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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>
* [[19-edo]] itself (in which the octave is just but the fifth significantly flat).
* [[Carlos Beta]] (in which the just perfect fifth is divided into 11 equal parts, making the octave about 12 cents sharp.
* [[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).


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.
__FORCETOC__
== New intervals ==
19-EDO tempers out the large 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:
 
'''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.
 
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"
{| class="wikitable"
|-
|-
| | Number of steps
! rowspan="3" | Number of steps
| | Interval name
! rowspan="3" | Interval name
| | Approximation
! rowspan="3" | JI intervals represented
| | Scale degree name
! colspan="3" | Scale degree
| | Scale degree symbol
|-
| | Scale degree Roman numeral
! rowspan="2" | Name
! colspan="2" | Symbol
|-
|-
| | 0
! Number
| | Unison
! Roman numeral
| | 1:1
| | Tonic
| | 1
| | I
|-
|-
| | 1
| 0
| | Augmented unison
| Unison
| | <span style="background-color: #ffffff;">25/24, 21/20, 28/27, 26/25, 27/26</span>
| 1/1
| | Upper bleeding tone
| Tonic
| | 1#
| 1
| | <span style="vertical-align: super;">I#</span>
| I
|-
|-
| | 2
| 1
| | Minor second
| Augmented unison
| | <span style="background-color: #ffffff;">15/14, 16/15, 13/12, 14/13</span>
| 25/24, 21/20, 28/27, 26/25, 27/26
| | Upper leading tone
| Upper bleeding tone
| | 2<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>
| 1♯
| | II<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>
| I♯
|-
|-
| | 3
| 2
| | Major second
| Minor second
| | <span style="background-color: #ffffff;">9/8, 10/9</span>
| 15/14, 16/15, 13/12, 14/13
| | Supertonic
| Upper leading tone
| | 2
| 2♭
| | II
| II♭
|-
|-
| | 4
| 3
| | Supermajor second; subminor third
| Major second
| | <span style="background-color: #ffffff;">7/6, 8/7, 15/13</span>
| 9/8, 10/9
| | Caesiant
| Supertonic
| | 2# ; 3<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>
| 2
| | II# , III<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>
| II
|-
|-
| | 5
| 4
| | Minor third
| Supermajor second; subminor third
| | <span style="background-color: #ffffff;">6/5, 25/21</span>
| 7/6, 8/7, 15/13
| | Minor mediant
| Caesiant
| | <u>3</u>
| 2♯ ; 3♭
| | <u>III</u>
| II♯ , III♭
|-
|-
| | 6
| 5
| | Major third
| Minor third
| | <span style="background-color: #ffffff;">5/4, 16/13, 26/21</span>
| 6/5, 25/21
| | Major mediant
| Minor mediant
| | <span style="text-decoration: overline;">3</span>
| <u>3</u>
| | <span style="text-decoration: overline;">III</span>
| <u>III</u>
|-
|-
| | 7
| 6
| | Supermajor third, subfourth
| Major third
| | <span style="background-color: #ffffff;">32/25, 9/7, 13/10</span>
| 5/4, 16/13, 26/21
| | Rubric
| Major mediant
| | 3# , 4<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>
| {{overline|3}}
| | III# , IV<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>
| {{overline|III}}
|-
|-
| | 8
| 7
| | Perfect fourth
| Supermajor third, subfourth
| | <span style="background-color: #ffffff;">4/3</span>
| 32/25, 9/7, 13/10
| | Subdominant
| Rubric
| | 4
| 3♯, 4♭
| | IV
| III♯ , IV♭
|-
|-
| | 9
| 8
| | Augmented fourth
| Perfect fourth
| | <span style="background-color: #ffffff;">25/18, 7/5, 18/13</span>
| 4/3
| | Hygrant
| Subdominant
| | 4#
| 4
| | IV#
| IV
|-
|-
| | 10
| 9
| | Diminished fifth
| Augmented fourth
| | <span style="background-color: #ffffff;">36/25, 10/7, 13/9</span>
| 25/18, 7/5, 18/13
| | Subhygrant
| Hygrant
| | 5<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>
| 4♯
| | V<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>
| IV♯
|-
|-
| | 11
| 10
| | Perfect fifth
| Diminished fifth
| | 3/2
| 36/25, 10/7, 13/9
| | Dominant
| Subhygrant
| | 5
| 5♭
| | V
| V♭
|-
|-
| | 12
| 11
| | Augmented fifth, subminor sixth
| Perfect fifth
| | <span style="background-color: #ffffff;">25/16, 14/9, 20/13</span>
| 3/2
| | Subrubric
| Dominant
| | 5#, 6<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>
| 5
| | V#, VI<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>
| V
|-
|-
| | 13
| 12
| | Minor sixth
| Augmented fifth, subminor sixth
| | <span style="background-color: #ffffff;">8/5, 13/8, 21/13</span>
| 25/16, 14/9, 20/13
| | Minor submediant
| Subrubric
| | <u>6</u>
| 5♯, 6♭
| | <u>VI</u>
| V♯, VI♭
|-
|-
| | 14
| 13
| | Major sixth
| Minor sixth
| | <span style="background-color: #ffffff;">5/3</span>
| 8/5, 13/8, 21/13
| | Major submediant
| Minor submediant
| | <span style="text-decoration: overline;">6</span>
| <u>6</u>
| | <span style="text-decoration: overline;">VI</span>
| <u>VI</u>
|-
|-
| | 15
| 14
| | Supermajor sixth, subminor seventh, harmonic seventh
| Major sixth
| | <span style="background-color: #ffffff;">7/4, 12/7, 26/15</span>
| 5/3
| | Subcaesiant
| Major submediant
| | 6#, 7<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>
| {{overline|6}}
| | VI#, VII<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>
| {{overline|VI}}
|-
|-
| | 16
| 15
| | Minor seventh
| Supermajor sixth, subminor seventh, harmonic seventh
| | <span style="background-color: #ffffff;">9/5, 16/9</span>
| 7/4, 12/7, 26/15
| | Subtonic
| Subcaesiant
| | 7
| 6♯
| | VII
| VI♯
|-
|-
| | 17
| 16
| | Major seventh
| Minor seventh
| | <span style="background-color: #ffffff;">15/8, 13/7, 28/15, 24/13</span>
| 9/5, 16/9
| | Lower leading tone
| Subtonic
| | 7#
| 7♭
| | VII#
| VII♭
|-
|-
| | 18
| 17
| | Diminished octave
| Major seventh
| | <span style="background-color: #ffffff;">27/14, 25/13</span>
| 15/8, 13/7, 28/15, 24/13
| | Lower bleeding tone
| Lower leading tone
| | 1<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>
| 7
| | <span style="background-color: #ffffff;">I</span><span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>
| VII
|-
| 18
| Diminished octave
| 27/14, 25/13
| Lower bleeding tone
| 1♭
| I♭
|}
|}


