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Lhearne (talk | contribs)
autopatrolled, emailconfirmed
1,636 edits
added chords to diatonic and octatonic
Line 354: Line 354:


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|}
{| class="wikitable"
|+Tertian triads of the porcutone diatonic on D
!Root note
!Triad notes
!Meantone triad
!Porcupine triad
!Porcutone triad
!JI chord approximated by triad
|-
!D
|D-F-A
|minor
|minor
|minor
|10:12:15
|-
!E
|E-G-B
|minor
|minor
|minor
|10:12:15
|-
!F
|F-A-C
|major
|major
|major
|4:5:6
|-
!G
|G-B-D
|major
|major
|major
|4:5:6
|-
!A
|A-C-E
|minor
|diminished
|minor diminished
|15:18:22
|-
!B
|B-D-F
|diminished
|diminished
|diminished
|25:30:36
|-
!C
|C-E-G
|major
|diminished
|major diminished
|27:33:40
|}
Porcupine tetrads in the table below are named after the third above the tonic and the third above the fifth, apart from tetrads with a diminished fifth.
{| class="wikitable"
|+Tertian tetrads of the porcutone diatonic on D
!Root note
!Triad notes
!Meantone tetrad
!Porcupine tetrad
!Porcutone tetrad
!JI chord approximated by tetrad
|-
!D
|D-F-A-C
|minor 7
|minor 7
|minor 7
|10:12:15:18
|-
!E
|E-G-B-D
|minor 7
|minor 7
|minor 7
|10:12:15:18
|-
!F
|F-A-C-E
|major 7
|major minor 7
|major major-minor 7
|12:15:18:22
|-
!G
|G-B-D-F
|major minor 7
|major minor 7
|major minor 7
|20:25:30:36
|-
!A
|A-C-E-G
|minor 7
|diminished 7
|minor diminished 7
|45:54:66:80
|-
!B
|B-D-F-A
|half diminished 7
|half diminished 7
|half diminished 7
|25:30:36:45
|-
!C
|C-E-G-B
|major 7
|half diminished 7
|major half diminished 7
|27:33:40:50
|}
Also of interest are the quartal triads of the porcutone diatonic. We describe these as stacked 3-step intervals (fourths) of the scale, perhaps an unusual interval to write quartal triads in, but it makes more sense here given the naming scheme I've introduced for the Porcupine[7] 3-step (quartal) triads.
{| class="wikitable"
|+3-step stacked triads of the porcutone diatonic on D
!Root note
!Triad notes
!Meantone triad
!Porcupine[7] triad
!Porcutone triad
!JI chord approximated by triad
|-
!D
|D-G-C
|sus
|3-step minor major
|sus minor major
|15:20:27
|-
!E
|E-A-D
|sus
|3-step major minor
|sus major minor
|11:15:20
|-
!F
|F-B-E
|sus ♭2
|3-step major minor
|sus ♭2 major minor
|24:33:44
|-
!G
|G-C-F
|sus
|3-step major minor
|sus major minor
|11:15:20
|-
!A
|A-D-G
|sus
|3-step minor minor
|sus minor minor
|9:12:16
|-
!B
|B-E-A
|sus
|3-step minor major
|sus minor major
|15:20:27
|-
!C
|C-F-B
|sus ♯4
|3-step minor major
|sus ♯4 minor major
|6:8:11
|}
|}


Line 658: Line 836:
!3-step stacked triad on root (with G♯)
!3-step stacked triad on root (with G♯)
!(with A♭ = H)
!(with A♭ = H)
!Triad name
!JI triad approximated
!JI triad approximated
|-
|-
Line 666: Line 845:
|G♯-C-F
|G♯-C-F
|A-D-G
|A-D-G
|3-step major major
|9:12:16
|9:12:16
|-
|-
Line 674: Line 854:
|A-D-G
