User:BudjarnLambeth/Batch 89 temperaments: Difference between revisions
Added normalised subgroup bases as per recommendation on the talk page; will further edit the rest of the page to use the normalised bases in the near future |
m Neatened article structure |
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| Line 18: | Line 18: | ||
Normalised subgroup bases: 2.3.11.89 | Normalised subgroup bases: 2.3.11.89 | ||
=== Mappings === | |||
Equal Temperament Mappings | Equal Temperament Mappings | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 42: | Line 42: | ||
|] ⟩ | |] ⟩ | ||
|} | |} | ||
Reduced Mapping | Reduced Mapping | ||
| Line 67: | Line 66: | ||
|] ⟩ | |] ⟩ | ||
|} | |} | ||
=== TE and POTE tunings === | |||
| Line 88: | Line 89: | ||
⟨0.511, 1.196, 6.223, -13.002] | ⟨0.511, 1.196, 6.223, -13.002] | ||
| Line 169: | Line 121: | ||
|} | |} | ||
=== Vectors and ET sequence === | |||
Unison Vectors | Unison Vectors | ||
* [-3, 1, -1, 1⟩ (89:88) | * [-3, 1, -1, 1⟩ (89:88) | ||
* [0, -5, 0, 2⟩ (7921:7776) | * [0, -5, 0, 2⟩ (7921:7776) | ||
* [3, -6, 1, 1⟩ (979:972) | * [3, -6, 1, 1⟩ (979:972) | ||
* [-6, 7, -2, 0⟩ (243:242) | * [-6, 7, -2, 0⟩ (243:242) | ||
{{Optimal ET sequence|legend=1| 7, 17, 24, 41* }} | {{Optimal ET sequence|legend=1| 7, 17, 24, 41* }} | ||
| Line 206: | Line 156: | ||
Normalised subgroup bases: 2.5.11.89 | Normalised subgroup bases: 2.5.11.89 | ||
=== Mappings === | |||
Equal Temperament Mappings | Equal Temperament Mappings | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 229: | Line 180: | ||
|] ⟩ | |] ⟩ | ||
|} | |} | ||
Reduced Mapping | Reduced Mapping | ||
| Line 255: | Line 205: | ||
|} | |} | ||
=== TE and POTE tunings === | |||
TE Generator Tunings (cents) | TE Generator Tunings (cents) | ||
| Line 306: | Line 256: | ||
|} | |} | ||
=== Vectors and ET sequence === | |||
Unison Vectors | Unison Vectors | ||
* [-5, 1, -1, 1⟩ (89:88) | * [-5, 1, -1, 1⟩ (89:88) | ||
* [0, 3, 0, -2⟩ (8000:7921) | * [0, 3, 0, -2⟩ (8000:7921) | ||
* [-5, 4, -1, -1⟩ (1000:979) | * [-5, 4, -1, -1⟩ (1000:979) | ||
* [-5, -2, -1, 3⟩ (704969:704000) | * [-5, -2, -1, 3⟩ (704969:704000) | ||
{{Optimal ET sequence|legend=1| 5*, 6, 13, 19, 32 }} | {{Optimal ET sequence|legend=1| 5*, 6, 13, 19, 32 }} | ||
| Line 345: | Line 293: | ||
Normalised subgroup bases: 2.3.31.89 | Normalised subgroup bases: 2.3.31.89 | ||
=== Mappings === | |||
Equal Temperament Mappings | Equal Temperament Mappings | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 368: | Line 317: | ||
|] ⟩ | |] ⟩ | ||
|} | |} | ||
Reduced Mapping | Reduced Mapping | ||
| Line 394: | Line 342: | ||
|} | |} | ||
=== TE and POTE tunings === | |||
TE Generator Tunings (cents) | TE Generator Tunings (cents) | ||
| Line 414: | Line 362: | ||
⟨0.853, -1.050, -5.200, 2.022] | ⟨0.853, -1.050, -5.200, 2.022] | ||
| Line 495: | Line 394: | ||
|} | |} | ||
=== Vectors and ET sequence === | |||
Unison Vectors | Unison Vectors | ||
* [7, 0, 1, -2⟩ (7936:7921) | * [7, 0, 1, -2⟩ (7936:7921) | ||
* [-9, 1, 2, -1⟩ (2883:2848) | * [-9, 1, 2, -1⟩ (2883:2848) | ||
* [-16, 1, 1, 1⟩ (8277:8192) | * [-16, 1, 1, 1⟩ (8277:8192) | ||
* [-2, 1, 3, -3⟩ (714984:704969) | * [-2, 1, 3, -3⟩ (714984:704969) | ||
{{Optimal ET sequence|legend=1| 2, 13, 15, 17, 19, 36, 55, 129* }} | {{Optimal ET sequence|legend=1| 2, 13, 15, 17, 19, 36, 55, 129* }} | ||
| Line 534: | Line 431: | ||
Normalised subgroup bases: 2.9+.9-.89 (contains a dual harmonic 9) | Normalised subgroup bases: 2.9+.9-.89 (contains a dual harmonic 9) | ||
=== Mappings === | |||
Equal Temperament Mappings | Equal Temperament Mappings | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 557: | Line 455: | ||
|] ⟩ | |] ⟩ | ||
|} | |} | ||
Reduced Mapping | Reduced Mapping | ||
| Line 583: | Line 480: | ||
|} | |} | ||
=== TE and POTE tunings === | |||
TE Generator Tunings (cents) | TE Generator Tunings (cents) | ||
| Line 634: | Line 531: | ||
|} | |} | ||
=== Vectors and ET sequence === | |||
Unison Vectors | Unison Vectors | ||
| Line 641: | Line 538: | ||
* [-6, 3, 0, -1⟩ (729:712) | * [-6, 3, 0, -1⟩ (729:712) | ||
* [-8, 2, 1, -1⟩ (729:712) | * [-8, 2, 1, -1⟩ (729:712) | ||
{{Optimal ET sequence|legend=1| 4*, 5*, 6, 13, 19 }} | {{Optimal ET sequence|legend=1| 4*, 5*, 6, 13, 19 }} | ||