User:Lhearne/Extra-Diatonic Intervals: Difference between revisions

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=== Common microtonal interval names ===

Dating back at least to 1880, after Alexander Ellis and John Land, the interval [[7/6]] has been associated with the label ''subminor third''. in a generalisation of this idea, [[9/7]] is most commonly reffered to as a ''supermajor third,'' [[12/7]] a ''supermajor sixth'', [[14/9]] a ''subminor sixths,'' [[8/7]] a ''supermajor second,'' [[7/4]] a ''subminor seventh'', [[27/14]] a ''supermajor seventh'' and [[28/27]] a ''subminor second.'' This system was further generalised by some theorists and musicians such that an interval a bit smaller than a major is referred to as a ''subminor third'', and an interval a bit larger than a minor third as a ''supraminor third''. Notice that 'supra' is used instead of 'super', but 'sub' is still used. Similarly defined are submajor and supraminor seconds, sixths and sevenths. 'Sub' and 'super' prefixes have also seen occasional application to the perfect scale degrees. Like in the case of the submajor 3rd, etc., super and sub unisons, fourths, fifths and octaves are not associated with particular frequency ratio by all or most microtonal musicians and theorists. In the case of seconds, thirds, sixths and sevenths, intervals half way between major and minor are often called ''neutral''. Finally, in limited use are 'intermediates', where an interval in-between a major 3rd and a perfect fourth, for example, is referred to as a 'third-fourth'. There are undoubtedly other interval naming practice that exists that are not as well known to the author, which are likely to be less commonly used. Although all these microtonal interval naming concepts are in common use, there is not yet a complete system that defined them, only complete systems that depart from them.

Dating back at least to 1880, after Alexander Ellis and John Land, the interval [[7/6]] has been associated with the label ''subminor third''. in a generalisation of this idea, [[9/7]] is most commonly reffered to as a ''supermajor third,'' [[12/7]] a ''supermajor sixth'', [[14/9]] a ''subminor sixths,'' [[8/7]] a ''supermajor second,'' [[7/4]] a ''subminor seventh'', [[27/14]] a ''supermajor seventh'' and [[28/27]] a ''subminor second.'' This system was further generalised by some theorists and musicians such that an interval a bit smaller than a major is referred to as a ''subminor third'', and an interval a bit larger than a minor third as a ''supraminor third''. Notice that 'supra' is used instead of 'super', but 'sub' is still used. Similarly defined are submajor and supraminor seconds, sixths and sevenths. 'Sub' and 'super' prefixes have also seen occasional application to the perfect scale degrees. Like in the case of the submajor 3rd, etc., super and sub unisons, fourths, fifths and octaves are not associated with particular frequency ratio by all or most microtonal musicians and theorists. In the case of seconds, thirds, sixths and sevenths, intervals half way between major and minor are often called ''neutral''. Finally, in limited use are 'intermediates', where an interval in-between a major 3rd and a perfect fourth, for example, is referred to as a 'third-fourth'. There are undoubtedly other interval naming practice that exists that are not as well known to the author, which are likely to be less commonly used. Although all these microtonal interval naming concepts are in common use, there is not yet a complete system that defined them, only complete systems that depart from them.

=== [[Sagittal notation|Sagittal]] - [http://forum.sagittal.org/viewforum.php?f=9 sagispeak] ===

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To provide native support for [[Semaphore]], [[Pajara]] and [[Injera]], intermediates are also added to the system. It should be noted immediately that intermediates are not as common to common microtonal interval naming as neutrals and though are a useful addition to this scheme, may be left out if desired. The appendix includes the MOS scales and edos from 'lists of all edos and MOS Scales', but without any intermediates.

‘2-3’ lies exactly half-way between M2 and m3 and divides the P4 in half. It may be read ‘second-third’ or ‘serd’. ‘6-7’, it’s octave-inverse lies exactly half-way between M6 and m7 and may be read ‘sixths-seventh’ or ‘sinth’.

‘2-3’ lies exactly half-way between M2 and m3 and divides the P4 in half. It may be read ‘second-third’ or ‘serd’. ‘6-7’, it’s octave-inverse lies exactly half-way between M6 and m7 and may be read ‘sixths-seventh’ or ‘sinth’.

‘1-2’ lies exactly half-way between P1 and m2, dividing the m2 in half. It may be read ‘unison-second’ or ‘unicond’. Its octave-inverse, ‘7-8’, lies exactly half-way between M7 and P8 and may be read ‘seventh-octave’ or ‘sevtave’.

