Douglas Blumeyer's RTT How-To: Difference between revisions

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=== generators ===

[[File:Generator sizes in PTS.png|800px|thumb|'''Figure 4b.''' Generator sizes of linear temperaments in PTS. Don't worry too much about the valid ranges yet; we'll discuss that part later. And I didn’t break down what’s happening along the blackwood, compton, augmented, dimipent, and some other lines which are labelled on the original PTS diagram. In some cases, it’s just because I got lazy and didn’t want to deal with fitting more numbers on this thing. But in the case of all those that I just listed, it’s because although they are rank-2, those temperaments all have non-octave periods and are therefore not linear, and so it doesn't make enough sense to compare their generators here. You'll learn about periods in the next section.]]

The answer to both of those questions is: it’s the generator (in this case, the meantone generator).

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Here’s a diagram that shows how the generator size changes gradually across each line in PTS. It may seem weird how the same generator size appears in multiple different places across the space. But keep in mind that pretty much any generator is possible pretty much anywhere here. This is simply the generator size pattern you get when you lock the octave to exactly 1200 cents, to establish a common basis for comparison. This is what enables us to produce maps of temperaments such as the one found at [[Map_of_linear_temperaments|this Xen wiki page]], or this chart here ''(see Figure 4b)''.

[[File:Generator sizes in PTS.png|800px|thumb|'''Figure 4b.''' Generator sizes of linear temperaments in PTS. Don't worry too much about the valid ranges yet; we'll discuss that part later. And I didn’t break down what’s happening along the blackwood, compton, augmented, dimipent, and some other lines which are labelled on the original PTS diagram. In some cases, it’s just because I got lazy and didn’t want to deal with fitting more numbers on this thing. But in the case of all those that I just listed, it’s because although they are rank-2, those temperaments all have non-octave periods and are therefore not linear, and so it doesn't make enough sense to compare their generators here. You'll learn about periods in the next section.]]

=== periods and generators ===

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 === generators ===
+[[File:Generator sizes in PTS.png|800px|thumb|'''Figure 4b.''' Generator sizes of linear temperaments in PTS. Don't worry too much about the valid ranges yet; we'll discuss that part later. And I didn’t break down what’s happening along the blackwood, compton, augmented, dimipent, and some other lines which are labelled on the original PTS diagram. In some cases, it’s just because I got lazy and didn’t want to deal with fitting more numbers on this thing. But in the case of all those that I just listed, it’s because although they are rank-2, those temperaments all have non-octave periods and are therefore not linear, and so it doesn't make enough sense to compare their generators here. You'll learn about periods in the next section.]]
 The answer to both of those questions is: it’s the generator (in this case, the meantone generator).
@@ Line 413: / Line 415: @@
 Here’s a diagram that shows how the generator size changes gradually across each line in PTS. It may seem weird how the same generator size appears in multiple different places across the space. But keep in mind that pretty much any generator is possible pretty much anywhere here. This is simply the generator size pattern you get when you lock the octave to exactly 1200 cents, to establish a common basis for comparison. This is what enables us to produce maps of temperaments such as the one found at [[Map_of_linear_temperaments|this Xen wiki page]], or this chart here ''(see Figure 4b)''.
-[[File:Generator sizes in PTS.png|800px|thumb|'''Figure 4b.''' Generator sizes of linear temperaments in PTS. Don't worry too much about the valid ranges yet; we'll discuss that part later. And I didn’t break down what’s happening along the blackwood, compton, augmented, dimipent, and some other lines which are labelled on the original PTS diagram. In some cases, it’s just because I got lazy and didn’t want to deal with fitting more numbers on this thing. But in the case of all those that I just listed, it’s because although they are rank-2, those temperaments all have non-octave periods and are therefore not linear, and so it doesn't make enough sense to compare their generators here. You'll learn about periods in the next section.]]
 === periods and generators ===