Microtheory

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.......There are an infinite number of ways to choose your tonal resources.......

( John Starrett )

 - A model for tuning systems classification

 - Some tuning models

 - About 24-EDO

- Extended sori-koron microtonal notation  for 96-EDO based on Ali-Naghi Vaziri's 24-EDO notation system

A model for hexatonic scales

 

                                Systems and Tuning 

 

System                                           

The world is full of sounds , in a range of musical to noise.All two musical sounds which can be used in melodic lines can make interval. now , we can arrange intervals to make scale , mode , maqam , dastgah and ......... to satisfy musical ( melodic and harmonic )aesthetics.

Musical aesthetics is a very important factor in selecting intervals with their specific melodic and harmonic functions to make a tuning system.

What is tuning system? in wikipedia , we can see meaning of system :

 System (from the Latin (systēma), and this from the Greek σύστημα (sustēma)) is an assemblage of elements comprising a whole, and that each element is related to other elements. Any element which has no relationship with any other element of the system, cannot be a part of that system. A subsystem is then a set of elements which is a proper subset of the whole system."                    

 Now , we see that in a tuning system , each degree of system is related to other degrees and elements. The realtioship between degrees depends on how we want to make system.some systems are mathematical models and some others , acoustical. If we accept a tuning system as a set of degrees , then scales , modes and .... besed on this system , are sub-systems and sub-sets.

 Tuning

Tuning is the process of producing or preparing to produce a certain pitch in relation to another, usually matched at the unison but often at some other interval relationship. Out of tune refers to a pitch that is too high or too low, corresponding to sharp or flat, respectively. Different methods of sound production require different methods of adjustment:

         Tuning to a pitch with one's voice is called matching pitch and is the most basic skill learned in ear training.

         Turning the pegs on a guitar (on the machine head) or violin to increase or decrease the tension on the strings so as to make them higher or lower in pitch.

         Modifying the length or width of the tube of a wind instrument, brass instrument, pipe, bell, or similar instrument to adjust the pitch.

Some instruments do not have a regular harmonic series, and are known as inharmonic. This makes their tuning complicated, and usually compromised. The tuning of bells, for instance, is extremely involved.

Tuning may be done aurally by sounding two pitches and adjusting one of them to match or relate to the other. A tuning fork or electronic tuning device may be used as a reference pitch, though in ensemble rehearsals often a piano is used (as its pitch cannot be adjusted for each rehearsal). Symphony orchestras tend to tune to an A provided by the principal oboist.

Interference beats are used to objectively measure the accuracy of tuning. As the two pitches approach a harmonic relationship, the frequency of beating decreases. When tuning a unison or octave it is desired to reduce the beating frequency until it cannot be detected. For other intervals, this is dependent on the tuning system being used.

Harmonics may be used to check the tuning of strings which are not tuned to the unison. For example, lightly touching the highest string of a cello at halfway

down its length (at a node) while bowing produces the same pitch as doing the same one third of the way down its second highest string.

Tuning system

A tuning system is the system used to define which tones, or pitches, to use when playing music. In other words, it is the choice of number and spacing of frequency values which are used.

Due to the psychoacoustic properties of tones, various pitch combinations will sound more or less "natural" when used in combination. For example, a tone caused by a vibration twice the speed of another (the ratio of 1:2) forms the natural sounding octave. Another natural resonance found in musical scales the world over is the ratio of 1:3 (2:3 when octave reduced) which is often called a perfect fifth. More complex musical effects can be created through other relationships.

The creation of a tuning system is complicated because musicians want to make music with more than just a few differing tones. As the number of tones is increased, conflicts arise in how each tone combines with every other. Finding a successful combination of tunings has been the cause of debate, and has lead to the creation of many different tuning systems across the world. Each tuning system has its own characteristics, strengths and weaknesses.

(From : http://en.wikipedia.org/wiki/Musical_tuning)

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From :http://launch.groups.yahoo.com/group/tuning/message/67919 -George D. Secor

.....I believe I need to clarify the distinction between a scale and a tuning. I define a scale as a set of tones that may be used to write a melody, in which the tones are related by (more or less) specific interval-classes. A tuning is a set of tones for which specific frequencies or frequency-ratios (either rational or irrational) are given; tunings may be defined by one or more generating intervals, in which case they may consist of an indefinite number of tones.
Examples of scales are: 1) a diatonic major scale (either just or tempered), and 2) a pentatonic scale consisting of a single chain of fifths (exact size unspecified). Examples of tunings are Pythagorean tuning, 12-ET, 1/4-comma meantone temperament, 19-ET, 31-ET, 17-ET, etc. A diatonic or pentatonic scale is contained in each of those tunings, and those scales will sound somewhat different in each tuning.
Some scales (such as the Blackjack scale) are organized in such a way that they are capable of being played only in certain tunings, so the choice of a tuning will determine which scales are available, and vice versa -- or one's choice of tuning may be determined by how well a particular scale sounds in that tuning.
Generally, one will choose a scale with a particular tuning (or family of tunings) in mind, or one may devise (or choose) a tuning so that (or because) it in some way optimizes a particular scale.