Xenharmonic Wiki

Quindromeda family: Difference between revisions

← Older editNewer edit →
VisualWikitext
Tag: Manual revert
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,030 edits
No edit summary
Tags: Mobile edit Mobile web edit
Line 1: Line 1:
{{Technical data page}}
{{Technical data page}}
The '''quindromeda family''' tempers out {{monzo| 56 -28 -5 }}, equating the [[Pythagorean comma]] with a stack of five [[schisma]]s, making it a member of the [[schismic–Pythagorean equivalence continuum]].  
The '''quindromeda family''' tempers out {{monzo| 56 -28 -5 }}, equating the [[Pythagorean comma]] with a stack of five [[schisma]]s, making it a member of the [[schismic–Pythagorean equivalence continuum]]. It does not split the octave but splits the fourth in five, making it a member of [[Ploidacot/Omega-pentacot|omega-pentacot]] temperaments.  


== Quindromeda ==
== Quindromeda ==
Line 11: Line 11:
[[Mapping]]: [{{val| 1 2 0 }}, {{val| 0 -5 28 }}]
[[Mapping]]: [{{val| 1 2 0 }}, {{val| 0 -5 28 }}]


[[POTE generator]]: ~4428675/4194304 = 99.526
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.854¢, ~4428675/4194304 = 99.514¢
* [[CWE]]: ~2 = 1200.000¢, ~4428675/4194304 = 99.523¢


{{Optimal ET sequence|legend=1| 12, 169, 181, 193, 205, 217, 422 }}
{{Optimal ET sequence|legend=1| 12, 169, 181, 193, 205, 217, 422 }}


[[Badness]]: 0.399849
[[Badness]] (Sintel): 9.380


=== Subgroup temperament ===
=== Subgroup temperament ===
Line 32: Line 34:
[[Mapping|Sval mapping]]: [{{val| 1 2 0 5 }}, {{val| 0 -5 28 -11 }}]
[[Mapping|Sval mapping]]: [{{val| 1 2 0 5 }}, {{val| 0 -5 28 -11 }}]


[[Tp tuning|POL2 generator]]: ~18/17 = 99.524
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.878¢, ~18/17 = 99.513¢
* [[CWE]]: ~2 = 1200.000¢, ~18/17 = 99.523¢


{{Optimal ET sequence|legend=1| 12, 169, 181, 193, 205, 422 }}
{{Optimal ET sequence|legend=1| 12, 169, 181, 193, 205, 422 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.0757 cents
[[Badness]] (Sintel): 0.768


==== 2.3.5.17.19 ====
==== 2.3.5.17.19 ====
Line 49: Line 53:
[[Mapping|Sval mapping]]: [{{val| 1 2 0 5 4 }}, {{val| 0 -5 28 -11 3 }}]
[[Mapping|Sval mapping]]: [{{val| 1 2 0 5 4 }}, {{val| 0 -5 28 -11 3 }}]


[[Tp tuning|POL2 generator]]: ~18/17 = 99.524
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.852¢, ~18/17 = 99.512¢
* [[CWE]]: ~2 = 1200.000¢, ~18/17 = 99.523¢


{{Optimal ET sequence|legend=1| 12, 169, 181, 193, 205, 422 }}
{{Optimal ET sequence|legend=1| 12, 169, 181, 193, 205, 422 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.0813 cents
[[Badness]] (Sintel): 0.348
 
[[Badness]]: 0.007140


== Quintagar ==
== Quintagar ==
Line 66: Line 70:
[[Mapping]]: [{{val| 1 2 0 -3 }}, {{val| 0 -5 28 70 }}]
[[Mapping]]: [{{val| 1 2 0 -3 }}, {{val| 0 -5 28 70 }}]


[[POTE generator]]: ~200/189 = 99.555
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.824¢, ~200/189 = 99.540¢
* [[CWE]]: ~2 = 1200.000¢, ~200/189 = 99.553¢


{{Optimal ET sequence|legend=1| 12, 217, 229, 446, 675c }}
{{Optimal ET sequence|legend=1| 12, 217, 229, 446, 675c }}


[[Badness]]: 0.142897
[[Badness]] (Sintel): 3.616


=== Quintoneum ===
=== Quintoneum ===
Line 81: Line 87:
Mapping: [{{val| 1 2 0 -3 -5 }}, {{val| 0 -5 28 70 102 }}]
Mapping: [{{val| 1 2 0 -3 -5 }}, {{val| 0 -5 28 70 102 }}]


