Kite's ups and downs notation: Difference between revisions
Wikispaces>TallKite **Imported revision 558220645 - Original comment: ** |
Wikispaces>TallKite **Imported revision 558221555 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2015-09-03 20: | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2015-09-03 20:18:09 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>558221555</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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There are some exceptions. Take this scale: | There are some exceptions. Take this scale: | ||
C Db Db^ Dv D Eb Eb^ Ev E F Gb Gb^ Gv G Ab Ab^ Av A Bb Bb^ Bv B C | C Db Db^ Dv D Eb Eb^ Ev E F Gb Gb^ Gv G Ab Ab^ Av A Bb Bb^ Bv B C | ||
Here's our fifths: C-G, Db-Ab, Db^-Ab^, Dv-Av, D-A, etc. Most fifths *look* like fifths and are easy to find. So do the 4ths. Our 4\22 maj 2nds are C-D, Db-Eb, Db^-Eb^, Dv-Ev, D-E, Eb-F, good until we reach Eb^-Gb, which | Here's our fifths: C-G, Db-Ab, Db^-Ab^, Dv-Av, D-A, etc. Most fifths *look* like fifths and are easy to find. So do the 4ths. Our 4\22 maj 2nds are C-D, Db-Eb, Db^-Eb^, Dv-Ev, D-E, Eb-F, good until we reach Eb^-Gb, which is a major 2nd that is spelled as a downminor 3rd. Here's this scale's chain of 5ths: | ||
Gb^ Db^ Ab^ Eb^ Bb^ Gb Db Ab Eb Bb F C G D A E B Gv Dv Av Ev Bv | Gb^ Db^ Ab^ Eb^ Bb^ Gb Db Ab Eb Bb F C G D A E B Gv Dv Av Ev Bv | ||
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Now that's an awful lot of sharps and flats, but that does make a neat and tidy notation (except for the Gbb-Gx fifth). And it exists as an alternative, embedded within our standard notation, with a key signature with circled X's on the B and E spots. | Now that's an awful lot of sharps and flats, but that does make a neat and tidy notation (except for the Gbb-Gx fifth). And it exists as an alternative, embedded within our standard notation, with a key signature with circled X's on the B and E spots. | ||
So the chain of fifths has a few spots to watch out for. You have to remember that B-something to G-something | So the chain of fifths has a few spots to watch out for. You have to remember that fifths sometimes appear as downminor 6ths, in the form of B-something to G-something. A little tricky, but manageable. Analogous to 12-ET, where G# to Eb is a fifth that looks like a sixth. | ||
__**Staff Notation**__ | __**Staff Notation**__ | ||
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fourthwards EDOs aka Mavila EDOs, with a fifth less than 686¢ | fourthwards EDOs aka Mavila EDOs, with a fifth less than 686¢ | ||
This is in addition to the trivial EDOs, 1, 2, 3, 4 and 6, which can be notated with standard notation as a subset of 12-EDO. The fifth is defined as the nearest approximation to 3/2. There is a little leeway to this in certain EDOs like 18 which have two possible fifths with nearly equal accuracy. | This is in addition to the trivial EDOs, 1, 2, 3, 4 and 6, which can be notated with standard notation as a subset of 12-EDO. The fifth is defined as the nearest approximation to 3/2. There is a little leeway to this in certain EDOs like 18 which have two possible fifths with nearly equal accuracy. | ||
This section will cover sweet EDOs and the other categories will be covered in other sections. | This section will cover sweet EDOs and the other categories will be covered in other sections. | ||
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In 22edo, the major chord is 0-8-13 = 0¢-436¢-709¢. In 19edo, it's 0-6-11 = 0¢-379¢-695¢. The two chords sound quite different, because "major 3rd" is defined only in terms of the fifth, not in terms of what JI ratios it approximates. To describe the sound of the chord, color notation can be used. 22edo major chords sound red and 19edo major chords sound yellow. | In 22edo, the major chord is 0-8-13 = 0¢-436¢-709¢. In 19edo, it's 0-6-11 = 0¢-379¢-695¢. The two chords sound quite different, because "major 3rd" is defined only in terms of the fifth, not in terms of what JI ratios it approximates. To describe the sound of the chord, color notation can be used. 22edo major chords sound red and 19edo major chords sound yellow. | ||
