Vishnu family: Difference between revisions

(2 intermediate revisions by the same user not shown)

Line 177:

Named by [[Godtone]] in 2026 after its inaccurate but simple interpretation of its half-octave period as [[7/5]][[~]][[10/7]], vishy tempers out [[50/49]] and represents the absolute simplest way to reach prime 7 by interpreting three ~25/24 generators as a significantly flat [[~]][[8/7]]. Its mapping might be deemed favorable because of all primes being reached in a negative number of generators, with the most complex, 11, being reached in -9 (as in vishnean). In fact, this temperament's mapping is identical to that of [[vishnean]] up to a simpler, higher-damage mapping of 7 in the same direction as all the other primes.

~~It might be worth noting that~~ the ~~[[CEE]] optima~~ (~~~71.954{{c}}, 7-limit; ~72.021{{c}}, 11-limit~~) ~~give more accurate tunings for prime 7~~, but ~~damage~~ 3 ~~and~~ 7/3 significantly more than CWE. ~~[[50edo]] is very close to these tunings~~, ~~via the 50d val. It is also recommendable~~ in [[84edo]] via the 84dd val, where 7 is ~1.7{{c}} sharper but everything else is significantly more accurate.

The extreme tuning 50edo tunes 11 approximately pure and 7 a little better via the 50d val (= 16 + 34d), but damages 3, 7/3 and 11/7 significantly more than CWE, and has a dubiously flat-tending 5-limit. However, in light of this, one might consider [[84edo]] via the 84dd val (= 34d + 50d), where 7 is ~1.7{{c}} sharper but everything else is significantly more accurate, with the exception of a sharper 11; especially, the 5-limit is approximately in-tune, so that with its more accurate 11 (and marginally more accurate 7) it is a good alternative to 34edo.

Therefore, it should be noted that as only the mapping of 7 differs from vishnean, using both mappings in any of [[34edo]], [[50edo]] and [[84edo]] (with [[2.3.5.11 subgroup]] fixed) could be seen as the primary and opportunistic utility of this temperament, by using whichever mapping of 7 happens to be more convenient or convincing in a given harmonic situation.

Therefore, it should be noted that as only the mapping of 7 differs from vishnean, using both mappings in any of [[34edo]], [[50edo]] and [[84edo]] (with [[2.3.5.11 subgroup]] fixed) could be seen as the primary and opportunistic utility of this temperament, by using whichever mapping of 7 happens to be more convenient or convincing in a given harmonic situation (if indeed the 7 is felt to be accurate enough).

[[Subgroup]]: 2.3.5.7

@@ Line 177: / Line 177: @@
 Named by [[Godtone]] in 2026 after its inaccurate but simple interpretation of its half-octave period as [[7/5]][[~]][[10/7]], vishy tempers out [[50/49]] and represents the absolute simplest way to reach prime 7 by interpreting three ~25/24 generators as a significantly flat [[~]][[8/7]]. Its mapping might be deemed favorable because of all primes being reached in a negative number of generators, with the most complex, 11, being reached in -9 (as in vishnean). In fact, this temperament's mapping is identical to that of [[vishnean]] up to a simpler, higher-damage mapping of 7 in the same direction as all the other primes.
-It might be worth noting that the [[CEE]] optima (~71.954{{c}}, 7-limit; ~72.021{{c}}, 11-limit) give more accurate tunings for prime 7, but damage 3 and 7/3 significantly more than CWE. [[50edo]] is very close to these tunings, via the 50d val. It is also recommendable in [[84edo]] via the 84dd val, where 7 is ~1.7{{c}} sharper but everything else is significantly more accurate.
+The extreme tuning 50edo tunes 11 approximately pure and 7 a little better via the 50d val (= 16 + 34d), but damages 3, 7/3 and 11/7 significantly more than CWE, and has a dubiously flat-tending 5-limit. However, in light of this, one might consider [[84edo]] via the 84dd val (= 34d + 50d), where 7 is ~1.7{{c}} sharper but everything else is significantly more accurate, with the exception of a sharper 11; especially, the 5-limit is approximately in-tune, so that with its more accurate 11 (and marginally more accurate 7) it is a good alternative to 34edo.
-Therefore, it should be noted that as only the mapping of 7 differs from vishnean, using both mappings in any of [[34edo]], [[50edo]] and [[84edo]] (with [[2.3.5.11 subgroup]] fixed) could be seen as the primary and opportunistic utility of this temperament, by using whichever mapping of 7 happens to be more convenient or convincing in a given harmonic situation.
+Therefore, it should be noted that as only the mapping of 7 differs from vishnean, using both mappings in any of [[34edo]], [[50edo]] and [[84edo]] (with [[2.3.5.11 subgroup]] fixed) could be seen as the primary and opportunistic utility of this temperament, by using whichever mapping of 7 happens to be more convenient or convincing in a given harmonic situation (if indeed the 7 is felt to be accurate enough).
 [[Subgroup]]: 2.3.5.7