Mason Green's New Common Practice Notation: Difference between revisions

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This is ~~my (~~Mason Green's) proposed notation for chord progressions in scales related to ~~19edo. Scales for which this notation works include~~:

This is Mason Green's proposed notation for chord progressions in scales related to:

<ul><li>~~19edo~~ itself (in which the octave is just but the fifth significantly flat).</li><li>[[Carlos_Beta|Carlos Beta]] (in which the just perfect fifth is divided into 11 equal parts, making the octave about 12 cents sharp.</li><li>[[Phoenix|Phoenix]] (~~my favorite:~~ a compromise between the two in which the just 9:5 interval is divided into 16 equal parts. Thus the octaves and the fifths are both flat but less so than in Carlos beta and 19edo respectively. The octave here is about 9 cents sharp).</li></ul>

<ul><li>[[19-edo]] itself (in which the octave is just but the fifth significantly flat).</li><li>[[Carlos_Beta|Carlos Beta]] (in which the just perfect fifth is divided into 11 equal parts, making the octave about 12 cents sharp.</li><li>[[Phoenix|Phoenix]] (a compromise between the two in which the just 9:5 interval is divided into 16 equal parts. Thus the octaves and the fifths are both flat but less so than in Carlos beta and 19edo respectively. The octave here is about 9 cents sharp).</li></ul>

~~I refer~~ to ~~this notation~~ as "New Common Practice" (NCP) in that it extends the Roman numeral analysis used for common practice to a 19-tone system.

This notation is referred to as "New Common Practice" (NCP), in that it extends the Roman numeral analysis used for common practice to a 19-tone system. It should not be confused with standard Roman Numeral notation, which can also apply to 19-EDO and other tuning methods as well.

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'''New intervals'''

~~These scales all temper~~ out the septimal diesis (49:48). Therefore, the septimal whole tone and septimal minor third are combined into the ''same'' interval, which is considered a third in some contexts and a second in others. The same is true for the harmonic seventh, which may be ~~considered either a seventh or a sixth.~~

19-EDO tempers out the septimal diesis (49:48). Some tones can be seen as enharmonically equivalent to other tones

Designating a particular pitch as the tonal center enables the other notes to be named relative to it. These names, which are independent of the notation used for the actual notes*, are as follows:

Designating a particular pitch as the tonal center enables the other notes to be named relative to it. These names, which are independent of the notation used for the actual notes, are as follows:

{| class="wikitable"

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| | 7/4, 12/7, 26/15

| | Subcaesiant

| | 6#~~, 7♭~~

| | 6#

| | VI#~~, VII♭~~

| | VI#

|-

| | 16

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| | 9/5, 16/9

| | Subtonic

| | 7

| | 7♭

| | VII

| | VII♭

|-

| | 17

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| | 15/8, 13/7, 28/15, 24/13

| | Lower leading tone

| | 7#

| | 7

| | VII#

| | VII

|-

| | 18

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'''Expanding Beyond Triads'''

~~In 12edo, triads~~ containing the tonic, mediant (third) and fifth are considered the basic chordal harmonies. Occasionally tetrads (seventh chords) appear ~~but they are wildly out of tune and considered unstable~~.

Triads containing the tonic, mediant (third) and fifth are considered the basic chordal harmonies. Occasionally tetrads (seventh chords) appear.

In NCP, triads may be considered incomplete depending on the context, and pentads, hexads, and even higher-order chords can appear and sound great. Also, there are ''many'' different possible chords, rather than just the major and minor. As a result, generalizing Roman numeral analysis presents problems.

My solution is to add a string of subscripted lowercase letters to the Roman numeral.

The proposed solution is to add a string of subscripted lowercase letters to the Roman numeral.

For otonal chords, such as the common major triad and its variants, the first letter denotes the harmonic corresponding to the lowest (bass) note of the chord. The second letter denotes the harmonic corresponding to the highest (treble) note of the chord. The third and subsequent letters (if present) correspond to all the harmonics "skipped" (i. e., not present) between the root and the bass. If there are only two letters, it means that all the (sub)harmonics between the treble and bass (excepting those which are automatically skipped, see below) are present.

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'''Chord progressions'''

''Porting'' is the process of translating chord progressions from ~~12edo~~ to ~~enneadecimal~~. Most chord progressions can be ported in some way, although it's important to note that some commas are not tempered out anymore, and there are chord progressions that close in ~~12edo~~ that don't close in 19 (so that you will end up one semitone higher or lower than where you started). Most of the time, however, this can easily be remedied. For instance, the [https://en.wikipedia.org/wiki/Coltrane_changes Coltrane changes] no longer work as before because three major thirds do not make an octave. However, a variant can be constructed in which one of the major thirds is replaced with a supermajor third; this version ''does'' close.

