Octoid: Difference between revisions
m Recategorize |
Removed redirect to Ragismic microtemperaments#Octoid Tags: Removed redirect Mobile edit Mobile web edit |
||
| Line 1: | Line 1: | ||
{{Infobox regtemp | |||
| Title = Octoid | |||
| Subgroups = 2.3.5.7, 2.3.5.7.11 | |||
| Comma basis = [[4375/4374]], [[16875/16807]] (7-limit); <br>[[540/539]], [[1375/1372]], [[4000/3993]] (11-limit) | |||
| Edo join 1 = 72 | Edo join 2 = 80 | |||
| Mapping = 8; 3 4 5 3 | |||
| Generators = 7/5 | |||
| Generators tuning = 583.948 | |||
| Optimization method = CWE | |||
| MOS scales = [[8L 64s]], [[72L 8s]] | |||
| Pergen = (P8/8, P4/3) | |||
| Color name = | |||
| Odd limit 1 = 11 | Mistuning 1 = 1.286 | Complexity 1 = 56 | |||
| Odd limit 2 = 11-limit 15 | Mistuning 2 = 1.473 | Complexity 2 = 64 | |||
}} | |||
'''Octoid''' is a [[regular temperament]] which takes a [[period]] of [[8edo|1/8 octave]], which represents [[12/11]], and adds a single [[generator]] which represents [[6/5]], [[7/5]], [[9/7]] or [[11/10]]. It [[tempering out|tempers out]] [[4375/4374]] and [[16875/16807]] in the 7-limit, and [[540/539]], [[1375/1372]], and [[4000/3993]] in the 11-limit. | |||
There are some extensions for the 13-limit including tridecimal octoid {{nowrap|(72 & 224)}} and octopus {{nowrap|(72 & 80)}}. | |||
See [[Ragismic microtemperaments #Octoid]] for technical details. | |||
== Interval chain == | |||
{| class="wikitable center-1" | |||
! rowspan="2" | Generator | |||
! colspan="2" | Period 1 | |||
! colspan="2" | Period 2 | |||
! colspan="2" | Period 3 | |||
! colspan="2" | Period 4 | |||
! colspan="2" | Period 5 | |||
! colspan="2" | Period 6 | |||
! colspan="2" | Period 7 | |||
! colspan="2" | Period 8 | |||
|- | |||
! Cents | |||
! Approx. ratios | |||
! Cents | |||
! Approx. ratios | |||
! Cents | |||
! Approx. ratios | |||
! Cents | |||
! Approx. ratios | |||
! Cents | |||
! Approx. ratios | |||
! Cents | |||
! Approx. ratios | |||
! Cents | |||
! Approx. ratios | |||
! Cents | |||
! Approx. ratios | |||
|- | |||
| 0 | |||
| 150.000 | |||
| [[12/11]] | |||
| 300.000 | |||
| [[25/21]] | |||
| 450.000 | |||
| [[35/27]] | |||
| 600.000 | |||
| [[99/70]], [[140/99]] | |||
| 750.000 | |||
| [[54/35]] | |||
| 900.000 | |||
| [[42/25]] | |||
| 1050.000 | |||
| [[11/6]] | |||
| 1200.000 | |||
| [[2/1]] | |||
|- | |||
| 1 | |||
| 133.948 | |||
| [[27/25]] | |||
| 283.948 | |||
| [[33/28]] | |||
| 433.948 | |||
| [[9/7]] | |||
| 583.948 | |||
| [[7/5]] | |||
| 733.948 | |||
| | |||
| 883.948 | |||
| [[5/3]] | |||
| 1033.948 | |||
| [[20/11]] | |||
| 1183.948 | |||
| | |||
|- | |||
| 2 | |||
| 117.895 | |||
| [[15/14]] | |||
| 267.895 | |||
| [[7/6]] | |||
| 417.895 | |||
| [[14/11]] | |||
| 567.895 | |||
| [[25/18]] | |||
| 717.895 | |||
| [[50/33]] | |||
| 867.895 | |||
| [[33/20]] | |||
| 1017.895 | |||
| [[9/5]] | |||
| 1167.895 | |||
| [[49/25]] | |||
|- | |||
| 3 | |||
| 101.843 | |||
| [[35/33]] | |||
| 251.843 | |||
| | |||
| 401.843 | |||
| | |||
| 551.843 | |||
| [[11/8]] | |||
| 701.843 | |||
