Beethoven in the temperaments-historical tunings on the modern concert grand.
"Temperament" is both the process and result of making slight changes to the pitches of a pure musical scale, so that the octave may be conveniently divided into a usable number of notes and intervals. In the history of Western music's 12-note octave tradition, there have been several, fundamentally different forms of temperament applied to the developing keyboard. Music suffers when performed in a tuning that is different than that which the composer used in its creation...
tuning, pianos, pianos beethoven, temperaments
The biological calendar that predicts the season for birth is a lunar calendar that, in humans, has somehow become the diatonic scale of music. A four-way correlation will be shown between the Meton lunar calendar, Fibonacci’s rabbit sequence, coral spawning record and both major and natural minor diatonic scales of music....
There must be a strong psychoacoustical basis for stability conditions. For pitch collections, this entails intervals that proceed gradually from very small to comparatively large frequency ratios.
It seems likely Lerdahl's point here is that intervals proceed gradually from small frequency ratios to larger frequency ones rather than suddenly. The classic Just diatonic scale does this and, to a lesser extent, so does the Pythagorean scale....
A practice in the mathematics of tuning instruments and analyzing scales.
The Chrysalis Foundation.
We are a 501(c)3 nonprofit arts and education foundation that supports the work of master builder, writer, and composer Cris Forster, whose original acoustic instruments facilitate new tunings in just intonation.
Cris Forster, Chrysalis Foundation, Musical Mathematics, just intonation, intonation, new music, microtone, microtonal music, tuning, scales, harmonic series, temperament, meantone, music history, tuning history, acoustic instrument, instrument construction, musical acoustics, musical glass, simple flute, marimba, canon, Marin Mersenne, Max F. Meyer, Harry Partch, Al-Jurjani, Ishaq Al-Kindi, Al-Farabi, Bharata, Ramamatya, Philolaus, Euclid, Safi Al-Din, Bartolomeo Ramis, Chris Forster.
The 8-Tone Quarto-Modes Concept is a special study into the diminished and its application for mainstream jazz players, advanced improvisators, and notational composers. Ten years in development, and written by an internationally acclaimed musician for musicians already familiar with standard scaletone harmony, it is a new paradigm for further possibilities in jazz and improvisational music.
jazz, music theory, improvised music.
8-Tone Quarto-Modes Concept by G. F. Mlely, new music theory for
jazz improvisator.
Music Theory for Songwriters: Many songwriters have questions about chords and how they flow. This site helps to unlock the mysteries of music theory.
Part One - Scales, Note Numbers, Roman Numerals
Part Two - I, IV, and V chords, Keys, Chords in D
Part Three - ii, iii, and vi chords, The Simple Map
Part Four - Chord Variations, Complex Chords
Part Five - Secondary Chords and The Big Map
Chord Charts and Maps - All 12 Maps plus 24 pages
of keyboard chord diagrams.
Part Six - Major Scales - I
Part Seven - Major Scales - II
Part Eight - Major Scales - III
Part Nine - The Circle Of Fifths
1st Steps in Keyboard - Keyboard Basics
Part Ten - Understanding Modes
Part Eleven - Minor Keys - I
Part Twelve - Minor Keys - II ...