''Porting'' is the process of translating chord progressions from one tuning system to another. Most chord progressions can be ported in some way, although it's important to note that some commas are not tempered out anymore, and there are chord progressions that close in one tuning (for example: 12-edo) that don't close in another (for example: 19-edo) (so that you will end up one semitone higher or lower than where you started). Most of the time, however, this can easily be remedied. For instance, the [https://en.wikipedia.org/wiki/Coltrane_changes Coltrane changes] no longer work as before because three major thirds do not make an octave. However, a variant can be constructed in which one of the major thirds is replaced with a supermajor third; this version ''does'' close.

Porting the following progressions is trivial:

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<ul><li>All progressions using only I, IV, and V.</li><li>The circle progression (vi - ii- V - I).</li></ul>

~~The following progressions can be ported in more than one way:~~

<ul><li>The 50s progression (I – vi - IV - V)</li><li>"Axis of Awesome" (I - V - vi - IV).</li><li>Pachelbel's Canon (I - V - vi - iii - IV - I - IV - V)</li></ul>

<ul><li>The 50s progression (~~can become~~ I – vi ~~- IV - V, or I - vi#~~ - IV - V)</li><li>"Axis of Awesome" (~~can become~~ I - V - vi ~~- IV, or I - V - vi#~~ - IV).</li><li>Pachelbel (~~several ways, some of which close and some don't~~)</li></ul>

There are also many new possibilities that don't have any close analogues in 12edo. In general, enneadecimal scales offer more flexibility as well as orders of magnitude more possibilities for chord progressions, due to the greater diversity of both chords and scale degrees.

