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15edo: Difference between revisions

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→Augmented Notation (Nonatonic): Changed the seconds’ names. I am already starting to regret that I made this.
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→Notation: Removed augmented notation because it was inaccurate, added kleismic/orgone notation
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There are a variety of other ways to notate 15edo, and the choice of notation depends heavily on which rank-2 temperament or MOS scale one wishes to treat as being the "main focus" of 15edo composition.
There are a variety of other ways to notate 15edo, and the choice of notation depends heavily on which rank-2 temperament or MOS scale one wishes to treat as being the "main focus" of 15edo composition.


=== Augmented Notation (Nonatonic) ===
=== Blackwood Notation (Pentatonic) ===
Augmented notation can be based on the Augmented[9] LssLssLss scale. By representing the 3|3 mode (sLssLssLs) with a chain of fifths (D E F F# G A Bb B C D) and using sharps and flats (#/b) to represent a step up or down respectively, 15edo’s notes and intervals can be named with respect to some diatonic intervals.
For note names, [[Kite Giedraitis]] proposes a possible alternative to heptatonic names, pentatonic names that omit B and merge E and F into a new letter, "eef" (it rhymes with leaf). Eef, like E, is a 5th above A. Eef, like F, is a 4th above C. The circle of 5ths is C G D A Eef C. Eef is written like an E, but with the bottom horizontal line going not right but left from the vertical line. Eef can be typed as ꘙ (unicode A619) or ⊧ (unicode 22A7) or 𐐆 (unicode 10406).  
{| class="wikitable"
{| class="wikitable"
|+
| C
| ^C
| vD
| D
|  ^D
| vꘙ
| ꘙ
| ^ꘙ
| vG
| G
| ^G
| vA
| A
| ^A
| vC
| C
|-
| P1
| ^1
| v2
| P2
| ^2
| v3
| P3
| ^3
| v4
| P4
| ^4
| v5
| P5
| ^5
| v6
| P6
|}
=== Blackwood Notation (Decatonic) ===
* '''Decimal Version:''' Using the nominals 1-0 (with 0 representing "10"), one of the three chains of 5edo is represented by the odd numbers, the second by the even numbers, and the third by numbers with accidentals (either odd numbers with sharps, or even numbers with flats).
* '''Guitar Version:''' On a 15edo guitar, because the "perfect fourth" comes from 5edo, all of the open strings can be tuned a perfect fourth apart and still span exactly two octaves. If one starts the [[circle of fourths]] on B — B-E-A-D-G-(B) — then the open strings of the guitar can be notated as usual (E-A-D-G-B-E). However, because the circle of fourths closes at five, and does not continue to circulate through the other 10 notes of 15edo, it is necessary to use accidentals to notate intervals on the other two chains of 5edo. This notation is not particularly ideal as a basis for a staff notation (as it requires all non-5edo chords to be notated with accidentals). It is nevertheless useful because it reflects an intuitive approach to 15edo on the guitar, since 5edo provides a useful set of 3-limit landmarks (or "perfect fourths" and "perfect fifths") that can be used to navigate the fretboard. It's especially convenient for writing chord charts, where the funky accidental-laden spellings can be more or less ignored.
=== Kleismic/Orgone Notation (Heptatonic) ===
Kleismic/Orgone notation can be based on the Kleismic/Orgone[7] LLsLsLs scale. If we try to represent the 3|3 mode (LsLsLsL) with a chain of fifths (D E F G A B C D) and use sharps and flats (#/b) to denote two steps up or down respectively, 15edo’s notes and intervals are out of order as 15edo has a hard 4L3s.
|-
|-
| | Cents
| | Cents
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|-
|-
| | 80
| | 80
| | Minor Second
| | Diminished Second
| | E
| | Eb
|-
|-
| | 160
| | 160
| | Major Second
| | Augmented Unison
| | E#
| | D#
|-
|-
