User:Eli5121/3L 4s Theory: Difference between revisions

(2 intermediate revisions by 2 users not shown)

Line 95:

| LsLsLss

| P1 M2 P3 M4 M5 A6 M7 P8

| ~~<nowiki>~~6|0~~</nowiki>~~

| style="text;" | 6|0

|-

| LsLssLs

| P1 M2 P3 M4 M5 P6 M7 P8

| ~~<nowiki>~~5|1~~</nowiki>~~

| style="text;" | 5|1

|-

| LssLsLs

| P1 M2 P3 m4 M5 P6 M7 P8

| ~~<nowiki>~~4|2~~</nowiki>~~

| style="text;" | 4|2

|-

| sLsLsLs

| P1 m2 P3 m4 M5 P6 M7 P8

| ~~<nowiki>~~3|3~~</nowiki>~~

| style="text;" | 3|3

|-

| sLsLssL

| P1 m2 P3 m4 M5 P6 m7 P8

| ~~<nowiki>~~2|4~~</nowiki>~~

| style="text;" | 2|4

|-

| sLssLsL

| P1 m2 P3 m4 m5 P6 m7 P8

| ~~<nowiki>~~1|5~~</nowiki>~~

| style="text;" | 1|5

|-

| ssLsLsL

| P1 m2 d3 m4 m5 P6 m7 P8

| ~~<nowiki>~~0|6~~</nowiki>~~

| style="text;" | 0|6

|}

== 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.

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 would 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:

Line 175:

| Minor #3

| C E# Gb

|}

{| class="wikitable center-all"

|-

! Mode

! Chords

|-

| style="text;" | 6|0

| I II III #iv V #viº VII

|-

| style="text;" | 5|1

| I ii III #ivº V VI VII

|-

| style="text;" | 4|2

| I iiº III IV V VI vii

|-

| style="text;" | 3|3

| I bII III IV v VI viiº

|-

| style="text;" | 2|4

| I bII iii IV vº VI bVII

|-

| style="text;" | 1|5

| i bII iiiº IV bV VI bVII

|-

| style="text;" | 0|6

| iº bII bIII IV bV vi bVII

|}

== 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.

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"

|-

Line 454:

Line 480:

| C

|}

To Do: add intro, key signatures

== Key Signatures ==

Using key signatures first requires a chain of generators for adding sharps and flats. In diatonic, the chain of fifths for sharps is FCGDAEB and the chain of fourths for flats is BEADGCF. In 3L 4s, the chain of thirds for sharps is FACEGBD and the chain of sixths for flats is DBGECAF. I think is also helpful to designate one key signature as representing the natural scale for multiple different notes. For example, in diatonic a key signature corresponds to a major and a minor scale for some two notes. Major is ionian and minor is aeolian. This makes it easier to write scores in different modes without using large amount of accidentals; if a key signature was only for a minor scale, writing in lydian would require 4 alterations, with major and minor scales you can minimize the difference between the natural scale in the key signature and the mode you're writing in. Now, the example of lydian only requires 2 sharps. Here, I am assigning the modes LssLsLs to major and sLssLsL to minor. This makes C major the relative major key of B minor. Here is a table describing keys from Ab major to E# major. The amount of sharps or flats is found from the distance in generators from C major or B minor and which notes are altered is found by the chain of thirds/sixths.

{| class="wikitable center-all"

|-

! Number of sharps/flats

! Which notes are altered relative to C/b

! Relative major key

! Relative minor key

|-

| None

| C major

| B minor

|-

| 1 sharp

| F#

| E major

| D minor

|-

| 1 flat

| Db

| A major

| G minor

|-

| 2 sharps

| F#A#

| G major

| F# minor

|-

| 2 flats

| DbBb

| F major

| E minor

|-

| 3 sharps

| F#A#C#

| B major

| A# minor

|-

| 3 flats

| DbBbGb

| Db major

| C minor

|-

| 4 sharps

| F#A#C#E#

| D major

| C# minor

|-

| 4 flats

| DbBbGbEb

| Bb major

| A minor

|-

| 5 sharps

| F#A#C#E#G#

| F# major

| E# minor

|-

| 5 flats

| DbBbGbEbCb

| Gb major

| F minor

|-

| 6 sharps

| F#A#C#E#G#B#

| A# major

| G# minor

|-

| 6 flats

| DbBbGbEbCbAb

| Eb major

| Db minor

|-

| 7 sharps

| F#A#C#E#G#B#D#

| C# major

| B# minor

|-

| 7 flats

| DbBbGbEbCbAbFb

| Cb major

| Bb minor

|-

| 8 sharps

| FxA#C#E#G#B#D#

| E# major

| D# minor

|-

| 8 flats

| DbbBbGbEbCbAbFb

| Ab major

| Gb minor

|}

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]]