@@ Line 1: / Line 1: @@
-This is my (Mason Green's) proposed notation for chord progressions in scales related to 19edo. Scales for which this notation works include:
+This is Mason Green's proposed notation for chord progressions in scales related to:
-<ul><li>19edo itself (in which the octave is just but the fifth significantly flat).</li><li>[[Carlos_Beta|Carlos Beta]] (in which the just perfect fifth is divided into 11 equal parts, making the octave about 12 cents sharp.</li><li>[[Phoenix|Phoenix]] (my favorite: a compromise between the two in which the just 9:5 interval is divided into 16 equal parts. Thus the octaves and the fifths are both flat but less so than in Carlos beta and 19edo respectively. The octave here is about 9 cents sharp).</li></ul>
+<ul><li>[[19-edo]] itself (in which the octave is just but the fifth significantly flat).</li><li>[[Carlos_Beta|Carlos Beta]] (in which the just perfect fifth is divided into 11 equal parts, making the octave about 12 cents sharp.</li><li>[[Phoenix|Phoenix]] (a compromise between the two in which the just 9:5 interval is divided into 16 equal parts. Thus the octaves and the fifths are both flat but less so than in Carlos beta and 19edo respectively. The octave here is about 9 cents sharp).</li></ul>
-I refer to this notation as "New Common Practice" (NCP) in that it extends the Roman numeral analysis used for common practice to a 19-tone system.
+This notation is referred to as "New Common Practice" (NCP), in that it extends the Roman numeral analysis used for common practice to a 19-tone system.  It should not be confused with standard Roman Numeral notation, which can also apply to 19-EDO and other tuning methods as well.
 -----
@@ Line 9: / Line 9: @@
 '''New intervals'''
-These scales all temper out the septimal diesis (49:48). Therefore, the septimal whole tone and septimal minor third are combined into the ''same'' interval, which is considered a third in some contexts and a second in others. The same is true for the harmonic seventh, which may be considered either a seventh or a sixth.
+-EDO tempers out the septimal diesis (49:48). Some tones can be seen as enharmonically equivalent to other tones
-Designating a particular pitch as the tonal center enables the other notes to be named relative to it. These names, which are independent of the notation used for the actual notes*, are as follows:
+Designating a particular pitch as the tonal center enables the other notes to be named relative to it. These names, which are independent of the notation used for the actual notes, are as follows:
 {| class="wikitable"
@@ Line 131: / Line 131: @@
 | | <span style="background-color: #ffffff;">7/4, 12/7, 26/15</span>
 | | Subcaesiant
-| | 6#, 7<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>
+| | 6#
-| | VI#, VII<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>
+| | VI#
 |-
 | | 16
@@ Line 138: / Line 138: @@
 | | <span style="background-color: #ffffff;">9/5, 16/9</span>
 | | Subtonic
-| | 7
+| | 7<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>
-| | VII
+| | VII<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>
 |-
 | | 17
@@ Line 145: / Line 145: @@
 | | <span style="background-color: #ffffff;">15/8, 13/7, 28/15, 24/13</span>
 | | Lower leading tone
-| | 7#
+| | 7
-| | VII#
+| | VII
 |-
 | | 18
@@ Line 170: / Line 170: @@
 '''Expanding Beyond Triads'''
-In 12edo, triads containing the tonic, mediant (third) and fifth are considered the basic chordal harmonies. Occasionally tetrads (seventh chords) appear but they are wildly out of tune and considered unstable.
+Triads containing the tonic, mediant (third) and fifth are considered the basic chordal harmonies. Occasionally tetrads (seventh chords) appear.
 In NCP, triads may be considered incomplete depending on the context, and pentads, hexads, and even higher-order chords can appear and sound great. Also, there are ''many'' different possible chords, rather than just the major and minor. As a result, generalizing Roman numeral analysis presents problems.
-My solution is to add a string of subscripted lowercase letters to the Roman numeral.
+The proposed solution is to add a string of subscripted lowercase letters to the Roman numeral.
 For otonal chords, such as the common major triad and its variants, the first letter denotes the harmonic corresponding to the lowest (bass) note of the chord. The second letter denotes the harmonic corresponding to the highest (treble) note of the chord. The third and subsequent letters (if present) correspond to all the harmonics "skipped" (i. e., not present) between the root and the bass. If there are only two letters, it means that all the (sub)harmonics between the treble and bass (excepting those which are automatically skipped, see below) are present.
@@ Line 263: / Line 263: @@
 '''<span style="font-family: Arial,Helvetica,sans-serif;">Chord progressions</span>'''
-''<span style="font-family: Arial,Helvetica,sans-serif;">Porting</span>''<span style="font-family: Arial,Helvetica,sans-serif;"> is the process of translating chord progressions from 12edo to enneadecimal. Most chord progressions can be ported in some way, although it's important to note that some commas are not tempered out anymore, and there are chord progressions that close in 12edo that don't close in 19 (so that you will end up one semitone higher or lower than where you started). Most of the time, however, this can easily be remedied. For instance, the [https://en.wikipedia.org/wiki/Coltrane_changes Coltrane changes] no longer work as before because three major thirds do not make an octave. However, a variant can be constructed in which one of the major thirds is replaced with a supermajor third; this version ''does'' close.</span>
+''<span style="font-family: Arial,Helvetica,sans-serif;">Porting</span>''<span style="font-family: Arial,Helvetica,sans-serif;"> is the process of translating chord progressions from one tuning system to another. Most chord progressions can be ported in some way, although it's important to note that some commas are not tempered out anymore, and there are chord progressions that close in one tuning (for example: 12-edo) that don't close in another (for example: 19-edo) (so that you will end up one semitone higher or lower than where you started). Most of the time, however, this can easily be remedied. For instance, the [https://en.wikipedia.org/wiki/Coltrane_changes Coltrane changes] no longer work as before because three major thirds do not make an octave. However, a variant can be constructed in which one of the major thirds is replaced with a supermajor third; this version ''does'' close.</span>
 <span style="font-family: Arial,Helvetica,sans-serif;">Porting the following progressions is trivial:</span>
@@ Line 269: / Line 269: @@
 <ul><li>All progressions using only I, IV, and V.</li><li>The circle progression (<span style="text-decoration: overline;">vi</span> - ii- V - I).</li></ul>
-The following progressions can be ported in more than one way:
+<ul><li>The 50s progression (I – <span style="text-decoration: overline;">vi</span> - IV - V)</li><li>"Axis of Awesome" (I - V - <span style="text-decoration: overline;">vi </span>- IV).</li><li>Pachelbel's Canon (I - V - <span style="text-decoration: overline;">vi </span>- <span style="text-decoration: overline;">iii </span>- IV - I - IV - V)</li></ul>
-<ul><li>The 50s progression (can become I – <span style="text-decoration: overline;">vi</span> - IV - V, or I - vi# - IV - V)</li><li>"Axis of Awesome" (can become I - V - <span style="text-decoration: overline;">vi </span>- IV, or I - V - vi# - IV).</li><li>Pachelbel (several ways, some of which close and some don't)</li></ul>
 There are also many new possibilities that don't have any close analogues in 12edo. In general, enneadecimal scales offer more flexibility as well as orders of magnitude more possibilities for chord progressions, due to the greater diversity of both chords and scale degrees.