The name "major" refers not to the sound but to the function of the chord. If you want to play a I - VIm - IIm - V - I progression without pitch shifts or tonic drift, you can do that in any edo, as long as you use major and minor chords. The notation tells you what kind of chord can be used to play that progression. In 22edo, the chord that you need sounds like a red chord. | The name "major" refers not to the sound but to the function of the chord. If you want to play a I - VIm - IIm - V - I progression without pitch shifts or tonic drift, you can do that in any edo, as long as you use major and minor chords. The notation tells you what kind of chord can be used to play that progression. In 22edo, the chord that you need sounds like a red chord. | ||
In other words, I - VIm - IIm - V - I in JI implies Iy - VIg - IIg - Vy - Iy, but this implication only holds in certain EDOs. The notation tells you which ones. | In other words, I - VIm - IIm - V - I in JI implies Iy - VIg - IIg - Vy - Iy, but this implication only holds in certain EDOs. The notation tells you which ones. | ||
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P1 - m2 - M2 - m3 - M3 - P4 - A4/d5 - P5 - m6 - M6 - m7 - M7 - P8 | P1 - m2 - M2 - m3 - M3 - P4 - A4/d5 - P5 - m6 - M6 - m7 - M7 - P8 | ||
perfect = white, major = red, yellow and fifthward white, minor = green, blue and fourthwards white | perfect = white, major = red, yellow and fifthward white, minor = green, blue and fourthwards white | ||
**__17edo__:** sharp = 2 keys: C Db C# C | **__17edo__:** sharp = 2 keys: C Db C# C | ||
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D - D# - Eb - E - E#/Fb - F - F# - Gb - G - G# - Ab - A - A# - Bb - B - B#/Cb - C - C# - Db - D | D - D# - Eb - E - E#/Fb - F - F# - Gb - G - G# - Ab - A - A# - Bb - B - B#/Cb - C - C# - Db - D | ||
P1 - A1/d2 - m2 - M2 - A2/d3 - m3 - M3 - A3/d4 - P4 - A4 - d5 - P5 - A5/d6 - m6 - M6 - A6/d7 - m7 - M7 - A7/d8 - P8 | P1 - A1/d2 - m2 - M2 - A2/d3 - m3 - M3 - A3/d4 - P4 - A4 - d5 - P5 - A5/d6 - m6 - M6 - A6/d7 - m7 - M7 - A7/d8 - P8 | ||
perfect = white, major = yellow and fifthward white, minor = green and fourthward white, aug/dim = red/blue. | |||
**__22edo__:** sharp = 3 keys: C Db * C# C | **__22edo__:** sharp = 3 keys: C Db * C# C | ||
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There are some exceptions. Take this scale:<br /> | There are some exceptions. Take this scale:<br /> | ||
C Db Db^ Dv D Eb Eb^ Ev E F Gb Gb^ Gv G Ab Ab^ Av A Bb Bb^ Bv B C<br /> | C Db Db^ Dv D Eb Eb^ Ev E F Gb Gb^ Gv G Ab Ab^ Av A Bb Bb^ Bv B C<br /> | ||
Here's our fifths: C-G, Db-Ab, Db^-Ab^, Dv-Av, D-A, etc. Most fifths *look* like fifths and are easy to find. So do the 4ths. Our 4\22 maj 2nds are C-D, Db-Eb, Db^-Eb^, Dv-Ev, D-E, Eb-F, good until we reach Eb^-Gb, which | Here's our fifths: C-G, Db-Ab, Db^-Ab^, Dv-Av, D-A, etc. Most fifths *look* like fifths and are easy to find. So do the 4ths. Our 4\22 maj 2nds are C-D, Db-Eb, Db^-Eb^, Dv-Ev, D-E, Eb-F, good until we reach Eb^-Gb, which is a major 2nd that is spelled as a downminor 3rd. Here's this scale's chain of 5ths:<br /> | ||
<br /> | <br /> | ||
Gb^ Db^ Ab^ Eb^ Bb^ Gb Db Ab Eb Bb F C G D A E B Gv Dv Av Ev Bv<br /> | Gb^ Db^ Ab^ Eb^ Bb^ Gb Db Ab Eb Bb F C G D A E B Gv Dv Av Ev Bv<br /> | ||
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Now that's an awful lot of sharps and flats, but that does make a neat and tidy notation (except for the Gbb-Gx fifth). And it exists as an alternative, embedded within our standard notation, with a key signature with circled X's on the B and E spots.<br /> | Now that's an awful lot of sharps and flats, but that does make a neat and tidy notation (except for the Gbb-Gx fifth). And it exists as an alternative, embedded within our standard notation, with a key signature with circled X's on the B and E spots.<br /> | ||
<br /> | <br /> | ||
So the chain of fifths has a few spots to watch out for. You have to remember that B-something to G-something | So the chain of fifths has a few spots to watch out for. You have to remember that fifths sometimes appear as downminor 6ths, in the form of B-something to G-something. A little tricky, but manageable. Analogous to 12-ET, where G# to Eb is a fifth that looks like a sixth.<br /> | ||
<br /> | <br /> | ||
<u><strong>Staff Notation</strong></u><br /> | <u><strong>Staff Notation</strong></u><br /> | ||
