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The equal-tempered version of the Bohlen–Pierce scale consists of the ratio 3:1 (1902 cents) conventionally a perfect fifth plus an octave (that is, a perfect twelfth), called in this theory a tritave (play ⓘ), and split into 13 equal parts.
Musical temperament. Comparison of notes derived from, or near, twelve perfect fifths (B ♯). In musical tuning, a temperament is a tuning system that slightly compromises the pure intervals of just intonation to meet other requirements. Most modern Western musical instruments are tuned in the equal temperament system.
12 equal temperament (12-ET) [a] is the musical system that divides the octave into 12 parts, all of which are equally tempered (equally spaced) on a logarithmic scale, with a ratio equal to the 12th root of 2 (12 √ 2 ≈ 1.05946).
To satisfy equal temperament and inharmonicity in piano tuning, complex and subtle adjustments are made. This paper explores the theoretical and practical details and challenges involved in piano tuning.
In this section we’ll look at an alternative method for constructing scales that dates back to Pythagoras in the sixth century B. C. – just tempered intonation – a tuning in which frequency intervals are chosen based upon their harmonic relationships. First let’s look more closely and the equal tempered scales as a point of comparison.
The equal tempered scale is the common musical scale used at present, used for the tuning of pianos and other instruments of relatively fixed scale. It divides the octave into 12 equal semitones. It is common practice to state musical intervals in cents, where 100¢ is defined as one equal tempered
A precise equal temperament is possible using the 17th-century Sabbatini method of splitting the octave first into three tempered major thirds. This was also proposed by several writers during the Classical era.
