Oolong: Difference between revisions
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See [[Starling temperaments #Oolong]]. | See [[Starling temperaments #Oolong]] for more technical data. | ||
== Interval chain == | == Interval chain == | ||
{| class="wikitable center- | In the following table, prime harmonics are in '''bold'''. | ||
{| class="wikitable center-1 right-2" | |||
! # | ! # | ||
! Cents* | ! Cents* | ||
| Line 8: | Line 10: | ||
|- | |- | ||
| 0 | | 0 | ||
| 0. | | 0.0 | ||
| 1/1 | | 1/1 | ||
|- | |- | ||
| 1 | | 1 | ||
| 311. | | 311.7 | ||
| 6/5 | | 6/5 | ||
|- | |- | ||
| 2 | | 2 | ||
| 623. | | 623.3 | ||
| 10/7 | | 10/7 | ||
|- | |- | ||
| 3 | | 3 | ||
| 935. | | 935.0 | ||
| 12/7 | | 12/7 | ||
|- | |- | ||
| 4 | | 4 | ||
| 46. | | 46.7 | ||
| 36/35 | | 36/35, 40/39 | ||
|- | |- | ||
| 5 | | 5 | ||
| 358. | | 358.3 | ||
| 16/13 | | '''16/13''' | ||
|- | |- | ||
| 6 | | 6 | ||
| 670. | | 670.0 | ||
| | | 96/65 | ||
|- | |- | ||
| 7 | | 7 | ||
| 981. | | 981.7 | ||
| | | 160/91 | ||
|- | |- | ||
| 8 | | 8 | ||
| 93. | | 93.4 | ||
| | | 96/91 | ||
|- | |- | ||
| 9 | | 9 | ||
| 405. | | 405.0 | ||
| | | 91/72 | ||
|- | |- | ||
| 10 | | 10 | ||
| 716. | | 716.7 | ||
| | | 91/60 | ||
|- | |- | ||
| 11 | | 11 | ||
| 1028. | | 1028.4 | ||
| | | 49/27, 65/36 | ||
|- | |- | ||
| 12 | | 12 | ||
| 140. | | 140.0 | ||
| 13/12 | | 13/12 | ||
|- | |- | ||
| 13 | | 13 | ||
| 451. | | 451.7 | ||
| 13/10 | | 13/10 | ||
|- | |- | ||
| 14 | | 14 | ||
| 763. | | 763.4 | ||
| 14/9 | | 14/9 | ||
|- | |- | ||
| 15 | | 15 | ||
| 1075. | | 1075.0 | ||
| | | 13/7, 28/15, 50/27 | ||
|- | |- | ||
| 16 | | 16 | ||
| 186. | | 186.7 | ||
| 10/9 | | 10/9, 28/25 | ||
|- | |- | ||
| 17 | | 17 | ||
| 498. | | 498.4 | ||
| 4/3 | | '''4/3''' | ||
|- | |- | ||
| 18 | | 18 | ||
| 810. | | 810.0 | ||
| 8/5 | | '''8/5''' | ||
|- | |- | ||
| 19 | | 19 | ||
| 1121. | | 1121.7 | ||
| 48/25 | | 40/21, 48/25 | ||
|- | |- | ||
| 20 | | 20 | ||
| 233. | | 233.4 | ||
| 8/7 | | '''8/7''' | ||
|} | |} | ||
<nowiki>*</nowiki> In 2.3.5.7.13 POTE tuning | <nowiki>*</nowiki> In 2.3.5.7.13 POTE tuning | ||
| Line 174: | Line 176: | ||
|} | |} | ||
[[Category:Oolong]] | [[Category:Temperament]] | ||
[[Category: | [[Category:Oolong| ]] <!-- main article --> | ||
[[Category:Starling]] | |||
Revision as of 12:39, 12 April 2021
See Starling temperaments #Oolong for more technical data.
Interval chain
In the following table, prime harmonics are in bold.
| # | Cents* | Approximate Ratios |
|---|---|---|
| 0 | 0.0 | 1/1 |
| 1 | 311.7 | 6/5 |
| 2 | 623.3 | 10/7 |
| 3 | 935.0 | 12/7 |
| 4 | 46.7 | 36/35, 40/39 |
| 5 | 358.3 | 16/13 |
| 6 | 670.0 | 96/65 |
| 7 | 981.7 | 160/91 |
| 8 | 93.4 | 96/91 |
| 9 | 405.0 | 91/72 |
| 10 | 716.7 | 91/60 |
| 11 | 1028.4 | 49/27, 65/36 |
| 12 | 140.0 | 13/12 |
| 13 | 451.7 | 13/10 |
| 14 | 763.4 | 14/9 |
| 15 | 1075.0 | 13/7, 28/15, 50/27 |
| 16 | 186.7 | 10/9, 28/25 |
| 17 | 498.4 | 4/3 |
| 18 | 810.0 | 8/5 |
| 19 | 1121.7 | 40/21, 48/25 |
| 20 | 233.4 | 8/7 |
* In 2.3.5.7.13 POTE tuning
Spectrum of oolong tunings
| Eigenmonzo | Generator |
|---|---|
| 7/5 | 308.744 |
| 7/6 | 311.043 |
| (7\27) | 311.111 |
| 10/9 | 311.400 |
| 14/13 | 311.447 |
| 49/48 | 311.491 |
| (27\104) | 311.538 |
| 13/12 | 311.548 |
| 8/7 | 311.559 |
| (47\181) | 311.602 |
| 13/9 | 311.608 |
| 4/3 | 311.650 |
| (20\77) | 311.688 |
| 28/27 | 311.708 |
| 15/13 | 311.742 |
| 16/15 | 311.764 |
| 9/7 | 311.780 |
| 13/10 | 311.863 |
| 5/4 | 311.871 |
| 16/13 | 311.894 |
| (13\50) | 312.000 |
| 15/14 | 312.037 |
| 25/24 | 312.070 |
| (6\23) | 313.043 |
| 6/5 | 315.641 |