Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Musical intervals under 12-note equal temperament: a geometrical
  interpretation   Musical intervals in multiple of semitones under 12-note equal temperament,
or more specifically pitch-class subsets of assigned cardinality ($n$-chords)
are conceived as positive integer points within an Euclidean $n$-space. The
number of distinct $n$-chords is inferred from combinatorics with the extension
to $n=0$, involving an Euclidean 0-space. The number of repeating $n$-chords,
or points which are turned into themselves during a circular permutation,
$T_n$, of their coordinates, is inferred from algebraic considerations.
Finally, the total number of $n$-chords and the number of $T_n$ set classes are
determined. Palindrome and pseudo palindrome $n$-chords are defined and
included among repeating $n$-chords, with regard to an equivalence relation,
$T_n/T_nI$, where reflection is added to circular permutation. To this respect,
the number of $T_n$ set classes is inferred concerning palindrome and pseudo
palindrome $n$-chords and the remaining $n$-chords. The above results are
reproduced within the framework of a geometrical interpretation, where positive
integer points related to $n$-chords of cardinality, $n$, belong to a regular
inclined $n$-hedron, $\Psi_{12}^n$, the vertexes lying on the coordinate axes
of a Cartesian orthogonal reference frame at a distance, $x_i=12$, $1\le i\le
n$, from the origin. Considering $\Psi_{12}^n$ as special cases of lattice
polytopes, the number of related nonnegative integer points is also determined
for completeness. A comparison is performed with the results inferred from
group theory.

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The categories of this paper are: dg-ga
18
The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th