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== Ups and down notation ==
== Ups and down notation ==
{| class="wikitable"
 
{| class="wikitable center-all"
|-
|-
| style="text-align:center;" | Degree
! Degree
| style="text-align:center;" | Cents
! Cents
| style="text-align:center;" | Approximate Ratios*
! Approximate Ratios<ref>based on treating 24-EDO as a 2.3.11.17.19 [[subgroup]]; other approaches are possible.</ref>
| colspan="3" style="text-align:center;" | [[Ups_and_Downs_Notation|ups and downs notation]]
! colspan="3" | [[ups and downs notation]]
|-
|-
| colspan="2" style="text-align:center;" | 0
| 0
| style="text-align:center;" | 1/1
| 0
| style="text-align:center;" | P1
| 1/1
| style="text-align:center;" | unison
| P1
| style="text-align:center;" | C
| unison
| C
|-
|-
| style="text-align:center;" | 1
| 1
| style="text-align:center;" | 50
| 50
| style="text-align:center;" | 33/32, 34/33
| 33/32, 34/33
| style="text-align:center;" | ^P1, vm2
| ^P1, vm2
| style="text-align:center;" | up-unison, downminor 2nd
| up-unison, downminor 2nd
| style="text-align:center;" | ^C, vDb
| ^C, vDb
|-
|-
| style="text-align:center;" | 2
| 2
| style="text-align:center;" | 100
| 100
| style="text-align:center;" | 17/16, 18/17
| 17/16, 18/17
| style="text-align:center;" | A1, m2
| A1, m2
| style="text-align:center;" | aug unison, minor 2nd
| aug unison, minor 2nd
| style="text-align:center;" | C#, Db
| C#, Db
|-
|-
| style="text-align:center;" | 3
| 3
| style="text-align:center;" | 150
| 150
| style="text-align:center;" | 12/11
| 12/11
| style="text-align:center;" | ~2
| ~2
| style="text-align:center;" | mid 2nd
| mid 2nd
| style="text-align:center;" | vD
| vD
|-
|-
| style="text-align:center;" | 4
| 4
| style="text-align:center;" | 200
| 200
| style="text-align:center;" | 9/8
| 9/8
| style="text-align:center;" | M2
| M2
| style="text-align:center;" | major 2nd
| major 2nd
| style="text-align:center;" | D
| D
|-
|-
| style="text-align:center;" | 5
| 5
| style="text-align:center;" | 250
| 250
| style="text-align:center;" | 22/19
| 22/19
| style="text-align:center;" | ^M2, vm3
| ^M2, vm3
| style="text-align:center;" | upmajor 2nd, downminor 3rd
| upmajor 2nd, downminor 3rd
| style="text-align:center;" | ^D, vEb
| ^D, vEb
|-
|-
| style="text-align:center;" | 6
| 6
| style="text-align:center;" | 300
| 300
| style="text-align:center;" | 19/16
| 19/16
| style="text-align:center;" | m3
| m3
| style="text-align:center;" | minor 3rd
| minor 3rd
| style="text-align:center;" | Eb
| Eb
|-
|-
| style="text-align:center;" | 7
| 7
| style="text-align:center;" | 350
| 350
| style="text-align:center;" | 11/9, 27/22
| 11/9, 27/22
| style="text-align:center;" | ~3
| ~3
| style="text-align:center;" | mid 3rd
| mid 3rd
| style="text-align:center;" | vE
| vE
|-
|-
| style="text-align:center;" | 8
| 8
| style="text-align:center;" | 400
| 400
| style="text-align:center;" | 24/19
| 24/19
| style="text-align:center;" | M3
| M3
| style="text-align:center;" | major 3rd
| major 3rd
| style="text-align:center;" | E
| E
|-
|-
| style="text-align:center;" | 9
| 9
| style="text-align:center;" | 450
| 450
| style="text-align:center;" | 22/17
| 22/17
| style="text-align:center;" | ^M3, v4
| ^M3, v4
| style="text-align:center;" | upmajor 3rd, down-4th
| upmajor 3rd, down-4th
| style="text-align:center;" | ^E, vF
| ^E, vF
|-
|-
| style="text-align:center;" | 10
| 10
| style="text-align:center;" | 500
| 500
| style="text-align:center;" | 4/3
| 4/3
| style="text-align:center;" | P4
| P4
| style="text-align:center;" | fourth
| fourth
| style="text-align:center;" | F
| F
|-
|-
| style="text-align:center;" | 11
| 11
| style="text-align:center;" | 550
| 550
| style="text-align:center;" | 11/8
| 11/8
| style="text-align:center;" | ^4, ~4
| ^4, ~4
| style="text-align:center;" | up-4th, mid-4th