| [[3/2]] | |||
| 851.843 | |||
| [[18/11]] | |||
| 1001.843 | |||
| [[25/14]] | |||
| 1151.843 | |||
| [[35/18]] | |||
|- | |||
| 4 | |||
| style="text-align:right" | 85.791 | |||
| [[21/20]] | |||
| 235.791 | |||
| | |||
| 385.791 | |||
| [[5/4]] | |||
| 535.791 | |||
| [[15/11]] | |||
| 685.791 | |||
| | |||
| 835.791 | |||
| | |||
| style="text-align:right" | 985.791 | |||
| | |||
| 1135.791 | |||
| [[27/14]] | |||
|- | |||
| 5 | |||
| style="text-align:right" | 69.739 | |||
| [[25/24]] | |||
| 219.739 | |||
| [[25/22]] | |||
| 369.739 | |||
| | |||
| 519.739 | |||
| [[27/20]] | |||
| 669.739 | |||
| | |||
| 819.739 | |||
| [[45/28]] | |||
| style="text-align:right" | 969.739 | |||
| [[7/4]] | |||
| 1119.739 | |||
| [[21/11]] | |||
|- | |||
| 6 | |||
| style="text-align:right" | 53.686 | |||
| [[33/32]] | |||
| 203.686 | |||
| [[9/8]] | |||
| 353.686 | |||
| [[27/22]] | |||
| 503.686 | |||
| | |||
| 653.686 | |||
| [[35/24]] | |||
| 803.686 | |||
| [[35/22]] | |||
| style="text-align:right" | 953.686 | |||
| | |||
| 1103.686 | |||
| | |||
|- | |||
| 7 | |||
| style="text-align:right" | 37.634 | |||
| [[45/44]], [[49/48]] | |||
| 187.634 | |||
| | |||
| 337.634 | |||
| | |||
| 487.634 | |||
| | |||
| 637.634 | |||
| | |||
| 787.634 | |||
| | |||
| style="text-align:right" | 937.634 | |||
| | |||
| 1087.634 | |||
| [[15/8]] | |||
|- | |||
| 8 | |||
| style="text-align:right" | 21.582 | |||
| [[81/80]] | |||
| 171.582 | |||
| | |||
| 321.582 | |||
| | |||
| 471.582 | |||
| [[21/16]] | |||
| 621.582 | |||
| | |||
| 771.582 | |||
| | |||
| style="text-align:right" | 921.582 | |||
| | |||
| 1071.582 | |||
| | |||
|} | |||
<nowiki>*</nowiki> in 11-limit CWE tuning | |||
== Scales == | |||
* [[Octoid72]] | |||
* [[Octoid80]] | |||
== Tunings == | |||
=== Norm-based tunings === | |||
{| class="wikitable mw-collapsible mw-collapsed" | |||
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings | |||
|- | |||
! rowspan="2" | | |||
! colspan="3" | Euclidean | |||
|- | |||
! Constrained | |||
! Constrained & skewed | |||
! Destretched | |||
|- | |||
! Tenney | |||
| CTE: ~7/5 = 583.9418{{c}} | |||
| CWE: ~7/5 = 583.9411{{c}} | |||
| POTE: ~7/5 = 583.9404{{c}} | |||
|} | |||
{| class="wikitable mw-collapsible mw-collapsed" | |||
|+ style="font-size: 105%; white-space: nowrap;" | 11-limit norm-based tunings | |||
|- | |||
! rowspan="2" | | |||
! colspan="3" | Euclidean | |||
|- | |||
! Constrained | |||
! Constrained & skewed | |||
! Destretched | |||
|- | |||
! Tenney | |||
| CTE: ~7/5 = 583.9297{{c}} | |||
| CWE: ~7/5 = 583.9477{{c}} | |||
| POTE: ~7/5 = 583.9622{{c}} | |||
|} | |||
== Music == | |||
* ''Dreyfus'' (archived 2010) by [[Gene Ward Smith]] – [https://soundcloud.com/genewardsmith/genewardsmith-dreyfus SoundCloud] | [https://www.archive.org/details/Dreyfus details] | [https://www.archive.org/download/Dreyfus/Genewardsmith-Dreyfus.mp3 play] – Octoid[72] in 224edo tuning | |||
[[Category:Octoid| ]] <!-- main article --> | [[Category:Octoid| ]] <!-- main article --> | ||