Extended-diatonic interval names: Difference between revisions

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Microtonal theorist [[Aaron Andrew Hunt]] devised [http://musictheory.zentral.zone/huntsystem4.html the Hunt system], which includes interval name assignments for JI (just intonation) and edos based on [[41edo]]. Compared to Keenan's 72 interval names, Aaron's system includes 41. His system is based directly on 41-tET, and unlike Keenan's system, interval are given the name of the closest step of 41-tET, and no account is taken of the size of the edos fifth. In 41-tET, Major, minor, augmented and diminished intervals are those obtained through the approximately Pythagorean cycle of fifths. Intervals one step of 41-tET above these are given the prefix 'small', one step larger are given the prefix 'large', two steps smaller the prefix 'narrow' and two larger the prefix 'wide'. As a result, 5/4 is labelled a 'small major 3rd', or SM3 (not to be confused with a super major third, a label that does not exist in this system).

Neo-medieval ~~musicians~~ and early music historian and theorist [[Margo Schulter]] described her own [http://www.bestii.com/~mschulter/IntervalSpectrumRegions.txt interval naming scheme] built on approximations to JI intervals. Each interval names corresponds to an approximate size, and no particular ET is referenced. In her scheme middle major thirds range in size from 400-423 cents, and small major thirds from 372-400c. 5/4 is labelled a small major third, 81/64 a middle major third and 9/7 a large major third. Margo's scheme includes small, middle and large varieties of major, minor and neutral 2nds, 3rds, 6ths, 7ths; perfect fourth and fifths; and tritones, as well as a sub fifth and super fourth; a dieses and comma and an octave less dieses and comma; and ''interseptimals'', which correspond to intermediates, her name referencing the fact that they may each approximate two ratios of 7.

Neo-medieval musician and early music historian and theorist [[Margo Schulter]] described her own [http://www.bestii.com/~mschulter/IntervalSpectrumRegions.txt interval naming scheme] built on approximations to JI intervals. Each interval names corresponds to an approximate size, and no particular ET is referenced. In her scheme middle major thirds range in size from 400-423 cents, and small major thirds from 372-400c. 5/4 is labelled a small major third, 81/64 a middle major third and 9/7 a large major third. Margo's scheme includes small, middle and large varieties of major, minor and neutral 2nds, 3rds, 6ths, 7ths; perfect fourth and fifths; and tritones, as well as a sub fifth and super fourth; a dieses and comma and an octave less dieses and comma; and ''interseptimals'', which correspond to intermediates, her name referencing the fact that they may each approximate two ratios of 7.

In Hunt's system when used in 41-tET or JI diatonic interval arithmetic is conserved, but in other tunings it may not be, and Margo's system may not conserve diatonic interval arithmetic either. Both systems may be applied to arbitrary tunings, but the same intervals (defined, perhaps by a MOS scale) may not be given the same interval names across different tunings. [[User:PiotrGrochowski/Extra-Diatonic Intervals|Other]] size-based systems also exist, but are less thoroughly described and less well known. In all these systems, interval arithmetic is not conserved across all tunings.

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 Microtonal theorist [[Aaron Andrew Hunt]] devised [http://musictheory.zentral.zone/huntsystem4.html the Hunt system], which includes interval name assignments for JI (just intonation) and edos based on [[41edo]]. Compared to Keenan's 72 interval names, Aaron's system includes 41. His system is based directly on 41-tET, and unlike Keenan's system, interval are given the name of the closest step of 41-tET, and no account is taken of the size of the edos fifth. In 41-tET, Major, minor, augmented and diminished intervals are those obtained through the approximately Pythagorean cycle of fifths. Intervals one step of 41-tET above these are given the prefix 'small', one step larger are given the prefix 'large', two steps smaller the prefix 'narrow' and two larger the prefix 'wide'. As a result, 5/4 is labelled a 'small major 3rd', or SM3 (not to be confused with a super major third, a label that does not exist in this system).
-Neo-medieval musicians and early music historian and theorist [[Margo Schulter]] described her own [http://www.bestii.com/~mschulter/IntervalSpectrumRegions.txt interval naming scheme] built on approximations to JI intervals. Each interval names corresponds to an approximate size, and no particular ET is referenced. In her scheme middle major thirds range in size from 400-423 cents, and small major thirds from 372-400c. 5/4 is labelled a small major third, 81/64 a middle major third and 9/7 a large major third. Margo's scheme includes small, middle and large varieties of major, minor and neutral 2nds, 3rds, 6ths, 7ths; perfect fourth and fifths; and tritones, as well as a sub fifth and super fourth; a dieses and comma and an octave less dieses and comma; and ''interseptimals'', which correspond to intermediates, her name referencing the fact that they may each approximate two ratios of 7.
+Neo-medieval musician and early music historian and theorist [[Margo Schulter]] described her own [http://www.bestii.com/~mschulter/IntervalSpectrumRegions.txt interval naming scheme] built on approximations to JI intervals. Each interval names corresponds to an approximate size, and no particular ET is referenced. In her scheme middle major thirds range in size from 400-423 cents, and small major thirds from 372-400c. 5/4 is labelled a small major third, 81/64 a middle major third and 9/7 a large major third. Margo's scheme includes small, middle and large varieties of major, minor and neutral 2nds, 3rds, 6ths, 7ths; perfect fourth and fifths; and tritones, as well as a sub fifth and super fourth; a dieses and comma and an octave less dieses and comma; and ''interseptimals'', which correspond to intermediates, her name referencing the fact that they may each approximate two ratios of 7.
 In Hunt's system when used in 41-tET or JI diatonic interval arithmetic is conserved, but in other tunings it may not be, and Margo's system may not conserve diatonic interval arithmetic either. Both systems may be applied to arbitrary tunings, but the same intervals (defined, perhaps by a MOS scale) may not be given the same interval names across different tunings. [[User:PiotrGrochowski/Extra-Diatonic Intervals|Other]] size-based systems also exist, but are less thoroughly described and less well known. In all these systems, interval arithmetic is not conserved across all tunings.