Semaphore and godzilla: Difference between revisions
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{{ | {{Interwiki | ||
| en = Semaphore and godzilla | | en = Semaphore and godzilla | ||
| de = Semiphor, Semaphor, Godzilla | | de = Semiphor, Semaphor, Godzilla | ||
| Line 12: | Line 12: | ||
| Mapping = 1; 2 8 1 11 | | Mapping = 1; 2 8 1 11 | ||
| Generators = 7/4 | | Generators = 7/4 | ||
| Generators tuning = | | Generators tuning = 948.0 | ||
| Optimization method = CWE | | Optimization method = CWE | ||
| Pergen = (P8, P4/2) | | Pergen = (P8, P4/2) | ||
| Line 20: | Line 20: | ||
| Odd limit 2 = 2.3.5.7.13 15 | Mistuning 2 = 20.5 | Complexity 2 = 14 | | Odd limit 2 = 2.3.5.7.13 15 | Mistuning 2 = 20.5 | Complexity 2 = 14 | ||
}} | }} | ||
'''Semaphore''', of the [[semaphoresmic clan]], is characterized by [[49/48]] being [[tempering out|tempered out]], so the [[generator]] represents [[7/4]] and [[12/7]] (or [[8/7]] and [[7/6]]) equally. This results in a very low [[complexity]] 2.3.7- | '''Semaphore''', of the [[semaphoresmic clan]], is characterized by [[49/48]] being [[tempering out|tempered out]], so the [[generator]] represents [[7/4]] and [[12/7]] (or [[8/7]] and [[7/6]]) equally. This results in a very low [[complexity]] [[2.3.7 subgroup|2.3.7-subgroup]] [[regular temperament|temperament]], with the drawback that most intervals of 7 must be out of tune by at least half of the comma 49/48, or about 18 [[cent]]s. ''Semaphore'' is a play on the words "semi-" and "fourth". | ||
If the [[5/1|5th harmonic]]'s intervals are desired, [[5/4]] can be sensibly mapped to +8 generators by tempering out [[81/80]], making it a [[ | If the [[5/1|5th harmonic]]'s intervals are desired, [[5/4]] can be sensibly mapped to +8 generators by tempering out [[81/80]], making it a [[meantone family #Extensions|meantone temperament]]. This temperament is '''godzilla'''. Moreover, the generator can be taken to be [[26/15]], which maps [[13/8]] to +11 generators by tempering out [[91/90]] and [[105/104]]. This extends the temperament to the 2.3.5.7.13 subgroup, with an abundance of harmonic resource and little additional damage. | ||
A more accurate but complex mapping of 5 can be found in [[immunity]], or 5/4 itself can be made the period by tempering out [[128/125]], resulting in [[triforce]]. | A more accurate but complex mapping of 5 can be found in [[immunity]], or 5/4 itself can be made the period by tempering out [[128/125]], resulting in [[triforce]]. | ||
For technical information, see [[Semaphoresmic clan #Semaphore]] and [[Semaphoresmic clan #Godzilla|#Godzilla]]. For a discussion on 11- and 13-limit extensions, see [[Godzilla extensions]]. | |||
== Interval chains == | == Interval chains == | ||
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| CWE: ~7/4 = 947.8216{{c}} | | CWE: ~7/4 = 947.8216{{c}} | ||
| POTE: ~7/4 = 947.3650{{c}} | | POTE: ~7/4 = 947.3650{{c}} | ||
|} | |||
{| class="wikitable mw-collapsible mw-collapsed" | |||
|+ style="font-size: 105%; white-space: nowrap;" | 2.3.5.7.13-subgroup norm-based tunings | |||
|- | |||
! rowspan="2" | | |||
! colspan="3" | Euclidean | |||
|- | |||
! Constrained | |||
! Constrained & skewed | |||
! Destretched | |||
|- | |||
! Tenney | |||
| CTE: ~7/4 = 948.9311{{c}} | |||
| CWE: ~7/4 = 948.0037{{c}} | |||
| POTE: ~7/4 = 947.5708{{c}} | |||
|} | |} | ||
| Line 216: | Line 232: | ||
{| class="wikitable center-all left-4" | {| class="wikitable center-all left-4" | ||
|- | |- | ||
! Edo<br>generator | ! Edo <br>generator | ||
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]* | ! [[Eigenmonzo|Unchanged interval <br>(eigenmonzo)]]* | ||
! Generator (¢) | ! Generator (¢) | ||
! Comments | ! Comments | ||
| Line 254: | Line 270: | ||
| | | | ||
| 947.368 | | 947.368 | ||
| Lower bound of no-11 13-odd-limit diamond monotone<br>No-11 15-odd-limit diamond monotone (singleton) | | Lower bound of {{nowrap|no-11}} 13-odd-limit diamond monotone <br>{{nowrap|No-11}} 15-odd-limit diamond monotone (singleton) | ||
|- | |- | ||
| | | | ||
| Line 269: | Line 285: | ||
| 5/4 | | 5/4 | ||
| 948.289 | | 948.289 | ||
| | | 7-, 9-odd-limit, {{nowrap|no-11}} 13- and 15-odd-limit minimax | ||
|- | |- | ||
| | | | ||
| Line 299: | Line 315: | ||
| | | | ||
| 960.000 | | 960.000 | ||
| Upper bound of 7-, 9-odd-limit, | | Upper bound of 7-, 9-odd-limit, and {{nowrap|no-11}} 13-odd-limit diamond monotone | ||
|- | |- | ||
| | | | ||