POTE generator: ~35/33 = 99.539
Optimal tunings:
* WE: ~2 = 1199.864¢, ~35/33 = 99.528¢
* CWE: ~2 = 1200.000¢, ~35/33 = 99.538¢


{{Optimal ET sequence|legend=1| 12, 205d, 217 }}
{{Optimal ET sequence|legend=1| 12, 205d, 217 }}


Badness: 0.087157
Badness (Sintel): 2.881


==== 13-limit ====
==== 13-limit ====
Line 174: Line 182:
Mapping: [{{val| 1 2 0 -3 13 }}, {{val| 0 -5 28 70 -115 }}]
Mapping: [{{val| 1 2 0 -3 13 }}, {{val| 0 -5 28 70 -115 }}]


POTE generator: ~200/189 = 99.551
Optimal tunings:
* WE: ~2 = 1199.867¢, ~200/189 = 99.540¢
* CWE: ~2 = 1200.000¢, ~200/189 = 99.551¢


{{Optimal ET sequence|legend=1| 12e, 217, 446 }}
{{Optimal ET sequence|legend=1| 12e, 217, 446 }}


Badness: 0.109908
Badness (Sintel): 3.633


==== 13-limit ====
==== 13-limit ====
Line 226: Line 236:
Mapping: [{{val| 1 2 0 -3 -6 }}, {{val| 0 -5 28 70 114 }}]
Mapping: [{{val| 1 2 0 -3 -6 }}, {{val| 0 -5 28 70 114 }}]


POTE generator: ~200/189 = 99.570
Optimal tunings:
* WE: ~2 = 1199.770¢, ~200/189 = 99.551¢
* CWE: ~2 = 1200.000¢, ~200/189 = 99.568¢


{{Optimal ET sequence|legend=1| 12, 217e, 229, 470cd, 699cd }}
{{Optimal ET sequence|legend=1| 12, 217e, 229, 470cd, 699cd }}


Badness: 0.093971
Badness (Sintel): 3.107


==== 13-limit ====
==== 13-limit ====
Line 319: Line 331:
[[Mapping]]: [{{val| 1 2 0 -2 }}, {{val| 0 -5 28 58 }}]
[[Mapping]]: [{{val| 1 2 0 -2 }}, {{val| 0 -5 28 58 }}]


[[POTE generator]]: ~625/588 = 99.483
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.876¢, ~625/588 = 99.473¢
* [[CWE]]: ~2 = 1200.000¢, ~625/588 = 99.482¢


{{Optimal ET sequence|legend=1| 12, 169, 181, 193 }}
{{Optimal ET sequence|legend=1| 12, 169, 181, 193 }}


[[Badness]]: 0.155536
[[Badness]] (Sintel): 3.936


=== 11-limit ===
=== 11-limit ===
Line 332: Line 346:
Mapping: [{{val| 1 2 0 -2 -4 }}, {{val| 0 -5 28 58 90 }}]
Mapping: [{{val| 1 2 0 -2 -4 }}, {{val| 0 -5 28 58 90 }}]


POTE generator: ~35/33 = 99.472
Optimal tunings:
* WE: ~2 = 1199.906¢, ~35/33 = 99.464¢
* CWE: ~2 = 1200.000¢, ~35/33 = 99.470¢


{{Optimal ET sequence|legend=1| 12, 181, 193, 374, 567ce }}
{{Optimal ET sequence|legend=1| 12, 181, 193, 374, 567ce }}


Badness: 0.073158
Badness (Sintel): 2.419


==== 13-limit ====
==== 13-limit ====
Line 464: Line 480:
[[Mapping]]: [{{val| 1 2 0 15 }}, {{val| 0 -5 28 -147 }}]
[[Mapping]]: [{{val| 1 2 0 15 }}, {{val| 0 -5 28 -147 }}]


[[POTE generator]]: ~4428675/4194304 = 99.529
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.843¢, ~4428675/4194304 = 99.516¢
* [[CWE]]: ~2 = 1200.000¢, ~4428675/4194304 = 99.529¢


{{Optimal ET sequence|legend=1| 205, 217, 422, 639, 1061 }}
{{Optimal ET sequence|legend=1| 205, 217, 422, 639, 1061 }}


