Vishnu family: Difference between revisions

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== 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 is also supported by [[50edo]] via the 50d [[val]], recommendable for its lower damage on prime 7, being close to an optimal tuning of it. It is also recommendable in [[84edo]] via the 84dd val, where 7 is ~1.7{{c}} sharper but everything else is significantly more accurate.

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.

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.

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 (if indeed the 7 is felt to be accurate enough).

[[Subgroup]]: 2.3.5.7

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=== 11-limit ===

Other than [[176/175]], 11-limit vishy also tempers out [[625/616]] and [[1331/1323]].

Subgroup: 2.3.5.7.11

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Optimal tunings:

* WE: ~7/5 = 598.8234{{c}}, ~25/24 = 70.7100{{c}}

: error map: {{val| -2.353 -1.631 -4.327 +11.984 +2.879 }}

* CWE: ~7/5 = 600.0000{{c}}, ~25/24 = 71.1044{{c}}

: error map: {{val| 0.000 -6.099 -2.375 +15.113 +0.498 }}

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 == 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 is also supported by [[50edo]] via the 50d [[val]], recommendable for its lower damage on prime 7, being close to an optimal tuning of it. It is also recommendable in [[84edo]] via the 84dd val, where 7 is ~1.7{{c}} sharper but everything else is significantly more accurate.
+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.
-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.
+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 (if indeed the 7 is felt to be accurate enough).
 [[Subgroup]]: 2.3.5.7
@@ Line 196: / Line 198: @@
 === 11-limit ===
+Other than [[176/175]], 11-limit vishy also tempers out [[625/616]] and [[1331/1323]].
 Subgroup: 2.3.5.7.11
@@ Line 204: / Line 208: @@
 Optimal tunings:
 * WE: ~7/5 = 598.8234{{c}}, ~25/24 = 70.7100{{c}}
+: error map: {{val| -2.353 -1.631 -4.327 +11.984 +2.879 }}
 * CWE: ~7/5 = 600.0000{{c}}, ~25/24 = 71.1044{{c}}
+: error map: {{val| 0.000 -6.099 -2.375 +15.113 +0.498 }}
 {{Optimal ET sequence|legend=0| 16, 18e, 34d }}