User:Ganaram inukshuk/Notes: Difference between revisions
→On various mosses, with extended scale names: Added mos names for newly-named 11-note mosses |
Added notes: UDP notation as two notations |
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This also describes a property of the generating intervals: they appear in one specific size in all but one mode; for 5L 2s's perfect 4th, it appears as the smaller size except in the lydian mode where it appears as an augmented 4th, and for the perfect 5th, it appears as the larger size except in the locrian mode where it's a diminished 5th. | This also describes a property of the generating intervals: they appear in one specific size in all but one mode; for 5L 2s's perfect 4th, it appears as the smaller size except in the lydian mode where it appears as an augmented 4th, and for the perfect 5th, it appears as the larger size except in the locrian mode where it's a diminished 5th. | ||
== Interpreting UDP as two mode enumeration methods == | |||
[[Modal UDP notation|UDP notation]] is one of many mode notation systems that primarily focuses on how to organize the modes of a mos by modal brightness. This notation necessarily requires the notation to distinguish between the chroma-positive and chroma-negative generators of a mos. One issue with this focus on only its chroma-positive generator is that the generators may "flip". As an example, 5L 2s is said to have a perfect 5th as its generator, but although 2L 3s (the pentatonic scale) is said to have a perfect 4th as its chroma-positive generator, it's common to think of its generator as a perfect 5th regardless. | |||
{| class="wikitable sortable" | |||
! colspan="9" |Modes of 5L 2s | |||
|- | |||
! rowspan="2" |UDP | |||
! rowspan="2" |Mode names | |||
! colspan="7" |Scale degrees (starting at C) | |||
|- | |||
!1st | |||
!2nd | |||
!3rd | |||
!4th | |||
!5th | |||
!6th | |||
!7th | |||
|- | |||
|<nowiki>6|0</nowiki> | |||
|Lydian | |||
|C | |||
|D | |||
|E | |||
|F# | |||
|G | |||
|A | |||
|B | |||
|- | |||
|<nowiki>5|1</nowiki> | |||
|Ionian | |||
|C | |||
|D | |||
|E | |||
|F | |||
|G | |||
|A | |||
|B | |||
|- | |||
|<nowiki>4|2</nowiki> | |||
|Mixolydian | |||
|C | |||
|D | |||
|E | |||
|F | |||
|G | |||
|A | |||
|Bb | |||
|- | |||
|<nowiki>3|3</nowiki> | |||
|Dorian | |||
|C | |||
|D | |||
|Eb | |||
|F | |||
|G | |||
|A | |||
|Bb | |||
|- | |||
|<nowiki>2|4</nowiki> | |||
|Aeolian | |||
|C | |||
|D | |||
|Eb | |||
|F | |||
|G | |||
|Ab | |||
|Bb | |||
|- | |||
|<nowiki>1|5</nowiki> | |||
|Phrygian | |||
|C | |||
|Db | |||
|Eb | |||
|F | |||
|G | |||
|Ab | |||
|Bb | |||
|- | |||
|<nowiki>0|6</nowiki> | |||
|Locrian | |||
|C | |||
|Db | |||
|Eb | |||
|F | |||
|Gb | |||
|Ab | |||
|Bb | |||
|} | |||
{| class="wikitable sortable" | |||
|+ | |||
! colspan="14" |Modes of 2L 3s | |||
|- | |||
! rowspan="2" |UDP | |||
! rowspan="2" |Mode "names" | |||
! colspan="5" |Scale degrees (independent of 5L 2s) | |||
! colspan="7" |Scale degrees (in relation to 5L 2s) | |||
|- | |||
!0d | |||
!1d | |||
!2d | |||
!3d | |||
!4d | |||
!1st | |||
!2nd | |||
!3rd | |||
!4th | |||
!5th | |||
!6th | |||
!7th | |||
|- | |||
|<nowiki>4|0</nowiki> | |||
|Pentatonic Phrygian (default mode for sake of example) | |||
|J | |||
|K | |||
|L | |||
|M | |||
|N | |||
|C | |||
| - | |||
|Eb | |||
|F | |||
| - | |||
|Ab | |||
|Bb | |||
|- | |||
|<nowiki>3|1</nowiki> | |||
|Pentatonic Aeolian (minor pentatonic) | |||
|J | |||
|K | |||
|L | |||
|M@ | |||
|N | |||
|C | |||
| - | |||
|Eb | |||
|F | |||
|G | |||
| - | |||
|Bb | |||
|- | |||
|<nowiki>2|2</nowiki> | |||
|Pentatonic Dorian | |||
|J | |||
|K@ | |||
|L | |||
|M@ | |||
|N | |||
|C | |||
|D | |||
| - | |||
|F | |||
|G | |||
| - | |||
|Bb | |||
|- | |||
|<nowiki>1|3</nowiki> | |||
|Pentatonic Mixolydian | |||
|J | |||
|K@ | |||
|L | |||
|M@ | |||
|N@ | |||
|C | |||
|D | |||
| - | |||
|F | |||
|G | |||
|A | |||
| - | |||
|- | |||
|<nowiki>0|4</nowiki> | |||
|Pentatonic Ionian (major pentatonic) | |||
|J | |||
|K@ | |||
|L@ | |||
|M@ | |||
|N@ | |||
|C | |||
|D | |||
|E | |||
| - | |||
|G | |||
|A | |||
| - | |||
|} | |||
This ironically means that major pentatonic is the darkest mode of 2L 3s, though this irony comes from specifying which generator is which. | |||
UDP notation denotes how a scale is produced in terms of how many chroma-positive generators going up (u) and down (d) are needed, notated as "u|d". This can also be interpreted as how many chroma-negative generators are needed going down (d') and up (u'), where the notation is otherwise identical (since d' = u and u' = d). As of writing, TAMNAMS has a proposed mode-naming scheme that drops the number of generators going down, where modes are notated as "u|" instead. An equivalent system that favors a chroma-negative generator can thereby be notated as "|d". In relation to UDP, this is basically the notation of "u|d" separated into two: "u|" and "|d". | |||
In the case of the modes of 2L 3s, even though the perfect 4th is the chroma-positive generator, enumerating modes either using standard UDP notation ("u|d") or the proposed TAMNAMS mode-naming scheme ("u|") and sorting by brightness results in mode 0|4 as being the "last" mode, whereas notating modes as "|d" notates mode 0|4 as the first mode. | |||
This notion of favoring a generator can also extend to mosses that come after a specific mos, such as the chromatic mosses of 5L 7s and 7L 5s for 5L 2s, where the chroma-positive generators (relative to 5L 2s) are the perfect 5th and perfect 4th respectively, though it may be possible to think of the generator of either mos as being the perfect 5th regardless. | |||