Pythagorean tuning
Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2. This ratio, also known as the "pure" perfect fifth, is chosen because it is one of the most consonant and easiest to tune by ear and because of importance attributed to the integer 3. As Novalis put it, "The musical proportions seem to me to be particularly correct natural proportions." Alternatively, it can be described as the tuning of the syntonic temperament in which the generator is the ratio 3:2 (i.e., the untempered perfect fifth), which is ≈702 cents wide.
- Caption
- enA series of fifths generated can give seven notes: a diatonic major scale on C in Pythagorean tuning .
- enDiatonic scale on C 12-tone equal tempered and just intonation.
- Comment
- enPythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2. This ratio, also known as the "pure" perfect fifth, is chosen because it is one of the most consonant and easiest to tune by ear and because of importance attributed to the integer 3. As Novalis put it, "The musical proportions seem to me to be particularly correct natural proportions." Alternatively, it can be described as the tuning of the syntonic temperament in which the generator is the ratio 3:2 (i.e., the untempered perfect fifth), which is ≈702 cents wide.
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- Has abstract
- enPythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2. This ratio, also known as the "pure" perfect fifth, is chosen because it is one of the most consonant and easiest to tune by ear and because of importance attributed to the integer 3. As Novalis put it, "The musical proportions seem to me to be particularly correct natural proportions." Alternatively, it can be described as the tuning of the syntonic temperament in which the generator is the ratio 3:2 (i.e., the untempered perfect fifth), which is ≈702 cents wide. The system dates to Ancient Mesopotamia; see Music of Mesopotamia § Music theory. The system is named, and has been widely misattributed, to Ancient Greeks, notably 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 × 9:8 × 9:8), to Eratosthenes. The so-called "Pythagorean tuning" was used by musicians up to the beginning of the 16th century. "The Pythagorean system would appear to be ideal because of the purity of the fifths, but some consider other intervals, particularly the major third, to be so badly out of tune that major chords [may be considered] a dissonance." The Pythagorean scale is any scale which can be constructed from only pure perfect fifths (3:2) and octaves (2:1). In Greek music it was used to tune tetrachords, which were composed into scales spanning an octave. A distinction can be made between extended Pythagorean tuning and a 12-tone Pythagorean temperament. Extended Pythagorean tuning corresponds 1-on-1 with western music notation and there is no limit to the number of fifths. In 12-tone Pythagorean temperament however one is limited by 12-tones per octave and one cannot play most music according to the Pythagorean system corresponding to the enharmonic notation, instead one finds that for instance the diminished sixth becomes a "wolf fifth".
- Hypernym
- Ratio
- Image
- enDiatonic scale on C.png
- enPythagorean diatonic scale on C.png
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- Pythagorean tuning
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- enPythagorean tuning
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- www.academia.edu/875113%7Cpublisher=Tadema
- in.music.sc.edu/fs/bain/atmi02/pst/index.html
- www.medieval.org/emfaq/harmony/pyth.html
- www.youtube.com/watch%3Fv=V4cvpBxaN54
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- 53 equal temperament
- 5-limit tuning
- Augmented fourth
- Augmented second
- Augmented unison
- Bartolomé Ramos de Pareja
- Boethius
- Boldface
- Bragod
- Category:3-limit tuning and intervals
- Category:Greek music
- Category:Pythagorean philosophy
- Cent (music)
- Christopher Page
- Comma (music)
- Consonance and dissonance
- Crwth
- Daniel Leech-Wilkinson
- Diatonic scale
- Diesis
- Diminished fifth
- Diminished fourth
- Diminished second
- Diminished sixth
- Ditone
- Enharmonic
- Enharmonically equivalent
- Enharmonic scale
- Epogdoon
- Equal temperament
- Eratosthenes
- File:Interval ratios in D-based symmetric Pythagorean tuning (powers for large numbers).PNG
- File:Music intervals frequency ratio equal tempered pythagorean comparison.svg
- File:Pythagorean major chord on C.png
- File:Rank-2 temperaments with the generator close to a fifth and period an octave.jpg
- File:Size of intervals in D-based symmetric Pythagorean tuning.PNG
- Five-limit tuning
- Frequency
- Frequency ratio
- Generator (music)
- Gothic Voices
- Harmonic series (music)
- Harmony
- Hertz
- Interval (music)
- Interval ratio
- John Bergamo
- John Schneider (guitarist)
- Just intonation
- Key (music)
- List of meantone intervals
- List of pitch intervals
- Lou Harrison
- Lyre
- Major scale
- Major second
- Major seventh
- Major sixth
- Major third
- Meantone temperament
- Minor second
- Minor seventh
- Minor sixth
- Minor third
- Musical temperament
- Musical tuning
- Music of ancient Greece
- Novalis
- Octave
- Octave equivalence
- Perfect fifth
- Perfect fourth
- Piano keyboard
- Ptolemy
- Pythagoras
- Pythagorean apotome
- Pythagorean comma
- Pythagorean limma
- Quarter-comma meantone
- Regular diatonic tuning
- Regular temperament
- Scale (music)
- Semiditone
- Semitone
- Sesquioctavum
- Sesquiquartum
- Sesquiquintum
- Sesquitertium
- Shí-èr-lǜ
- Superparticular number
- Tetrachord
- Timaeus (dialogue)
- Twelve tone equal temperament
- Unison
- Violin family
- Well temperament
- Whole-tone scale
- Wolf interval
- Zarlino
- SameAs
- 4ziA3
- Accord pythagoricien
- Afinação pitagórica
- Afinación pitagórica
- Escala pitagòrica
- Intonazio pitagoriko
- m.0bsjt
- Pitagora agordo
- Pitagoro darna
- Püthagoraszi hangolás
- Pytagoreisk stemming
- Pythagorase häälestus
- Pythagorean tuning
- Pythagorean tuning
- Pythagoreische Stimmung
- Pythagoreisk stämning
- Pythagorejské ladění
- Q836135
- Scala pitagorica
- Sistemul Pitagora (muzică)
- Stemming van Pythagoras
- Пифагоров строй
- Піфагорійський стрій
- کوک فیثاغورثی
- ピタゴラス音律
- 五度相生律
- 피타고라스 음률
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- Category:3-limit tuning and intervals
- Category:Greek music
- Category:Pythagorean philosophy
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