Bozuji tuning: Difference between revisions
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== Summary == | == Summary == | ||
Bozuji tuning is a [[5-limit|5-limit just intonation]] tuning set with specified intervals proposed by [[Bostjan Zupancic]] ('''Bo'''stjan '''Zu'''pancic '''J'''ust '''I'''ntonation), which are closely related to the tones available in meantone temperament. The approach to generating the intervals is somewhat unique, as all intervals were generated by choosing adaptive step sizes (which have been shown to work with software keyboards) and stepping through scales with different tonalities. The tuning contains 23 intervals per [[octave]], and it is intended to be an expansion of [[wikipedia:Ptolemy's_intense_diatonic_scale|Ptolemy's Intense Diatonic Scale]]. | Bozuji tuning is a [[5-limit|5-limit just intonation]] tuning set with specified intervals proposed by [[Bostjan Zupancic]] ('''Bo'''stjan '''Zu'''pancic '''J'''ust '''I'''ntonation), which are closely related to the tones available in meantone temperament. The [[Bathomotonic|approach]] to generating the intervals is somewhat unique, as all intervals were generated by choosing adaptive step sizes (which have been shown to work with software keyboards, see AdaptiveJI) and stepping through scales with different tonalities. The tuning contains 23 intervals per [[octave]], and it is intended to be an expansion of [[wikipedia:Ptolemy's_intense_diatonic_scale|Ptolemy's Intense Diatonic Scale]]. | ||
== Interval Base == | == Interval Base == | ||
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== Step Sizes == | == Step Sizes == | ||
Ptolemy's work generated a scale with seven degrees and used three step sizes between adjacent intervals. Zarlino later expanded Ptolemy's scale into a more generalized 5-limit just intonation tuning with four step sizes. This approach proposes a matrix of two kinds each of five types of step sizes. | Ptolemy's work generated a scale with seven degrees and used three step sizes between adjacent intervals. Zarlino later expanded Ptolemy's scale into a more generalized 5-limit just intonation tuning with four step sizes. This approach proposes a matrix of two kinds each of five types of step sizes. | ||
The "type" of the step is determined by the musical context and the desired tonality of the interval after the step versus the tonality of the proceeding step. For example, going from the perfect interval to a major interval is achieved by using a whole step, whilst a minor interval is achieved by using a half step, a diminished interval by a quarter step, and an augmented interval by a grown step. The "kind" of step is determined by the positions of the intervals within the scale, in order to minimize the creation of new intervals by accounting for commas and such. | |||
The two kinds of step sizes are lesser steps and greater steps. The lesser steps being indicated with a lowercase letter and the greater steps indicated with an uppercase letter. The five types of step sizes are: quarter (q), half (h), whole (w), grown (g), and expanded (x). | The two kinds of step sizes are lesser steps and greater steps. The lesser steps being indicated with a lowercase letter and the greater steps indicated with an uppercase letter. The five types of step sizes are: quarter (q), half (h), whole (w), grown (g), and expanded (x). | ||
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In Ptolemy's system, whole and half steps were used to step through the major diatonic scale. In this system, the steps are used to generate scales based on the choice of which step to use. If you think of diminished, minor, major/perfect, then augmented scale degrees as decreasing in "flatness," or increasing in "sharpness," relative to one another, then, broadly speaking, quarter steps are used to increase flatness, half steps are used to either increase flatness or maintain flatness, whole steps are used to generally maintain flatness (might change by one unit of flatness in either direction, though), grown steps are used to decrease flatness, and expanded steps are used to greatly decrease flatness. | In Ptolemy's system, whole and half steps were used to step through the major diatonic scale. In this system, the steps are used to generate scales based on the choice of which step to use. If you think of diminished, minor, major/perfect, then augmented scale degrees as decreasing in "flatness," or increasing in "sharpness," relative to one another, then, broadly speaking, quarter steps are used to increase flatness, half steps are used to either increase flatness or maintain flatness, whole steps are used to generally maintain flatness (might change by one unit of flatness in either direction, though), grown steps are used to decrease flatness, and expanded steps are used to greatly decrease flatness. | ||
Such a general set of steps is difficult to notate using the more familiar (to those more steeped in xenharmonic music theory) symbols akin to "L" and "s" (see [[MOS scale|MOS]]), simply because there are necessarily multiple kinds and multiple types of steps. | |||
The general approach of defining step sizes and generating scales based off of those sizes is called the [[Bathomotonic|"bathomotonic approach"]]. | |||
== Generating the Intervals from Both Step Sizes and From Simplest Ratios == | == Generating the Intervals from Both Step Sizes and From Simplest Ratios == | ||
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[[Category:23-tone]] | [[Category:23-tone]] | ||
[[Category:Ergotonic]] | [[Category:Ergotonic]] | ||
[[Category:Bathomotonic]] | |||