Projection: Difference between revisions

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===Units===

The units of a prime-count vector are typically understood to be "primes", which is natural enough given their name. But the units of the generator embedding <math>G</math> are better taken to be ~~<math>\text{~~p}/~~\text{~~g~~}</math>~~, read "primes ''per generator''." This makes sense because their job is to translate temperament generators back into terms of primes.

The units of a prime-count vector are typically understood to be "primes", which is natural enough given their name. But the units of the generator embedding <math>G</math> are better taken to be '''p'''/'''g''', read "primes ''per generator''." This makes sense because their job is to translate temperament generators back into terms of primes.

Here is an example generator embedding for a [[5-limit]], [[Tour_of_Regular_Temperaments#Rank-2_temperaments|rank-2 temperament]], with units given for each entry:

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The subscripts indicate which primes and which generators are related. So the columns, as previously stated, correspond to the two generators of the temperament, ~~<math>\text{g}_1</math>~~ and ~~<math>\text{g}_2</math>~~, while the rows correspond to the three primes for this temperament, ~~<math>\text{p}_1</math>~~, ~~<math>\text{p}_2</math>~~, and ~~<math>\text{p}_3</math>~~, which are primes 2, 3, and 5, respectively.

The subscripts indicate which primes and which generators are related. So the columns, as previously stated, correspond to the two generators of the temperament, g₁ and g₂, while the rows correspond to the three primes for this temperament, p₁, p₂, and p₃, which are primes 2, 3, and 5, respectively.

See also [[Dave Keenan & Douglas Blumeyer's guide to RTT: units analysis]].

@@ Line 259: / Line 259: @@
 ===Units===
-The units of a prime-count vector are typically understood to be "primes", which is natural enough given their name. But the units of the generator embedding <math>G</math> are better taken to be <math>\text{p}/\text{g}</math>, read "primes ''per generator''." This makes sense because their job is to translate temperament generators back into terms of primes.
+The units of a prime-count vector are typically understood to be "primes", which is natural enough given their name. But the units of the generator embedding <math>G</math> are better taken to be '''p'''/'''g''', read "primes ''per generator''." This makes sense because their job is to translate temperament generators back into terms of primes.
 Here is an example generator embedding for a [[5-limit]], [[Tour_of_Regular_Temperaments#Rank-2_temperaments|rank-2 temperament]], with units given for each entry:
@@ Line 273: / Line 273: @@
-The subscripts indicate which primes and which generators are related. So the columns, as previously stated, correspond to the two generators of the temperament, <math>\text{g}_1</math> and <math>\text{g}_2</math>, while the rows correspond to the three primes for this temperament, <math>\text{p}_1</math>, <math>\text{p}_2</math>, and <math>\text{p}_3</math>, which are primes 2, 3, and 5, respectively.
+The subscripts indicate which primes and which generators are related. So the columns, as previously stated, correspond to the two generators of the temperament, g₁ and g₂, while the rows correspond to the three primes for this temperament, p₁, p₂, and p₃, which are primes 2, 3, and 5, respectively.
 See also [[Dave Keenan & Douglas Blumeyer's guide to RTT: units analysis]].