Homothetic just intonation: Difference between revisions
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Homothetic just intonation is a kind of extended [[just intonation]] conceived by Sui-hin Mak. The term 'homothetic' refers to the [[wikipedia:Homothetic_center#Computing_homothetic_centers|homothetic formula]] '''x₀ = (r₂x₁ + r₁x₂) / (r₁ + r₂)'''. The | Homothetic just intonation is a kind of extended [[just intonation]] conceived by Sui-hin Mak. The term 'homothetic' refers to the [[wikipedia:Homothetic_center#Computing_homothetic_centers|homothetic formula]] for circles. The tuning aims at producing the pitches between notes of an existing prime limit JI pitch collection. | ||
Circles are drawn at all points of the existing pitches as their centres, with its size determined by its prime factors. The homothetic formula '''x₀ = (r₂x₁ + r₁x₂) / (r₁ + r₂)''' is used to find the intersection of common tangents of two given circles. The new pitch between two successive existing pitches is determined by the homothetic centre of the two circles. | |||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|+Octave-equivalent 31-tone homothetic just scale generated by 11-limit JI | |||
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! frequency | ! frequency | ||