<!-- Soft edit: "Note that it conflicts with [[User:PiotrGrochowski/Extra-Diatonic Intervals — 50edo]]'s unison–second."

<!-- Soft edit by Piotr: "Note that it conflicts with [[User:PiotrGrochowski/Extra-Diatonic Intervals — 50edo]]'s unison–second."

should this be rejected, accepted, or accepted with delay until Piotr's 50edo based notation is complete?

Hi Piotr ~~(I'm guessing)~~ Cool use of comments for 'soft edits'. Good place to talk here about it. My use of 1-2 is more aligned with 2-3 and 3-4 (common uses) than your is, where it splits the limma, the Pythagorean diatonic semitone. Half of the whole-tone, as you are using it isn't really ambiguously a unison or a second or both, it's very close to a minor second, and in 19edo, equivalent to it. -->

Gareth: Hi Piotr Cool use of comments for 'soft edits'. Good place to talk here about it. My use of 1-2 is more aligned with 2-3 and 3-4 (common uses) than your is, where it splits the limma, the Pythagorean diatonic semitone. Half of the whole-tone, as you are using it isn't really ambiguously a unison or a second or both, it's very close to a minor second, and in 19edo, equivalent to it.

Piotr: The difference is that my systems include the augmented unison, while yours don't. With the 100 cents being both in the 12edo, 24edo and 36edo meantones, I settled on unison–second as the name for 4\50, which is 96 cents. 3\50 is augmented unison, and 5\50 is diminished second. The unison–second and fourth–fifth could be perceived as splits of the diesis in half. They're in the middle of semitones and tritones respectively. Many systems seem to abuse (no offense) the name "minor second" for any semitone, when in fact minor second and augmented unison are separate intervals in the circle of fifths. An octave is made of 7 minor seconds and 5 augmented unisons. While it can be said that three octaves is 8 major thirds and 4 diminished fourths, I excluded the diminished fourth from my notation because it's considered wolf in 5–limit meantone and 9/7 in septimal meantone, which is a supermajor third. -->

‘3-4’ lies exactly half-way between M3 and P4, dividing the M6 in half. It may be read ‘third-fourth’ or ‘thourth’. It’s octave-inverse, ‘5-6’, lies exactly half-way between P5 and m6 and may be read ‘fifth-sixth’ or ‘fixth’. <!-- plural?!

