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Pythagorean tuning

Pythagorean tuning
The syntonic tuning continuum, showing Pythagorean tuning at 702 cents.[1] Diatonic scale on C Play 12-tone equal tempered and Play just intonation. Pythagorean (tonic) major chord on C Play (compare Play equal tempered and Play just). Comparison of equal-tempered (black) and Pythagorean (green) intervals showing the relationship between frequency ratio and the intervals' values, in cents. The system had been mainly attributed to Pythagoras (sixth century BC) by modern authors of music theory, while Ptolemy, and later Boethius, ascribed the division of the tetrachord by only two intervals, called "semitonium", "tonus", "tonus" in Latin (256:243 x 9:8 x 9:8), to Eratosthenes. Method[edit] Pythagorean tuning is based on a stack of intervals called perfect fifths, each tuned in the ratio 3:2, the next simplest ratio after 2:1. This succession of eleven 3:2 intervals spans across a wide range of frequency (on a piano keyboard, it encompasses 77 keys). Size of intervals[edit] (e.g. between E♭ and E)

http://en.wikipedia.org/wiki/Pythagorean_tuning

Related:  figurative artjust and other tuningsharmonic theory

Why the circle of fourths is so important when learning major scales Playing your major scales should be a part of your daily practice regimen. However, practicing them in a “circle of fourths” or “circle of fifths” pattern is even better. Let’s focus more on circle of fourths. If you type “circle of fourths” or “circle of fifths” in google, you can actually find a host of other examples.

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Untitled Document Mathematics, astronomy, geometry, geography, art, music and religion were all integrated in ancient times. Numerous surviving examples suggest that ancient Egyptian art was based on a strict canon that was followed for over 3,000 years. According to Plato, this was also true of ancient Egyptian music. 5 Ways to Use Non-Diatonic Notes in Jazz Improvisation You want to play exciting solos… Ones that will make the audience sit on the edge of their seats, that’ll make you stand out from every other musician in the room. …except when you improvise everything ends up sounding exactly the same. Many musicians share this frustration and for many it goes right back to the standard approach to improvisation that you find in most books. The mentality that each chord has a designated scale: Major scales for major chordsDorian for minor chordsMixolydian for V7 chords

LucyTuning*LucyScaleDevelopments*Pi tuning*LucyTuned Lullabies*John "Longitude" Harrison Setting tuning and harmonic standards into the future. Have fun with them. LucyTuned Lullabies (from around the world) New LucyTune site (May 2005) BBC Radio 4 interview with Robert Sandall about LucyTuning mp3 - (3min 54 seconds) LucyTuning - musical tuning, harmonic, composition, practice, specifications, and theory

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