Understanding Basic Music Theory - Catherine Schmidt-Jones [87]
It should also be noted that some music traditions around the world do not use the type of precision tunings described above, not because they can't, but because of an aesthetic preference for wide tuning. In these traditions, the sound of many people playing precisely the same pitch is considered a thin, uninteresting sound; the sound of many people playing near the same pitch is heard as full, lively, and more interesting.
Some music traditions even use an extremely precise version of wide tuning. The gamelan orchestras of southeast Asia, for example, have an aesthetic preference for the "lively and full" sounds that come from instruments playing near, not on, the same pitch. In some types of gamelans, pairs of instruments are tuned very precisely so that each pair produces beats, and the rate of the beats is the same throughout the entire range of that gamelan. Long-standing traditions allow gamelan craftsmen to reliably produce such impressive feats of tuning.
Further Study
As of this writing:
The Just Intonation Network has much information about Just Intonation, including some audio examples.
Kyle Gann's An Introduction to Historical Tunings is a good source about both the historical background and more technical information about various tunings. It also includes some audio examples.
The Huygens-Fokker Foundation has a very large on-line bibliography of tuning and temperament.
Musemath has several animations illustrating equal temperament and the math necessary to understand it.
Alfredo Capurso, a researcher in Italy, has developed the Circular Harmonic System (c.ha.s), a tempered tuning system that solves the wolf fifth problem by adjusting the size of the octave as well as the fifth. It also provides an algorithm for generating microtonal scales. You can read about it at the Circular Harmonic System website or download a paper on the subject. You can also listen to piano performances using this tuning by searching for "CHAS tuning" at YouTube.
Note
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6.3. Modes and Ragas*
Note
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Introduction
In many music traditions, including Western music, the list of all the notes that are expected or allowed in a particular piece of music is a scale. A long tradition of using scales in particular ways has trained listeners to expect certain things from a piece of music. If you hear a song in C major, for example, not only will your ear/brain expect to hear the notes from the C major scale, it will expect to hear them grouped into certain chords, and it will expect the chords to follow each other in certain patterns (chord progressions) and to end in a certain way (a cadence). You don't have to have any musical training at all to have these expectations; you only need to have grown up in a culture that listens to this kind of music.
The expectations for music in a minor key are a little different than for music in a major key. But it is important to notice that you can move that song in C major to E major, G flat major, or any other major key. It will sound basically the same, except that it will sound higher or lower. In the same way, all minor keys are so alike that music can easily be transposed from one minor key to another. (For more on this subject, see Major Scales, Minor Scales, Scales that aren't Major or Minor, and Transposition.)