South Bay Chapter
November Meeting:
Date: Tues. 11/12/2024
Time: 7:00 pm
Location:
Kawai America
2055 E. University
Rancho Dominguez CA 90220
In October the South Bay Chapter continued our ongoing temperament discussion with an excellent presentation from Ryan Ellison. Ryan gave a thorough explanation of "The Roadmap," a 3-step circular temperament pattern based on 4ths and 5ths. Ryan's clear explanation, followed by a demonstration of the temperament process, prompted helpful discussion and questions from newer techs as well as our veteran members.
Continuing our deep dive into temperament, our November meeting will feature a Zoom presentation by Fred Sturm from the Albuquerque Chapter. The meeting will take place at Kawai (as usual), and we will set-up a screen projector to display Fred's video and slides. Fred’s class is entitled, “A Brief Look at Temperament and Temperament History,” and is described as follows:
The problem of temperament arises from the incompatibility of "consonant" intervals: Octave (2:1), fifth (3:2), fourth (4:3), major third (5:4), and minor third (6:5).
We use an octave divided into twelve half steps. Three major thirds "sort of" equal an octave, but not quite. They fall short by over 41 cents. So every stack of three major thirds must be wide by about 41 cents in total, or about 12 cents each. Making any third more narrow means the other two thirds must be that much wider.
Tuning has typically been done via a series of fifths (eg, CG, GD, DA, AE). A series of four fifths like that example ends up producing a major third (CE) that is wide of a just (pure, beatless) major third by about 21 cents. (This wide major third is commonly called a "Pythagorean third"). That 21 cent difference is called a syntonic comma.
The predominant temperament for centuries (Renaissance through much of the Baroque) is called "mean tone." Music of the Renaissance favored major thirds, so they were tuned beatless. This was done by tuning a series of fifths that were ¼ of a syntonic comma (about 5 cents) narrow, in a series that went from E flat through G sharp. This system yields four stacks of major thirds, of which two will be just and the other 41 cents wide. Eg, CE, EG#, G#C. G#C cannot be used as AflatC, G sharp is definitely not A flat. Key signatures are limited to a maximum of two flats and three sharps.
The style of composition exemplified by J. S. Bach moved from key to key without limitation: it required that all notes could be used in every way (natural, sharp, flat, double sharp, double flat). This required a circular tuning that offered compromises, leading to adoption of equal temperament, in which every interval except the octave is "least bad" (eg, all major thirds equally wide)."