Xenharmonic Wiki

User:Moremajorthanmajor/Hierarchy of soid-family modes: Difference between revisions

← Older editNewer edit →
VisualWikitext
No edit summary
No edit summary
Line 14: Line 14:
|+
|+
!Quantity (±13¢)
!Quantity (±13¢)
!Mode
! colspan="3" |Mode
|-
|-
|''1\1edo-22\21edo''
|''1\1edo-22\21edo''
|''Perfect Soft Phrygian''
| rowspan="12" |Perfect Minor
| rowspan="4" |Neapolitan
|''Soft Phrygian''
|-
|-
|''22\21-16\15''
|''22\21-16\15''
Line 25: Line 27:
|-
|-
|11\10-10\9
|11\10-10\9
|Perfect Intense Phrygian
|Intense Phrygian
|-
|-
|10\9-9\8
|10\9-9\8
|Perfect Intense Phrygian-Soft Aeolian
|Neapolitan/Natural-Harmonic
|Intense Phrygian-Soft Aeolian
|-
|-
|9\8-8\7
|9\8-8\7
|Perfect Soft Aeolian
| rowspan="3" |Natural-Harmonic
|Soft Aeolian
|-
|-
|8\7-7\6
|8\7-7\6
Line 37: Line 41:
|-
|-
|7\6-6\5
|7\6-6\5
|Perfect Intense Aeolian
|Intense Aeolian
|-
|-
|6\5-11\9
|6\5-11\9
|Perfect Intense Aeolian-Dorian
|Natural-Harmonic/Melodic
|Intense Aeolian-Subpental Dorian
|-
|-
|11\9-5\4
|11\9-5\4
|Perfect Subpental Dorian
| rowspan="3" |Melodic
|Subpental Dorian
|-
|-
|5\4-14\11
|5\4-14\11
|Perfect Pental Dorian
|Pental Dorian
|-
|-
|14\11-9\7
|14\11-9\7
|Perfect Superpental Dorian
|Superpental Dorian
|-
|-
|9\7-13\10
|9\7-13\10
|Perfect Dorian-Mixolydian
| colspan="2" |Perfect Neutral
|Dorian-Mixolydian
|-
|-
|13\10-21\16
|13\10-21\16
|Perfect Subpental Mixolydian
| rowspan="7" |Perfect Major
| rowspan="4" |Melodic
|Subpental Mixolydian
|-
|-
|21\16-4\3
|21\16-4\3
|Perfect Pental Mixolydian
|Pental Mixolydian
|-
|-
|4\3-39\29
|4\3-39\29
|Perfect Soft Superpental Mixolydian
|Soft Superpental Mixolydian
|-
|-
|39\29-40\29
|39\29-40\29
|Perfect Intense Superpental Mixolydian
|Intense Superpental Mixolydian
|-
|-
|40\29-7\5
|40\29-7\5
|Perfect Mixolydian-Soft Ionian
|Melodic/Natural-Harmonic
|Superpental Mixolydian-Soft Ionian
|-
|-
|7\5-17\12
|7\5-17\12
|Perfect Soft Ionian
| rowspan="2" |Natural-Harmonic
|Soft Ionian
|-
|-
|17\12-10\7
|17\12-10\7
|Perfect Intense Ionian
|Intense Ionian
|-
|-
|10\7-22\15
|10\7-22\15
| colspan="2" rowspan="3" |Ambiguous
|Intense Ionian-Lydian/Locrian
|Intense Ionian-Lydian/Locrian
|-
|-
Line 85: Line 97:
|-
|-
|11\7-19\12
|11\7-19\12
|Pluperfect Soft Phrygian
| rowspan="11" |Pluperfect/Abundant Minor
| rowspan="2" |Neapolitan
|Soft Phrygian
|-
|-
|19\12-8\5
|19\12-8\5
|Pluperfect Phrygian
|Intense Phrygian
|-
|-
|8\5-47\29
|8\5-47\29
|Pluperfect Phrygian-Aeolian
|Neapolitan/Natural-Harmonic
|Intense Phrygian-Subpental Aeolian
|-
|-
|47\29-48\29
|47\29-48\29
|Pluperfect Intense Subpental Aeolian
| rowspan="4" |Natural-Harmonic
|Intense Subpental Aeolian
|-
|-
|48\29-5\3
|48\29-5\3
|Pluperfect Soft Subpental Aeolian
|Soft Subpental Aeolian
|-
|-
|5/3-27\16
|5/3-27\16
|Pluperfect Pental Aeolian
|Pental Aeolian
|-
|-
|27\16-17\10
|27\16-17\10
|Pluperfect Subpental Aeolian
|Superpental Aeolian
|-
|-
|17\10-12\7
|17\10-12\7
|Pluperfect Aeolian-Dorian
|Natural-Harmonic/Melodic
|Aeolian-Dorian
|-
|-
|12\7-19\11
|12\7-19\11
|Pluperfect Subpental Dorian
| rowspan="3" |Melodic
|Subpental Dorian
|-
|-
|19\11-7\4
|19\11-7\4
|Pluperfect Pental Dorian
|Pental Dorian
|-
|-
|7\4-16\9
|7\4-16\9
|Pluperfect Superpental Dorian
|Superpental Dorian
|-
|-
|16\9-9\5
|16\9-9\5
|Pluperfect Dorian-Soft Mixolydian
| colspan="2" |Pluperfect/Abundant "Neutral"
|Superpental Dorian-Soft Mixolydian
|-
|-
|9\5-11\6
|9\5-11\6
| rowspan="8" |Pluperfect/Abundant Major
| rowspan="3" |Melodic
|Pluperfect Soft Mixolydian
|Pluperfect Soft Mixolydian
|-
|-
Line 130: Line 151:
|-
|-
|15\8-17\9
|15\8-17\9
|Melodic/Natural-Harmonic
|Pluperfect Intense Mixolydian-Soft Ionian
|Pluperfect Intense Mixolydian-Soft Ionian
|-
|-
|17\9-19\10
|17\9-19\10
| rowspan="4" |Natural-Harmonic
|Pluperfect Soft Ionian
|Pluperfect Soft Ionian
|-
|-
Line 143: Line 166:
|''Pluperfect Intense Ionian''
|''Pluperfect Intense Ionian''
|}
|}
The names "Perfect" and "Pluperfect" refer to the common limitation of a vocal melody to within a tenth for the sake of overall perceptual coherence. The "Perfect" modes also match where LCP may consider just a triad (or tetrad) to be reasonably complete and therefore the basic chordal harmony.  
The names "Perfect" and "Pluperfect/Abundant" refer to the common limitation of a vocal melody to within an eleventh for the sake of overall perceptual coherence. The "Perfect" modes also match where LCP may consider just a triad (or tetrad) to be reasonably complete and therefore the basic chordal harmony.  


