Philip Pennance, Commutative Diagrams and the Construction of Musical Scales. Sept. 12, 2025. Philip Pennance, Guitar Chord Sequences Totally Ordered by Pitch, May 2026. Philip Pennance, A Mathematical Introduction to Melody, Aug. 11, 2026. Tables of Guitar Chords Philip Pennance, Guitar Chord Triads, Ordered by Pitch, May 2026. Philip Pennance, …

Brutal Analysis by Grok Ah, the 2022 Marco Curricular de Matemáticas from Puerto Rico’s Departamento de Educación. A bureaucratic masterpiece that takes the noble subject of mathematics — the one discipline built on irrefutable logic, precise definitions, deductive proof, and universal abstraction — and buries it alive under a mountain of mandated …

The Puerto Rico Mathematics Curriculum Framework Unidad 1: Fundamentos de Geometría

Under construction. See here for the mathematical theory behind these tables, G Major Closed Triads on Frets 1–12 in Ascending Pitch Order G Major Closed Triads with Bass Note on String 4 in Ascending Pitch Order G Major Closed Triads with Bass Note on String 5 in Ascending Pitch Order …

Agreement concerning basic definitions, models, and measurement procedures is an objective of good science. Below are some questions and a paper concerning GMST. It is left to the reader to ascertain if these answers by Grok are reasonable. Question 1. Consider, for example, the concept of length in a Galilean …

Restrictions on admissible changes of scale are often overlooked in science education. Ironically, this topic receives far more attention in philosophy, psychology, and sociology texts than in the natural sciences. In fact, it was the Harvard psychologist S.~S.~Stevens who introduced the now-classic taxonomy of measurement scales, classifying variables according to …

According to United Nations and Guttmacher Institute projections, there were approximately 19,087 live births, 34,745 deaths, and 17,510 abortions in Puerto Rico in 2025. The following graph shows the ratio of abortions to birth over time. Abortions caused by in-vitro fertilization procedures are not included. Since fertility per woman in …

el lunes 19 de enero  a las 10 AM  (Día Feriado del Dr. Martin Luther King)   frente a las Escalinatas Norte del Capitolio en San Juan, Puerto Rico.  Trae a tu familia y amigos. #PuertoRicoEsProVida

This article is intended as a minimal introduction to some basic musical ideas which fall within the intersection of mathematics and music. We discuss the science underlying the construction of Pythagorean and other tunings, giving mathematically clear definitions of the necessary musical terms. Careful distinction is made between the frequential …