Fredg999: Text replacement - "Ups and Downs Notation" to "Ups and downs notation"

2025-08-20T01:13:17Z

Text replacement - "Ups and Downs Notation" to "Ups and downs notation"

← Older revision		Revision as of 01:13, 20 August 2025
Line 203:		Line 203:
	\|}		\|}
	== Notating EDOs ==		== Notating EDOs ==
	This notation can be used for EDOs that support 3L 4s to assign every degree of the EDO can be assigned a nominal/nominal plus accidental and interval names relative to a root. When a sharp/flat is greater than one degree of the EDO, [[Ups and ~~Downs Notation~~]] can be added to avoid using large amounts of sharps and flats. They can also be used when notating a multiple of an EDO that already supports 3L 4s as a superset of the smaller EDO. Here are examples of EDOs supporting basic, hard, and soft 3L 4s.		This notation can be used for EDOs that support 3L 4s to assign every degree of the EDO can be assigned a nominal/nominal plus accidental and interval names relative to a root. When a sharp/flat is greater than one degree of the EDO, [[Ups and downs notation]] can be added to avoid using large amounts of sharps and flats. They can also be used when notating a multiple of an EDO that already supports 3L 4s as a superset of the smaller EDO. Here are examples of EDOs supporting basic, hard, and soft 3L 4s.
	{\| class="wikitable center-all"		{\| class="wikitable center-all"
	\|-		\|-

Lériendil: deploying new cat

2025-02-09T15:46:09Z

deploying new cat

← Older revision		Revision as of 15:46, 9 February 2025
Line 575:		Line 575:
	\|}		\|}
	To Do: add intro, EDOs notated using sharps/flats and up;s/downs, images for examples of key signatures		To Do: add intro, EDOs notated using sharps/flats and up;s/downs, images for examples of key signatures

			[[Category:Approaches to tuning systems]]
			[[Category:Method]]

Eli5121: Key signatures section

2021-12-17T13:32:55Z

Key signatures section

Show changes

Eli5121: Created page with "== Intervals == Names for these intervals come from their degree in the scale and how "bright" or "dark" they are. Degree comes from ordering the intervals by pitch after redu..."

2021-12-15T00:01:19Z

Created page with "== Intervals == Names for these intervals come from their degree in the scale and how "bright" or "dark" they are. Degree comes from ordering the intervals by pitch after redu..."