Two noted potential bugs of the RCM are that only the tenths, in reference to their value as the compound form of the third which is ''the'' modal degree of the diatonic scale, are in reformed modes which match their qualities and Lydian and Locrian are technically two names of the same reformed mode. On the other hand, one noted feature of the RCM (unlike the common-practice church modes) is that they, by definition, ''do not'' refer to a specific gamut (or subgamut of a larger whole gamut) of notes to which a composition is presumed to be confined.  
Two noted potential bugs of the RCM are that only the tenths, in reference to their value as the compound form of the third which is ''the'' modal degree of the diatonic scale, are in reformed modes which match their qualities and Lydian and Locrian are technically two names of the same reformed mode. On the other hand, one noted feature of the RCM (unlike the common-practice church modes) is that they, by definition, ''do not'' refer to a specific gamut (or subgamut of a larger whole gamut) of notes to which a composition is presumed to be confined.  
Line 153: Line 176:
----
----
'''Extending common practice diatonic scales to repeat beyond the octave'''
'''Extending common practice diatonic scales to repeat beyond the octave'''
In syntonic temperaments, the seven notes of the diatonic scale are considered the basic components of linear melody and relatively easy to stabilize over most chords of the key.
In syntonic temperaments, the seven notes of the diatonic scale are considered the basic components of linear melody and relatively easy to stabilize over most chords of the key.


