Xenharmonic Wiki

15edo: Difference between revisions

← Older editNewer edit →
VisualWikitext
ArrowHead294 (talk | contribs)
15,220 edits
ArrowHead294 (talk | contribs)
15,220 edits
mNo edit summary
Line 380: Line 380:
There are a variety of 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 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.


===Sagittal notation===
=== Sagittal notation ===
This notation uses the same sagittal sequence as EDOs [[22edo#Sagittal notation|22]] and [[29edo#Sagittal notation|29]], is a subset of the notation for [[30edo#Sagittal notation|30-EDO]], and is a superset of the notation for [[5edo#Sagittal notation|5-EDO]].
This notation uses the same sagittal sequence as EDOs [[22edo#Sagittal notation|22]] and [[29edo#Sagittal notation|29]], is a subset of the notation for [[30edo#Sagittal notation|30-EDO]], and is a superset of the notation for [[5edo#Sagittal notation|5-EDO]].


Line 393: Line 393:


=== Blackwood Notation (Pentatonic) ===
=== 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).  
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
| ^C
| ^C
Line 437: Line 438:
=== 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 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.
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"
|-
|-
| | Cents
| Cents
| | Interval Name(s)
| Interval Name(s)
| | Note name(s)
| Note name(s)
|-
|-
| | 0
| 0
| | Unison
| Unison
| | D
| D
|-
|-
| | 80
| 80
| | Augmented Unison / Minor Second
| Augmented Unison / Minor Second
| | D# / Eb
| D# / Eb
|-
|-
| | 160
| 160
| | Major Second
| Major Second
| | E
| E
|-
|-
| | 240
| 240
| | Augmented Second / Diminished Third
| Augmented Second / Diminished Third
| | E# / Fb
| E# / Fb
|-
|-
| | 320
| 320
| | Minor Third
| Minor Third
| | F
| F
|-
|-
| | 400
| 400
| | Major Third / Diminished Fourth
| Major Third / Diminished Fourth
| | F# / Gb
| F# / Gb
|-
|-
| | 480
| 480
| | Perfect Fourth
| Perfect Fourth
| | G
| G
|-
|-
| | 560
| 560
| | Augmented Fourth
| Augmented Fourth
| | G#
| G#
|-
|-
| | 640
| 640
| | Diminished Fifth
| Diminished Fifth
| | Ab
| Ab
|-
|-
| | 720
| 720
| | Perfect Fifth
| Perfect Fifth
| | A
| A
|-
|-
| | 800
| 800
| | Augmented Fifth / Minor Sixth
| Augmented Fifth / Minor Sixth
| | A# / Bb
| A# / Bb
|-
|-
| | 880
| 880
| | Major Sixth
| Major Sixth
| | B
| B
|-
|-
| | 960
| 960
| | Augmented Sixth / Diminished Seventh
| Augmented Sixth / Diminished Seventh
| | B# / Cb
| B# / Cb
|-
|-
| | 1040
| 1040
| | Minor Seventh
| Minor Seventh
| | C
| C
|-
|-
| | 1120
| 1120
| | Major Seventh / Diminished Octave
| Major Seventh / Diminished Octave
| | C# / Db
| C# / Db
|-
|-
| | 1200
| 1200
| | Octave
| Octave
| | D
| D
|}
|}
One neat thing about using this notation system is that its notated major scale, D E F# G A B C# D, directly corresponds to 15edo’s LH Nice-Ionian scale.
One neat thing about using this notation system is that its notated major scale, D E F# G A B C# D, directly corresponds to 15edo’s LH Nice-Ionian scale.


Line 515: Line 518:
{| class="wikitable"
{| class="wikitable"
|-
|-
| | Cents
| Cents
| | Interval Name
| Interval Name
| | Note names
| Note names
|-
|-
| | 0
| 0
| | Zeroquill
| Zeroquill
| | α - α
| α - α
|-
|-
| | 80
| 80
| | Small Quill / Half Quill
| Small Quill / Half Quill
| | α - β\
| α - β\
|-
|-
| | 160
| 160
| | Quill
| Quill
| | α - β
| α - β
|-
|-
| | 240
| 240
| | Small Diquill
| Small Diquill
| | α - χ\
| α - χ\
|-
|-
| | 320
| 320
| | Large Diquill
| Large Diquill
| | α - χ
| α - χ
|-
|-
| | 400
| 400
| | Small Triquill
| Small Triquill
| | α - δ\
| α - δ\
|-
|-
| | 480
| 480
| | Large Triquill
| Large Triquill
| | α - δ
| α - δ
|-
|-
| | 560
| 560
| | Small Fourquill
| Small Fourquill
| | α - ε\
| α - ε\
|-
|-
| | 640
| 640
| | Large Fourquill
| Large Fourquill
| | α - ε
| α - ε
|-
|-
| | 720
| 720
| | Small Fivequill
| Small Fivequill
| | α - φ\
| α - φ\
|-
|-
| | 800
| 800
| | Large Fivequill
| Large Fivequill
| | α - φ
| α - φ
|-
|-
| | 880
| 880
| | Small Sixquill
| Small Sixquill
| | α - γ\
| α - γ\
|-
|-
| | 960
| 960
| | Large Sixquill
| Large Sixquill
| | α - γ
| α - γ
|-
|-
| | 1040
| 1040
| | Small Sevenquill
| Small Sevenquill
| | α - η\
| α - η\
|-
|-
| | 1120
| 1120
| | Large Sevenquill
| Large Sevenquill
| | α - η
| α - η
|-
|-
| | 1200
| 1200
| | Octoquill
| Octoquill
| | α - α
| α - α
|}
|}
A regular keyboard can be designed using this system by placing 7 black keys as Porcupine[7] and 8 whites as Porcupine[8]. In fact, [https://www.stephenweigelcomposerperformer.com/ Stephen Weigel] has already done this with his pink Halberstadt keyboard.
A regular keyboard can be designed using this system by placing 7 black keys as Porcupine[7] and 8 whites as Porcupine[8]. In fact, [https://www.stephenweigelcomposerperformer.com/ Stephen Weigel] has already done this with his pink Halberstadt keyboard.


===MisterShafXen's notation===
=== MisterShafXen's notation ===
This is a pentatonic notation, with the following note names: A A# Bb B B# Cb C C# Db D D# Eb E E# Ab A. A 1-4-5-1 progression in A would have chords A (A Cb D, Am), C (C Eb A, Cm), and D (D Ab B, Dm). The C# minor chord can be spelled C# Eb A#.
This is a pentatonic notation, with the following note names: A A# Bb B B# Cb C C# Db D D# Eb E E# Ab A. A 1-4-5-1 progression in A would have chords A (A Cb D, Am), C (C Eb A, Cm), and D (D Ab B, Dm). The C# minor chord can be spelled C# Eb A#.


Retrieved from "https://en.xen.wiki/w/15edo"