13edo scales: Difference between revisions
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J (F#) = 180 Hz (approximately 16/11 or 7 edosteps below standard middle C of 261.6255653 Hz) | J (F#) = 180 Hz (approximately 16/11 or 7 edosteps below standard middle C of 261.6255653 Hz) | ||
==Intervals== | |||
{| class="wikitable" | |||
|- | |||
! | Degree | |||
! | Cents | |||
! | Approximated 21-limit Ratios* | |||
! | Kentaku notation | |||
! | Pseudo-Diatonic Category | |||
|- | |||
| style="text-align:center;" | 0 | |||
| style="text-align:right;" | 0.00 | |||
| style="text-align:center;" | Unison (P1) | |||
|- | |||
| style="text-align:center;" | 1 | |||
| style="text-align:right;" | 92.31 | |||
| style="text-align:center;" | Minor second (m2) | |||
|- | |||
| style="text-align:center;" | 2 | |||
| style="text-align:right;" | 184.615 | |||
| style="text-align:center;" | Major second (M2) | |||
|- | |||
| style="text-align:center;" | 3 | |||
| style="text-align:right;" | 276.92 | |||
| style="text-align:center;" | Minor third (m3) | |||
|- | |||
| style="text-align:center;" | 4 | |||
| style="text-align:right;" | 369.23 | |||
| style="text-align:center;" | Major third (M3)/Diminished fourth (d4) | |||
|- | |||
| style="text-align:center;" | 5 | |||
| style="text-align:right;" | 461.54 | |||
| style="text-align:center;" | Minor fourth (m4) | |||
|- | |||
| style="text-align:center;" | 6 | |||
| style="text-align:right;" | 553.85 | |||
| style="text-align:center;" | Major fourth (M4)/Minor tritone (mt) | |||
|- | |||
| style="text-align:center;" | 7 | |||
| style="text-align:right;" | 646.15 | |||
| style="text-align:center;" | Minor fifth (m5)/Major tritone (Mt) | |||
|- | |||
| style="text-align:center;" | 8 | |||
| style="text-align:right;" | 738.46 | |||
| style="text-align:center;" | Major fifth (M5) | |||
|- | |||
| style="text-align:center;" | 9 | |||
| style="text-align:right;" | 830.77 | |||
| style="text-align:center;" | Minor sixth (m6)/Augmented fifth (A5) | |||
|- | |||
| style="text-align:center;" | 10 | |||
| style="text-align:right;" | 923.08 | |||
| style="text-align:center;" | Major sixth (M6) | |||
|- | |||
| style="text-align:center;" | 11 | |||
| style="text-align:right;" | 1015.385 | |||
| style="text-align:center;" | Minor seventh (m7) | |||
|- | |||
| style="text-align:center;" | 12 | |||
| style="text-align:right;" | 1107.69 | |||
| style="text-align:center;" | Major seventh (M7) | |||
|- | |||
| style="text-align:center;" | 13 | |||
| style="text-align:right;" | 1200 | |||
| style="text-align:center;" | 2/1 | |||
| style="text-align:center;" | J | |||
| style="text-align:center;" | Octave (P8) | |||
|} | |||
==Archaeotonic (6L 1s)== | ==Archaeotonic (6L 1s)== | ||
The archaeotonic scale is overall brighter, more "majory" and more concordant than the oneirotonic scale: there are more 4:5:9 chords and chords involving the 11th and 13th harmonics, and extremely dissonant intervals such as 16/11 and 32/21 are less common. | The archaeotonic scale is overall brighter, more "majory" and more concordant than the oneirotonic scale: there are more 4:5:9 chords and chords involving the 11th and 13th harmonics, and extremely dissonant intervals such as 16/11 and 32/21 are less common. | ||