But this reform leaves the requirement of diatonicity, if retaining it, under-specified, and it would be nice to have some form of full specificity to apply anywhere in the spectrum ([[Bohlen-Pierce]] is fine, but it leaves one out of luck where the tritave is not chroma-equivalent).
But this reform leaves the requirement of diatonicity, if retaining it, under-specified, and it would be nice to have some form of full specificity to apply anywhere in the spectrum ([[Bohlen-Pierce]] is fine, but it leaves one out of luck where the tritave is not to be chroma-equivalent).


This is where LCP comes into the picture. It provides these names for the extensions of the common practice diatonic scales to repeat beyond the octave:
This is where LCP comes into the picture. It provides these names for the extensions of the common practice diatonic scales to repeat beyond the octave, that is the Reformed Authentic modes:


''Minor Ninths (F-G-A-B-H-C-D-E; da/fo-ro/se-ma/li-fi/ta/sa-bu/ku-so/da-le/ra-ti/si/mi) - Phrygian Mode New Neapolitan Scale:''
''Minor Ninths (G-A-B-C-Q-D-E-F) - Phrygian Mode New Neapolitan Scale:''


Major Ninths (F-G-A-B-H-C-D-E; da/fo-ro/se-ma/li-fi/ta/sa-bu/ku-so/da-le/ra-ti/si/mi) - Aeolian Mode New Neapolitan Scale:
Major Ninths (F-G-A-B-H-C-D-E) - Aeolian Mode New Neapolitan Scale:
 
'''2L 6s and 6L 2s - Symmetric, Tetrachordal Major'''


'''2L 6s and 6L 2s -'''
{| class="wikitable"
|+
|
|
|I
|II
|III
|IV
|V
|VI
|VII
|VIII
|-
| rowspan="2" |'''Symmetric Major'''
|''Phrygian''
|''so''
|''le''
|''ti/si''
|''du''
|''bo/k''o
|''re''
|''mi''
|''fa''
|-
|Aeolian
|fo
|se
|li
|ta/sa
|bu/ku
|do
|ra
|mi
|-
| rowspan="2" |'''Tetrachordal Major'''
|''Phrygian''
|''do''
|''ra''
|''mi''
|''fu''
|''bo/k''o
|''se''
|''li''
|''ta/sa''
|-
|Aeolian
|da
|ro
|ma
|fi
|bu/ku
|so
|le
|ti/si
|}
4L 4s - Macro-diminished
4L 4s - Macro-diminished


'''3L 5s and 5L 3s - Grandfather'''
'''3L 5s and 5L 3s - Grandfather'''


Minor Tenths - Dorian Mode Middletown (F-G[-J]-A-B-H-C-D[-S]-E; da/fo-ro/se[-bu]-ma/li-fi/ta/sa-bu/ku-so/da-le/ra[-ku]-ti/si/mi)
Minor Tenths (G[-J]-A-B-C-Q-D[-S]-E-F) - Dorian Mode Middletown


Major Tenths - Mixolydian Mode Middletown (F-G[-J]-A-B-H-C-D[-S]-E; da/fo-ro/se[-bu]-ma/li-fi/ta/sa-bu/ku-so/da-le/ra[-ku]-ti/si/mi)
Major Tenths (F-G[-J]-A-B-H-C-D[-S]-E) - Mixolydian Mode Middletown