New page

== Intervals ==
Names for these intervals come from their degree in the scale and how "bright" or "dark" they are. Degree comes from ordering the intervals by pitch after reducing by the period. Bright and dark compare the pitch of the interval. Bright intervals include major and augmented, as well as the "bright" perfect generator. The bright generator is the one which generates intervals higher in pitch; those intervals are bright. Conversely, dark intervals are lower in pitch than their bright counterparts and include minor and diminished and the "dark" perfect generator that generates them. An example for this naming system comes from the diatonic scale, MOS 5L 2s. The generators are the perfect fourth and perfect fifth, between 3\7 and 2\5, and 4\7 and 3\5, respectively, and the period is 2/1. Stacking perfect fifths creates a chain of bright intervals (P5 M2 M6 ...) and perfect fourths generate dark intervals (P4 m7 m3 ...). In 3L 4s, the perfect third between 1\3 and 2\7 is the bright generator and the perfect sixth between 2\3 and 5\7 is the dark generator. These are the intervals found in the 7 note MOS (LssLsLs and it's modes):
{| class="wikitable center-all"
|-
! colspan="2" | "Bright" Intervals
! Genchain Distance
! colspan="2" | "Dark" Intervals
! Genchain Distance
|-
| Perfect Unison
| P1
| 0
| Perfect Octave
| P8
| 0
|-
| Major Second
| M2
| +4
| Minor Seventh
| m7
| -4
|-
| Perfect Third
| P3
| +1
| Perfect Sixth
| P6
| -1
|-
| Major Fourth
| M4
| +5
| Minor Fifth
| m5
| -5
|-
| Major Fifth
| M5
| +2
| Minor Fourth
| m4
| -2
|-
| Augmented Sixth
| A6
| +6
| Diminished Third
| d3
| -6
|-
| Major 7th
| M7
| +3
| Minor 2nd
| m2
| -3
|}
The 10 note chromatic scales 3L 7s (LsssLssLss), 7L 3s (sLLLsLLsLL), and 10edo (equalized) add these intervals:
{| class="wikitable center-all"
|-
! colspan="2" | "Bright" Intervals
! Genchain Distance
! colspan="2" | "Dark" Intervals
! Genchain Distance
|-
| Augmented Unison
| A1
| +7
| Diminished Octave
| d8
| -7
|-
| Augmented Third
| A3
| +8
| Diminished Sixth
| d6
| -8
|-
| Augmented Fifth
| A5
| +9
| Diminished Fourth
| d4
| -9
|}
== Modes ==
{| class="wikitable center-all"
|-
! Mode in step patterns
! Mode in intervals
! [[Modal UDP Notation]]
|-
| LsLsLss
| P1 M2 P3 M4 M5 A6 M7 P8
| <nowiki>6|0</nowiki>
|-
| LsLssLs
| P1 M2 P3 M4 M5 P6 M7 P8
| <nowiki>5|1</nowiki>
|-
| LssLsLs
| P1 M2 P3 m4 M5 P6 M7 P8
| <nowiki>4|2</nowiki>
|-
| sLsLsLs
| P1 m2 P3 m4 M5 P6 M7 P8
| <nowiki>3|3</nowiki>
|-
| sLsLssL
| P1 m2 P3 m4 M5 P6 m7 P8
| <nowiki>2|4</nowiki>
|-
| sLssLsL
| P1 m2 P3 m4 m5 P6 m7 P8
| <nowiki>1|5</nowiki>
|-
| ssLsLsL
| P1 m2 d3 m4 m5 P6 m7 P8
| <nowiki>0|6</nowiki>
|}
== Nominals and Accidentals ==
3L 4s is heptatonic and can be notated using the familiar letters of A, B, C, D, E, F, and G. Sharps and flats can be used as accidentals to signify altering pitch. The amount that they alter can be defined as the difference between a minor interval and its major counterpart, also equal to a generator * the number of notes in the scale, reduced by the period, in this case stacking 7 P3's = a sharp and 7 P6's = a flat. In diatonic, CDEFGABC corresponds to LLsLLLs, P1 M2 M3 P4 P5 M6 M7 P8. Here, CDEFGABC in 3L 4s is used as LssLsLs, P1 M2 P3 m4 M5 P6 M7 P8. For example, if you wanted to write the mode LsLsLss on C, you'd write CDEF#GA#BC. sLsLsLs on C is CDbEFGABC. LssLsLs on B is BC#DEF#GA#B. This can also be used to write altered scales, such as <nowiki>4|2<nowiki> #6. The step pattern is LssLLss and on C that wpuld be CDEFGA#BC. This approach is structurally similar to traditional notation, extrapolating familiar concepts to new applications. The differences are in note relations, as in a diatonic C-E is different than C-E in 3L 4s, so it must be specified what scales are being used in order to avoid confusion.
== Chords ==
