Pentatonic Functional Just System: Difference between revisions
→The 11- and 13-limits: new formal commas '''again''', delete outdated names |
→The 11- and 13-limits: half-complete the names |
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== The 11- and 13-limits == | == The 11- and 13-limits == | ||
We now look at the entire [[15-odd-limit]] [[tonality diamond]]. Here, we will use different formal commas than in the FJS: The formal comma for 11 is [[729/704|704/729]] (11/8 is <sub>5</sub>s4<sup>11</sup>), and the formal comma for 13 is [[27/26|26/27]] (13/8 is <sub>5</sub>m5<sup>13</sup>). | We now look at the entire [[15-odd-limit]] [[tonality diamond]]. Here, we will use different formal commas than in the FJS: The formal comma for 11 is [[729/704|704/729]] (11/8 is <sub>5</sub>s4<sup>11</sup>), and the formal comma for 13 is [[27/26|26/27]] (13/8 is <sub>5</sub>m5<sup>13</sup>). | ||
{| class="wikitable right-all mw-collapsible" | {| class="wikitable right-all left-3 mw-collapsible" | ||
|+ {{nowrap|15-odd-limit by PFJS}} | |+ {{nowrap|15-odd-limit by PFJS}} | ||
|- | |- | ||
! Ratio !! Cents !! | ! Ratio !! Cents !! Name | ||
|- | |- | ||
| 1/1 || 0.0 || <sub>5</sub>P1 | | 1/1 || 0.0 || <sub>5</sub>P1 | ||
| Line 256: | Line 256: | ||
| 15/14 || 119.4 || <sub>5</sub>s2<sup>5</sup><sub>7</sub> | | 15/14 || 119.4 || <sub>5</sub>s2<sup>5</sup><sub>7</sub> | ||
|- | |- | ||
| 14/13 || 128.3 || | | 14/13 || 128.3 || <sub>5</sub>S1<sup>7</sup><sub>13</sub> | ||
|- | |- | ||
| 13/12 || 138.6 || | | 13/12 || 138.6 || <sub>5</sub>m2<sup>13</sup> | ||
|- | |- | ||
| 12/11 || 150.6 || | | 12/11 || 150.6 || <sub>5</sub>S1<sub>11</sub> | ||
|- | |- | ||
| 11/10 || 165.0 || | | 11/10 || 165.0 || <sub>5</sub>m2<sup>11</sup><sub>5</sub> | ||
|- | |- | ||
| 10/9 || 182.4 || <sub>5</sub>m2<sup>5</sup> | | 10/9 || 182.4 || <sub>5</sub>m2<sup>5</sup> | ||
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| 7/6 || 266.9 || <sub>5</sub>M2<sup>7</sup> | | 7/6 || 266.9 || <sub>5</sub>M2<sup>7</sup> | ||
|- | |- | ||
| 13/11 || 289.2 || | | 13/11 || 289.2 || <sub>5</sub>M2<sup>13</sup><sub>111</sub> | ||
|- | |- | ||
| 6/5 || 315.6 || <sub>5</sub>M2<sub>5</sub> | | 6/5 || 315.6 || <sub>5</sub>M2<sub>5</sub> | ||
|- | |- | ||
| 11/9 || 347.4 || | | 11/9 || 347.4 || <sub>5</sub>s3<sup>11</sup> | ||
|- | |- | ||
| 16/13 || 359.3 || | | 16/13 || 359.3 || <sub>5</sub>M2<sub>13</sub> | ||
|- | |- | ||
| 5/4 || 386.3 || <sub>5</sub>s3<sup>5</sup> | | 5/4 || 386.3 || <sub>5</sub>s3<sup>5</sup> | ||
|- | |- | ||
| 14/11 || 417.5 || | | 14/11 || 417.5 || <sub>5</sub>S2<sup>7</sup><sub>11</sub> | ||
|- | |- | ||
| 9/7 || 435.1 || | | 9/7 || 435.1 || <sub>5</sub>s3<sub>7</sub> | ||
|- | |- | ||
| 13/10 || 454.2 || | | 13/10 || 454.2 || <sub>5</sub>P3<sup>13</sup><sub>5</sub> | ||
|- | |- | ||
| 4/3 || 498.0 || | | 4/3 || 498.0 || <sub>5</sub>P3 | ||
|- | |- | ||
| 15/11 || 537.0 || | | 15/11 || 537.0 || <sub>5</sub>P3<sup>5</sup><sub>11</sub> | ||
|- | |- | ||
| 11/8 || 551.3 || | | 11/8 || 551.3 || <sub>5</sub>s4<sup>11</sup> | ||
|- | |- | ||
| 18/13 || 563.4 || | | 18/13 || 563.4 || <sub>5</sub>P3<sub>13</sub> | ||
|- | |- | ||
| 7/5 || 582.5 || | | 7/5 || 582.5 || <sub>5</sub>S3<sup>7</sup><sub>5</sub> | ||
|- | |- | ||
| 10/7 || 617.5 || | | 10/7 || 617.5 || | ||