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fourthwards EDOs aka Mavila EDOs, with a fifth less than 686¢<br /> | fourthwards EDOs aka Mavila EDOs, with a fifth less than 686¢<br /> | ||
<br /> | <br /> | ||
This is in addition to the trivial EDOs, 1, 2, 3, 4 and 6, which can be notated with standard notation as a subset of 12-EDO. The fifth is defined as the nearest approximation to 3/2. There is a little leeway to this in certain EDOs like 18 which have two possible fifths with nearly equal accuracy. <br /> | This is in addition to the trivial EDOs, 1, 2, 3, 4 and 6, which can be notated with standard notation as a subset of 12-EDO. The fifth is defined as the nearest approximation to 3/2. There is a little leeway to this in certain EDOs like 18 which have two possible fifths with nearly equal accuracy.<br /> | ||
<br /> | <br /> | ||
This section will cover sweet EDOs and the other categories will be covered in other sections.<br /> | This section will cover sweet EDOs and the other categories will be covered in other sections.<br /> | ||
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In 22edo, the major chord is 0-8-13 = 0¢-436¢-709¢. In 19edo, it's 0-6-11 = 0¢-379¢-695¢. The two chords sound quite different, because &quot;major 3rd&quot; is defined only in terms of the fifth, not in terms of what JI ratios it approximates. To describe the sound of the chord, color notation can be used. 22edo major chords sound red and 19edo major chords sound yellow.<br /> | In 22edo, the major chord is 0-8-13 = 0¢-436¢-709¢. In 19edo, it's 0-6-11 = 0¢-379¢-695¢. The two chords sound quite different, because &quot;major 3rd&quot; is defined only in terms of the fifth, not in terms of what JI ratios it approximates. To describe the sound of the chord, color notation can be used. 22edo major chords sound red and 19edo major chords sound yellow.<br /> | ||
<br /> | <br /> | ||
The name &quot;major&quot; refers not to the sound but to the function of the chord. If you want to play a I - VIm - IIm - V - I progression without pitch shifts or tonic drift, you can do that in any edo, as long as you use major and minor chords. The notation tells you what kind of chord can be used to play that progression. In 22edo, the chord that you need sounds like a red chord. <br /> | The name &quot;major&quot; refers not to the sound but to the function of the chord. If you want to play a I - VIm - IIm - V - I progression without pitch shifts or tonic drift, you can do that in any edo, as long as you use major and minor chords. The notation tells you what kind of chord can be used to play that progression. In 22edo, the chord that you need sounds like a red chord.<br /> | ||
<br /> | <br /> | ||
In other words, I - VIm - IIm - V - I in JI implies Iy - VIg - IIg - Vy - Iy, but this implication only holds in certain EDOs. The notation tells you which ones.<br /> | In other words, I - VIm - IIm - V - I in JI implies Iy - VIg - IIg - Vy - Iy, but this implication only holds in certain EDOs. The notation tells you which ones.<br /> | ||
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P1 - m2 - M2 - m3 - M3 - P4 - A4/d5 - P5 - m6 - M6 - m7 - M7 - P8<br /> | P1 - m2 - M2 - m3 - M3 - P4 - A4/d5 - P5 - m6 - M6 - m7 - M7 - P8<br /> | ||
perfect = white, major = red, yellow and fifthward white, minor = green, blue and fourthwards white<br /> | perfect = white, major = red, yellow and fifthward white, minor = green, blue and fourthwards white<br /> | ||
<br /> | <br /> | ||
<strong><u>17edo</u>:</strong> sharp = 2 keys: C Db C# C<br /> | <strong><u>17edo</u>:</strong> sharp = 2 keys: C Db C# C<br /> | ||
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D - D# - Eb - E - E#/Fb - F - F# - Gb - G - G# - Ab - A - A# - Bb - B - B#/Cb - C - C# - Db - D<br /> | D - D# - Eb - E - E#/Fb - F - F# - Gb - G - G# - Ab - A - A# - Bb - B - B#/Cb - C - C# - Db - D<br /> | ||
P1 - A1/d2 - m2 - M2 - A2/d3 - m3 - M3 - A3/d4 - P4 - A4 - d5 - P5 - A5/d6 - m6 - M6 - A6/d7 - m7 - M7 - A7/d8 - P8<br /> | P1 - A1/d2 - m2 - M2 - A2/d3 - m3 - M3 - A3/d4 - P4 - A4 - d5 - P5 - A5/d6 - m6 - M6 - A6/d7 - m7 - M7 - A7/d8 - P8<br /> | ||
perfect = white, major = yellow and fifthward white, minor = green and fourthward white, aug/dim = red/blue.<br /> | |||
<br /> | <br /> | ||
<strong><u>22edo</u>:</strong> sharp = 3 keys: C Db * C# C<br /> | <strong><u>22edo</u>:</strong> sharp = 3 keys: C Db * C# C<br /> | ||