|A-D-G
|B-E-A♭ = B-E-H
|B-E-A♭ = B-E-H
|3-step major major
|9:12:16
|9:12:16
|-
|-
Line 682: Line 863:
|B-E-G♯
|B-E-G♯
|C-F-A
|C-F-A
|3-step major minor
|3:4:5
|3:4:5
|-
|-
Line 690: Line 872:
|C-F-A
|C-F-A
|D-G-B
|D-G-B
|3-step major minor
|3:4:5
|3:4:5
|-
|-
Line 698: Line 881:
|D-G-B
|D-G-B
|E-A♭-C = E-H-C
|E-A♭-C = E-H-C
|3-step major minor
|3:4:5
|3:4:5
|-
|-
Line 706: Line 890:
|E-G♯-C
|E-G♯-C
|F-A-D
|F-A-D
|3-step minor major
|12:15:20
|12:15:20
|-
|-
Line 714: Line 899:
|F-A-D
|F-A-D
|G-B-E
|G-B-E
|3-step minor major
|12:15:20
|12:15:20
|-
|-
Line 722: Line 908:
|G-B-E
|G-B-E
|A♭-C-F = H-C-F
|A♭-C-F = H-C-F
|3-step minor major
|12:15:20
|12:15:20
|}
|}
Line 736: Line 923:
!UDP
!UDP
!Mode name
!Mode name
!3-step stacked triad on root
!JI triads approximated by  
!JI triads approximated by  
3-step stacked triad on root
3-step stacked triad on root
Line 743: Line 931:
|<nowiki>7|0</nowiki>
|<nowiki>7|0</nowiki>
|Dylathian (də-LA(H)TH-iən)
|Dylathian (də-LA(H)TH-iən)
|3-step major major
|3:4:5, 9:12:16
|3:4:5, 9:12:16
|-
|-
Line 749: Line 938:
|<nowiki>6|1</nowiki>
|<nowiki>6|1</nowiki>
|Illarnekian (ill-ar-NEK-iən)
|Illarnekian (ill-ar-NEK-iən)
|3-step major major
|3:4:5, 9:12:16
|3:4:5, 9:12:16
|-
|-
Line 755: Line 945:
|<nowiki>5|2</nowiki>
|<nowiki>5|2</nowiki>
|Celephaïsian (kel-ə-FAY-zhən)
|Celephaïsian (kel-ə-FAY-zhən)
|3-step major major
|3:4:5, 9:12:16
|3:4:5, 9:12:16
|-
|-
Line 761: Line 952:
|<nowiki>4|3</nowiki>
|<nowiki>4|3</nowiki>
|Ultharian (ul-THA(I)R-iən)
|Ultharian (ul-THA(I)R-iən)
|3-step major major
|3:4:5, 9:12:16
|3:4:5, 9:12:16
|-
|-
Line 767: Line 959:
|<nowiki>3|4</nowiki>
|<nowiki>3|4</nowiki>
|Mnarian (mə-NA(I)R-iən)
|Mnarian (mə-NA(I)R-iən)
|3-step major major
|3:4:5, 9:12:16
|3:4:5, 9:12:16
|-
|-
Line 773: Line 966:
|<nowiki>2|5</nowiki>
|<nowiki>2|5</nowiki>
|Kadathian (kə-DA(H)TH-iən)
|Kadathian (kə-DA(H)TH-iən)
|3-step major major
|3:4:5, 9:12:16
|3:4:5, 9:12:16
|-
|-
Line 779: Line 973:
|<nowiki>1|6</nowiki>
|<nowiki>1|6</nowiki>
|Hlanithian (lə-NITH-iən)
|Hlanithian (lə-NITH-iən)
|3-step major minor
|160:200:243
|160:200:243
|-
|-
Line 785: Line 980:
|<nowiki>0|7</nowiki>
|<nowiki>0|7</nowiki>
|Sarnathian (sar-NA(H)TH-iən), can be shortened to "Sarn"
|Sarnathian (sar-NA(H)TH-iən), can be shortened to "Sarn"
|3-step minor major
|200:243:324
|200:243:324
|}
|}
Line 1,050: Line 1,246:
!Step pattern
!Step pattern
!3-step stacked triad on root
!3-step stacked triad on root
!Oneirotonic name
!Porcupine name
!Porcutone name
!JI triad approximated
!JI triad approximated
|-
|-
Line 1,055: Line 1,254:
|LMLLMLsM
|LMLLMLsM
|A-D-G
|A-D-G
|3-step major major
|3-step major major
|3-step major major
|9:12:16
|9:12:16
|-
|-
Line 1,060: Line 1,262:
|MLMLLMLs
|MLMLLMLs
|G♯-C-F
|G♯-C-F
|30:39:52 (7:9:12 Thrasher, 16:21:28 Supermagic)
|3-step minor major
|3-step major major
|3-step minor-major major
