|
|
|
|
| LEADER |
01421nam a2200217Ia 4500 |
| 001 |
10.1080-17459737.2019.1605626 |
| 008 |
220511s2019 CNT 000 0 und d |
| 020 |
|
|
|a 17459737 (ISSN)
|
| 245 |
1 |
0 |
|a 2:3:4 Harmony within the tritave
|
| 260 |
|
0 |
|b Taylor and Francis Ltd.
|c 2019
|
| 856 |
|
|
|z View Fulltext in Publisher
|u https://doi.org/10.1080/17459737.2019.1605626
|
| 520 |
3 |
|
|a In the Pythagorean tuning system, the fifth is used to generate a scale of 12 notes per octave. In this paper, we use the octave to generate a scale of 19 notes per tritave; one can play this scale on a traditional piano. In this system, the octave becomes a proper interval and the 2:3:4 chord a proper chord. We study harmonic properties obtained from the 2:3:4 chord, in particular composition elements using dominants, inversions, major and minor chords, and diminished chords. The Tonnetz (array notation) turns out to be an effective tool to visualize the harmonic development in a composition based on these elements. 2:3:4 harmony may sound pure, yet sparse, as we illustrate in a short piece. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.
|
| 650 |
0 |
4 |
|a Bohlen-Pierce
|
| 650 |
0 |
4 |
|a composition
|
| 650 |
0 |
4 |
|a continued fractions
|
| 650 |
0 |
4 |
|a Harmony
|
| 650 |
0 |
4 |
|a neo-Riemannian Tonnetz
|
| 650 |
0 |
4 |
|a scales
|
| 650 |
0 |
4 |
|a tritave
|
| 700 |
1 |
|
|a Schmidmeier, M.
|e author
|
| 773 |
|
|
|t Journal of Mathematics and Music
|
