TUNING SYSTEMS, SOUND & FREQUENCIES
WHAT "MAKES" A TUNING SYSTEM?
A "Concert Pitch" is a tone used as REFERENCE for musical instruments to tune to. This tone / frequency does NOT tell us anything about the relationship between this tone and any other tone that might be used.
A "Tuning System" is the combination of: Concert Pitch (the reference point), the Musical Interval System (the range of notes within the system / the number of actual tones available to use) and the Temperament (the interval distances between the tones).
NOTE: Even though all (proper) tuning system can be explained / described using mathematical formulas, not every mathematical formula will "generate" a proper (harmonious) tuning system!
Concert pitch refers to the pitch reference to which a group of musical instruments are tuned for a performance. Concert pitch may vary from ensemble to ensemble, and has varied widely over musical history. In the literature this is also called international standard pitch. The reference note most commonly used is the "A" above middle C.
During historical periods when instrumental music rose in prominence (relative to the voice), there was a continuous tendency for pitch levels to rise. This "pitch inflation" seemed largely a product of instrumentalists' competing with each other, each attempting to produce a brighter, more "brilliant", sound than that of their rivals. This tendency was also prevalent with wind instrument manufacturers, who crafted their instruments to play generally at a higher pitch than those made by the same craftsmen years earlier.
"Pitch inflation" can also been looked at as the "acoustic loudness war". In modern times the "loudness" can be created with for example the use of "Compressors". But in the time before electric amplification and electronic tools existed, raising the pitch created a "louder" appearance sound-wise.
At the beginning of the 17th century, Michael Praetorius reported in his encyclopedic "Syntagma Musicum" that pitch levels had become so high that singers were experiencing severe throat strain and lutenists and violin players were complaining of snapped strings.
PITCH REFERENCE TOOLS:
Until 1711, musicians and directors had no clear reference point to tune their instruments. This all changed with the invention of the “tuning fork” in England by Royal trumpeter John Shore in 1711.
ROELS WORLD ARTICLES ABOUT CONCERT PITCH:
A tuning system has two main "elements": the "Music Interval System" and the "Temperament".
By musical interval system is meant a range of notes or musical intervals theoretically available to a composer. The qualification "theoretically" is important, as such systems could include notes or intervals which are not actually audible for human beings.
The most basic of distinctions among such systems is between open and closed systems, where a closed system has a finite set of possible musical intervals, and an open system has an infinite set.
More information: XenHarmonic
In musical tuning, a temperament is a system of tuning which slightly compromises the pure intervals of just intonation in order to meet other requirements of the system. Most instruments in modern Western music are tuned with the equal temperament system.
In Twelve-Tone Equal Temperament (12-TET or 12-EDO - EDO = Equal Divisions of the Octave) divides the octave into 12 equal parts, the width of a semitone, i.e. the frequency ratio of the interval between two adjacent notes, is the twelfth root of two:
There are many other Musical Temperaments (most more complicated then 12-TET), using various mathematical formulas to create other ratios then 1.059463. The most know Temperaments are the: Pythagorean Tuning, Meantone Temperament, Well Temperament, Just Intonation and Five-Limit Tuning.
ROELS WORLD ARTICLES ABOUT TEMPERAMENT
OTHER PITCH AND TUNING RELATED ARTICLES ON ROELS WORLD: