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In harmony, the tonus is the ratio 9:8 between a pair of frequencies or, equivalently, the ratio 8:9 between a pair of wavelengths. It is the arithmetic mean of unison and ditono: Harmony is the use and study of pitch simultaneity and chords, actual or implied, in music. ...
In mathematics and statistics, the arithmetic mean of a set of numbers is the sum of all the members of the set divided by the number of items in the set. ...
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In harmony, the ditonus (Latin for double tone — plural ditoni) is the ratio 5:4 (sesquiquartum) between a pair of frequencies or, equivalently, the ratio 4:5 between a pair of wavelengths. ...
It is equal to diapente divided by diatessaron: In harmony, diapente is the ratio 3:2 (sesquialterum) between a pair of frequencies or, equivalently, the ratio 2:3 between a pair of wavelengths. ...
See diatessaron (interval) for the musical term. ...
This means that a diapente is equal to a diatessaron and a tonus, put together.
The tonus is 1.001 in binary — 1 + 2−3 — and it is the inversion of the eptadem minus (minor seventh) (16:9), The musical interval of a minor seventh the first note (the root or tonic) and the seventh in a minor scale. ...
Notice also that the eptadem minus is a pair of diatessarons put together: The eptadem minus is the sum of the first eight reciprocals of triangular numbers: The tonus is also called major second. The musical interval of a major second — also called a whole-tone — is the relationship between the first note (the root or tonic) and the second note in a major scale (and also a minor scale). ...
Major and Minor
The tonus comes in two slightly different versions: the tuono maggiore (9:8) and the tuono minore (10:9).
The tuono minore is the harmonic mean of unison and ditono: In mathematics, the harmonic mean is one of several methods of calculating an average. ...
In binary, the tuono minore is equal to 1.000111000111000111000111...
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