@@ Line 95: / Line 95: @@
 | LsLsLss
 | P1 M2 P3 M4 M5 A6 M7 P8
-| <nowiki>6|0</nowiki>
+| style="text;" | 6|0
 |-
 | LsLssLs
 | P1 M2 P3 M4 M5 P6 M7 P8
-| <nowiki>5|1</nowiki>
+| style="text;" | 5|1
 |-
 | LssLsLs
 | P1 M2 P3 m4 M5 P6 M7 P8
-| <nowiki>4|2</nowiki>
+| style="text;" | 4|2
 |-
 | sLsLsLs
 | P1 m2 P3 m4 M5 P6 M7 P8
-| <nowiki>3|3</nowiki>
+| style="text;" | 3|3
 |-
 | sLsLssL
 | P1 m2 P3 m4 M5 P6 m7 P8
-| <nowiki>2|4</nowiki>
+| style="text;" | 2|4
 |-
 | sLssLsL
 | P1 m2 P3 m4 m5 P6 m7 P8
-| <nowiki>1|5</nowiki>
+| style="text;" | 1|5
 |-
 | ssLsLsL
 | P1 m2 d3 m4 m5 P6 m7 P8
-| <nowiki>0|6</nowiki>
+| style="text;" | 0|6
 |}
 == Nominals and Accidentals ==
-L 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.
+L 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 would 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:
@@ Line 175: / Line 175: @@
 | Minor #3
 | C E# Gb
+|}
+{| class="wikitable center-all"
+|-
+! Mode
+! Chords
+|-
+| style="text;" | 6|0
+| I II III #iv V #viº VII
+|-
+| style="text;" | 5|1
+| I ii III #ivº V VI VII
+|-
+| style="text;" | 4|2
+| I iiº III IV V VI vii
+|-
+| style="text;" | 3|3
+| I bII III IV v VI viiº
+|-
+| style="text;" | 2|4
+| I bII iii IV vº VI bVII
+|-
+| style="text;" | 1|5
+| i bII iiiº IV bV VI bVII
+|-
+| style="text;" | 0|6
+| iº bII bIII IV bV vi bVII
 |}
 == 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.
+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"
 |-
@@ Line 454: / Line 480: @@
 | C
 |}
-To Do: add intro, key signatures
+== Key Signatures ==
+Using key signatures first requires a chain of generators for adding sharps and flats. In diatonic, the chain of fifths for sharps is FCGDAEB and the chain of fourths for flats is BEADGCF. In 3L 4s, the chain of thirds for sharps is FACEGBD and the chain of sixths for flats is DBGECAF. I think is also helpful to designate one key signature as representing the natural scale for multiple different notes. For example, in diatonic a key signature corresponds to a major and a minor scale for some two notes. Major is ionian and minor is aeolian. This makes it easier to write scores in different modes without using large amount of accidentals; if a key signature was only for a minor scale, writing in lydian would require 4 alterations, with major and minor scales you can minimize the difference between the natural scale in the key signature and the mode you're writing in. Now, the example of lydian only requires 2 sharps. Here, I am assigning the modes LssLsLs to major and sLssLsL to minor. This makes C major the relative major key of B minor. Here is a table describing keys from Ab major to E# major. The amount of sharps or flats is found from the distance in generators from C major or B minor and which notes are altered is found by the chain of thirds/sixths.
+{| class="wikitable center-all"
+|-
+! Number of sharps/flats
+! Which notes are altered relative to C/b
+! Relative major key
+! Relative minor key
+|-
+| None
+| None
+| C major
+| B minor
+|-
+| 1 sharp
+| F#
+| E major
+| D minor
+|-
+| 1 flat
+| Db
+| A major
+| G minor
+|-
+| 2 sharps
+| F#A#
+| G major
+| F# minor
+|-
+| 2 flats
+| DbBb
+| F major
+| E minor
+|-
+| 3 sharps
+| F#A#C#
+| B major
+| A# minor
+|-
+| 3 flats
+| DbBbGb
+| Db major
+| C minor
+|-
+| 4 sharps
+| F#A#C#E#
+| D major
+| C# minor
+|-
+| 4 flats
+| DbBbGbEb
+| Bb major
+| A minor
+|-
+| 5 sharps
+| F#A#C#E#G#
+| F# major
+| E# minor
+|-
+| 5 flats
+| DbBbGbEbCb
+| Gb major
+| F minor
+|-
+| 6 sharps
+| F#A#C#E#G#B#
+| A# major
+| G# minor
+|-
+| 6 flats
+| DbBbGbEbCbAb
+| Eb major
+| Db minor
+|-
+| 7 sharps
+| F#A#C#E#G#B#D#
+| C# major
+| B# minor
+|-
+| 7 flats
+| DbBbGbEbCbAbFb
+| Cb major
+| Bb minor
+|-
+| 8 sharps
+| FxA#C#E#G#B#D#
+| E# major
+| D# minor
+|-
+| 8 flats
+| DbbBbGbEbCbAbFb
+| Ab major
+| Gb minor
+|}
+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]]