Yer: Difference between revisions

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So every point in the first cube is connected to the analogous node in the second cube. Normally the node for 19 would not have any direct connection with the node 11, 13, 17. It only directly connects with one node in the other cube, its analogous one, the unison. But here we see that not only is there another effect going on connecting these two nodes, that effect goes beyond connecting them, it straight up conflates them.

But that's not all; recall that there were two other pairs of pitches that were almost the same, too. One of those pairs has such simple sounding members, it may surprise you: 13 and 11 * 19. In this view, we can see that they are nowhere near each other. So we’ll have to nudge our lattice around a little bit more; that's how we arrive at the final lattice shown in the introduction.

But that's not all; recall that there were two other pairs of pitches that were almost the same, too. One of those pairs has such simple sounding members, it may surprise you: 13 and 11 * 19. In this view, we can see that they are nowhere near each other. So we’ll have to nudge our lattice around a little bit more; that's how we arrive at the final lattice shown in the introduction. There, the three pairs of intervals in the center connected by short solid black lines can be modulated between almost unnoticed.

[[File:Yer - other comma conflation.png|none|thumb|

Blume comma conflation - before

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Blume comma visualized

]]

Another consequence of the Blume comma is that a couple “extra” lattice connections appear. These are drawn in dotted green on the lattices in the introduction.

The idea is that if you were to try to go from 11 * 17 by an eleventh to 11 * 11 * 17, well, you’re not really allowed to do that because the EFG does not duplicate factors (you can’t have two 11’s), but since 11 * 11 * 17 is essentially 1, we’ll permit it.

Analogously, you can move from 11 * 13 * 17 * 19 by an eleventh to 11 * 11 * 13 * 17 * 19, or just 13 * 19. Though, for symmetry, we actually do 13 * 19 / 11 rather than 11 * 11 * 13 * 17 * 19.

And as long as we're changing the angle we look on the cube to bring the right pairs of pitches together, we have also taken care to balance these dotted lines with the real 11 lines, so that it’s the zig to the zag of the real 11, more strongly suggesting the dimension of the 11th harmonic’s relationship to that of the 17th (i.e that two 11's make a 17).

Now we could have drawn dotted lines connecting 11 * 13 * 17 to 13, but declined,

considering that the ability to move between these two pitches is already achievable

by modulating from from 11 * 13 * 17 to 19, then moving by that 11 to 11 * 19, then modulating to 13. The same goes for the connection between 11 * 17 * 19 and 19. This would be pretty obvious on the cycle view, because we’d just be drawing a dotted line right alongside an existing solid one.

Here’s something else interesting: we can move by four 11’s in a row. We can move from 17 * 19 to 11 * 17 * 19, which can be shifted to 13 * 17, then move to 11 * 13 * 17, which can be shifted to 19, then move to 11 * 19, which can be shifted to 13, then move to 11 * 13.

You can also move by 3 11’s in a row on the left and right edges; for the other factors, you can only ever move by two of them in a row (in sad 17’s case, only one spot where you can do that, which happens to be in parallel to the spot where you can 4x by 11).

== Comma pumps ==

Yer is pure JI, but due to the five places where it boasts two pitches very close together but with very different harmonic compositions, it can achieve [[Zero comma pump|zero comma pumps]] by “comma shifting” at those key points, returning to exactly their original pitch.

In Yer, there are three classes of pumps of the Blumeyer comma. One way of defining them is by which harmonic is opposite the 19. So in class a, it’s the 11, in b it’s the 13, and in c it’s the 17.

This diagram shows real instances of these pumps in Yer and then rotates each of these three diagrams by a different amount so that the 19 would be horizontal across the top in each one, in order to better bring out their differences in shape.

== Scala file ==

@@ Line 143: / Line 143: @@
 So every point in the first cube is connected to the analogous node in the second cube. Normally the node for 19 would not have any direct connection with the node 11, 13, 17. It only directly connects with one node in the other cube, its analogous one, the unison. But here we see that not only is there another effect going on connecting these two nodes, that effect goes beyond connecting them, it straight up conflates them.
-But that's not all; recall that there were two other pairs of pitches that were almost the same, too. One of those pairs has such simple sounding members, it may surprise you: 13 and 11 * 19. In this view, we can see that they are nowhere near each other. So we’ll have to nudge our lattice around a little bit more; that's how we arrive at the final lattice shown in the introduction.
+But that's not all; recall that there were two other pairs of pitches that were almost the same, too. One of those pairs has such simple sounding members, it may surprise you: 13 and 11 * 19. In this view, we can see that they are nowhere near each other. So we’ll have to nudge our lattice around a little bit more; that's how we arrive at the final lattice shown in the introduction. There, the three pairs of intervals in the center connected by short solid black lines can be modulated between almost unnoticed.
 [[File:Yer - other comma conflation.png|none|thumb|
 Blume comma conflation - before
@@ Line 165: / Line 166: @@
 Blume comma visualized
 ]]
+Another consequence of the Blume comma is that a couple “extra” lattice connections appear. These are drawn in dotted green on the lattices in the introduction.
+The idea is that if you were to try to go from 11 * 17 by an eleventh to 11 * 11 * 17, well, you’re not really allowed to do that because the EFG does not duplicate factors (you can’t have two 11’s), but since 11 * 11 * 17 is essentially 1, we’ll permit it.
+Analogously, you can move from 11 * 13 * 17 * 19 by an eleventh to 11 * 11 * 13 * 17 * 19, or just 13 * 19. Though, for symmetry, we actually do 13 * 19 / 11 rather than 11 * 11 * 13 * 17 * 19.
+And as long as we're changing the angle we look on the cube to bring the right pairs of pitches together, we have also taken care to balance these dotted lines with the real 11 lines, so that it’s the zig to the zag of the real 11, more strongly suggesting the dimension of the 11th harmonic’s relationship to that of the 17th (i.e that two 11's make a 17).
+Now we could have drawn dotted lines connecting 11 * 13 * 17 to 13, but declined,
+considering that the ability to move between these two pitches is already achievable
+by modulating from from 11 * 13 * 17 to 19, then moving by that 11 to 11 * 19, then modulating to 13. The same goes for the connection between 11 * 17 * 19 and 19. This would be pretty obvious on the cycle view, because we’d just be drawing a dotted line right alongside an existing solid one.
+Here’s something else interesting: we can move by four 11’s in a row. We can move from 17 * 19 to 11 * 17 * 19, which can be shifted to 13 * 17, then move to 11 * 13 * 17, which can be shifted to 19, then move to 11 * 19, which can be shifted to 13, then move to 11 * 13.
+You can also move by 3 11’s in a row on the left and right edges; for the other factors, you can only ever move by two of them in a row (in sad 17’s case, only one spot where you can do that, which happens to be in parallel to the spot where you can 4x by 11).
+== Comma pumps ==
+Yer is pure JI, but due to the five places where it boasts two pitches very close together but with very different harmonic compositions, it can achieve [[Zero comma pump|zero comma pumps]] by “comma shifting” at those key points, returning to exactly their original pitch.
+In Yer, there are three classes of pumps of the Blumeyer comma. One way of defining them is by which harmonic is opposite the 19. So in class a, it’s the 11, in b it’s the 13, and in c it’s the 17.
+This diagram shows real instances of these pumps in Yer and then rotates each of these three diagrams by a different amount so that the 19 would be horizontal across the top in each one, in order to better bring out their differences in shape.
 == Scala file ==