User:Aura/Aura's introduction to 159edo: Difference between revisions
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Added some more data on 159edo's Ionian mode as optimized for 5-limit |
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This mode- along the corresponding tonality- is optimized for 5-limit using a variation on the Didymian diatonic scale. | This mode- along the corresponding tonality- is optimized for 5-limit using a variation on the Didymian diatonic scale. | ||
{| class="mw-collapsible mw-collapsed wikitable center-1" | |||
|+ style="font-size: 105%; white-space: nowrap;" | Table of Ionian notes and intervals | |||
|- | |||
! Interval Name | |||
! Notation (from D) | |||
! Steps from Tonic | |||
! Function | |||
! Corresponding JI | |||
|- | |||
| Perfect Unison | |||
| D | |||
| 0 | |||
| Tonic | |||
| [[1/1]] | |||
|- | |||
| Pythagorean Major Second | |||
| E | |||
| 27 | |||
| Supertonic (Bidominant) | |||
| [[9/8]] | |||
|- | |||
| Ptolemaic Major Third | |||
| F#↓ | |||
| 51 | |||
| Mesodistomediant | |||
| [[5/4]] | |||
|- | |||
| Perfect Fourth | |||
| G | |||
| 66 | |||
| Servient (Subdominant) | |||
| [[4/3]] | |||
|- | |||
| Perfect Fifth | |||
| A | |||
| 93 | |||
| Dominant | |||
| [[3/2]] | |||
|- | |||
| Pythagorean Major Sixth | |||
| B | |||
| 120 | |||
| Proximocontramediant (Tridominant) | |||
| [[27/16]] | |||
|- | |||
| Ptolemaic Major Seventh | |||
| C#↓ | |||
| 144 | |||
| Distosubcollocant | |||
| [[15/8]] | |||
|- | |||
| Perfect Octave | |||
| D | |||
| 159 | |||
| Tonic | |||
| [[2/1]] | |||
|} | |||
As a consequence of this particular scale structure, you have the following chords... | |||
{| class="mw-collapsible mw-collapsed wikitable center-1" | {| class="mw-collapsible mw-collapsed wikitable center-1" | ||
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| 45:54:64 | | 45:54:64 | ||
| This dissonant triad is one of two possible diatonic diminished triads in the 5-limit | | This dissonant triad is one of two possible diatonic diminished triads in the 5-limit | ||
|- | |||
| Pythagorean Suspended 2 | |||
| D, E, A | |||
| 0, 27, 93 | |||
| I, IV, V | |||
| 8:9:12 | |||
| This dissonant triad is a common suspension in both 3-limit and 5-limit diatonic music | |||
|- | |||
| Pythagorean Suspended 4 | |||
| D, G, A | |||
| 0, 66, 93 | |||
| I, II, V | |||
| 1/(8:9:12) | |||
| This dissonant triad is a common suspension in both 3-limit and 5-limit diatonic music | |||
|- | |||
| Ptolemaic Suspended 2 | |||
| D, E↓, A | |||
| 0, 24, 93 | |||
| II | |||
| 18:20:27 | |||
| This dissonant triad is an uncommon suspension in 5-limit diatonic music | |||
|- | |||
| Ptolemaic Suspended 4 | |||
| D, G↑, A | |||
| 0, 69, 93 | |||
| III | |||
| 1/(18:20:27) | |||
| This dissonant triad is an uncommon suspension in 5-limit diatonic music | |||
|- | |||
|} | |||
{| class="mw-collapsible mw-collapsed wikitable center-1" | |||
|+ style="font-size: 105%; white-space: nowrap;" | Table of Ionian tetrads | |||
|- | |||
! Name | |||
! Notation (from D) | |||
! Steps | |||
! Occur(s) on Scale Degree(s) | |||
! Approximate JI | |||
! Notes | |||
|- | |||
| Ptolemaic Major Seventh | |||
| D, F#↓, A, C#↓ | |||
| 0, 51, 93, 144 | |||
| I | |||
| 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 | |||
|- | |||
| Ptolemaic Minor Seventh | |||
| D, F↑, A, C↑ | |||
| 0, 42, 93, 135 | |||
| III | |||
| 1/(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 | |||
|- | |||
|} | |} | ||
With the above scale steps and chords, this variation of Ionian in 159edo is considerably more tonally stable than its more familiar counterpart from 12edo and 24edo. | |||
== Notes == | |||
<references group="note" /> | |||