Monzo: Difference between revisions
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=== Subgroup monzos === | === Subgroup monzos === | ||
{{Main| | {{Main|Subgroup monzos and vals}} | ||
A subgroup monzo is like a standard monzo, except that it is in a just intonation [[subgroup]] that is not a prime limit. It is usually provided along with the subgroup it is in, such as 2.3.7 [1 -2 1⟩ for 14/9 or 2.3.13/5 [1 -1 1⟩ for 26/15. For subgroups with primes as basis elements (such as 2.3.7), a subgroup monzo can be seen as a standard monzo abbreviated to hide zeroes. To make this more clear, the abbreviated sections may be replaced with ellipses, such as 2.3.7 [1 -2 ... 1⟩ for 14/9. | A subgroup monzo is like a standard monzo, except that it is in a just intonation [[subgroup]] that is not a prime limit. It is usually provided along with the subgroup it is in, such as 2.3.7 [1 -2 1⟩ for 14/9 or 2.3.13/5 [1 -1 1⟩ for 26/15. For subgroups with primes as basis elements (such as 2.3.7), a subgroup monzo can be seen as a standard monzo abbreviated to hide zeroes. To make this more clear, the abbreviated sections may be replaced with ellipses, such as 2.3.7 [1 -2 ... 1⟩ for 14/9. | ||
=== Tempered monzos === | === Tempered monzos === | ||
{{Main| | {{Main|Tempered monzos and vals}} | ||
A tempered monzo represents a tempered interval, or an interval in a regular temperament. It functions similarly to a subgroup monzo, except each entry represents not a JI interval but a generator for that regular temperament. For example, the tmonzo for the major third in meantone (or more generally, the diatonic major third in a fifth-generated temperament) is ~2.~3 [-6 4⟩. (Note that we write the generators with tildes to indicate that they are tempered intervals). This means that to find the major third, you go up four perfect twelfths (~3/1) and down six octaves (~2/1). | A tempered monzo represents a tempered interval, or an interval in a regular temperament. It functions similarly to a subgroup monzo, except each entry represents not a JI interval but a generator for that regular temperament. For example, the tmonzo for the major third in meantone (or more generally, the diatonic major third in a fifth-generated temperament) is ~2.~3 [-6 4⟩. (Note that we write the generators with tildes to indicate that they are tempered intervals). This means that to find the major third, you go up four perfect twelfths (~3/1) and down six octaves (~2/1). | ||