[[Badness]]: 0.316850
[[Badness]] (Sintel): 8.019


=== 11-limit ===
=== 11-limit ===
Line 477: Line 495:
Mapping: [{{val| 1 2 0 15 -5 }}, {{val| 0 -5 28 -147 102 }}]
Mapping: [{{val| 1 2 0 15 -5 }}, {{val| 0 -5 28 -147 102 }}]


POTE generator: ~17325/16384 = 99.529
Optimal tunings:
* WE: ~2 = 1199.839¢, ~17325/16384 = 99.515¢
* CWE: ~2 = 1200.000¢, ~17325/16384 = 99.529¢


{{Optimal ET sequence|legend=1| 205, 217, 422, 639, 1061e }}
{{Optimal ET sequence|legend=1| 205, 217, 422, 639, 1061e }}


Badness: 0.085219
Badness (Sintel): 2.817


=== 13-limit ===
=== 13-limit ===
Line 529: Line 549:
[[Mapping]]: [{{val|1 2 0 6}}, {{val|0 -10 56 -77}}]
[[Mapping]]: [{{val|1 2 0 6}}, {{val|0 -10 56 -77}}]


[[POTE generator]]: ~36/35 = 49.756
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.925¢, ~36/35 = 49.753¢
* [[CWE]]: ~2 = 1200.000¢, ~36/35 = 49.757¢


{{Optimal ET sequence|legend=1| 24, 169d, 193, 217, 410 }}
{{Optimal ET sequence|legend=1| 24, 169d, 193, 217, 410 }}


[[Badness]]: 0.244589
[[Badness]] (Sintel): 6.190


=== 11-limit ===
=== 11-limit ===
Line 542: Line 564:
Mapping: [{{val|1 2 0 6 4}}, {{val|0 -10 56 -77 -13}}]
Mapping: [{{val|1 2 0 6 4}}, {{val|0 -10 56 -77 -13}}]


POTE generator: ~36/35 = 49.757
Optimal tunings:
* WE: ~2 = 1199.834¢, ~36/35 = 49.750¢
* CWE: ~2 = 1200.000¢, ~36/35 = 49.757¢


{{Optimal ET sequence|legend=1| 24, 169d, 193, 217, 410e }}
{{Optimal ET sequence|legend=1| 24, 169d, 193, 217, 410e }}


Badness: 0.093130
Badness (Sintel): 3.079


=== 13-limit ===
=== 13-limit ===
Line 595: Line 619:


[[Mapping]]: [{{val| 2 4 0 -5 }}, {{val| 0 -5 28 64 }}]
[[Mapping]]: [{{val| 2 4 0 -5 }}, {{val| 0 -5 28 64 }}]
: Mapping generators: ~10125/7168, ~1323/1250


[[POTE generator]]: ~1323/1250 = 99.521
[[Optimal tuning]]s:
* [[WE]]: ~10125/7168 = 599.929¢, ~1323/1250 = 99.509¢
* [[CWE]]: ~10125/7168 = 600.000¢, ~1323/1250 = 99.519¢


{{Optimal ET sequence|legend=1| 12, 398, 410, 422, 832, 1254d, 2086bd }}
{{Optimal ET sequence|legend=1| 12, 398, 410, 422, 832, 1254d, 2086bd }}


[[Badness]]: 0.233140
[[Badness]] (Sintel): 5.900


=== 11-limit ===
=== 11-limit ===
Line 609: Line 636:
Mapping: [{{val| 2 4 0 -5 -10 }}, {{val| 0 -5 28 64 102 }}]
Mapping: [{{val| 2 4 0 -5 -10 }}, {{val| 0 -5 28 64 102 }}]


POTE generator: ~1323/1250 = 99.525
Optimal tunings:
* WE: ~99/70 = 599.922¢, ~1323/1250 = 99.512¢
* CWE: ~99/70 = 600.000¢, ~1323/1250 = 99.523¢


{{Optimal ET sequence|legend=1| 12, 410, 422 }}
{{Optimal ET sequence|legend=1| 12, 410, 422 }}


Badness: 0.093926
Badness (Sintel): 3.105


=== 13-limit ===
=== 13-limit ===
Retrieved from "https://en.xen.wiki/w/Quindromeda_family"