Xenharmonic Wiki

19edo: Difference between revisions

← Older editNewer edit →
VisualWikitext
Francium (talk | contribs)
4,840 edits
→Music: Added music
→Intervals: ratio first; sectioning
Line 46: Line 46:
Standard 12edo notation can be used, whether it is staff notation (with five lines), letter notation (with standard accidentals), solfege, or sargam. Note that D# and Eb are two different notes.
Standard 12edo notation can be used, whether it is staff notation (with five lines), letter notation (with standard accidentals), solfege, or sargam. Note that D# and Eb are two different notes.


{| class="wikitable right-1 right-2 center-4 center-6 center-7"
{| class="wikitable right-1 right-2 center-5 center-7 center-8"
! Degree
! #
! Cents
! Cents
! Approximate Ratios*
! colspan="3" | Interval
! colspan="3" | Interval
! [[Solfege]]
! [[Solfege]]
! Dodecatonic notation
! Dodecatonic Notation
! Ratios*
|-
|-
| 0
| 0
| 0.00
| 0.00
| [[1/1]]
| unison
| unison
| P1
| P1
Line 61: Line 62:
| Do
| Do
| P1
| P1
| [[1/1]]
|-
|-
| 1
| 1
| 63.16
| 63.16
| [[25/24]], [[28/27]], [[26/25]]
| aug 1sn, dim 2nd
| aug 1sn, dim 2nd
| A1, d2
| A1, d2
Line 70: Line 71:
| Di/Ro
| Di/Ro
| A1, m2
| A1, m2
| [[25/24]], [[28/27]], [[26/25]]
|-
|-
| 2
| 2
| 126.32
| 126.32
| [[15/14]], [[16/15]], [[13/12]], [[14/13]]
| minor 2nd
| minor 2nd
| m2
| m2
Line 79: Line 80:
| Ra
| Ra
| M2, m3
| M2, m3
| [[15/14]], [[16/15]], [[13/12]], [[14/13]]
|-
|-
| 3
| 3
| 189.47
| 189.47
| [[9/8]], [[10/9]], [[125/112]]
| major 2nd
| major 2nd
| M2
| M2
Line 88: Line 89:
| Re
| Re
| M3
| M3
| [[9/8]], [[10/9]], [[125/112]]
|-
|-
| 4
| 4
| 252.63
| 252.63
| [[7/6]], [[8/7]], [[15/13]]
| aug 2nd, dim 3rd
| aug 2nd, dim 3rd
| A2, d3
| A2, d3
Line 97: Line 98:
| Ri/Ma
| Ri/Ma
| m4, a3
| m4, a3
| [[7/6]], [[8/7]], [[15/13]]
|-
|-
| 5
| 5
| 315.79
| 315.79
| [[6/5]]
| minor 3rd
| minor 3rd
| m3
| m3
Line 106: Line 107:
| Me
| Me
| M4, m5
| M4, m5
| [[6/5]]
|-
|-
| 6
| 6
| 378.95
| 378.95
| [[5/4]], [[16/13]], [[56/45]]
| major 3rd
| major 3rd
| M3
| M3
Line 115: Line 116:
| Mi
| Mi
| M5
| M5
| [[5/4]], [[16/13]], [[56/45]]
|-
|-
| 7
| 7
| 442.11
| 442.11
| [[32/25]], [[9/7]], [[13/10]]
| aug 3rd, dim 4th
| aug 3rd, dim 4th
| A3, d4
| A3, d4
Line 124: Line 125:
| Mo/Fe
| Mo/Fe
| A5, d6
| A5, d6
| [[32/25]], [[9/7]], [[13/10]]
|-
|-
| 8
| 8
| 505.26
| 505.26
| [[4/3]], [[75/56]]
| perfect 4th
| perfect 4th
| P4
| P4
Line 133: Line 134:
| Fa
| Fa
| P6
| P6
| [[4/3]], [[75/56]]
|-
|-
| 9
| 9
| 568.42
| 568.42
| [[25/18]], [[7/5]], [[18/13]]
| aug 4th
| aug 4th
| A4
| A4
Line 142: Line 143:
| Fi
| Fi
| A6, m7
| A6, m7
| [[25/18]], [[7/5]], [[18/13]]
|-
|-
| 10
| 10
| 631.58
| 631.58
| [[36/25]], [[10/7]], [[13/9]]
| dim 5th
| dim 5th
| d5
| d5
Line 151: Line 152:
| Se
| Se
| M7, d8
| M7, d8
| [[36/25]], [[10/7]], [[13/9]]
|-
|-
| 11
| 11
| 694.74
| 694.74
| [[3/2]], [[112/75]]
| perfect 5th
| perfect 5th
| P5
| P5
Line 160: Line 161:
| So
| So
| P8
| P8
| [[3/2]], [[112/75]]
|-
|-
| 12
| 12
| 757.89
| 757.89
| [[25/16]], [[14/9]], [[20/13]]
| aug 5th, dim 6th
| aug 5th, dim 6th
| A5, d6
| A5, d6
Line 169: Line 170:
| Si/Lo
| Si/Lo
| A8, m9
| A8, m9
| [[25/16]], [[14/9]], [[20/13]]
|-
|-
| 13
| 13
| 821.05
| 821.05
| [[8/5]], [[13/8]], [[45/28]]
| minor 6th
| minor 6th
| m6
| m6
Line 178: Line 179:
| Le
| Le
| M9, m10
| M9, m10
| [[8/5]], [[13/8]], [[45/28]]
|-
|-
| 14
| 14
| 884.21
| 884.21
| [[5/3]]
| major 6th
| major 6th
| M6
| M6
Line 187: Line 188:
| La
| La
| M10
| M10
| [[5/3]]
|-
|-
| 15
| 15
| 947.37
| 947.37
| [[7/4]], [[12/7]], [[26/15]]
| aug 6th, dim 7th
| aug 6th, dim 7th
| A6, d7
| A6, d7
Line 196: Line 197:
| Li/Ta
| Li/Ta
| m11, A10
| m11, A10
| [[7/4]], [[12/7]], [[26/15]]
|-
|-
| 16
| 16
| 1010.53
| 1010.53
| [[9/5]], [[16/9]], [[224/125]]
| minor 7th
| minor 7th
| m7
| m7
Line 205: Line 206:
| Te
| Te
| M11, m12
| M11, m12
| [[9/5]], [[16/9]], [[224/125]]
|-
|-
| 17
| 17
| 1073.68
| 1073.68
| [[15/8]], [[13/7]], [[28/15]], [[24/13]]
| major 7th
| major 7th
| M7
| M7
Line 214: Line 215:
| Ti
| Ti
| M12
| M12
| [[15/8]], [[13/7]], [[28/15]], [[24/13]]
|-
|-
| 18
| 18
| 1136.84
| 1136.84
| [[48/25]], [[27/14]], [[25/13]]
| aug 7th, dim 8ve
| aug 7th, dim 8ve
| A7, d8
| A7, d8
Line 223: Line 224:
| To/Da
| To/Da
| A12, d13
| A12, d13
| [[48/25]], [[27/14]], [[25/13]]
|-
|-
| 19
| 19
| 1200.00
| 1200.00
| [[2/1]]
| perfect 8ve
| perfect 8ve
| P8
| P8
Line 232: Line 233:
| Do
| Do
| P13
| P13
| [[2/1]]
|}
|}
<nowiki>*</nowiki> based on treating 19edo as a 2.3.5.7.13 subgroup temperament; other approaches are possible.
<nowiki>*</nowiki> based on treating 19edo as a 2.3.5.7.13 subgroup temperament; other approaches are possible.


