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

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

<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 17 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>

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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.

| | Number of steps

| | Interval name

| | Approximation

| | Scale degree name

| | Scale degree symbol

| | Scale degree Roman numeral

|-

| | 0

| | Unison

| | 1:1

| | Tonic

| | 1

| | I

|-

| | 1

| | Augmented unison

| | <span style="background-color: #ffffff;">25/24, 21/20, 28/27, 26/25, 27/26</span>

| | Upper bleeding tone

| | 1#

| | <span style="vertical-align: super;">I#</span>

|-

| | 2

| | Minor second

| | <span style="background-color: #ffffff;">15/14, 16/15, 13/12, 14/13</span>

| | Upper leading tone

| | 2<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>

| | II<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>

|-

| | 3

| | Major second

| | <span style="background-color: #ffffff;">9/8, 10/9</span>

| | Supertonic

| | 2

| | II

|-

| | 4

| | Supermajor second; subminor third

| | <span style="background-color: #ffffff;">7/6, 8/7, 15/13</span>

| | Caesiant

| | 2# ; 3<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>

| | II# , III<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>

|-

| | 5

| | Minor third

| | <span style="background-color: #ffffff;">6/5, 25/21</span>

| | Minor mediant

| | <u>3</u>

| | <u>III</u>

|-

| | 6

| | Major third

| | <span style="background-color: #ffffff;">5/4, 16/13, 26/21</span>

| | Major mediant

| | <span style="text-decoration: overline;">3</span>

| | <span style="text-decoration: overline;">III</span>

|-

| | 7

| | Supermajor third, subfourth

| | <span style="background-color: #ffffff;">32/25, 9/7, 13/10</span>

| | Rubric

| | 3# , 4<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>

| | III# , IV<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>

|-

| | 8

| | Perfect fourth

| | <span style="background-color: #ffffff;">4/3</span>

| | Subdominant

| | 4

| | IV

|-

| | 9

| | Augmented fourth

| | <span style="background-color: #ffffff;">25/18, 7/5, 18/13</span>

| | Hygrant

| | 4#

| | IV#

|-

| | 10

| | Diminished fifth

| | <span style="background-color: #ffffff;">10/7, 13/9</span>

| | Subhygrant

| | 5<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>

| | V<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>

|-

| | 11

| | Perfect fifth

| | 3/2

| | Dominant

| | 5

| | V

|-

| | 12

| | Augmented fifth, subminor sixth

| | <span style="background-color: #ffffff;">25/16, 14/9, 20/13</span>

| | Subrubric

| | 5#, 6<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>

| | V#, VI<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>

|-

| | 13

| | Minor sixth

| | <span style="background-color: #ffffff;">8/5, 13/8, 21/13</span>

| | Minor submediant

| | <u>6</u>

| | <u>VI</u>

|-

| | 14

| | Major sixth

| | <span style="background-color: #ffffff;">5/3</span>

| | Major submediant

| | <span style="text-decoration: overline;">6</span>

| | <span style="text-decoration: overline;">VI</span>

|-

| | 15

| | Supermajor sixth, subminor seventh, harmonic seventh

| | <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>

| | VI#, VII<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>

|-

| | 16

| | Minor seventh

| | <span style="background-color: #ffffff;">9/5, 16/9</span>

| | Subtonic

| | 7

| | VII

|-

| | 17

| | Major seventh

| | <span style="background-color: #ffffff;">15/8, 13/7, 28/15, 24/13</span>

| | Lower leading tone

| | 7#

| | VII#

|-

| | 18

| | Diminished octave

| | <span style="background-color: #ffffff;">27/14, 25/13</span>

| | Lower bleeding tone

| | 1<span style="background-color: #ffffff; color: #252525; font-family: 'Arial Unicode MS','Lucida Sans Unicode'; font-size: 14px;">♭</span>

| | <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>

|}

One noted feature of NCP (unlike standard common practice) is that compositions are ''not'' confined to the notes of the diatonic scale, or even to the "superdiatonic" (12-note subset of 19) extension. Both of these are fundamentally 5-limit systems, and modulation by 7-limit intervals will quickly take us outside of these confines.

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'''Expanding Beyond Triads'''

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.

The 11th, 17th, 19th, 23rd, and 29th harmonics have no letters assigned to them and are automatically assumed to be skipped since enneadecimal scales do not approximate them easily. The 13th is not skipped because it ''is'' approximated fairly well, particularly if the octave is stretched a bit.

| | Symbol

| | Name

| | Just approximation

|-

| | I<span style="vertical-align: sub;">(ae)</span>

| | Major pentad

| | Otonal 4:5:6:7:8

|-

| | i<span style="vertical-align: sub;">(ae)</span>

| | Minor pentad

| | Utonal 4:5:6:7:8

|-

| | I<span style="vertical-align: sub;">(ch)</span>

| | Major hexad

| | Otonal 6:7:8:9:10:12

|-

| | i<span style="vertical-align: sub;">(ch)</span>

| | Minor hexad

| | 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>

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'''<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 the following progressions is trivial:</span>

<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>

<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.