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Entries found for search: tonic

syntonic comma :The error arising in any just intonation, due to the fact that the octave is incompatible with the simple frequency ratios of the intervals of the diatonic scale. If is the frequency of the tonic C, the first sixth produces A, with a frequency of . In going to D, an interval of a fourth is required, and this is a frequency ratio of , so its frequency will be of A, which is of , or , which is . The descending fifth gives G, at a frequency of = . The last fifth results in the tonic, C, with a frquency of = . This discrepancy is called the syntonic comma, and is equal to about one-fourth of a half-step. It results in the fact that, after the above simple five-chord progression, the tonic is no longer at the same frequency at which it started. Intervals of major thirds are not commensurate with a perfect fifth, the difference being the syntonic comma. The following integer equation must, therefore, be false for all integers:

where X, Y, n, and m are integers, and is the frequency of the tonic. The left-hand side represents successive steps of musical intervals, and the right-hand side represents octave transpositions. It can be shown that this equation can never be satisfied. See also the diatonic comma."

pentatonic : A scale in which the octave is divided into five notes.

tonic : The reference (lowest) pitch on which a musical scale is built, i.e., the "do" of do-re-mi. It is defined in terms of the musical note rather than in terms of absolute frequency. For example, if one changes the key of a musical selection from C to AB this is a change of the tonic from the note C to the note AB..

diatonic : A musical scale of eight notes spanning one octave, consisting of an ascending pattern of two whole-steps, a half-step, three whole-steps and another half-step. There are two types of diatonic scale in common use in western music: the diatonic major scale and the diatonic minor scale. Music which includes notes outside of the diatonic in which the piece is written is said to be chromatic.

diatonic comma : After playing the Circle of Fifths, i.e., twelve ascending perfect fifths, followed by seven descending octaves, the pitch discrepancy between the ending note and the starting note is called the diatonic comma, or the Comma of Pythagoras. This discrepancy amounts to a little over 1%, or about one-sixth of a half-step and gives rise to various temperaments in an attempt to distribute the error as harmoniously as possible. See scale construction, syntonic comma.

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