Naming tertian chords in 3L 4s can be done similarly to diatonic names for tertian chords. In both systems triads are made of a root, a major or minor interval, and a perfect or imperfect generator. The difference is that in diatonic the fifth is the generator whereas in 3L 4s the third is the generator. When a chord contains a perfect generator, it is named after the major or minor interval. When it's made up of an imperfect generator and an "agreeing" minor or major interval, you name it after the imperfect generator. Other chords are named as alterations of the prior types of chords described. Extensions can be named with the intervals used. Here are examples of naming triads, with diatonic as an example:
{| class="wikitable center-all"
|-
! colspan="3" | Diatonic
! colspan="3" | 3L 4s
|-
| colspan="6" | Natural Triads
|-
| P1 M3 P5
| Major
| C E G
| P1 P3 M5
| Major
| C E G
|-
| P1 m3 P5
| Minor
| C Eb G
| P1 P3 m5
| Minor
| C E Gb
|-
| P1 m3 d5
| Diminished
| C Eb Gb
| P1 d3 m5
| Diminished
| C Eb Gb
|-
| colspan="6" | Other Triads
|-
| P1 M3 A5
| Augmented
| C E G#
| P1 A3 M5
| Augmented
| C E# G
|-
| P1 M3 d5
| Major b5
| C E Gb
| P1 d3 M5
| Major b3
| C Eb G
|-
| P1 m3 A5
| Minor #5
| C Eb G#
| P1 A3 m5
| Minor #3
| C E# Gb
|}
== Notating EDOs ==
This notation can be used for EDOs that support 3L 4s to assign every degree of the EDO can be assigned a nominal/nominal plus accidental and interval names relative to a root. When a sharp/flat is greater than one degree of the EDO, [[Ups and Downs Notation]] can be added to avoid using large amounts of sharps and flats. Here are examples of EDOs supporting basic, hard, and soft 3L 4s.
{| class="wikitable center-all"
|-
! #\10edo (basic)
! Cents
! colspan="3" | Notation
|-
| 0
| 0
| Perfect Unison
| P1
| C
|-
| 1
| 120
| Minor Second
| m2
| Db
|-
| 2
| 240
| Major Second, Diminished Third
| M2, d3
| D, Eb
|-
| 3
| 360
| Perfect Third
| P3
| E
|-
| 4
| 480
| Minor Fourth
| m4
| F
|-
| 5
| 600
| Major Fourth, Minor Fifth
| M4, m5
| F#, Gb
|-
| 6
| 720
| Major Fifth
| M5
| G
|-
| 7
| 840
| Perfect Sixth
| P6
| A
|-
| 8
| 960
| Augmented Sixth, Minor Seventh
| A6, m7
| A#, Bb
|-
| 9
| 1080
| Major Seventh
| M7
| B
|-
| 10
| 1200
| Perfect Octave
| P8
| C
|}
{| class="wikitable center-all"
|-
! #\13edo (hard)
! Cents
! colspan="3" | Notation
|-
| 0
| 0
| Perfect Unison
| P1
| C
|-
| 1
| 92.31
| Minor Second
| m2
| Db
|-
| 2
| 184.62
| Diminished Third
| d3
| Eb
|-
| 3
| 276.92
| Major Second
| M2
| D
|-
| 4
| 369.23
| Perfect Third
| P3
| E
|-
| 5
| 461.54
| Minor Fourth
| m4
| F
|-
| 6
| 553.85
| Minor Fifth
| m5
| Gb
|-
| 7
| 646.15
| Major Fourth
| M4
| F#
|-
| 8
| 738.46
| Major Fifth
| M5
| G
|-
| 9
| 830.77
| Perfect Sixth
| P6
| A
|-
| 10
| 923.08
| Minor Seventh
| m7
| Bb
|-
| 11
| 1015.38
| Augmented Sixth
| A6
| A#
|-
| 12
| 1107.69
| Major Seventh
| M7
| B
|-
| 13
| 1200
| Perfect Octave
| P8
| C
|}
{| class="wikitable center-all"
|-
! #\17edo (soft)
! Cents
! colspan="3" | Notation
|-
| 0
| 0
| Perfect Unison
| P1
| C
|-
| 1
| 70.59
| Augmented Unison, Diminished Second
| A1, d2
| C#, Dbb
|-
| 2
| 141.18
| Minor 2nd
| m2
| Db
|-
| 3
| 211.76
| Major Second
| M2
| D
|-
| 4
| 282.35
| Diminished Third
| d3
| Eb
|-
| 5
| 352.94
| Perfect Third
| P3
| E
|-
| 6
| 423.53
| Augmented Third, Diminished Fourth
| A3, d4
| E#, Fb
|-
| 7
| 494.12
| Minor Fourth
| m4
| F
|-
| 8
| 564.71
| Major Fourth
| M4
| F#
|-
| 9
| 635.29
| Minor Fifth
| m5
| Gb
|-
| 10
| 705.88
| Major Fifth
| M5
| G
|-
| 11
| 776.47
| Augmented Fifth, Diminished Sixth
| A5, d6
| G#, Ab
|-
| 12
| 847.06
| Perfect Sixth
| P6
| A
|-
| 13
| 917.65
| Augmented Sixth
| A6
| A#
|-
| 14
| 988.24
| Minor 7th
| m7
| Bb
|-
| 15
| 1058.82
| Major Seventh
| M7
| B
|-
| 16
| 1129.41
| Augmented Seventh, Diminished Octave
| A7, d8
| B#, Cb
|-
| 17
| 1200
| Perfect Octave
| P8
| C
|}
To Do: add intro, key signatures

User:Eli5121/3L 4s Theory - Revision history

Fredg999: Text replacement - "Ups and Downs Notation" to "Ups and downs notation"

Lériendil: deploying new cat

Eli5121: Key signatures section

Eli5121: Created page with "== Intervals == Names for these intervals come from their degree in the scale and how "bright" or "dark" they are. Degree comes from ordering the intervals by pitch after redu..."