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5-limit Tonnetz. Five-limit tuning, 5-limit tuning, or 5-prime-limit tuning (not to be confused with 5-odd-limit tuning), is any system for tuning a musical instrument that obtains the frequency of each note by multiplying the frequency of a given reference note (the base note) by products of integer powers of 2, 3, or 5 (prime numbers limited to 5 or lower), such as 2 −3 ·3 1 ·5 1 = 15/8.
The intervals of 5-limit just intonation (prime limit, not odd limit) are ratios involving only the powers of 2, 3, and 5. The fundamental intervals are the superparticular ratios 2/1 (the octave), 3/2 (the perfect fifth) and 5/4 (the major third). That is, the notes of the major triad are in the ratio 1:5/4:3/2 or 4:5:6.
Open E ♭ 5 tuning – E ♭-B ♭-e ♭-b ♭-e ♭ ' This is achieved by removing the fourth (G) string, tuning both Es and the B down a half step, and the A and D strings up a half-step. This creates a five-string power chord. Jacob Collier's "mirrored" tuning – D-A-e-a-d' As explained to the guitarist Paul Davids in a YouTube video [68].
Video 2: generating the syntonic temperament's note space. The valid tuning range of the syntonic temperament is show in Figure 1. Figure 1: The valid tuning range of the syntonic temperament, noting its valid tuning ranges at different p-limits and some notable tunings within those ranges.
Pages in category "5-limit tuning and intervals" The following 10 pages are in this category, out of 10 total. This list may not reflect recent changes. ...
[1] 3-limit 9:8 major tone 5-limit 10:9 minor tone. In music theory, the syntonic comma, also known as the chromatic diesis, the Didymean comma, the Ptolemaic comma, or the diatonic comma [2] is a small comma type interval between two musical notes, equal to the frequency ratio 81 / 80 (= 1.0125) (around 21.51 cents).
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Thus Pythagorean tuning, which uses only the perfect fifth (3/2) and octave (2/1) and their multiples (powers of 2 and 3), is represented through a two-dimensional lattice (or, given octave equivalence, a single dimension), while standard (5-limit) just intonation, which adds the use of the just major third (5/4), may be represented through a ...