15edo: Difference between revisions

Line 383:

* '''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) ===

[To be added later]

=== Porcupine Notation (Octotonic) ===

Porcupine notation ~~bases~~ porcupine[8] LLLLLLLs scale using eight nominals α β χ δ ε φ γ η. Others have proposed ABCDEFGHA, but conflicts with european notation have caused many to reject this approach. Thus greek letters can be used in their place with a close resemblance to the spelling of ABCDEFGHA. The letters are not in greek alphabetic order.

Porcupine notation can also be based on the porcupine[8] LLLLLLLs scale using eight nominals: α β χ δ ε φ γ η. Others have proposed ABCDEFGHA, but conflicts with european notation have caused many to reject this approach. Thus greek letters can be used in their place with a close resemblance to the spelling of ABCDEFGHA. The letters are not in greek alphabetic order.

The eight nominals form the base diatonic scale. In this sense, the "quill" is the name given to the two-edostep interval (160¢) of 15edo while the "small quill" (80¢) is the chroma of 15edo. This produces a very consistent notation for both porcupine[8] and Blackwood[10], moreso than putting 15edo into a 5L 2s framework. See the main [[Porcupine Notation|porcupine notation]] page.

@@ Line 383: / Line 383: @@
 * '''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) ===
+[To be added later]
 === Porcupine Notation (Octotonic) ===
-Porcupine notation bases porcupine[8] LLLLLLLs scale using eight nominals α β χ δ ε φ γ η. Others have proposed ABCDEFGHA, but conflicts with european notation have caused many to reject this approach. Thus greek letters can be used in their place with a close resemblance to the spelling of ABCDEFGHA. The letters are not in greek alphabetic order.
+Porcupine notation can also be based on the porcupine[8] LLLLLLLs scale using eight nominals: α β χ δ ε φ γ η. Others have proposed ABCDEFGHA, but conflicts with european notation have caused many to reject this approach. Thus greek letters can be used in their place with a close resemblance to the spelling of ABCDEFGHA. The letters are not in greek alphabetic order.
 The eight nominals form the base diatonic scale. In this sense, the "quill" is the name given to the two-edostep interval (160¢) of 15edo while the "small quill" (80¢) is the chroma of 15edo. This produces a very consistent notation for both porcupine[8] and Blackwood[10], moreso than putting 15edo into a 5L 2s framework. See the main [[Porcupine Notation|porcupine notation]] page.