| up-4th, mid-4th
| style="text-align:center;" | ^F
| ^F
|-
|-
| style="text-align:center;" | 12
| 12
| style="text-align:center;" | 600
| 600
| style="text-align:center;" | 17/12
| 17/12
| style="text-align:center;" | A4, d5
| A4, d5
| style="text-align:center;" | aug 4th, dim 5th
| aug 4th, dim 5th
| style="text-align:center;" | F#, Gb
| F#, Gb
|-
|-
| style="text-align:center;" | 13
| 13
| style="text-align:center;" | 650
| 650
| style="text-align:center;" | 16/11
| 16/11
| style="text-align:center;" | v5, ~5
| v5, ~5
| style="text-align:center;" | down-5th, mid-5th
| down-5th, mid-5th
| style="text-align:center;" | vG
| vG
|-
|-
| style="text-align:center;" | 14
| 14
| style="text-align:center;" | 700
| 700
| style="text-align:center;" | 3/2
| 3/2
| style="text-align:center;" | P5
| P5
| style="text-align:center;" | fifth
| fifth
| style="text-align:center;" | G
| G
|-
|-
| style="text-align:center;" | 15
| 15
| style="text-align:center;" | 750
| 750
| style="text-align:center;" | 17/11
| 17/11
| style="text-align:center;" | ^5, vm6
| ^5, vm6
| style="text-align:center;" | up-fifth, downminor 6th
| up-fifth, downminor 6th
| style="text-align:center;" | ^G, vAb
| ^G, vAb
|-
|-
| style="text-align:center;" | 16
| 16
| style="text-align:center;" | 800
| 800
| style="text-align:center;" | 19/12
| 19/12
| style="text-align:center;" | m6
| m6
| style="text-align:center;" | minor 6th
| minor 6th
| style="text-align:center;" | Ab
| Ab
|-
|-
| style="text-align:center;" | 17
| 17
| style="text-align:center;" | 850
| 850
| style="text-align:center;" | 18/11, 44/27
| 18/11, 44/27
| style="text-align:center;" | ~6
| ~6
| style="text-align:center;" | mid 6th
| mid 6th
| style="text-align:center;" | vA
| vA
|-
|-
| style="text-align:center;" | 18
| 18
| style="text-align:center;" | 900
| 900
| style="text-align:center;" | 32/19
| 32/19
| style="text-align:center;" | M6
| M6
| style="text-align:center;" | major 6th
| major 6th
| style="text-align:center;" | A
| A
|-
|-
| style="text-align:center;" | 19
| 19
| style="text-align:center;" | 950
| 950
| style="text-align:center;" | 19/11
| 19/11
| style="text-align:center;" | ^M6, vm7
| ^M6, vm7
| style="text-align:center;" | upmajor 6th, downminor 7th
| upmajor 6th, downminor 7th
| style="text-align:center;" | ^A, vBb
| ^A, vBb
|-
|-
| style="text-align:center;" | 20
| 20
| style="text-align:center;" | 1000
| 1000
| style="text-align:center;" | 16/9
| 16/9
| style="text-align:center;" | m7
| m7
| style="text-align:center;" | minor 7th
| minor 7th
| style="text-align:center;" | Bb
| Bb
|-
|-
| style="text-align:center;" | 21
| 21
| style="text-align:center;" | 1050
| 1050
| style="text-align:center;" | 11/6
| 11/6
| style="text-align:center;" | ~7
| ~7
| style="text-align:center;" | mid 7th
| mid 7th
| style="text-align:center;" | vB
| vB
|-
|-
| style="text-align:center;" | 22
| 22
| style="text-align:center;" | 1100
| 1100
| style="text-align:center;" | 17/9, 32/17
| 17/9, 32/17
| style="text-align:center;" | M7
| M7
| style="text-align:center;" | major 7th
| major 7th
| style="text-align:center;" | B
| B
|-
|-
| style="text-align:center;" | 23
| 23
| style="text-align:center;" | 1150
| 1150
| style="text-align:center;" | 33/17, 64/33
| 33/17, 64/33
| style="text-align:center;" | ^M7, vP8
| ^M7, vP8
| style="text-align:center;" | upmajor 7th, down-8ve
| upmajor 7th, down-8ve
| style="text-align:center;" | ^B, vC
| ^B, vC
|-
|-
| style="text-align:center;" | 24
| 24
| style="text-align:center;" | 1200
| 1200
| style="text-align:center;" | 2/1
| 2/1
| style="text-align:center;" | P8
| P8
| style="text-align:center;" | perfect 8ve
| perfect 8ve
| style="text-align:center;" | C
| C
|}
|}
*based on treating 24-EDO as a 2.3.11.17.19 subgroup; other approaches are possible.
 
