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understanding temperaments
Description
Overview of historical temperaments on keyboard instruments.
The need for temperament arises because it is impossible to have octaves, fifths, thirds, etc., all pure at once, or, in other words, because the ratios of the different pure intervals are incompatible....
temperament, tuning, Pythagore, just intonation, Aaron, Silbermann, Salinas, Kirnberger, Vallotti, Werckmeister, LewareQC
The need for temperament arises because it is impossible to have octaves, fifths, thirds, etc., all pure at once, or, in other words, because the ratios of the different pure intervals are incompatible....
temperament, tuning, Pythagore, just intonation, Aaron, Silbermann, Salinas, Kirnberger, Vallotti, Werckmeister, LewareQC
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Date
May 2, 2005
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8151
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by edward g. dunne.
It is an old (and well-understood) problem in music that you can't tune a piano perfectly. To understand why takes a tiny bit of mathematics and a smattering of physics (acoustics, namely).
Let me begin by explaining the way a scale is constructed. To avoid sharps and flats (and to make the diagrams easier to draw), I'll use the key of C.
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It is an old (and well-understood) problem in music that you can't tune a piano perfectly. To understand why takes a tiny bit of mathematics and a smattering of physics (acoustics, namely).
Let me begin by explaining the way a scale is constructed. To avoid sharps and flats (and to make the diagrams easier to draw), I'll use the key of C.
So-called middle C represents a particular frequency. There are various standards for fixing the starting frequency...
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Intonation Study:
Experiments in interval perception often reveal an astonishingly wide range of acceptability as far as mistuning is concerned. Mistunings of 20–40 cents seem to be acceptable in adjustment or evaluation tasks, yet this wide range of tolerance towards intonation deviation contrasts with the demands made on the intonation skills of expert musicians. Within the framework of a top-down approach, it is hypothesized that expert musicians use all acoustical cues available, such as timbre or musical context, in order to achieve optimal task adaptation and therefore are able to adapt to different tuning systems to a significant degree. On this hypothesis, it was decided to carry out an experiment which includes a "realistic" musical setting. The experimental conditions of this study used the paradigm of controlled varied condition with a 2 (tuning systems) * 2 (players) * 5 (renditions) * 5 (interval categories) design. Two professional musicians (trumpet players) were chosen as subjects to play the missing upper voice of a 4-part sound-example whilst listening via headphones to the remaining 3 parts in adaptive just intonation (JI) and equal temperament (ET). An analysis of variance showed a non-significant difference between the mean deviation of intonation in the two systems used. The results revealed a mean deviation of 4.9 cents in the ET condition (sd = 6.5) and 6.7 cents in the JI condition (sd = 8.1) and no significant differences were found between players. Results are based on the assumption of an unconscious "always the same" strategy, which means that the same intonation is employed for ET and JI versions. This overall tendency is interpreted as a "burn in"-effect and is the consequence of long term intonation practice in ET. Additionally, a factor analysis revealed four components which determine intonation patterns: these are 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 acoustic of the particular musical instrument and deviation patterns in specific intervals ...
Experiments in interval perception often reveal an astonishingly wide range of acceptability as far as mistuning is concerned. Mistunings of 20–40 cents seem to be acceptable in adjustment or evaluation tasks, yet this wide range of tolerance towards intonation deviation contrasts with the demands made on the intonation skills of expert musicians. Within the framework of a top-down approach, it is hypothesized that expert musicians use all acoustical cues available, such as timbre or musical context, in order to achieve optimal task adaptation and therefore are able to adapt to different tuning systems to a significant degree. On this hypothesis, it was decided to carry out an experiment which includes a "realistic" musical setting. The experimental conditions of this study used the paradigm of controlled varied condition with a 2 (tuning systems) * 2 (players) * 5 (renditions) * 5 (interval categories) design. Two professional musicians (trumpet players) were chosen as subjects to play the missing upper voice of a 4-part sound-example whilst listening via headphones to the remaining 3 parts in adaptive just intonation (JI) and equal temperament (ET). An analysis of variance showed a non-significant difference between the mean deviation of intonation in the two systems used. The results revealed a mean deviation of 4.9 cents in the ET condition (sd = 6.5) and 6.7 cents in the JI condition (sd = 8.1) and no significant differences were found between players. Results are based on the assumption of an unconscious "always the same" strategy, which means that the same intonation is employed for ET and JI versions. This overall tendency is interpreted as a "burn in"-effect and is the consequence of long term intonation practice in ET. Additionally, a factor analysis revealed four components which determine intonation patterns: these are 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 acoustic of the particular musical instrument and deviation patterns in specific intervals ...
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A Digital Audio Primer:
Many people don’t care about the technology behind their stereo system. As long as it sounds good and they can press a button and listen to music, everything is fine. However, when you start working with audio on computers and the Internet, it’s important to understand a few key principles to achieve good results.
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Sound reaches our ears as waves of rapidly varying air pressure caused by a vibrating object, such as a guitar string. As the string moves in one direction, it pushes on nearby air molecules, causing them to move closer together. This creates a small region of high pressure on one side of the string and low pressure on the opposite side. As the string moves in the opposite direction, the areas of high and low pressure reverse ...
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