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User:Aura/Aura's introduction to 159edo: Difference between revisions

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Begin second table for Dorian
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As can be seen in the above table, As a consequence of this particular scale structure, you have the following basic chords...
As a consequence of this particular scale structure, you have the following basic chords...


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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.
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.  It is also only one of two traditional diatonic modes in which one is able to perform a complete [[Wikipedia: Vi–ii–V–I|circle progression]].


==== Dorian ====
==== Dorian ====


This mode is optimized for 5-limit by means of a different scale.
Unlike what is expected, the form of Dorian mode optimized for 5-limit is not symmetrical, owing to the need to maintain [[Rothenberg propriety]].  


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| [[9/8]]
| [[9/8]]
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|-
| Ptolemaic Major Third
| Ptolemaic Minor Third
| F↑
| F↑
| 51
| 42
| Mesoproximomediant
| Mesoproximomediant
| [[6/5]]
| [[6/5]]
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| [[27/16]]
| [[27/16]]
|-
|-
| Ptolemaic Major Seventh
| Pythagorean Minor Seventh
| C
| C
| 132
| 132
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Unlike what is expected, the optimized form of Dorian mode is not symmetrical, owing to the need to maintain [[Rothenberg propriety]].  As a consequence of this particular scale structure, you have the following basic chords...
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 Dorian triads
|-
! Name
! Notation (from D)
! Steps
! Occur(s) on Scale Degree(s)
! Approximate JI
! Notes
|-
| Ptolemaic Minor
| D, F↑, A
| 0, 42, 93
| I
| 1/(4:5:6)
| This is the second of two triads that can be considered fully-resolved in Western Classical Harmony
|-
| Pythagorean Major
| D, F#, A
| 0, 54, 93
| IV, VII
| 1/(54:64:81)
| This dissonant triad is common in Western Classical, Medieval, and Neo-Medieval Harmony
|-
| Pythagorean Minor
| D, F, A
| 0, 39, 93
| II, V
| 54:64:81
| This dissonant triad is common in Western Classical, Medieval, and Neo-Medieval Harmony
|-
| Supradusthumic Ptolemaic Major
| D, F#↓, A↓
| 0, 51, 90
| 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
| VI
| 1/(45:54:64)
| This dissonant triad is one of two possible diatonic diminished triads in the 5-limit
|}
 
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|+ style="font-size: 105%; white-space: nowrap;" | Table of basic Dorian tetrads
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! Name
! Notation (from D)
! Steps
! Occur(s) on Scale Degree(s)
! Approximate JI
! Notes
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