| | 240
| | 240
| | Diminished Third
| | Perfect Second
| | Fb
| | E
|-
|-
| | 320
| | 320
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|-
|-
| | 400
| | 400
| | Minor Fourth
| | Gb
|-
| | 480
| | Major Third
| | Major Third
| | F#
| | F#
|-
|-
| | 480
| | 560
| | Perfect Fourth
| | Major Fourth
| | G
| | G
|-
| | 560
| | Augmented Fourth
| | G#
|-
|-
| | 640
| | 640
| | Diminished Fifth
| | Minor Fifth
| | Ab
| | A
|-
|-
| | 720
| | 720
| | Perfect Fifth
| | Minor Sixth
| | A
| | Bb
|-
|-
| | 800
| | 800
| | Minor Sixth
| | Major Fifth
| | Bb
| | A#
|-
|-
| | 880
| | 880
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|-
|-
| | 960
| | 960
| | Augmented Sixth
| | Perfect Seventh
| | B#
| | C
|-
|-
| | 1040
| | 1040
| | Minor Seventh
| | Diminished Octave
| | Cb
| | B# / Db
|-
|-
| | 1120
| | 1120
| | Major Seventh
| | Augmented Seventh
| | C
| | C#
|-
|-
| | 1200
| | 1200
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| | D
| | D
|}
|}
=== Blackwood Notation (Pentatonic) ===
For note names, [[Kite Giedraitis]] proposes a possible alternative to heptatonic names, pentatonic names that omit B and merge E and F into a new letter, "eef" (it rhymes with leaf). Eef, like E, is a 5th above A. Eef, like F, is a 4th above C. The circle of 5ths is C G D A Eef C. Eef is written like an E, but with the bottom horizontal line going not right but left from the vertical line. Eef can be typed as ꘙ (unicode A619) or ⊧ (unicode 22A7) or 𐐆 (unicode 10406).
{| class="wikitable"
|+
| C
| ^C
| vD
| D
|  ^D
| vꘙ
| ꘙ
| ^ꘙ
| vG
| G
| ^G
| vA
| A
| ^A
| vC
| C
|-
| P1
| ^1
| v2
| P2
| ^2
| v3
| P3
| ^3
| v4
| P4
| ^4
| v5
| P5
| ^5
| v6
| P6
|}
=== Blackwood Notation (Decatonic) ===
* '''Decimal Version:''' Using the nominals 1-0 (with 0 representing "10"), one of the three chains of 5edo is represented by the odd numbers, the second by the even numbers, and the third by numbers with accidentals (either odd numbers with sharps, or even numbers with flats).
* '''Guitar Version:''' On a 15edo guitar, because the "perfect fourth" comes from 5edo, all of the open strings can be tuned a perfect fourth apart and still span exactly two octaves. If one starts the [[circle of fourths]] on B — B-E-A-D-G-(B) — then the open strings of the guitar can be notated as usual (E-A-D-G-B-E). However, because the circle of fourths closes at five, and does not continue to circulate through the other 10 notes of 15edo, it is necessary to use accidentals to notate intervals on the other two chains of 5edo. This notation is not particularly ideal as a basis for a staff notation (as it requires all non-5edo chords to be notated with accidentals). It is nevertheless useful because it reflects an intuitive approach to 15edo on the guitar, since 5edo provides a useful set of 3-limit landmarks (or "perfect fourths" and "perfect fifths") that can be used to navigate the fretboard. It's especially convenient for writing chord charts, where the funky accidental-laden spellings can be more or less ignored.


=== Porcupine Notation (Heptatonic) ===
=== Porcupine Notation (Heptatonic) ===
Porcupine notation can be based on the Porcupine[7] Lssssss scale. By representing the 3|3 mode (sssLsss) with a chain of fifths (D E F G A B C D) and using sharps and flats (#/b) to represent a step up or down respectively, 15edo can be notated using standard notation. Its intervals can likewise be named with respect to diatonic intervals.
Porcupine notation can be based on the Porcupine[7] Lssssss scale. By representing the 3|3 mode (sssLsss) with a chain of fifths (D E F G A B C D) and using sharps and flats (#/b) to denote a step up or down respectively, 15edo can be notated using standard notation. Its intervals can likewise be named with respect to diatonic intervals.
{| class="wikitable"
{| class="wikitable"
|-
|-
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