Yer: Difference between revisions

Line 110:

As an EFG, it has no subharmonic factors, that is, no division - only multiplication of them together, which leads to it being [https://en.xen.wiki/w/Otonality_and_utonality#Ambitonal ambitonal], not otonal or utonal leaning. While it is nicely “balanced/symmetrical” as all CPSs are, pitches in the resultant system are not evenly distributed. There are two massive gaps of 185 cents, and two places where pitches land almost directly on top of each other.

Since the EFG system of Yer includes both 11 * 13 * 17 and 19 as pitches, that means the comma exists as an interval in the scale. Since it’s so tiny, though, the two notes related by it can hardly be treated as separate. This means that when you go to draw this tuning out as a JI lattice, you can do something you wouldn’t normally do, which is set a couple points right together.

~~[[File:Yer comma conflation.png|thumb|~~

~~Blumeyer comma conflation~~

~~|none]]~~

You could think of this lattice as a pair of cubes. One is an Euler-Fokker genus of [11, 13, 17]. The other is that same Euler-Fokker genus, just with every node multiplied by 19. That’s why every point in the second cube has the same set of circles colored in as the analogous one in the other cube, just with the magenta 19 filled in as well.

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.

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

~~Blume comma conflation~~

]]

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.

== Commas ==

Those pitches right on top of each other are a feature, not a bug. The pitch 11 * 13 * 17 is 2431, only one off from the pitch 19, which when octave adjusted is 2432. So we end up with this superparticular ratio, 2432:2431, the Blumeyer comma.

Those pitches right on top of each other are a feature, not a bug. The pitch 11 * 13 * 17 is 2431, only one off from the pitch 19, which when octave adjusted is 2432. So we end up with this superparticular ratio, 2432:2431, called the Blumeyer comma.

{| class="wikitable"

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Yer supports 240 possible comma pumps (which are [[Zero comma pump|zero comma pumps]] via comma shifts by the comma-wide intervals present in the tuning).

Yer supports 240 possible comma pumps (which are [[Zero comma pump|zero comma pumps]] via comma shifts by the comma-wide intervals present in the tuning). More on that later.

== Lattice Play ==

Since the EFG system of Yer includes both 11 * 13 * 17 and 19 as pitches, that means the comma exists as an interval in the scale. Since it’s so tiny, though, the two notes related by it can hardly be treated as separate. This means that when you go to draw this tuning out as a JI lattice, you can do something you wouldn’t normally do, which is set a couple points right together.

[[File:Yer comma conflation.png|thumb|

Blumeyer comma conflation

|none]]

You could think of this lattice as a pair of cubes. One is an Euler-Fokker genus of [11, 13, 17]. The other is that same Euler-Fokker genus, just with every node multiplied by 19. That’s why every point in the second cube has the same set of circles colored in as the analogous one in the other cube, just with the magenta 19 filled in as well.

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.

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

Blume comma conflation

]]

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.

== Scala file ==

@@ Line 110: / Line 110: @@
 As an EFG, it has no subharmonic factors, that is, no division - only multiplication of them together, which leads to it being [https://en.xen.wiki/w/Otonality_and_utonality#Ambitonal ambitonal], not otonal or utonal leaning. While it is nicely “balanced/symmetrical” as all CPSs are, pitches in the resultant system are not evenly distributed. There are two massive gaps of 185 cents, and two places where pitches land almost directly on top of each other.
-Since the EFG system of Yer includes both 11 * 13 * 17 and 19 as pitches, that means the comma exists as an interval in the scale. Since it’s so tiny, though, the two notes related by it can hardly be treated as separate. This means that when you go to draw this tuning out as a JI lattice, you can do something you wouldn’t normally do, which is set a couple points right together.
-[[File:Yer comma conflation.png|thumb|
-Blumeyer comma conflation
-|none]]
-You could think of this lattice as a pair of cubes. One is an Euler-Fokker genus of [11, 13, 17]. The other is that same Euler-Fokker genus, just with every node multiplied by 19. That’s why every point in the second cube has the same set of circles colored in as the analogous one in the other cube, just with the magenta 19 filled in as well.
-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.
-[[File:Yer - other comma conflation.png|none|thumb|
-Blume comma conflation
-]]
-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.
 == Commas ==
-Those pitches right on top of each other are a feature, not a bug. The pitch 11 * 13 * 17 is 2431, only one off from the pitch 19, which when octave adjusted is 2432. So we end up with this superparticular ratio, 2432:2431, the Blumeyer comma.
+Those pitches right on top of each other are a feature, not a bug. The pitch 11 * 13 * 17 is 2431, only one off from the pitch 19, which when octave adjusted is 2432. So we end up with this superparticular ratio, 2432:2431, called the Blumeyer comma.
 {| class="wikitable"
@@ Line 147: / Line 133: @@
 |}
-Yer supports 240 possible comma pumps (which are [[Zero comma pump|zero comma pumps]] via comma shifts by the comma-wide intervals present in the tuning).
+Yer supports 240 possible comma pumps (which are [[Zero comma pump|zero comma pumps]] via comma shifts by the comma-wide intervals present in the tuning). More on that later.
+== Lattice Play ==
+Since the EFG system of Yer includes both 11 * 13 * 17 and 19 as pitches, that means the comma exists as an interval in the scale. Since it’s so tiny, though, the two notes related by it can hardly be treated as separate. This means that when you go to draw this tuning out as a JI lattice, you can do something you wouldn’t normally do, which is set a couple points right together.
+[[File:Yer comma conflation.png|thumb|
+Blumeyer comma conflation
+|none]]
+You could think of this lattice as a pair of cubes. One is an Euler-Fokker genus of [11, 13, 17]. The other is that same Euler-Fokker genus, just with every node multiplied by 19. That’s why every point in the second cube has the same set of circles colored in as the analogous one in the other cube, just with the magenta 19 filled in as well.
+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.
+[[File:Yer - other comma conflation.png|none|thumb|
+Blume comma conflation
+]]
+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.
 == Scala file ==