@@ Line 36: / Line 36: @@
 === Common microtonal interval names ===
-Dating back at least to 1880, after Alexander Ellis and John Land, the interval [[7/6]] has been associated with the label ''subminor third''. in a generalisation of this idea, [[9/7]] is most commonly reffered to as a ''supermajor third,'' [[12/7]] a ''supermajor sixth'', [[14/9]] a ''subminor sixths,'' [[8/7]] a ''supermajor second,'' [[7/4]] a ''subminor seventh'', [[27/14]] a ''supermajor seventh'' and [[28/27]] a ''subminor second.'' This system was further generalised by some theorists and musicians such that an interval a bit smaller than a major is referred to as a ''subminor third'', and an interval a bit larger than a minor third as a ''supraminor third''. Notice that 'supra' is used instead of 'super', but 'sub' is still used. Similarly defined are submajor and supraminor seconds, sixths and sevenths. 'Sub' and 'super' prefixes have also seen occasional application to the perfect scale degrees. Like in the case of the submajor 3rd, etc., super and sub unisons, fourths, fifths and octaves are not associated with particular frequency ratio by all or most microtonal musicians and theorists. In the case of seconds, thirds, sixths and sevenths, intervals half way between major and minor are often called ''neutral''. Finally, in limited use are 'intermediates', where an interval in-between a major 3rd and a perfect fourth, for example, is referred to as a 'third-fourth'. There are undoubtedly other interval naming practice that exists that are not as well known to the author, which are likely to be less commonly used. Although all these microtonal interval naming concepts are in common use, there is not yet a complete system that defined them, only complete systems that depart from them.
+Dating back at least to 1880, after Alexander Ellis and John Land, the interval [[7/6]] has been associated with the label ''subminor third''. in a generalisation of this idea, [[9/7]] is most commonly reffered to as a ''supermajor third,'' [[12/7]] a ''supermajor sixth'', [[14/9]] a ''subminor sixths,<!-- plural?! -->'' [[8/7]] a ''supermajor second,'' [[7/4]] a ''subminor seventh'', [[27/14]] a ''supermajor seventh'' and [[28/27]] a ''subminor second.'' This system was further generalised by some theorists and musicians such that an interval a bit smaller than a major is referred to as a ''subminor third'', and an interval a bit larger than a minor third as a ''supraminor third''. Notice that 'supra' is used instead of 'super', but 'sub' is still used. Similarly defined are submajor and supraminor seconds, sixths and sevenths. 'Sub' and 'super' prefixes have also seen occasional application to the perfect scale degrees. Like in the case of the submajor 3rd, etc., super and sub unisons, fourths, fifths and octaves are not associated with particular frequency ratio by all or most microtonal musicians and theorists. In the case of seconds, thirds, sixths and sevenths, intervals half way between major and minor are often called ''neutral''. Finally, in limited use are 'intermediates', where an interval in-between a major 3rd and a perfect fourth, for example, is referred to as a 'third-fourth'. There are undoubtedly other interval naming practice that exists that are not as well known to the author, which are likely to be less commonly used. Although all these microtonal interval naming concepts are in common use, there is not yet a complete system that defined them, only complete systems that depart from them.
 === [[Sagittal notation|Sagittal]] - [http://forum.sagittal.org/viewforum.php?f=9 sagispeak] ===
@@ Line 100: / Line 100: @@
 To provide native support for [[Semaphore]], [[Pajara]] and [[Injera]], intermediates are also added to the system. It should be noted immediately that intermediates are not as common to common microtonal interval naming as neutrals and though are a useful addition to this scheme, may be left out if desired. The appendix includes the MOS scales and edos from 'lists of all edos and MOS Scales', but without any intermediates.
-‘2-3’ lies exactly half-way between M2 and m3 and divides the P4 in half. It may be read ‘second-third’ or ‘serd’. ‘6-7’, it’s octave-inverse lies exactly half-way between M6 and m7 and may be read ‘sixths-seventh’ or ‘sinth’.
+‘2-3’ lies exactly half-way between M2 and m3 and divides the P4 in half. It may be read ‘second-third’ or ‘serd’. ‘6-7’, it’s octave-inverse lies exactly half-way between M6 and m7 and may be read ‘sixths<!-- plural?! -->-seventh’ or ‘sinth’.
 ‘1-2’ lies exactly half-way between P1 and m2, dividing the m2 in half. It may be read ‘unison-second’ or ‘unicond’. Its octave-inverse, ‘7-8’, lies exactly half-way between M7 and P8 and may be read ‘seventh-octave’ or ‘sevtave’.
-<!-- Soft edit: "Note that it conflicts with [[User:PiotrGrochowski/Extra-Diatonic Intervals — 50edo]]'s unison–second."
+<!-- Soft edit by Piotr: "Note that it conflicts with [[User:PiotrGrochowski/Extra-Diatonic Intervals — 50edo]]'s unison–second."
 should this be rejected, accepted, or accepted with delay until Piotr's 50edo based notation is complete?
-Hi Piotr (I'm guessing) Cool use of comments for 'soft edits'. Good place to talk here about it. My use of 1-2 is more aligned with 2-3 and 3-4 (common uses) than your is, where it splits the limma, the Pythagorean diatonic semitone. Half of the whole-tone, as you are using it isn't really ambiguously a unison or a second or both, it's very close to a minor second, and in 19edo, equivalent to it. -->
+Gareth: Hi Piotr Cool use of comments for 'soft edits'. Good place to talk here about it. My use of 1-2 is more aligned with 2-3 and 3-4 (common uses) than your is, where it splits the limma, the Pythagorean diatonic semitone. Half of the whole-tone, as you are using it isn't really ambiguously a unison or a second or both, it's very close to a minor second, and in 19edo, equivalent to it.
+Piotr: The difference is that my systems include the augmented unison, while yours don't. With the 100 cents being both in the 12edo, 24edo and 36edo meantones, I settled on unison–second as the name for 4\50, which is 96 cents. 3\50 is augmented unison, and 5\50 is diminished second. The unison–second and fourth–fifth could be perceived as splits of the diesis in half. They're in the middle of semitones and tritones respectively. Many systems seem to abuse (no offense) the name "minor second" for any semitone, when in fact minor second and augmented unison are separate intervals in the circle of fifths. An octave is made of 7 minor seconds and 5 augmented unisons. While it can be said that three octaves is 8 major thirds and 4 diminished fourths, I excluded the diminished fourth from my notation because it's considered wolf in 5–limit meantone and 9/7 in septimal meantone, which is a supermajor third. -->
 ‘3-4’ lies exactly half-way between M3 and P4, dividing the M6 in half. It may be read ‘third-fourth’ or ‘thourth’. It’s octave-inverse, ‘5-6’, lies exactly half-way between P5 and m6 and may be read ‘fifth-sixth’ or ‘fixth’. <!-- plural?!