|30:39:52 (7:9:12, 16:21:28)
|-
|-
|Dylathian middle major
|Dylathian middle major
|LLMLsMLM
|LLMLsMLM
|B-E-G♯
|C-F-A
|3-step major major
|3-step major minor
|3-step major major-minor
|3:4:5
|3:4:5
|-
|-
|Kadathian bright major
|Kadathian bright major
|MLLMLsML
|MLLMLsML
|C-F-A
|B-E-G♯
|3-step major major
|3-step major minor
|3-step major major-minor
|3:4:5
|3:4:5
|-
|-
Line 1,075: Line 1,286:
|LMLsMLML
|LMLsMLML
|D-G-B
|D-G-B
|3-step major major
|3-step major minor
|3-step major major-minor
|3:4:5
|3:4:5
|-
|-
Line 1,080: Line 1,294:
|LsMLMLLM
|LsMLMLLM
|F-A-D
|F-A-D
|3-step major major
|3-step minor major
|3-step major-minor major
|12:15:20
|12:15:20
|-
|-
Line 1,085: Line 1,302:
|MLsMLMLL
|MLsMLMLL
|E-G♯-C
|E-G♯-C
|3-step major minor
|3-step minor major
|3-step major-minor minor-major
|8:10:13
|8:10:13
|-
|-
Line 1,090: Line 1,310:
|sMLMLLML
|sMLMLLML
|G-B-E
|G-B-E
|3-step major major
|3-step minor major
|3-step major-minor major
|12:15:20
|12:15:20
|}
|}
Line 1,098: Line 1,321:
!Step pattern
!Step pattern
!3-step stacked triad on root
!3-step stacked triad on root
!Oneirotonic name
!Porcupine name
!Porcutone name
!JI triad approximated
!JI triad approximated
|-
|-
|Ultharian bright quartal
|Ultharian bright quartal
|LMLLMLsM
|LMLLMLMs
|A-D-G
|A-D-G
|3-step major major
|3-step major major
|3-step major major
|9:12:16
|9:12:16
|-
|-
|Illarnekian bright major
|Illarnekian bright major
|MLMLLMLs
|LLMLMsLM
|A♭-C-F
|9:12:16
|-
|Hlanithian dark quartal
|LLMLsMLM
|C-F-A
|C-F-A
|3-step major major
|3-step major minor
|3-step major major-minor
|3:4:5
|3:4:5
|-
|-
|Mnarian middle major
|Hlanithian dark quartal
|MLLMLsML
|MLLMLMsL
|B-E-A♭
|B-E-A♭
|27:36:44
|3-step major minor
|3-step major major
|3-step major major
|15:20:26 (12:16:21)
|-
|-
| Celephaïsian bright minor
|Mnarian middle major
|LMLsMLML
|LMLMsLML
|D-G-B
|D-G-B
|3-step major major
|3-step major minor
|3-step major major-minor
|3:4:5
|3:4:5
|-
|-
| Sarnathian dark major
| Celephaïsian bright minor
|LsMLMLLM
|LMsLMLLM
|F-A-D
|F-A-D
|3-step major major
|3-step minor major
|3-step major-minor major
|12:15:20
|12:15:20
|-
| Sarnathian dark major
|MLMsLMLL
|E-A♭-C
|3-step minor major
|3-step major minor
|3-step minor-major major-minor
|55:72:90 (16:21:26)
|-
|-
| Dylathian dark minor
| Dylathian dark minor
|MLsMLMLL
|sLMLLMLM
|E-A♭-C
|A♭-C-F
|99:121:162
|3-step major major
|3-step minor major
|3-step major-minor major
|12:15:20
|-
|-
| Kadathian middle minor
| Kadathian middle minor
|sMLMLLML
|MsLMLLML
|G-B-E
|G-B-E
|3-step major major
|3-step minor major
|3-step major-minor major
|12:15:20
|12:15:20
|}
|}
To me the left handed porcutone octatonic is superior because of the 3-step stacked triads it offers.


The following table gives all intervals of the porcutone octatonic.
The following table gives all intervals of the porcutone octatonic.
Retrieved from "https://en.xen.wiki/w/Pinetone"