<references/>


Combining ups and downs notation with [[Kite's_color_notation|color notation]], qualities can be loosely associated with colors:
Combining ups and downs notation with [[Kite's_color_notation|color notation]], qualities can be loosely associated with colors:


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | quality
! | quality
Line 209: Line 212:
! | examples
! | examples
|-
|-
| style="text-align:center;" | downminor
| downminor
| style="text-align:center;" | zo
| zo
| style="text-align:center;" | {a, b, 0, 1}
| {a, b, 0, 1}
| style="text-align:center;" | 7/6, 7/4
| 7/6, 7/4
|-
|-
| style="text-align:center;" | minor
| minor
| style="text-align:center;" | fourthward wa
| fourthward wa
| style="text-align:center;" | {a, b}, b &lt; -1
| {a, b}, b &lt; -1
| style="text-align:center;" | 32/27, 16/9
| 32/27, 16/9
|-
|-
| style="text-align:center;" | "
| "
| style="text-align:center;" | gu
| gu
| style="text-align:center;" | {a, b, -1}
| {a, b, -1}
| style="text-align:center;" | 6/5, 9/5
| 6/5, 9/5
|-
|-
| style="text-align:center;" | mid
| mid
| style="text-align:center;" | ilo
| ilo
| style="text-align:center;" | {a, b, 0, 0, 1}
| {a, b, 0, 0, 1}
| style="text-align:center;" | 11/9, 11/6
| 11/9, 11/6
|-
|-
| style="text-align:center;" | "
| "
| style="text-align:center;" | lu
| lu
| style="text-align:center;" | {a, b, 0, 0, -1}
| {a, b, 0, 0, -1}
| style="text-align:center;" | 12/11, 18/11
| 12/11, 18/11
|-
|-
| style="text-align:center;" | major
| major
| style="text-align:center;" | yo
| yo
| style="text-align:center;" | {a, b, 1}
| {a, b, 1}
| style="text-align:center;" | 5/4, 5/3
| 5/4, 5/3
|-
|-
| style="text-align:center;" | "
| "
| style="text-align:center;" | fifthward wa
| fifthward wa
| style="text-align:center;" | {a, b}, b &gt; 1
| {a, b}, b &gt; 1
| style="text-align:center;" | 9/8, 27/16
| 9/8, 27/16
|-
|-
| style="text-align:center;" | upmajor
| upmajor
| style="text-align:center;" | ru
| ru
| style="text-align:center;" | {a, b, 0, -1}
| {a, b, 0, -1}
| style="text-align:center;" | 9/7, 12/7
| 9/7, 12/7
|}
|}


