Search found 1177 matches

by Dave Keenan
Wed Feb 14, 2024 11:54 am
Forum: Linear Temperament notations
Topic: Negri temperament
Replies: 4
Views: 1581

Re: Negri temperament

Sorry Herman. I somehow missed your previous post until now. The F:\!/: notation does seem simpler, at least in those few bars. But I'd hate for the decision to be forced on you by the lack of a symbol for +11g (175 ¢ when the generator is 125 ¢, i.e. in 48edo). The only suggestion I have for +11g i...
by Dave Keenan
Thu Dec 28, 2023 7:41 pm
Forum: Linear Temperament notations
Topic: Negri temperament
Replies: 4
Views: 1581

Re: Negri temperament

Good to hear from you, Herman. I agree those are valid, except I get -18g, not +11g, for :(|||~: . One different suggestion I have is to use :/|\: for +10g, based on extending the mapping of the 124 to 126 cent generator to ⟨ 0 -4 3 -2 14]. :/|\: is used in 48edo which supports Negri temperament. Th...
by Dave Keenan
Mon Dec 18, 2023 6:50 pm
Forum: Mathematical theory
Topic: James algebra provides a clever notation for elementary functions
Replies: 3
Views: 4372

Re: James algebra provides a clever notation for elementary functions

A Unicode text version using brackets We don't always have access to MathJax or LaTeX. It would be good to still be able to write James algebra expressions in plain Unicode text in a way that can be mixed with traditional algebra. To do this, we need pairs of brackets that are never or rarely used ...
by Dave Keenan
Thu Dec 07, 2023 12:25 pm
Forum: Mathematical theory
Topic: James algebra provides a clever notation for elementary functions
Replies: 3
Views: 4372

Re: James algebra provides a clever notation for elementary functions

\def \ex #1{\enclose{top left}{#1} \, } \def \lo #1{\enclose{bottom left}{#1} \, } \def \ph #1{\enclose{phasorangle}{#1} \, } \def \re #1{\enclose{angletop}{#1} \, } \def \no #1{\enclose{top right}{#1} \, } About the enclosure for reciprocal The "angletop" enclosure \re{x} used for recipr...
by Dave Keenan
Wed Dec 06, 2023 3:11 pm
Forum: Mathematical theory
Topic: James algebra provides a clever notation for elementary functions
Replies: 3
Views: 4372

Re: James algebra provides a clever notation for elementary functions

How to typeset the James algebra expressions The enclosures shown in the preceding post are provided by the <menclose> element of the MathML web standard. They are accessed via the \enclose macro in the MathJax dialect of the LaTeX mathematical typesetting language. MathJax is installed on this for...
by Dave Keenan
Tue Dec 05, 2023 11:33 pm
Forum: Mathematical theory
Topic: James algebra provides a clever notation for elementary functions
Replies: 3
Views: 4372

James algebra provides a clever notation for elementary functions

James algebra can simplify and illuminate the relationships between elementary algebraic functions and numbers. Here's a brief introduction to James algebra using a notation I devised in discussions with Douglas Blumeyer cmloegcmluin . The advantage of this notation, over Jeff James' bracket notati...
by Dave Keenan
Mon Sep 04, 2023 11:50 pm
Forum: The lounge
Topic: aperiodic monotiles
Replies: 5
Views: 8350

Re: aperiodic monotiles

What counts as a heterochiral tiling when we have two tile shapes? In Douglas's first article above, we chose not to go into this question, but Craig Kaplan has asked us to elaborate. Clearly there is no problem defining homochiral versus heterochiral when there is a single chiral tile shape. If th...
by Dave Keenan
Wed Aug 30, 2023 11:40 pm
Forum: The lounge
Topic: aperiodic monotiles
Replies: 5
Views: 8350

Re: aperiodic monotiles

Of course the heptagons and triangles were actually obtained from the hurtles, by starting from one end of the pair of colinear edges and skipping every other vertex. The non-convex 14-sided hurtle thereby becomes a convex 7-sided "lemon" and some space is left over in the form of 45° righ...
by Dave Keenan
Wed Aug 30, 2023 11:10 pm
Forum: The lounge
Topic: aperiodic monotiles
Replies: 5
Views: 8350

Re: aperiodic monotiles

I discovered that the following homochirally aperiodic tiling of "lemons and leaves", is derivable from the homochirally aperiodic hurtle tiling. The set consists of two convex polyhedra: a chiral irregular 7-gon and a 45° right triangle, with matching rules enforced by requiring continuit...
by Dave Keenan
Sun Aug 27, 2023 5:34 pm
Forum: The lounge
Topic: aperiodic monotiles
Replies: 5
Views: 8350

Re: aperiodic monotiles

Parameterizations The scheme we use above, where we morph smoothly from the chevron to the comet, by deriving 𝑎 and 𝑏 as the sine and cosine of a single parameter θ, is not the only way to do this, although it's hard to imagine a simpler way. On the diagram below: https://forum.sagittal.org/downloa...