The purpose of this study was to determine the effectiveness of a computer-based training program for improving students' ability to make judgments of harmonic intonation. Twenty members of two undergraduate conducting classes participated in the Harmonic Intonation Training Program (HITP). An equivalent matched control group was selected from 156 other undergraduate music majors who had also taken the investigator-developed Harmonic Intonation Discrimination Test (HIDT). The HITP consisted of a body of drill-and-prac-tice exercises using intervals, triads, and brief three- and four-part musical passages. The exercises were played in both equal temperament and just intonation by a 16-voice digital synthesizer. After a 9-week treatment period, a two-way ANOVA on posttest HIDT scores revealed a difference (p= .005) in favor of the experimental group. Results of a questionnaire administered after the training to the experimental subjects indicated that attitudes toward the training program were mostly positive.

Comma 32 805/32 768

1998 ◽  
Vol 06 (03) ◽  
pp. 295-305 ◽  
Author(s):  
Ján Haluška
Keyword(s):  
Just Intonation ◽  
Equal Temperament ◽  
The One

We find a fifth approximation of the Just Intonation which generalizes Equal Temperament. The intervals causing a dilemma are the second and the minor seventh and the tritone because they are unambiguous in Just Intonation (the relative frequencies 10/9, 9/8, 8/7 and 7/4, 16/9, 18/10 and 45/32, 64/45, respectively). If we do not consider the second and seventh with the relative frequencies 8/7 and 7/4, respectively, all the music intervals in this approximation either coincide with he Just Intonation interval values (the octave, fifth, fourth, second (9/8) and the minor seventh (16/9)) or are exactly the one comma distant from the corresponding Just Intonation intervals. This comma is 32 805/32 768 ≈ 1.00112915, which is less than the ratio of frequencies of the perfect and the equal tempered fifths (≈ 1.00112989).

scholarly journals A Quantitative Analysis of Value-at-Risk based on Two-factor Pricing Model and GARCH Model

2021 ◽  
Vol 13 ◽  
pp. 338-340
Author(s):  
Qingqing Yu
Keyword(s):  
At Risk ◽  
Quantitative Analysis ◽  
Value At Risk ◽  
Garch Model ◽  
Theory And Practice ◽  
Financial Risks ◽  
Pricing Model ◽  
Gradual Improvement ◽  
New Instrument ◽  
Main Instrument

Value-at-risk has become the main instrument for the measurement and management of financial risks. With innovative construction of multi-level capital market system and gradual improvement of functions of financial system in China, financial risks demonstrate some new uncertainties. With regard to quantitative analysis and the management of risks in Chinese financial market, adoption of some methods for quantification of value-at-risk is of greatly importance in the fields of both theory and practice. The constant improvement in research of theory and practice concerning financial development gives birth to all kinds of new instruments for measurement and management of financial risks, among which value-at-risk is a common new instrument applied in measurement and management of modern finance. In this paper, an empirical analysis is conducted on quantification of financial value-at-risk based on Two-factor pricing model and GARCH model.

scholarly journals The effect of piano accompaniment type and harmonic context on the tuning performance of college-level choral musicians

2018 ◽  
Author(s):  
◽  
Tristan Frampton
Keyword(s):  
Just Intonation ◽  
College Level ◽  
Equal Temperament ◽  
Harmonic Context ◽  
Tuning Systems

This study was designed to evaluate the effect of piano accompaniment style on the intonation performance of college-level choral musicians. It was hypothesized that using a piano accompaniment comprised solely of referential tones (RT), as opposed to having all voice parts doubled by the piano (PD), would encourage more desirable intonation performance. Participants (N = 34) sang a researcher-composed melody harmonized with traditional Western functional harmony under both accompaniment conditions. Accompaniment type was not found to have a significant effect on the tuning performance of target intervals, but harmonic context did significantly affect the singers' intonation. Most notably, intonation of major 3rds in the I and IV chords closely approximated just intonation, regardless of accompaniment type. In the context of the V chord, performances more closely approximated the high Pythagorean 3rd, which was attributed to a tendency to heighten the leading tone. When comparing intonation performance to the just intonation, equal temperament, and Pythagorean tuning systems, results indicated that performances did not conform perfectly to any one tuning system, supporting the conclusion that the singers' intonation performance was dependent on harmonic context.

Intonation of Harmonic Intervals: Adaptability of Expert Musicians to Equal Temperament and Just Intonation

2003 ◽  
Vol 20 (4) ◽  
pp. 383-410 ◽  
Author(s):  
Reinhard Kopiez
Keyword(s):  
Factor Analysis ◽  
Theoretical Model ◽  
Musical Instrument ◽  
Just Intonation ◽  
Experimental Paradigm ◽  
Professional Musicians ◽  
Average Deviation ◽  
Equal Temperament ◽  
Nonsignificant Difference ◽  
Tuning Systems

This study examines the deviation in the intonation of simultaneously sounding tones under the condition of an embedded melody task. Two professional musicians (trumpet players) were chosen as subjects to play the missing upper voice of a four-part audio example, while listening via headphones to the remaining three parts in adaptive five-limit just intonation and equal temperament. The experimental paradigm was that of a controlled varied condition with a 2 (tuning systems) ×× 5 (interval categories) ×× 5 (renditions) ×× 2 (players) factorial design. An analysis of variance showed a nonsignificant difference between the average deviation of harmonic intonation in the two systems used. Mean deviations of 4.9 cents (SD = 6.5 cents) in the equal-temperament condition and of 6.7 cents (SD = 8.1 cents) in the just-intonation condition were found. Thus, we assume that the musicians employed the same intonation for equaltemperament and just-intonation versions (an unconscious "always the same" strategy) and could not successfully adapt their performances to the just-intonation tuning system. Fewer deviations could be observed in the equal-temperament condition. This overall tendency can be interpreted as a "burn in" effect and is probably the consequence of longterm intonation practice with equal-temperament. Finally, a theoretical model of intonation is developed by use of factor analysis. Four factors that determine intonation patterns were revealed: the "major third factor," the "minor third and partials factor," the "instrumental tuning factor," and the "octave-minor seventh factor." To summarize, even in expert musicians, intonation is not determined by abstract tuning systems but is the result of an interaction among compositional features, the acoustics of the particular musical instrument, and deviation patterns in specific intervals.

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