User:Eufalesio/Important Tables: Difference between revisions
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Data I deem important! | Data I deem important! | ||
== Temperament properties of Ultimate edos (I care about) == | == 13-limit Temperament properties of Ultimate edos (I care about) == | ||
'''217 & 270 & 311: Ultimate {S49*S55, S64, S65} = {2080/2079, 4096/4095, 35035/34992}''' | '''217 & 270 & 311: Ultimate {S49*S55, S64, S65} = {2080/2079, 4096/4095, 35035/34992}''' | ||
* '''270 & 311''': Newt {S49, S55, S64, S65} = {2080/2079, 2401/2400, 3025/3024, 4096/4095}; supported trivially by 41edo | * '''270 & 311''': Newt {S49, S55, S64, S65} = {2080/2079, 2401/2400, 3025/3024, 4096/4095}; supported trivially by 41edo | ||
* '''94 & 270''': Gariwizmic {S11/S12, S64, S65, S99) = {1716/1715, <span data-darkreader-inline-color="">2080/2079, 4096/4095, 35035/34992}</span> | * '''94 & 270''': Gariwizmic {S11/S12, S64, S65, S99) = {1716/1715, <span data-darkreader-inline-color="">2080/2079, 4096/4095, 35035/34992}</span> | ||
* ''' | * '''41g & 217''': Cotoneum {S21, S28<sup>2</sup>*S29, S64, S65} = {441/440, <span data-darkreader-inline-color="">2080/2079, 4096/4095, 10976/10935}</span> | ||
* ''' | * '''41g & 53''': Cassandra {S25*S26, S15, S64, S65} = {225/224, 325/324, 352/351, 385/384}; supported trivially by 12e | ||
** '''270:''' {S49, S55, S64, S65, S99} = {1001/1000, 2401/2400, 2080/2079, 3025/3024, 4096/4095} | ** '''270:''' {S49, S55, S64, S65, S99} = {1001/1000, 2401/2400, 2080/2079, 3025/3024, 4096/4095} | ||
** '''94:''' {S15, S11/S12, S64, S65, S99} = {225/224, 325/324, 352/351, 385/384, 1716/1715} | ** '''94:''' {S15, S11/S12, S64, S65, S99} = {225/224, 325/324, 352/351, 385/384, 1716/1715} | ||
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Which can implicitly be seen in this table: | Which can implicitly be seen in this table: | ||
{| class="wikitable" style="text-align:center; vertical-align:middle" | {| class="wikitable" style="text-align:center; vertical-align:middle" | ||
! colspan="2" |Newt | |||
! colspan="2" | | |||
! colspan="2" |Gariwizmic | |||
! | |||
! rowspan="3" |Ultimate r3 | |||
|- | |||
! | |||
! colspan="4" |Cassandra | |||
! colspan="2" |Vulture | |||
|- style="font-weight:bold;" | |- style="font-weight:bold;" | ||
! 311 | ! 311 | ||
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! 270 | ! 270 | ||
! 217 | ! 217 | ||
|- | |- | ||
| colspan="8" | 2080/2079 | | colspan="8" | 2080/2079 | ||
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Any other join of Ultimate edos is ommited because I either don't know or don't care. | Any other join of Ultimate edos is ommited because I either don't know or don't care. | ||
Ultimate can be easily defined in 19-limit as {S35, S64, S65, S76, S77} = {1225/1224, 1540/1539, 1729/1728, 2080/2079, 4096/4095}. | |||
== Table of Ultimate edos' intervals == | == Table of Ultimate edos' intervals == | ||
A good and regular set of intervals I care about. Doesn't include all, but many things. | A good and regular set of intervals I care about. Doesn't include all, but many things. | ||
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<span data-darkreader-inline-color="">Bolded has an equalized tuning with a telic convergent. Ending sequence at the biggest telic convergent below a thousand. The reason for doing this is that MOSes with record low softness have equalized tunings with convergent primes. MOSes with a hyperlink represent equalized tunings I deem notable.</span> | <span data-darkreader-inline-color="">Bolded has an equalized tuning with a telic convergent. Ending sequence at the biggest telic convergent below a thousand. The reason for doing this is that MOSes with record low softness have equalized tunings with convergent primes. MOSes with a hyperlink represent equalized tunings I deem notable.</span> | ||
Also note how p3 has the the shortest length out of all the primes. Shoutout to p11, it manages to build some good scales up until 37edo, on which it basically hits a dead end. | Also note how p3 has the the shortest length out of all the primes. Shoutout to p11, it manages to build some good scales up until 37edo, on which it basically hits a dead end. Luckily its triple, 111edo, is quite decent. | ||
{| class="wikitable mw-collapsible mw-collapsed" data-darkreader-inline-color="" style="text-align: center;" | {| class="wikitable mw-collapsible mw-collapsed" data-darkreader-inline-color="" style="text-align: center;" | ||
!'''Generation \ Prime''' | !'''Generation \ Prime''' | ||
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|<small>3L 19s</small> | |<small>3L 19s</small> | ||
|'''<small>[[53edo|41L 12s]]</small>''' | |'''<small>[[53edo|41L 12s]]</small>''' | ||
|'''<small>24L 13s</small>''' | |'''<small>[[111edo|24L 13s]]</small>''' | ||
|<small>2L 15s</small> | |<small>2L 15s</small> | ||
|- | |- | ||