Xenharmonic Wiki

Pinetone: Difference between revisions

← Older editNewer edit →
VisualWikitext
Lhearne (talk | contribs)
autopatrolled, emailconfirmed
1,636 edits
mNo edit summary
Lhearne (talk | contribs)
autopatrolled, emailconfirmed
1,636 edits
Line 599: Line 599:


{| class="wikitable"
{| class="wikitable"
|+Table 2.7. Tertian triads of the Ptolemismic Pinetone diatonic on D (dorian symmetric minor)
|+Table 2.7. Tertian triads of the Ptolemismic Pinetone diatonic in D (dorian symmetric minor)
!Root note
!Root note
!Triad notes
!Triad notes
Line 606: Line 606:
!Pinetone triad
!Pinetone triad
!JI chord approximated by triad
!JI chord approximated by triad
!Mode on root
|-
|-
!D
!D
Line 613: Line 614:
|minor
|minor
|10:12:15
|10:12:15
|Dorian symmetric minor
|-
|-
!E
!E
Line 620: Line 622:
|minor
|minor
|10:12:15
|10:12:15
|Phrygian bright minor
|-
|-
!F
!F
Line 627: Line 630:
|major
|major
|4:5:6
|4:5:6
|Lydian dark major
|-
|-
!G
!G
Line 634: Line 638:
|major
|major
|4:5:6
|4:5:6
|Mixolydian bright major
|-
|-
!A
!A
Line 641: Line 646:
|minor diminished
|minor diminished
| 15:18:22
| 15:18:22
|Aeolian magical seventh
|-
|-
!B
!B
Line 648: Line 654:
|diminished
|diminished
|25:30:36
|25:30:36
|Locrian dark diminished
|-
|-
!C
!C
Line 655: Line 662:
| major diminished
| major diminished
| 27:33:40
| 27:33:40
|Ionian bright diminished
|}
|}


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.
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"
{| class="wikitable"
|+Table 2.8. Tertian tetrads of the Ptolemismic Pinetone diatonic on D (dorian symmetric minor)
|+Table 2.8. Tertian tetrads of the Ptolemismic Pinetone diatonic in D (dorian symmetric minor)
!Root note
!Root note
!Triad notes
!Triad notes
Line 666: Line 674:
!Pinetone tetrad
!Pinetone tetrad
!JI chord approximated by tetrad
!JI chord approximated by tetrad
!Mode on root
|-
|-
!D
!D
Line 673: Line 682:
| minor 7
| minor 7
| 10:12:15:18
| 10:12:15:18
|Dorian symmetric minor
|-
|-
!E
!E
Line 680: Line 690:
| minor 7
| minor 7
| 10:12:15:18
| 10:12:15:18
|Phrygian bright minor
|-
|-
!F
!F
Line 687: Line 698:
|major major-minor 7
|major major-minor 7
|12:15:18:22
|12:15:18:22
|Lydian dark major
|-
|-
!G
!G
Line 694: Line 706:
|major minor 7
|major minor 7
|20:25:30:36
|20:25:30:36
|Mixolydian bright major
|-
|-
!A
!A
Line 701: Line 714:
|minor diminished 7
|minor diminished 7
|45:54:66:80
|45:54:66:80
|Aeolian magical seventh
|-
|-
!B
!B
Line 708: Line 722:
|half diminished 7
|half diminished 7
|25:30:36:45
|25:30:36:45
|Locrian dark diminished
|-
|-
!C
!C
Line 715: Line 730:
|major half diminished 7
|major half diminished 7
|27:33:40:50
|27:33:40:50
|Ionian bright diminished
|}
|}


