User talk:TallKite: Difference between revisions

Line 153:

Modifying by combinations of 1331/1296 and 1089/1024 yields interesting results, but I have yet to properly create the part of the system for dealing with these sorts of things. I think we could afford to work together to develop this and to fix remaining flaws if you have the time. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 17:22, 22 November 2020 (UTC)

: I can name every note and every interval in the 2.3.11 subgroup using only ^ and v. And knowing only that ^1 is slightly less than half a sharp, the size of any interval can easily be estimated.

: Here's a simple formula for converting a 2.3.11 monzo to ups and downs:

: (a, b, c) = c * (-5, 1, 1) + (a + 5c, b - c) = c ups (or -c downs) + pythagorean interval

: The pythagorean intervals are named conventionally as M2, m3, etc. So (0, -2, 1) = ^m3

: Here's simple formulas for converting an upped or downed pythagorean interval to a monzo:

: x ups + (a, b) = (a - 5x, b + x, x)

: x downs + (a, b) = (a + 5x, b - x, -x)

: Here's simple formulas for adding together two upped/downed intervals:

: [x ups + (a, b)] plus [y ups + (c, d)] = (x+y) ups + (a + c, b + d)

: [x ups + (a, b)] plus [y downs + (c, d)] = (x-y) ups + (a + c, b + d)

: You don't even need formulas for this, actually. You just add up the pythagorean intervals as usual, then add in the ups and downs. Adding an interval to a note works the same way, as does finding the interval between two notes.

: Here's the 2.3.11 lattice, with a vertical step equal to 33/32:

<tt>

^^F ^^C ^^G ^^D ^^A ^^E ^^B

^F ^C ^G ^D ^A ^E ^B

F C G D A E B

vF vC vG vD vA vE vB

vvF vvC vvG vvD vvA vvE vvB

</tt>

: Each row is a chain of 5ths. The top row is the double-up row, next is the up row, next plain, next down, next double-down.

: Another version of the lattice, with vertical steps of 11/8:

<tt>

^^Eb ^^Bb ^^F ^^C ^^G ^^D ^^A

^Bb ^F ^C ^G ^D ^A ^E

F C G D A E B

vC vG vD vA vE vB ^F#

vvG vvD vvA vvE vvB vvF# vvC#

</tt>

: Another version, with 1/1 - 11/9 - 3/2 and 1/1 - 27/22 - 3/2 triads forming triangles.

<tt>

^^Fb ^^Cb ^^Gb ^^Db ^^Ab ^^Eb ^^Bb

^Ab ^Eb ^Bb ^F ^C ^G ^D

F C G D A E B

vA vE vB vF# vC# vG# vD#

vvF# vvC# vvG# vvD# vvA# vvE# vvB#

</tt>

: See how simple and clear it all is? Everything follows directly from ^1 = 33/32. So it's quite possible to have a very simple nomenclature for everything.

: You have Alpharabian, Betarabian, Paramajor, Paraminor, Greater Neutral, Lesser Neutral, Supraminor and Submajor. And from your previous comments, Rastmic, Birastmic, and Trirastmic. Your nomenclature is way more complicated than it needs to be.

: I've read what you've written several times and I still have no idea which parts of the lattice are Alpharabian, which are Betarabian, and which are neither. I also have no idea how to add together two intervals, or what note I get from adding an interval to a note, or how to name the interval between two notes. I suspect formulas for those things would be impossible.

: So unfortunately, I don't see much point on working with you to improve your nomenclature. Because my first suggestion would be to drastically simplify it. We seem to have fundamentally different approaches. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 01:45, 26 November 2020 (UTC)

@@ Line 153: / Line 153: @@
 Modifying by combinations of 1331/1296 and 1089/1024 yields interesting results, but I have yet to properly create the part of the system for dealing with these sorts of things.  I think we could afford to work together to develop this and to fix remaining flaws if you have the time. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 17:22, 22 November 2020 (UTC)
+: I can name every note and every interval in the 2.3.11 subgroup using only ^ and v. And knowing only that ^1 is slightly less than half a sharp, the size of any interval can easily be estimated.
+: Here's a simple formula for converting a 2.3.11 monzo to ups and downs:
+: (a, b, c) = c * (-5, 1, 1) + (a + 5c, b - c) = c ups (or -c downs) + pythagorean interval
+: The pythagorean intervals are named conventionally as M2, m3, etc. So (0, -2, 1) = ^m3
+: Here's simple formulas for converting an upped or downed pythagorean interval to a monzo:
+: x ups + (a, b) = (a - 5x, b + x, x)
+: x downs + (a, b) = (a + 5x, b - x, -x)
+: Here's simple formulas for adding together two upped/downed intervals:
+: [x ups + (a, b)] plus [y ups + (c, d)] = (x+y) ups + (a + c, b + d)
+: [x ups + (a, b)] plus [y downs + (c, d)] = (x-y) ups + (a + c, b + d)
+: You don't even need formulas for this, actually. You just add up the pythagorean intervals as usual, then add in the ups and downs. Adding an interval to a note works the same way, as does finding the interval between two notes.
+: Here's the 2.3.11 lattice, with a vertical step equal to 33/32:
+<tt>
+ ^^F  ^^C  ^^G  ^^D  ^^A  ^^E  ^^B
+  ^F   ^C   ^G   ^D   ^A   ^E   ^B
+   F    C    G    D    A    E    B
+  vF   vC   vG   vD   vA   vE   vB
+ vvF  vvC  vvG  vvD  vvA  vvE  vvB
+</tt>
+: Each row is a chain of 5ths. The top row is the double-up row, next is the up row, next plain, next down, next double-down.
+: Another version of the lattice, with vertical steps of 11/8:
+<tt>
+ ^^Eb ^^Bb ^^F  ^^C  ^^G  ^^D  ^^A
+  ^Bb  ^F   ^C   ^G   ^D   ^A   ^E
+   F    C    G    D    A    E    B
+  vC   vG   vD   vA   vE   vB   ^F#
+ vvG  vvD  vvA  vvE  vvB  vvF# vvC#
+</tt>
+: Another version, with 1/1 - 11/9 - 3/2 and 1/1 - 27/22 - 3/2 triads forming triangles.
+<tt>
+ ^^Fb ^^Cb ^^Gb ^^Db ^^Ab ^^Eb ^^Bb
+     ^Ab  ^Eb  ^Bb  ^F   ^C   ^G   ^D
+   F    C    G    D    A    E    B
+     vA   vE   vB   vF#  vC#  vG#  vD#
+ vvF# vvC# vvG# vvD# vvA# vvE# vvB#
+</tt>
+: See how simple and clear it all is? Everything follows directly from ^1 = 33/32. So it's quite possible to have a very simple nomenclature for everything.
+: You have Alpharabian, Betarabian, Paramajor, Paraminor, Greater Neutral, Lesser Neutral, Supraminor and Submajor. And from your previous comments, Rastmic, Birastmic, and Trirastmic. Your nomenclature is way more complicated than it needs to be.
+: I've read what you've written several times and I still have no idea which parts of the lattice are Alpharabian, which are Betarabian, and which are neither. I also have no idea how to add together two intervals, or what note I get from adding an interval to a note, or how to name the interval between two notes. I suspect formulas for those things would be impossible.
+: So unfortunately, I don't see much point on working with you to improve your nomenclature. Because my first suggestion would be to drastically simplify it. We seem to have fundamentally different approaches. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 01:45, 26 November 2020 (UTC)