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As a result, the requirement of diatonicity is dropped and the whole 19-note gamut is accessible. There are therefore no "modes" in NCP, since all notes and chords are defined solely by their relationship to the tonic (the "home key"). This opens unusual possibilities, such as mixing major and minor tonality in the same composition.
As a result, the requirement of diatonicity is dropped and the whole 19-note gamut is accessible. There are therefore no "modes" in NCP, since all notes and chords are defined solely by their relationship to the tonic (the "home key"). This opens unusual possibilities, such as mixing major and minor tonality in the same composition.


-----
== Expanding beyond triads ==
 
Triads containing the tonic, mediant (third) and fifth are considered the basic chordal harmonies. Occasionally tetrads (seventh chords) appear.
'''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.


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.
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.
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 236: Line 236:
{| class="wikitable"
{| class="wikitable"
|-
|-
| | Symbol
! Symbol
| | Name
! Name
| | Just approximation
! Just approximation
|-
|-
| | I<span style="vertical-align: sub;">(ae)</span>
| I<sub>(ae)</sub>
| | Major pentad
| Major pentad
| | Otonal 4:5:6:7:8
| Otonal 4:5:6:7:8
|-
|-
| | i<span style="vertical-align: sub;">(ae)</span>
| i<sub>(ae)</sub>
| | Minor pentad
| Minor pentad
| | Utonal 4:5:6:7:8
| Utonal 4:5:6:7:8
|-
|-
| | I<span style="vertical-align: sub;">(ch)</span>
| I<sub>(ch)</sub>
| | Major hexad
| Major hexad
| | Otonal 6:7:8:9:10:12
| Otonal 6:7:8:9:10:12
|-
|-
| | i<span style="vertical-align: sub;">(ch)</span>
| i<sub>(ch)</sub>
| | Minor hexad
| Minor hexad
| | Otonal 6:7:8:9:10:12
| Otonal 6:7:8:9:10:12
|}
|}


<span style="font-family: Arial,Helvetica,sans-serif;">Due to tempering, some chords may be notated in more than one way. For example, the chord I</span><span style="font-family: Arial,Helvetica,sans-serif; vertical-align: sub;">(gkhj) </span><span style="font-family: Arial,Helvetica,sans-serif;">,</span><span style="font-family: Arial,Helvetica,sans-serif;">which corresponds to the otonal 10:13:15, is tempered to be the same as i</span><span style="font-family: Arial,Helvetica,sans-serif; vertical-align: sub;">(cfe) </span><span style="font-family: Arial,Helvetica,sans-serif;">(the utonal 6:7:9).</span>
Due to tempering, some chords may be notated in more than one way. For example, the chord I<sub>(gkhj) </sub>, which corresponds to the otonal 10:13:15, is tempered to be the same as i<sub>(cfe)</sub>(the utonal 6:7:9).


-----
== Chord progressions ==
''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.


'''<span style="font-family: Arial,Helvetica,sans-serif;">Chord progressions</span>'''
Porting the following progressions is trivial:


''<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>
* All progressions using only I, IV, and V.
* The circle progression ({{overline|vi}} - ii- V - I).
* The 50s progression (I – {{overline|vi}} - IV - V)
* "Axis of Awesome" (I - V - {{overline|vi}} - IV).
* Pachelbel's Canon (I - V - {{overline|vi}} - {{overline|iii}} - IV - I - IV - V)


<span style="font-family: Arial,Helvetica,sans-serif;">Porting the following progressions is trivial:</span>
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.


<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>
{{Navbox notation}}


The following progressions can be ported in more than one way:
<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.
[[Category:19edo]]
[[Category:19edo]]
[[Category:beta]]
[[Category:beta]]
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