Line 728: Line 744:
!Pinetone triad
!Pinetone triad
!JI chord approximated by triad
!JI chord approximated by triad
!Mode on root
|-
|-
!D
!D
Line 735: Line 752:
|sus minor major
|sus minor major
|15:20:27
|15:20:27
|Dorian symmetric minor
|-
|-
!E
!E
Line 742: Line 760:
|sus major minor
|sus major minor
|11:15:20
|11:15:20
|Phrygian bright minor
|-
|-
!F
!F
Line 749: Line 768:
|sus ♭2 major minor
|sus ♭2 major minor
|24:33:44
|24:33:44
|Lydian dark major
|-
|-
!G
!G
Line 756: Line 776:
|sus major minor
|sus major minor
|11:15:20
|11:15:20
|Mixolydian bright major
|-
|-
!A
!A
Line 763: Line 784:
|sus minor minor
|sus minor minor
|9:12:16
|9:12:16
|Aeolian magical seventh
|-
|-
!B
!B
Line 770: Line 792:
|sus minor major
|sus minor major
|15:20:27
|15:20:27
|Locrian dark diminished
|-
|-
!C
!C
Line 777: Line 800:
|sus ♯4 minor major
|sus ♯4 minor major
|6:8:11
|6:8:11
|Ionian bright diminished
|}
|}
We can see that compared to tertian (2-step stacked) chords, quartal (3-step stacked) chords are much more evenly spread in the Pinetone diatonic. 3-step pentads ala the quartal voicings of modern jazz harmony may also be of interest. Two octaves are spanned by four 3-step intervals and a 2-step remainder. Given that Pinetone cannot be generated by 4/3 perfect fourths like Meantone can these pentads have much more variety in Pinetone than in Meantone. As in modern jazz, variety is found through utilizing all inversions of the pentad. The root position and 2nd inversion are shown, where the second inversion spans an octave with a symmetric pattern of two 3-step intervals on either side of a 2-step interval. Root position pentads on A and B (2nd inversion on G and A) cover the notes of the [[The Pinetone System#Pinetone pentatonic|Pinetone major and minor pentatonics]] respectively, introduced below.  
We can see that compared to tertian (2-step stacked) chords, quartal (3-step stacked) chords are much more evenly spread in the Pinetone diatonic. 3-step pentads ala the quartal voicings of modern jazz harmony may also be of interest. Two octaves are spanned by four 3-step intervals and a 2-step remainder. Given that Pinetone cannot be generated by 4/3 perfect fourths like Meantone can these pentads have much more variety in Pinetone than in Meantone. As in modern jazz, variety is found through utilizing all inversions of the pentad. The root position and 2nd inversion are shown, where the second inversion spans an octave with a symmetric pattern of two 3-step intervals on either side of a 2-step interval. Root position pentads on A and B (2nd inversion on G and A) cover the notes of the [[The Pinetone System#Pinetone pentatonic|Pinetone major and minor pentatonics]] respectively, introduced below.  
Line 788: Line 812:
!JI chord approximated by triad
!JI chord approximated by triad
!JI Intervals
!JI Intervals
!Mode on root
|-
|-
!D
!D
Line 796: Line 821:
|15:20:27:36:50
|15:20:27:36:50
|4/3, 27/20, 4/3, 25/18, (6/5)
|4/3, 27/20, 4/3, 25/18, (6/5)
|Dorian symmetric minor
|-
|-
!E
!E
Line 804: Line 830:
| 20:27:36:48:65
| 20:27:36:48:65
|27/20, 4/3, 4/3, 65/48, (16/13)
|27/20, 4/3, 4/3, 65/48, (16/13)
|Phrygian bright minor
|-
|-
! F
! F
Line 812: Line 839:
|24:33:44:60:80
|24:33:44:60:80
|11/8, 4/3, 15/11, 4/3, (6/5)
|11/8, 4/3, 15/11, 4/3, (6/5)
|Lydian dark major
|-
|-
!G
!G
Line 820: Line 848:
|20:27:36:50:66
|20:27:36:50:66
|27/20, 4/3, 25/18, 33/25, (40/33)
|27/20, 4/3, 25/18, 33/25, (40/33)
|Mixolydian bright major
|-
|-
! A
! A
Line 828: Line 857:
|25:33:44:60:80
|25:33:44:60:80
|33/25, 4/3, 15/11, 4/3, (5/4)
|33/25, 4/3, 15/11, 4/3, (5/4)
|Aeolian magical seventh
|-
|-
!B
!B
Line 836: Line 866:
|15:20:27:36:48
|15:20:27:36:48
|4/3, 27/20, 4/3, 4/3, (5/4)
|4/3, 27/20, 4/3, 4/3, (5/4)
|Locrian dark diminished
|-
|-
!C
!C
Line 844: Line 875:
|18:24:33:44:60
|18:24:33:44:60
|4/3, 11/8, 4/3, 15/11, (6/5)
|4/3, 11/8, 4/3, 15/11, (6/5)
|Ionian bright diminished
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 854: Line 886:
!JI chord approximated by triad
!JI chord approximated by triad
!JI Intervals
!JI Intervals
!Mode on root
|-
|-
!D
!D
Line 862: Line 895:
|15:20:27:33:45:60
|15:20:27:33:45:60
|4/3, 27/20, 11/9, 15/11, 4/3
|4/3, 27/20, 11/9, 15/11, 4/3
|Dorian symmetric minor
|-
|-
!E
!E
Line 870: Line 904:
| 11:15:20:24:33:44
| 11:15:20:24:33:44
|15/11, 4/3, 6/5, 11/8, 4/3
|15/11, 4/3, 6/5, 11/8, 4/3
|Phrygian bright minor
|-
|-
!F
!F
Line 878: Line 913:
|18:25:33:40:54:72
|18:25:33:40:54:72
|25/18, 33/25, 40/33, 27/20, 4/3
|25/18, 33/25, 40/33, 27/20, 4/3
|Lydian dark major
|-
|-
!G
!G
Line 886: Line 922:
| 11:15:20:25:33:44
| 11:15:20:25:33:44
|15/11, 4/3, 5/4, 33/25, 4/3
|15/11, 4/3, 5/4, 33/25, 4/3
|Mixolydian bright major
|-
|-
!A
!A
Line 894: Line 931:
|27:36:48:60:80:108
|27:36:48:60:80:108
|4/3, 4/3, 5/4, 4/3, 27/20
|4/3, 4/3, 5/4, 4/3, 27/20
|Aeolian magical seventh
|-
|-
!B
!B
Line 902: Line 940:
| 33:44:60:72:96:132
| 33:44:60:72:96:132
|4/3, 15/11, 6/5, 4/3, 11/8
|4/3, 15/11, 6/5, 4/3, 11/8
|Locrian dark diminished
|-
|-
!C
!C
Line 910: Line 949:
|27:36:50:60:80:108
|27:36:50:60:80:108
|4/3, 25/18, 6/5, 4/3, 27/20
|4/3, 25/18, 6/5, 4/3, 27/20
|Ionian bright diminished
|}
|}
The mode names in the table below link to sequenced examples of the root position 3-step triads, and to root position, 1st inversion, 2nd inversion (with double octave), 3rd inversion, and 4th inversion 3-step pentads, on the tonic of each mode, tuned to [http://x31eq.com/cgi-bin/rt.cgi?ets=1ce_4p_2ce&limit=2_3_5_11 TE 2.3.5.11 Ptolemismic].
The mode names in the table below link to sequenced examples of the root position 3-step triads, and to root position, 1st inversion, 2nd inversion (with double octave), 3rd inversion, and 4th inversion 3-step pentads, on the tonic of each mode, tuned to [http://x31eq.com/cgi-bin/rt.cgi?ets=1ce_4p_2ce&limit=2_3_5_11 TE 2.3.5.11 Ptolemismic].
Retrieved from "https://en.xen.wiki/w/Pinetone"