'''3L 6s and 6L 3s - Symmetric, Tetrachordal Major, Macro-augmented[9]'''
'''3L 6s and 6L 3s - Macro-augmented[9]'''
{| class="wikitable"
|
|
|'''I'''
|'''II'''
|'''III'''
|'''IV'''
|'''V'''
|'''VI'''
|'''VII'''
|'''VIII'''
|IX
|-
| rowspan="2" |'''Symmetric Major'''
|Dorian
|so
|le
lu
|ti/si


ve
|du
ti/si
|bo
du
|re
ko
|mo
re
|ki
mi
|fa
|-
|Mixolydian
|'''fo'''
|'''se'''
|'''li'''
'''bu'''
|'''ta/sa'''
'''li'''
|'''bu'''
'''ta/sa'''
|'''do'''
'''ku'''
|'''ra'''
'''do'''
|'''ku'''
'''ra'''
|'''mi'''
|-
| rowspan="2" |'''Tetrachordal Major'''
|Dorian
|do
|ra
ru
|mi
ve
|fu
mi
|bo
fu
|se
ko
|lo
se
|ki
li
|ta/sa
|-
|Mixolydian
|'''da'''
|'''ro'''
|'''ma'''
'''bu'''
|'''fi'''
'''ma'''
|'''bu'''
'''fi'''
|'''so'''
'''ku'''
|'''le'''
'''so'''
|'''ku'''
'''le'''
|'''ti/si'''
|}
4L 5s and 5L 4s - Montrose
4L 5s and 5L 4s - Montrose


Line 213: Line 387:
''Major Fourteenths - Ionian Mode (aka Nagashi)''
''Major Fourteenths - Ionian Mode (aka Nagashi)''


Tetrad and Pentatonic - Mangan Temperament
''(Tetrad and Pentatonic - Mangan Temperament''


Hexa- and Heptatonic - Haneman Temperament
''Hexa- and Heptatonic - Haneman Temperament''


Enneatonic plus or minus one - Baiman Temperament
''Enneatonic plus or minus one - Baiman Temperament''


Hen- and dodecatonic - Sanbaiman Temperament
''Hen- and dodecatonic - Sanbaiman Temperament)''


Triskaidekatonic - Yakuman Temperament List
Triskaidekatonic - Yakuman Temperament List
Line 262: Line 436:
|Major - 7:9:12
|Major - 7:9:12
|}
|}
There are also "full" and "defective" ways of transliterating chord progressions into LCP modes which are ninths, elevenths and thirteenths due to the scale having a degree which is exactly at its midpoint. However, the ninths offer all the extra possibilities with no extra necessities unless you care about having great diversity of "defective" ways of transliterating chord progressions into the mode.
There are also "full" and "defective" ways of transliterating chord progressions into LCP modes which are ninths, elevenths and thirteenths due to the scale having a degree which is exactly at its midpoint. However, the ninths offer all the extra possibilities with no extra necessities unless you care about having great diversity of "defective" ways of transliterating chord progressions into the mode.Also, transliterations into ninths work as follows:
 
{| class="wikitable"
|+
!
!d5-v5
!P5
!^5-A5
|-
|m3
|Dorian - 6:7:10~Husayni (Persian) - 11:13:18
|Minor - 5:6:8
|
|-
|n3
|Bayati/Turkish Minor - 9:11:14
|Neutral - 22:27:36 (18:22:29)
|Rast - 9:11:15
|-
|M3
|
|Major - 7:9:12
|Chahargah (Persian) - 11:14:18~Hindu - 7:9:11
|}
 
The four reformed minor keys are as follows
 
{| class="wikitable"
|+
!
!
!I
!II
!III
!IV
!V
!VI
!VII
!VII
|-
! rowspan="2" |''Phrygian''
!''MOS''
! rowspan="2" |''G Major''
!''A Minor''
! rowspan="2" |''B Minor''
! rowspan="2" |''C Hindu''
!''Q Minor''
! rowspan="2" |''D Major''
!''E Minor''
! rowspan="2" |''F Minor''
|-
|''#7''
!''A Dorian''
!''Q Hindu''
!''E# Double Diminished''
|-
| rowspan="2" |Aeolian
!MOS
| rowspan="2" |F Major
|G Major
! rowspan="2" |A Dorian
!B Minor
| rowspan="2" |H Major
| rowspan="2" |C Major
!D Dorian
! rowspan="2" |E Minor
|-
|b4
|G Dorian
!Bb Major
!D Minor
|}
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/Hierarchy_of_soid-family_modes"