Hemififths: Difference between revisions
→Tunings: gencom is irrelevant to tunings. It being here seems like an artifact. It's also trivial to derive them in this case |
→Notation: the two notations aren't mutually exclusive. Improve wording and formatting. |
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== Notation == | == Notation == | ||
Hemififths can be notated in [[neutral | Hemififths can be notated in [[neutral chain-of-fifths notation]], in which case 5/4 is represented by a sesqui-augmented second (C–D{{sesquisharp2}}), and 7/4 by a semi-augmented sixth (C–A{{demisharp2}}). In the 13-limit extension, 11/8 is represented by the semi-augmented fourth (C–F{{demisharp2}}), and 13/8 by the neutral sixth (C–A{{demiflat2}}). This, of course, defies the tradition of tertian harmony. The just major triad on C is {{dash|C, D{{sesquisharp2}}, G|med}}, for example. One may want to adopt one or more additional modules of accidentals such as arrows or +/- signs to represent the comma steps. There are two notable comma steps: | ||
# | # The syntonic~septimal comma (-17 gensteps, semidiminished second); | ||
# | # The Pythagorean comma (+24 gensteps, inverse diminished second). | ||
Below is tabulated how to notate the prime harmonics with an arrow representing a syntonic~septimal comma. | Below is tabulated how to notate the prime harmonics with an arrow representing a syntonic~septimal comma. | ||
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| 3/2 | | 3/2 | ||
| Perfect fifth | | Perfect fifth | ||
| | | C–G | ||
|- | |- | ||
| 5/4 | | 5/4 | ||
| Down major third | | Down major third | ||
| | | C–vE | ||
|- | |- | ||
| 7/4 | | 7/4 | ||
| Down minor seventh | | Down minor seventh | ||
| | | C–vBb | ||
|- | |- | ||
| 11/8 | | 11/8 | ||
| Semi-augmented fourth | | Semi-augmented fourth | ||
| | | C–Ft | ||
|- | |- | ||
| 13/8 | | 13/8 | ||
| Neutral sixth | | Neutral sixth | ||
| | | C–Ad | ||
|} | |} | ||
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| 3/2 | | 3/2 | ||
| Perfect fifth | | Perfect fifth | ||
| | | C–G | ||
|- | |- | ||
| 5/4 | | 5/4 | ||
| Up neutral third | | Up neutral third | ||
| | | C–^Ed | ||
|- | |- | ||
| 7/4 | | 7/4 | ||
| Up semidiminished seventh | | Up semidiminished seventh | ||
| | | C–^Bdb | ||
|- | |- | ||
| 11/8 | | 11/8 | ||
| Semi-augmented fourth | | Semi-augmented fourth | ||
| | | C–Ft | ||
|- | |- | ||
| 13/8 | | 13/8 | ||
| Neutral sixth | | Neutral sixth | ||
| | | C–Ad | ||
|} | |} | ||