User:Jbcristian/The Average Tuning System: Difference between revisions
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While some files span multiple octaves or include [[Subharmonic|non-reduced intervals below the unison]], these instances are relatively rare. Most are periodic tunings in alignment with the [[octave]], the archive's most common interval. (Note: rather than relatively rare, some are intentionally wrong, since scala file definition specifies the omission of the 1, and conclude with the equave, implementations may totally ignore those values) | While some files span multiple octaves or include [[Subharmonic|non-reduced intervals below the unison]], these instances are relatively rare. Most are periodic tunings in alignment with the [[octave]], the archive's most common interval. (Note: rather than relatively rare, some are intentionally wrong, since scala file definition specifies the omission of the 1, and conclude with the equave, implementations may totally ignore those values) | ||
In a direct analysis of the files, the first key from each tuning, totaling 87,558 notes, reveals the octave as the most common, appearing with its exact representation in 4,481 total files and with close variations in practically all tunings. | In a direct analysis of the files, the first key from each tuning, totaling 87,558 notes, reveals the octave as the most common, appearing with its exact representation in 4,481 total files and with close variations in practically all tunings. | ||
The [[perfect fifth]] emerges as the second most popular interval, succeeded by the [[perfect fourth]] and major third. | The [[perfect fifth]] emerges as the second most popular interval, succeeded by the [[perfect fourth]] and major third. | ||
[[File:Scala archive intervals.jpg|thumb|none|Distribution of intervals. The two graphics depict identical data. The first graphic displays both vertical and horizontal axes on a linear scale, while the second utilizes a logarithmic scale for the vertical axis. This logarithmic scale highlights intervals that occur only once, significantly beyond the octave, as well as those appearing below a value of 1.|381x381px]] | |||
{| class="wikitable" | {| class="wikitable" | ||
|+Top 5 Intervals | |+Top 5 Intervals | ||
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When calculating all added tones, the complete interval matrix only for the octave-ending tunings yields a total of 2,641,310 intervals, and the list of the most frequent remains largely unchanged. | When calculating all added tones, the complete interval matrix only for the octave-ending tunings yields a total of 2,641,310 intervals, and the list of the most frequent remains largely unchanged. | ||
[[File:Intervals scan comparision.jpg|thumb|The two graphics present distinct datasets. The first graphic represents the scan of the initial key in each file, while the second illustrates the scan subsequent to computing all matrices. Both graphics showcase the top 17 intervals, which exhibit remarkable similarity. Each graph encompasses a single octave, with both vertical and horizontal axes set to a logarithmic scale.]] | [[File:Intervals scan comparision.jpg|thumb|none|The two graphics present distinct datasets. The first graphic represents the scan of the initial key in each file, while the second illustrates the scan subsequent to computing all matrices. Both graphics showcase the top 17 intervals, which exhibit remarkable similarity. Each graph encompasses a single octave, with both vertical and horizontal axes set to a logarithmic scale.|376x376px]] | ||
''(Why is it important to calculate the interval matrix and added tones to determine the most common intervals?'' | ''(Why is it important to calculate the interval matrix and added tones to determine the most common intervals?'' | ||
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The graph represents the tuning space horizontally and accumulates identical exact repetitions vertically. | The graph represents the tuning space horizontally and accumulates identical exact repetitions vertically. | ||
[[File:Truncation comparision.jpg|thumb|Both graphics portray identical data, but the second one illustrates the data after truncation (with a maximum error of approximately 0.2 cents). Both visuals display the top 17 intervals, which remained consistent even after truncation. This reduction resulted in 242,538 unique intervals being compressed to just 9,997. The logarithmic view in the graphic also highlights the uneven definition loss of musical notes post-truncation, which was executed on the decimal data.]] | [[File:Truncation comparision.jpg|thumb|none|Both graphics portray identical data, but the second one illustrates the data after truncation (with a maximum error of approximately 0.2 cents). Both visuals display the top 17 intervals, which remained consistent even after truncation. This reduction resulted in 242,538 unique intervals being compressed to just 9,997. The logarithmic view in the graphic also highlights the uneven definition loss of musical notes post-truncation, which was executed on the decimal data.|409x409px]] | ||
Progressively truncating the notes in this way, doesn't significantly alter popularity, even a 2-cent error proved insufficient to dislodge any peak prominence. | Progressively truncating the notes in this way, doesn't significantly alter popularity, even a 2-cent error proved insufficient to dislodge any peak prominence. | ||
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The first ~500 most frequent intervals comprise just, rational, and integer ratio intervals before cent-defined intervals like the octave at 1200 cents appear. | The first ~500 most frequent intervals comprise just, rational, and integer ratio intervals before cent-defined intervals like the octave at 1200 cents appear. | ||
====== How to: ====== | ======How to:====== | ||
The program developed for this analysis is open-source and available at [LINK]. It's designed for straightforward usage—simply load any .scl file or files, and it will promptly conduct and showcase statistics on them. The analysis comes in two modes: 'direct' examines files as they are, focusing on the first key, while 'full' generates interval matrices for all files. Notably, the 'full' analysis uses a fixed equave of 2:1, a setting implemented after discovering that 95% of the database concludes with a 2:1 equave. This equave parameter can be adjusted within the code for further exploration and customization." | The program developed for this analysis is open-source and available at [LINK]. It's designed for straightforward usage—simply load any .scl file or files, and it will promptly conduct and showcase statistics on them. The analysis comes in two modes: 'direct' examines files as they are, focusing on the first key, while 'full' generates interval matrices for all files. Notably, the 'full' analysis uses a fixed equave of 2:1, a setting implemented after discovering that 95% of the database concludes with a 2:1 equave. This equave parameter can be adjusted within the code for further exploration and customization." | ||