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As mentioned above, Pythagorean tuning defines all notes and intervals of a scale from a series of pure fifths with a ratio of 3:2. Thus it is not only a mathematically elegant system, but also one of the easiest to tune by ear.
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www.medieval.org/emfaq/harmony/pyth2.html
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In the West, as the name suggests, Pythagorean tuning was credited to the ancient Greek philosopher Pythagoras, known (like many of the pre-Socratics) mainly through quotations and anecdotes in later writers.
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www.medieval.org/emfaq/harmony/pyth.html
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Pythagorean tuning was widely used in medieval and Renaissance times. Major seconds and thirds are larger in Pythagorean intonation than in equal temperament, and minor seconds and thirds are smaller.
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cnx.org/content/m11639/latest/
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BAIN A Multimedia Approach to the Harmonic Series (A Pythagorean tuing of the diatonic scale) ... In the case of a Pythagorean tuning, the generating interval is a 3:2 fifth. Notice that a sequence of five consecutive upper 3:2 fifths based on C4, and one lower 3:2 fifth, produces a seven-tone scale, as shown in Fig.
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www.music.sc.edu/fs/bain/atmi02/pst/index.html
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Pythagoras devised a system of tuning based upon the interval of a fifth, the most consonant interval after the unison and the octave. It’s generally believed that ... In other words, twelve perfect fifths are not exactly equal to seven perfect octaves, and the Pythagorean comma is the amount of the discrepancy.
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www.microtonalguitar.com/tutorial/pythagorean/
www.microtonalguitar.com/tutorial/pythagorean/
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Soon the system of musical tuning in which frequency relationships are intervals based on a 3:2 ratio was born. This is the Pythagorean Tuning system.
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www.sciencefairadventure.com/ProjectDetail.aspx?Project...
www.sciencefairadventure.com/ProjectDetail.aspx?ProjectID=179
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JUST TUNING or JUST INTONATION ... The tuning of this system results in an absence of , but differences in the size of the ... Appendix C. Compare: INTONATION, PYTHAGOREAN SCALE, TEMPERED TUNING.
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www.sfu.ca/sonic-studio/handbook/Just_Tuning.html
www.sfu.ca/sonic-studio/handbook/Just_Tuning.html
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s of a pipe or string fit more closely to a scale of just intonation than to the Pythagorean. ... See: Appendix C. Compare: EQUAL TEMPERAMENT, INTONATION, TEMPERED TUNING.
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www.sfu.ca/sonic-studio/handbook/Pythagorean_Scale.html
www.sfu.ca/sonic-studio/handbook/Pythagorean_Scale.html
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Overview of historical temperaments on keyboard instruments ... Anyone seriously interested in temperaments must read Margo Schulter's remarkable Pythagorean Tuning and Medieval Polyphony. Notwithstanding the title, her discussion of Baroque meantones and irregular temperaments is also very thorough.
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pages.globetrotter.net/roule/temper.htm
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