## Search found 1177 matches

Wed Feb 14, 2024 11:54 am
Forum: Linear Temperament notations
Topic: Negri temperament
Replies: 4
Views: 1424

### 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...
Thu Dec 28, 2023 7:41 pm
Forum: Linear Temperament notations
Topic: Negri temperament
Replies: 4
Views: 1424

### 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...
Mon Dec 18, 2023 6:50 pm
Forum: Mathematical theory
Topic: James algebra provides a clever notation for elementary functions
Replies: 3
Views: 4276

### 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 ...
Thu Dec 07, 2023 12:25 pm
Forum: Mathematical theory
Topic: James algebra provides a clever notation for elementary functions
Replies: 3
Views: 4276

### 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...
Wed Dec 06, 2023 3:11 pm
Forum: Mathematical theory
Topic: James algebra provides a clever notation for elementary functions
Replies: 3
Views: 4276

### 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...
Tue Dec 05, 2023 11:33 pm
Forum: Mathematical theory
Topic: James algebra provides a clever notation for elementary functions
Replies: 3
Views: 4276

### 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...
Mon Sep 04, 2023 11:50 pm
Forum: The lounge
Topic: aperiodic monotiles
Replies: 5
Views: 8001

### 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...
Wed Aug 30, 2023 11:40 pm
Forum: The lounge
Topic: aperiodic monotiles
Replies: 5
Views: 8001

### 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...
Wed Aug 30, 2023 11:10 pm
Forum: The lounge
Topic: aperiodic monotiles
Replies: 5
Views: 8001

### 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...
Sun Aug 27, 2023 5:34 pm
Forum: The lounge
Topic: aperiodic monotiles
Replies: 5
Views: 8001

### 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...