User:Aura/Aura's introduction to 159edo: Difference between revisions
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| Line 1,614: | Line 1,614: | ||
| D, F#, A | | D, F#, A | ||
| 0, 54, 93 | | 0, 54, 93 | ||
| IV, | | IV, bVII | ||
| 1/(54:64:81) | | 1/(54:64:81) | ||
| This dissonant triad is common in Western Classical, Medieval, and Neo-Medieval Harmony | | This dissonant triad is common in Western Classical, Medieval, and Neo-Medieval Harmony | ||
| Line 1,628: | Line 1,628: | ||
| D, F#↓, A↓ | | D, F#↓, A↓ | ||
| 0, 51, 90 | | 0, 51, 90 | ||
| | | b↑III | ||
| 1/(27:32:40) | | 1/(27:32:40) | ||
| This dissonant triad is one of two possible diatonic wolf triads in the 5-limit | | This dissonant triad is one of two possible diatonic wolf triads in the 5-limit | ||
| Line 1,660: | Line 1,660: | ||
| D, F#, A, C# | | D, F#, A, C# | ||
| 0, 54, 93, 147 | | 0, 54, 93, 147 | ||
| | | bVII | ||
| 128:162:192:243 | | 128:162:192:243 | ||
| This dissonant tetrad is common in 3-limit music, but still has a role to play in 5-limit music | | This dissonant tetrad is common in 3-limit music, but still has a role to play in 5-limit music | ||
| Line 1,674: | Line 1,674: | ||
| D, F#↓, A↓, C#↓ | | D, F#↓, A↓, C#↓ | ||
| 0, 51, 90, 144 | | 0, 51, 90, 144 | ||
| | | b↑III | ||
| 240:256:320:405 | | 240:256:320:405 | ||
| This dissonant tetrad is one of a few diatonic tetrads to feature a wolf fifth | | This dissonant tetrad is one of a few diatonic tetrads to feature a wolf fifth | ||
| Line 1,714: | Line 1,714: | ||
| [[1/1]] | | [[1/1]] | ||
|- | |- | ||
| | | Ptolemaic Minor Second | ||
| Eb↑ | | Eb↑ | ||
| 15 | | 15 | ||
| Line 1,757: | Line 1,757: | ||
|} | |} | ||
As a consequence of this particular scale structure, you have the following basic chords... | |||
{| class="mw-collapsible mw-collapsed wikitable center-1" | |||
|+ style="font-size: 105%; white-space: nowrap;" | Table of basic Phrygian triads | |||
|- | |||
! Name | |||
! Notation (from D) | |||
! Steps | |||
! Occur(s) on Scale Degree(s) | |||
! Approximate JI | |||
! Notes | |||
|- | |||
| Ptolemaic Major | |||
| D, F#↓, A | |||
| 0, 51, 93 | |||
| b↑II, b↑VI | |||
| 4:5:6 | |||
| This is the first of two triads that can be considered fully-resolved in Western Classical Harmony | |||
|- | |||
| Ptolemaic Minor | |||
| D, F↑, A | |||
| 0, 42, 93 | |||
| I, IV, bVII | |||
| 1/(4:5:6) | |||
| This is the second of two triads that can be considered fully-resolved in Western Classical Harmony | |||
|- | |||
| Supradusthumic Ptolemaic Major | |||
| D, F#↓, A↓ | |||
| 0, 51, 90 | |||
| b↑III | |||
| 1/(27:32:40) | |||
| This dissonant triad is one of two possible diatonic wolf triads in the 5-limit | |||
|- | |||
| Lesser Ptolemaic Diminished | |||
| D, F, Ab↑ | |||
| 0, 39, 81 | |||
| V | |||
| 1/(45:54:64) | |||
| This dissonant triad is one of two possible diatonic diminished triads in the 5-limit | |||
|} | |||
{| class="mw-collapsible mw-collapsed wikitable center-1" | |||
|+ style="font-size: 105%; white-space: nowrap;" | Table of basic Phrygian tetrads | |||
|- | |||
! Name | |||
! Notation (from D) | |||
! Steps | |||
! Occur(s) on Scale Degree(s) | |||
! Approximate JI | |||
! Notes | |||
|- | |||
| Ptolemaic Minor with Pythagorean Minor Seventh | |||
| D, F↑, A, C | |||
| 0, 42, 93, 132 | |||
| I | |||
| 90:108:135:160 | |||
| This dissonant tetrad is perhaps best considered a cross between a suspension and a triad owing to the dissonance of the wolf fifth | |||
|- | |||
| Ptolemaic Major Seventh | |||
| D, F#↓, A, C#↓ | |||
| 0, 51, 93, 144 | |||
| b↑II | |||
| 8:10:12:15 | |||
| This tetrad is likely to decompose into a voicing variation on the corresponding triad if the same scale degree is used as a chord root multiple times in a row | |||
[[Category:Method]] | [[Category:Method]] | ||