=== Interval quality and chord names in color notation ===
Using [[color notation]], qualities can be loosely associated with colors:
Using [[color notation]], qualities can be loosely associated with colors:


{| class="wikitable" style="text-align: center"
{| class="wikitable" style="text-align: center"
! quality
! Quality
! [[color name]]
! [[Color name]]
! monzo format
! Monzo Format
! examples
! Examples
|-
|-
| diminished
| diminished
Line 275: Line 276:
Key signatures are the same, but with the extra notes and different enharmonic equivalents, some key signatures can get messy.  For example, the key of Bbb would have double-flats on B and E, and flats on C, D, F, G, and A.  Thinking of rewriting this key as A# might seem better, but then the key signature would contain double-sharps on C, F, and G, and sharps on A, B, D, and E, which is actually worse.
Key signatures are the same, but with the extra notes and different enharmonic equivalents, some key signatures can get messy.  For example, the key of Bbb would have double-flats on B and E, and flats on C, D, F, G, and A.  Thinking of rewriting this key as A# might seem better, but then the key signature would contain double-sharps on C, F, and G, and sharps on A, B, D, and E, which is actually worse.


=== Chord names ===
All 19edo chords can be named using conventional methods, expanded to include augmented and diminished 2nd, 3rds, 6ths and 7ths. Here are the zo, gu, yo and ru triads:
All 19edo chords can be named using conventional methods, expanded to include augmented and diminished 2nd, 3rds, 6ths and 7ths. Here are the zo, gu, yo and ru triads:


{| class="wikitable center-1 center-2 center-3 center-4"
{| class="wikitable center-1 center-2 center-3 center-4"
! [[Kite's color notation|color of the 3rd]]
! [[Kite's color notation|Color of the 3rd]]
! JI chord
! JI Chord
! edosteps
! Edosteps
! notes of C chord
! Notes of C Chord
! written name
! Written Name
! spoken name
! Spoken Name
|-
|-
| zo
| zo
Line 321: Line 321:
The last two chords illustrate how the 15\19 interval can be considered as either 7/4 or 12/7, and how 19edo tends to conflate zo and ru ratios.
The last two chords illustrate how the 15\19 interval can be considered as either 7/4 or 12/7, and how 19edo tends to conflate zo and ru ratios.


For a more complete list, see [[19edo Chord Names]] and [[Ups and Downs Notation #Chords and Chord Progressions]].
For a more complete list, see [[19edo Chord Names]] and [[Ups and downs notation #Chords and Chord Progressions]].


== JI approximation ==
== JI approximation ==
Retrieved from "https://en.xen.wiki/w/19edo"