Mason Green's New Common Practice Notation: Difference between revisions
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This is | This is [[Mason Green]]'s proposed notation for chord progressions in scales related to: | ||
* [[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). | |||
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: | |||
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 | |||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! rowspan="3" | Number of steps | |||
! rowspan="3" | Interval name | |||
| | ! rowspan="3" | JI intervals represented | ||
! colspan="3" | Scale degree | |||
| | | |- | ||
| | ! rowspan="2" | Name | ||
! colspan="2" | Symbol | |||
|- | |- | ||
! Number | |||
! Roman numeral | |||
|- | |- | ||
| | | 0 | ||
| | | Unison | ||
| | | 1/1 | ||
| | | Tonic | ||
| 1 | |||
| | | I | ||
|- | |- | ||
| | | 1 | ||
| | | Augmented unison | ||
| | | 25/24, 21/20, 28/27, 26/25, 27/26 | ||
| Upper bleeding tone | |||
| | | 1♯ | ||
| | | I♯ | ||
|- | |- | ||
| | | 2 | ||
| | | Minor second | ||
| | | 15/14, 16/15, 13/12, 14/13 | ||
| | | Upper leading tone | ||
| | | 2♭ | ||
| | | II♭ | ||
|- | |- | ||
| | | 3 | ||
| | | Major second | ||
| | | 9/8, 10/9 | ||
| | | Supertonic | ||
| 2 | |||
| II | |||
|- | |- | ||
| | | 4 | ||
| | | Supermajor second; subminor third | ||
| | | 7/6, 8/7, 15/13 | ||
| | | Caesiant | ||
| | | 2♯ ; 3♭ | ||
| | | II♯ , III♭ | ||
|- | |- | ||
| | | 5 | ||
| | | Minor third | ||
| | | 6/5, 25/21 | ||
| | | Minor mediant | ||
| <u>3</u> | |||
| <u>III</u> | |||
|- | |- | ||
| | | 6 | ||
| | | Major third | ||
| | | 5/4, 16/13, 26/21 | ||
| | | Major mediant | ||
| | 3 | | {{overline|3}} | ||
| | III | | {{overline|III}} | ||
|- | |- | ||
| | | 7 | ||
| | | Supermajor third, subfourth | ||
| | | 32/25, 9/7, 13/10 | ||
| | | Rubric | ||
| | | 3♯, 4♭ | ||
| | | III♯ , IV♭ | ||
|- | |- | ||
| | | 8 | ||
| | | Perfect fourth | ||
| | | 4/3 | ||
| | | Subdominant | ||
| 4 | |||
| IV | |||
|- | |- | ||
| | | 9 | ||
| | | Augmented fourth | ||
| | | 25/18, 7/5, 18/13 | ||
| | | Hygrant | ||
| | | 4♯ | ||
| | | IV♯ | ||
|- | |- | ||
| | | 10 | ||
| | | Diminished fifth | ||
| | | 36/25, 10/7, 13/9 | ||
| | | Subhygrant | ||
| | | 5♭ | ||
| | | V♭ | ||
|- | |- | ||
| | | 11 | ||
| | | Perfect fifth | ||
| | | 3/2 | ||
| | | Dominant | ||
| 5 | |||
| V | |||
|- | |- | ||
| | | 12 | ||
| | | Augmented fifth, subminor sixth | ||
| | | 25/16, 14/9, 20/13 | ||
| | | Subrubric | ||
| | | 5♯, 6♭ | ||
| | | V♯, VI♭ | ||
|- | |- | ||
| | | 13 | ||
| | | Minor sixth | ||
| | | 8/5, 13/8, 21/13 | ||
| | | Minor submediant | ||
| <u>6</u> | |||
| <u>VI</u> | |||
|- | |- | ||
| | | 14 | ||
| | | Major sixth | ||
| | | 5/3 | ||
| | | Major submediant | ||
| | 6 | | {{overline|6}} | ||
| | VI | | {{overline|VI}} | ||
|- | |- | ||
| | | 15 | ||
| | | Supermajor sixth, subminor seventh, harmonic seventh | ||
| | | 7/4, 12/7, 26/15 | ||
| | | Subcaesiant | ||
| | | 6♯ | ||
| | | VI♯ | ||
|- | |- | ||
| | | 16 | ||
| | | Minor seventh | ||
| | | 9/5, 16/9 | ||
| | | Subtonic | ||
| | | 7♭ | ||
| | | VII♭ | ||
|- | |- | ||
| | 18 | | 17 | ||
| Major seventh | |||
| | | 15/8, 13/7, 28/15, 24/13 | ||
| Lower leading tone | |||
| | | 7 | ||
| | | 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. | |||
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. | ||
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. | ||
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{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! Symbol | |||
! Name | |||
! Just approximation | |||
|- | |- | ||
| I<sub>(ae)</sub> | |||
| Major pentad | |||
| Otonal 4:5:6:7:8 | |||
|- | |- | ||
| i<sub>(ae)</sub> | |||
| Minor pentad | |||
| Utonal 4:5:6:7:8 | |||
|- | |- | ||
| I<sub>(ch)</sub> | |||
| Major hexad | |||
| Otonal 6:7:8:9:10:12 | |||
|- | |- | ||
| i<sub>(ch)</sub> | |||
| Minor hexad | |||
| Otonal 6:7:8:9:10:12 | |||
|} | |} | ||
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. | |||
Porting the following progressions is trivial: | |||
* 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) | |||
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. | |||
{{Navbox notation}} | |||
[[Category:19edo]] | [[Category:19edo]] | ||
[[Category:beta]] | [[Category:beta]] | ||