Vishnu family: Difference between revisions
m →Vishy: also is there a reason not to keep higher-limit errors to compare in brackets? |
The only thing I understand in these edits is that you prefer CEE tuning (but even that's very much questionable for this temp, as I'm noting hereby). Precision is 4 places following the other entries in this page. |
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== Vishy == | == Vishy == | ||
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 | 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. | |||
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. | ||
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[WE]]: ~7/5 = 598. | * [[WE]]: ~7/5 = 598.8702{{c}}, ~25/24 = 70.6439{{c}} | ||
: [[error map]]: {{val| -2.260 -0.982 -3.895 +12.463 | : [[error map]]: {{val| -2.260 -0.982 -3.895 +12.463 }} | ||
* [[CWE]]: ~7/5 = 600. | * [[CWE]]: ~7/5 = 600.0000{{c}}, ~25/24 = 71.9109{{c}} | ||
: error map: {{val| 0.000 +0.969 +0.654 +18.141 | : error map: {{val| 0.000 +0.969 +0.654 +18.141 }} | ||
{{Optimal ET sequence|legend=0| 16, 18, 34d }} | {{Optimal ET sequence|legend=0| 16, 18, 34d }} | ||
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Optimal tunings: | Optimal tunings: | ||
* WE: ~7/5 = 598. | * WE: ~7/5 = 598.8234{{c}}, ~25/24 = 70.7100{{c}} | ||
: error map: {{val| -2.353 -1.631 -4.327 +11.984 +2.879 }} | : error map: {{val| -2.353 -1.631 -4.327 +11.984 +2.879 }} | ||
* CWE: ~7/5 = 600. | * CWE: ~7/5 = 600.0000{{c}}, ~25/24 = 71.1044{{c}} | ||
: error map: {{val| 0.000 -6.099 -2.375 +15.113 +0.498 }} | : error map: {{val| 0.000 -6.099 -2.375 +15.113 +0.498 }} | ||