Thread: Eric Dollard
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Old 09-04-2015, 04:00 AM
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On dissonance and the equal temperament and Pythagorean scales

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An unstable tone combination is a dissonance; its tension demands an onward motion to a stable chord. Thus dissonant chords are "active"; traditionally they have been considered harsh and have expressed pain, grief, and conflict.
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The concept of dissonance does not belong to the domain of harmony as it is presented us by Nature [harmonic series], but is derived from voice leading [guidelines], which is an essential constituent of Art.
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In Western music, dissonance is the quality of sounds that seems unstable and has an aural need to resolve to a stable consonance.
Consonance and dissonance - Wikipedia, the free encyclopedia

A piano tuner uses the concept of dissonance as an indicator in order to tune the piano. When two oscillating strings are not precisely in tune with each other, what may be perceived as phasing or modulation effects occur, also known as beat frequencies. As each key on a piano consists of 3 individually tuned strings, each string must be perfectly in tune with the other two associated with the same key in order to sound good. In order to achieve this, the piano tuner makes adjustments until there are no perceivable beats or phasing. Only then is the piano key in tune with itself, and this is how incalculably fine adjustments are done by ear. Needless to say a piano tuner isn't considered a professional until he has many years of experience under his belt.

This is the concept that also allows us to look more closely at the different scales and ideas put forth in Eric's latest presentation "Power of Aether as Related to Music and Electricity".

For this purpose, the files 12_TET.tun 12 Tone Equal Temperament and PYTH_12.tun 12-Tone Pythagorean Scale listed in post #2371 are loaded as the scaling system for LinPlug Albino 3, which is a software virtual synthesizer plugin. It's possible to derive everything from the maths given in the presentation and to manually do everything, but someone has already done it for us and saved the mapping in a convenient file.

The beginning of the youtube video illustrates what happens when two oscillating sources are detuned from each other. Note the phasing effect, or beat frequencies and how the rate changes according to how much one oscillator is detuned from the other. The waveform used is a sawtooth, one single note C played, and two oscillators.

Next, C and the fourth is played using the equal temperament scale, and then the same with Pythagorean. Then C with the fifth in the same order. Note the same dissonance that was heard when the two oscillators were detuned. This time only one oscillator is used, the phasing or beat frequencies are the result of the fact that the equal temperament keys aren't precisely in tune with each other. Note how various frequencies appear and disappear displayed on the spectrum analyser. With the Pythagorean scaling, the keys match the natural harmonics. A sawtooth waveform is used with a single oscillator here again.

Then the waveform is changed to square, and distortion is added to emphasise the harmonics. Now the dissonance speaks for itself and becomes glaringly obvious.

Dissonance, Equal Temperament, And Pythagorean Scales (Obsolete Version) - YouTube

[edit]Updated video with less audio/video sync issues coming soon[/edit]

New version: Dissonance, Equal Temperament, And Pythagorean Scales - YouTube

An excellent addition to understanding some of the things Eric talks about in the presentation is this course:

How Music and Mathematics Relate | The Great Courses
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Last edited by dR-Green; 09-08-2015 at 04:40 PM.
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