14ed5: Difference between revisions

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'''The 14 equal divisions of [[5/1]]''' system divides the 5th harmoinc or pentave into 14 equal steps of 199.022 cents each.  It is essentially a compressed [[6edo]] whole tone scale with a tempered octave of 1194.13 cents.
'''The 14 equal divisions of [[5/1]]''' system divides the 5th harmoinc or pentave into 14 equal steps of 199.022 cents each.  It is essentially a compressed [[6edo]] whole tone scale with a tempered octave of 1194.13 cents.
== Theory ==
== Theory ==
14ed5 is the first ED5 which can reasonably be described as a 5.7.11 subgroup temperament, excluding harmonics 2 and 3 as implied by pentaves.
14ed5 is the first ED5 which can reasonably be described as a 5.7.11 subgroup temperament, excluding harmonics 2 and 3 as implied by pentaves. The best approximation of 7/5 is near 2edo's tritone at 597 cents, while the best approximation of 11/5 is a major ninth of 1393 cents, also being the square root of five.

Revision as of 07:30, 22 August 2023

← 13ed5 14ed5 15ed5 →
Prime factorization 2 × 7
Step size 199.022 ¢ 
Octave 6\14ed5 (1194.13 ¢) (→ 3\7ed5)
Twelfth 10\14ed5 (1990.22 ¢) (→ 5\7ed5)
Consistency limit 3
Distinct consistency limit 3

The 14 equal divisions of 5/1 system divides the 5th harmoinc or pentave into 14 equal steps of 199.022 cents each. It is essentially a compressed 6edo whole tone scale with a tempered octave of 1194.13 cents.

Theory

14ed5 is the first ED5 which can reasonably be described as a 5.7.11 subgroup temperament, excluding harmonics 2 and 3 as implied by pentaves. The best approximation of 7/5 is near 2edo's tritone at 597 cents, while the best approximation of 11/5 is a major ninth of 1393 cents, also being the square root of five.