18/17: Difference between revisions
Jump to navigation
Jump to search
Expansion |
Simplify the "terminology and notation" section since it's addressed in the 17-limit page |
||
| Line 8: | Line 8: | ||
== Terminology and notation == | == Terminology and notation == | ||
Conceptualization systems disagree on whether [[17/16]] should be a [[diatonic semitone]] or a [[chromatic semitone]], and as a result the disagreement propagates to all intervals of [[harmonic class|HC17]]. See [[17-limit]] for a detailed discussion. | |||
In | For 18/17 specifically: | ||
* In the [[Functional Just System]], it is a chromatic semitone, separated by [[4131/4096]] from the [[2187/2048|Pythagorean augmented unison (2187/2048)]]. | |||
* In [[Helmholtz-Ellis notation]], it is a diatonic semitone, separated by [[2187/2176]] from the [[256/243|Pythagorean minor second (256/243)]]. | |||
The term ''small septendecimal semitone'' omits the diatonic/chromatic part and only describes its melodic property i.e. the size. It is said in contrast to the large septendecimal semitone of 18/17. | |||
== See also == | == See also == | ||
| Line 17: | Line 21: | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
* [[ | * [[1ed18/17]] – equal multiplication of this interval | ||
[[Category:Second]] | [[Category:Second]] | ||
[[Category:Chroma]] | [[Category:Chroma]] | ||
[[Category:Semitone]] | [[Category:Semitone]] | ||
Revision as of 08:17, 4 January 2024
| Interval information |
reduced
[sound info]
In 17-limit just intonation, 18/17 is the small septendecimal semitone of about 99¢. It is very close to 12edo's "half step" of 100¢, and fairly close to the "large septendecimal semitone" of 17/16 (~105¢).
Terminology and notation
Conceptualization systems disagree on whether 17/16 should be a diatonic semitone or a chromatic semitone, and as a result the disagreement propagates to all intervals of HC17. See 17-limit for a detailed discussion.
For 18/17 specifically:
- In the Functional Just System, it is a chromatic semitone, separated by 4131/4096 from the Pythagorean augmented unison (2187/2048).
- In Helmholtz-Ellis notation, it is a diatonic semitone, separated by 2187/2176 from the Pythagorean minor second (256/243).
The term small septendecimal semitone omits the diatonic/chromatic part and only describes its melodic property i.e. the size. It is said in contrast to the large septendecimal semitone of 18/17.
See also
- 17/9 – its octave complement
- 17/12 – its fifth complement
- Gallery of just intervals
- List of superparticular intervals
- 1ed18/17 – equal multiplication of this interval