@inproceedings{5e7bd4094a5e4af8abf04484d71f98da,
title = "Distributional analysis of n-dimensional feature space for 7-note scales in 22-TET",
abstract = "Many scale features have been defined in an effort to account for the ubiquity of the diatonic scale in tonal music. In 12-TET, their relative influences have been difficult to disentangle. In 22-TET however, the features are spread differently across different scales. We sought here to to establish a set of 7-note scales in 22-TET that represent the major clusters within the whole population of scales. We first calculate numerous features of every 7-note scale in 22-TET that may relate to their perception in harmonic tonality. This feature space is then reduced by the step-by-step removal of features which may be most completely expressed as linear combinations of the others. A k-medoids cluster analysis leads finally to the selection of 11 exemplar scales, including approximations of four different tunings of the diatonic scale in just intonation.",
keywords = "algorithms, cluster analysis, musical intervals and scales",
author = "Gareth Hearne and Milne, {Andrew J.} and Dean, {Roger T.}",
year = "2019",
doi = "10.1007/978-3-030-21392-3_16",
language = "English",
isbn = "9783030213916",
publisher = "Springer",
pages = "201--212",
booktitle = "Mathematics and Computation in Music: 7th International Conference, MCM 2019, Madrid, Spain, June 18{\~A}¢€“21, 2019, Proceedings",
note = "International Conference on Mathematics and Computation in Music ; Conference date: 18-06-2019",
}