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What’s New 📩

• Milton Babbitt Occasional Variations
• Occasional Variations
• Occasional Variation

The allowances for variations are relative to the maximum permissible design pressure for the system. The allowances for variations are not used in sustained (longitudinal), occasional (wind, earthquake), or displacement (thermal expansion) stress evaluations. They are only used in pressure design. High variation wood floors come in an array of colors, from dark to light, and is available in both thin and wide planks. Like other wood flooring, high variation floors are easy to clean and maintain, requiring no sealing and just a sweep and occasional mop. A wide range of factors influences blood pressure, including anxiety, stress, and medications. High blood pressure can have severe complications, such as a heart attack or stroke. The other two works serve as variations with the string quartet form - 'Occasional Variations,' a 9'54 work for synthesizer from 1968-71, and 'Composition for.

Title

Phonetic Distance Between Words with Application to the International Spelling Alphabet 🔠

Summary

This post develops a robust quantitative method for measuring the distance (or difference) between: individual phonemes accounting for their type (consonant, vowel or diphthong) and their duration two words (i.e. two sequences of phonemes) a group of words

It describes how discrete convolution can be used to determine the distance between words which naturally accommodates variations in phoneme duration. Existing International Spelling Alphabet and US Phonetic Alphabet schemes are compared using several quality measures. Alternative word sets are generated that out perform the existing schemes using these quality measures.

Post Summary

Games 🏆

Bridge ♠️♥️♦️♣️

Title

Bridge Hand Probability Analysis

Summary

Considers the probability of holding various types of hand after the initial deal and before any other information is available. Several standard tables are generated that represent some key aspects of the game. A general algorithm is developed that allows a broad range of hand probabilities to be calculated including suit distribution, High Card Points (HCP) and honour holdings.

Downloads (see full post for context)

◻︎ Suit Distribution Probabilities (csv)

◻︎ High Card Point (HCP) Probabilities (csv)

◻︎ Suit Distribution by HCP (csv)

◻︎ HCP by Number of Aces (csv)

◻︎ HCP by Keycards (csv)

Title

Bridge Partnership (Two Hand) Probability Analysis

Summary

Extends the previous post on Bridge probability analysis from one hand to two hands that form a partnership. Various probability tables are generated for suit distributions and HCP holdings for two hands.

Downloads (see full post for context)

◻︎ Suit Distribution Probabilities for Two Combined Hands (csv)

◻︎ High Card Point (HCP) Probabilities for Two Combined Hands (csv)

◻︎ High Card Point (HCP) Probabilities for Two Separate Hands (csv)

Tic-Tac-Toe

Title

Tic-Tac-Toe Analysis using Clojure (Part 1)

Summary

Analysis of the Tic-Tac-Toe (aka Noughts and Crosses) game tree using Clojure. Shows how it can be significantly reduced in size by accounting for winning positions, duplications, symmetries and forced moves. The analysis “discovers” the notion of forked positions and that there are only three drawn positions. There are also game tree visualisations.

Downloads (see full post for context)

◻︎ Full Tic-Tac-Toe tree diagram (pdf)

◻︎ Corner first move branch (pdf)

◻︎ Edge first move branch (pdf)

◻︎ Centre first move branch (pdf)

Title

Tic-Tac-Toe Analysis using Clojure (Part 2)

Summary

Analysis of Tic-Tac-Toe (aka Noughts and Crosses) player strategy using Clojure. Building on Part 1, it develops opening theory, position evaluation and a “reduced” game tree that captures the essence of the game.

Downloads (see full post for context)

◻︎ Scored Reduced Game Tree – excludes duplicate nodes but has more cross links (pdf)

◻︎ Scored Reduced Game Tree – removes all cross links but has some nodes duplicated (pdf)

◻︎ Scored Reduced Game Tree – excluding symmetries and duplicates (pdf)

Miscellaneous 🗄

Milton Babbitt Occasional Variations

Title

Efficient Recursive Levenshtein (Edit) Distance Algorithm

Summary

A recursive algorithm for calculating the Levenshtein distance using an upper bound to significantly improve performance. Includes an implementation in Clojure with comparative benchmarks. An iterative “matrix” implementation is also included.

Title

High Quality HTML Tables using Text Only Layouts

Summary

A proposed specification, and basic Clojure implementation, is provided to create HTML tables from text only input. CSS inline styling of table HTML elements, including individual rows, columns and cells, is supported, as well as rowspan and colspan. The resulting HTML is suitable for inclusion in Markdown documents, for example. The specification allows the generation of high quality tables for blogs and similar Web-based documentation.

Code

◻︎ Basic Clojure Implementation

Title

Alternative Star Trek Warp Speed Scale and Related Equations

Summary

This post: Proposes an alternative base-10 log Warp scale that more realistically reflects the vastness of the Universe and makes it more navigable in human time frames Developes Warp Power, Energy and Efficiency pseudo-equations by combining relativistic and classical mechanics which provides a robust mathematical underpinning of a universal Warp speed limit Introduces the notion of engine endurance to restrict the distance Warp capable ships can travel before engine maintenance is required

Title

Phonetic Distance Between Words with Application to the International Spelling Alphabet 🔠

Summary

This post develops a robust quantitative method for measuring the distance (or difference) between: individual phonemes accounting for their type (consonant, vowel or diphthong) and their duration two words (i.e. two sequences of phonemes) a group of words

It describes how discrete convolution can be used to determine the distance between words which naturally accommodates variations in phoneme duration. Existing International Spelling Alphabet and US Phonetic Alphabet schemes are compared using several quality measures. Alternative word sets are generated that out perform the existing schemes using these quality measures.

In the past, Babbitt has always been the Big Scary Monster of 20th Century American music (not exactly a catchy nickname), though increasingly his reputation has risen through the good work of people who have actually heard his music.
In the 2nd (1952) and 6th (1993) string quartets (the real highlights of the disc, in my opinion), the ghost of Romanticism is constantly making it's presence felt. Babbitt's sonic palette in these quartets is conservative, alternating between bowed and plucked notes — no col legno, string snapping or rapping the side of the instrument here. The effect is not one of a conscious regression or hearkening to the past, but rather one feels that here Babbitt has absorbed and sublimated an entire history of the string quartet genre (one that has become in the past century even more of a cornerstone than the symphony). There are constant whisperings or 'memories' of tonality, happening almost as if by coincidence — like drifting clouds converging to form a familiar shape. More than 40 years separate the two quartets, but little obvious change in style can be discerned. It is almost as if Babbitt is (perhaps heretical to say!) a modern day Fauré, writing music that is solely his own long after it has become unfashionable.

Occasional Variations

The disc's title piece, Occasional Variations (1968-71), has suffered the same fate as other pieces of this genre — it sounds extremely dated. Even so, the pure timbres of the ancient synthesizer sound charming to these ears, and give one the feeling of listening directly to the score, free of the 'vagaries' of performance — similar to a MIDI transcription of a piece, but more interesting because of the extremely synthetic nature of the sounds.
Where in the two string quartets, Babbitt has sublimated a history of quartet writing, in Composition for Guitar (1984) it is the folk music of Spain and traditional jazz playing that is on display. Flamenco-like strumming alternates with softly plucked notes in a bed of silence in a way that is meditative without devolving into mere dinner table ambience (if indeed it is at all possible for music this abstract to do so!)

Occasional Variation

This disc is my introduction to this reputedly 'difficult' composer, but it certainly won't be the last. I'd recommend this to anyone interested in music that is challenging, but eminently rewarding.