Line 256: Line 259:
{| class="wikitable"
{| class="wikitable"
|-
|-
!edosteps
! edosteps
!notes
! notes
!written name
! written name
!spoken name
! spoken name
!JI chord, if any
! JI chord, if any
|-
|-
|0-5-14
| 0-5-14
|C vEb G
| C vEb G
|Cvm
| Cvm
|C downminor
| C downminor
|6:7:9
| 6:7:9
|-
|-
|0-6-14
| 0-6-14
|C Eb G
| C Eb G
|Cm
| Cm
|C minor
| C minor
|10:12:15 <u>or</u> 6/(6:5:4)
| 10:12:15 <u>or</u> 6/(6:5:4)
|-
|-
|0-7-14
| 0-7-14
|C vE G
| C vE G
|C~
| C~
|C mid
| C mid
|18:22:27
| 18:22:27
|-
|-
|0-8-14
| 0-8-14
|C E G
| C E G
|C
| C
|C major or C
| C major or C
|4:5:6
| 4:5:6
|-
|-
|0-9-14
| 0-9-14
|C ^E G
| C ^E G
|C^
| C^
|C upmajor or C up
| C upmajor or C up
|14:18:21 <u>or</u> 9/(9:7:6)
| 14:18:21 <u>or</u> 9/(9:7:6)
|-
|-
|0-8-13
| 0-8-13
|C E vG
| C E vG
|C(v5)
| C(v5)
|C down-five
| C down-five
|
|
|-
|-
|0-7-13
| 0-7-13
|C vE vG
| C vE vG
|C~(v5)
| C~(v5)
|C mid down-five
| C mid down-five
|22:27:32
| 22:27:32
|-
|-
|0-4-11-14
| 0-4-11-14
|C D ^F G
| C D ^F G
|C^4,9
| C^4,9
|C up-four add-nine
| C up-four add-nine
|8:9:11:12
| 8:9:11:12
|-
|-
|0-9-14-19
| 0-9-14-19
|C ^E G ^A
| C ^E G ^A
|C^6
| C^6
|C up-six
| C up-six
|14:18:21:24
| 14:18:21:24
|-
|-
|0-5-14-20
| 0-5-14-20
|C vEb G Bb
| C vEb G Bb
|Cvm,7
| Cvm,7
|C downminor add-seven
| C downminor add-seven
|
|
|-
|-
|0-5-14-19
| 0-5-14-19
|C vEb G vBb
| C vEb G vBb
|Cvm7
| Cvm7
|C downminor-seven
| C downminor-seven
|12:14:18:21
| 12:14:18:21
|-
|-
|0-7-14-21
| 0-7-14-21
|C vE G vB
| C vE G vB
|C~7
| C~7
|C mid-seven
| C mid-seven
|18:22:27:33
| 18:22:27:33
|-
|-
|0-7-14-21-28
| 0-7-14-21-28
|C vE G vB D
| C vE G vB D
|C~9
| C~9
|C mid-nine
| C mid-nine
|36:44:54:66:81
| 36:44:54:66:81
|-
|-
|0-7-14-21-28-35
| 0-7-14-21-28-35
|C vE G vB D ^F
| C vE G vB D ^F
|C~11
| C~11
|C mid-eleven
| C mid-eleven
|36:44:54:66:81:99
| 36:44:54:66:81:99
|-
|-
|0-7-14-21-28-35-42
| 0-7-14-21-28-35-42
|C vE G vB D ^F A
| C vE G vB D ^F A
|C~13
| C~13
|C mid-thirteen
| C mid-thirteen
|36:44:54:66:81:99:121
| 36:44:54:66:81:99:121
|-
|-
|0-8-14-28-35-42
| 0-8-14-28-35-42
|C E G D ^F vA
| C E G D ^F vA
|C9,~11~13no7
| C9,~11~13no7
|C nine mid-eleven mid-thirteen no-seven
| C nine mid-eleven mid-thirteen no-seven
|4:5:6:9:11:13
| 4:5:6:9:11:13
|}
|}
For a more complete list of chords, see [[Ups and Downs Notation#Chords and Chord Progressions|Ups and Downs Notation - Chords and Chord Progressions]].
 
For a more complete list of chords, see [[Ups and Downs Notation #Chords and Chord Progressions]].


==William Lynch's notation==
==William Lynch's notation==
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