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

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Line 10: Line 10:
! rowspan="2" | Step
! rowspan="2" | Step
! rowspan="2" | Cents
! rowspan="2" | Cents
! rowspan="2" colspan="3" | Interval names
! colspan="3" | Interval and Note names
! colspan="2" | Compatibility rating
! colspan="2" | Compatibility rating
|-
|-
! [[SKULO interval names|SKULO]]-based interval names
! [[2.3-equivalent class and Pythagorean-commatic interval naming system|Pythagorean-commatic]]-based interval names
! [[Syntonic-rastmic subchroma notation|SRS notation]]
! Harmonic
! Harmonic
! Melodic
! Melodic
Line 524: Line 527:
| k4
| k4
| Greater Grave Fourth
| Greater Grave Fourth
| G↓
| G↓, Abb
| -6
| -6
| -5
| -5
Line 620: Line 623:
| kkA4, RuA4, kd5
| kkA4, RuA4, kd5
| Diptolemaic Augmented Fourth, Retroptolemaic Diminished Fifth
| Diptolemaic Augmented Fourth, Retroptolemaic Diminished Fifth
| G#↓↓, Ab↓
| Gt>/, G#↓↓, Ab↓
| -3
| -3
| 4
| 4
Line 692: Line 695:
| KKd5, rUDd5, KA4
| KKd5, rUDd5, KA4
| Diptolemaic Diminished Fifth, Retroptolemaic Augmented Fourth
| Diptolemaic Diminished Fifth, Retroptolemaic Augmented Fourth
| Ab↑↑, G#↑
| Ad<\, Ab↑↑, G#↑
| -3
| -3
| 4
| 4
Line 716: Line 719:
| Rm5, rUA4
| Rm5, rUA4
| Wide Paraminor Fifth, Retrodiptolemaic Augmented Fourth
| Wide Paraminor Fifth, Retrodiptolemaic Augmented Fourth
| Ad<\, G#↑, Ab↑↑
| Ad>/, G#↑, Ab↑↑
| -1
| -1
| 6
| 6
Line 788: Line 791:
| K5
| K5
| Lesser Acute Fifth
| Lesser Acute Fifth
| A↑
| A↑, Gx
| -6
| -6
| -5
| -5
Line 1,004: Line 1,007:
| KM6
| KM6
| Lesser Supermajor Sixth
| Lesser Supermajor Sixth
| B↑, Cd<\, Cb↑↑, A##
| B↑, Cd<\, Cb↑↑, Ax
| -1
| -1
| 7
| 7
Line 1,012: Line 1,015:
| SM6, kUM6
| SM6, kUM6
| Greater Supermajor Second, Narrow Inframinor Seventh
| Greater Supermajor Second, Narrow Inframinor Seventh
| Cb<, Bt<↓, B↑/
| Cd<, Bt<↓, B↑/
| 0
| 0
| 7
| 7
Line 1,655: Line 1,658:
| I
| I
| 90:108:135:160
| 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
|  
|-
|-
| Pythagorean Major Seventh
| Pythagorean Major Seventh
Line 1,813: Line 1,816:
| I
| I
| 90:108:135:160
| 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
| Ptolemaic Major Seventh
Line 1,827: Line 1,830:
| b↑III
| b↑III
| 1/(45:54:64:80)
| 1/(45:54:64:80)
| This dissonant dominant tetrad has a different function than its more traditional counterpart
| This dissonant dominant tetrad has a slightly different function than its more traditional counterpart
|-
| Ptolemaic Minor Seventh
| D, F↑, A, C↑
| 0, 42, 93, 135
| IV, bVII
| 10:12:15:18
|
|-
| Ptolemaic Parallel Half-Diminished
| D, F, Ab↑, C
| 0, 39, 81, 132
| V
| 1/(36:45:54:64)
| This dissonant tetrad is an option for imperfect half cadences in the 5-limit
|-
| Ptolemaic Major Seventh
| D, F#↓, A, C#↓
| 0, 51, 93, 144
| b↑VI
| 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 Phrygian in 159edo actually presents unexpected possibilities compared to its more traditional counterpart.
 
==== Lydian ====
 
This mode is optimized for 5-limit using a variation on the right-handed Zarlino diatonic scale.
 
{| class="mw-collapsible mw-collapsed wikitable center-1"
|+ style="font-size: 105%; white-space: nowrap;" | Table of Lydian 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#↓
| 78
| Sycophant
| [[45/32]]
|-
| 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 basic chords...
 
{| class="mw-collapsible mw-collapsed wikitable center-1"
|+ style="font-size: 105%; white-space: nowrap;" | Table of basic Lydian triads
|-
! Name
! Notation (from D)
! Steps
! Occur(s) on Scale Degree(s)
! Approximate JI
! Notes
|-
| Ptolemaic Major
| D, F#↓, A
| 0, 51, 93
| I, II, V
| 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
| ↓III, ↓VII
| 1/(4:5:6)
| This is the second of two triads that can be considered fully-resolved in Western Classical Harmony
|-
| Supradusthumic Pythagorean Minor
| D, F, A↓
| 0, 39, 90
| VI
| 27:32:40
| This dissonant triad is one of two possible diatonic wolf triads in the 5-limit
|-
| Greater Ptolemaic Diminished
| D, F↑, Ab↑
| 0, 42, 81
| #↓IV
| 45:54:64
| This dissonant triad is one of two possible diatonic diminished triads in the 5-limit
|}
|}


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