Pinetone: Difference between revisions
→Intervals and triads: added mode 3 to table |
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| Line 1,030: | Line 1,030: | ||
Mode 3 has 4:5:6 major triads available above E♭, E, F, G♭, and G. | Mode 3 has 4:5:6 major triads available above E♭, E, F, G♭, and G. | ||
Tables 3.1. shows the (3, 4) and (4, 3) triads available of mode -3 and mode 3 of the Pinetone chromatic scale: | |||
{| class="wikitable" | {| class="wikitable" | ||
|+Table 3.1. (3, 4) and (4, 3) triads of the Ptolemismic Pinetone chromatic | |+Table 3.1. (3, 4) and (4, 3) triads of the Ptolemismic Pinetone chromatic modes -3 and 3 | ||
!Note | !Mode -3 Note | ||
!Mode 3 Note | |||
!Triad class | !Triad class | ||
!Triad in meantone | !Triad in meantone | ||
| Line 1,042: | Line 1,043: | ||
|- | |- | ||
! rowspan="2" |D | ! rowspan="2" |D | ||
! rowspan="2" |E♭ | |||
|(3, 4) | |(3, 4) | ||
| minor | | minor | ||
| Line 1,057: | Line 1,059: | ||
|- | |- | ||
! rowspan="2" |D♯ | ! rowspan="2" |D♯ | ||
! rowspan="2" |E | |||
|(3, 4) | |(3, 4) | ||
|minor | |minor | ||
| Line 1,072: | Line 1,075: | ||
|- | |- | ||
! rowspan="2" |E | ! rowspan="2" |E | ||
! rowspan="2" |F | |||
|(3, 4) | |(3, 4) | ||
| minor | | minor | ||
| Line 1,087: | Line 1,091: | ||
|- | |- | ||
! rowspan="2" |F | ! rowspan="2" |F | ||
! rowspan="2" |G♭ | |||
|(3, 4) | |(3, 4) | ||
| aug 2 | | aug 2 | ||
| Line 1,102: | Line 1,107: | ||
|- | |- | ||
! rowspan="2" |F♯ | ! rowspan="2" |F♯ | ||
! rowspan="2" |G | |||
|(3, 4) | |(3, 4) | ||
|minor | |minor | ||
| Line 1,117: | Line 1,123: | ||
|- | |- | ||
! rowspan="2" |G | ! rowspan="2" |G | ||
! rowspan="2" |A♭ | |||
|(3, 4) | |(3, 4) | ||
| aug 2 | | aug 2 | ||
| Line 1,132: | Line 1,139: | ||
|- | |- | ||
! rowspan="2" |G♯ | ! rowspan="2" |G♯ | ||
! rowspan="2" |A | |||
|(3, 4) | |(3, 4) | ||
|minor | |minor | ||
| Line 1,147: | Line 1,155: | ||
|- | |- | ||
! rowspan="2" |A | ! rowspan="2" |A | ||
! rowspan="2" |B♭ | |||
|(3, 4) | |(3, 4) | ||
| minor | | minor | ||
| Line 1,162: | Line 1,171: | ||
|- | |- | ||
! rowspan="2" |A♯ | ! rowspan="2" |A♯ | ||
! rowspan="2" |B | |||
|(3, 4) | |(3, 4) | ||
|minor dim 6 | |minor dim 6 | ||
| Line 1,177: | Line 1,187: | ||
|- | |- | ||
! rowspan="2" |B | ! rowspan="2" |B | ||
! rowspan="2" |C | |||
|(3, 4) | |(3, 4) | ||
|minor | |minor | ||
| Line 1,192: | Line 1,203: | ||
|- | |- | ||
! rowspan="2" |C | ! rowspan="2" |C | ||
! rowspan="2" |D♭ | |||
|(3, 4) | |(3, 4) | ||
| aug 2 | | aug 2 | ||
| Line 1,207: | Line 1,219: | ||
|- | |- | ||
! rowspan="2" |C♯ | ! rowspan="2" |C♯ | ||
! rowspan="2" |D | |||
|(3, 4) | |(3, 4) | ||
|minor | |minor | ||
| Line 1,221: | Line 1,234: | ||
|461.443, 704.101 | |461.443, 704.101 | ||
|} | |} | ||
<nowiki>*</nowiki> | <nowiki>*</nowiki> For tables 3.1. non-bracketed JI ratios are those approximated in 2.3.5.11.13 Ptolemismic Pinetone; bracketed JI ratios are the 2.3.7 interval approximated by additionally tempering out 105/104 or 245/243 as in Supermagic temperament. | ||
Note the major minor third approximating 11/9 and the minor major third approximating 27/22 are very similar in size in this tuning (351.784 and 352.317 respectively). If we equate these intervals, we additionally temper out 243/242, leading to an extension of Tetracot (Wollemia or Monkey if we also equate 13/10 with 9/7 or 21/16 respectively). | Note the major minor third approximating 11/9 and the minor major third approximating 27/22 are very similar in size in this tuning (351.784 and 352.317 respectively). If we equate these intervals, we additionally temper out 243/242, leading to an extension of Tetracot (Wollemia or Monkey if we also equate 13/10 with 9/7 or 21/16 respectively). | ||