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In music, just intonation or pure intonation is the tuning of musical intervals as whole number ratios of frequencies. An interval tuned in this way is said to be pure, and is called a just interval. Just intervals consist of tones from a single harmonic series of an implied fundamental. For example, in the diagram, if the notes G3 and C4 are tuned as members of the harmonic series of the lowest C, their frequencies will be 3 and 4 times the fundamental frequency. The interval ratio between C4 and G3 is therefore 4:3, a just fourth.
In music theory, a comma is a very small interval, the difference resulting from tuning one note two different ways. Traditionally, there are two most common comma; the syntonic comma, "the difference between a just major 3rd and four just perfect 5ths less two octaves", and the Pythagorean comma, "the difference between twelve 5ths and seven octaves". The word comma used without qualification refers to the syntonic comma, which can be defined, for instance, as the difference between an F♯ tuned using the D-based Pythagorean tuning system, and another F♯ tuned using the D-based quarter-comma meantone tuning system. Intervals separated by the ratio 81:80 are considered the same note because the 12-note Western chromatic scale does not distinguish Pythagorean intervals from 5-limit intervals in its notation. Other intervals are considered commas because of the enharmonic equivalences of a tuning system. For example, in 53TET, B♭ and A♯ are both approximated by the same interval although they are a septimal kleisma apart.
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References
- ↑ List of award winners, Villa Massimo.
- ↑ Archive notes to second biennale, 1990, Munich Biennale.
- 1 2 "Wolfgang von Schweinitz". CalArts. 7 February 1953. Retrieved 9 December 2024.
- ↑ "Wolfgang von Schweinitz Bio 2008". www.plainsound.org. Retrieved 2019-03-18.
- ↑ Sabat, Marc (2005). "The Extended Helmholtz-Ellis JI Pitch Notation" (PDF).
- ↑ "Schneider-Schott-Musikpreis". Landeshauptstadt Mainz (in German). 12 October 2018. Retrieved 9 December 2024.
- ↑ "SHMF Liste der Preisträger: Paul Hindemith". Startseite (in German). Retrieved 9 December 2024.
