Kite's Genchain mode numbering: Difference between revisions
Wikispaces>TallKite **Imported revision 593197474 - Original comment: ** |
Wikispaces>TallKite **Imported revision 593219602 - 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>2016-09-24 | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-09-24 19:59:42 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>593219602</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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If the scale is written using heptatonically using 7 /note names, the degree numbers are heptatonic. C D E G A# is written 1st Meantone [5] #6. If the scale were written pentatonically using 5 note names, perhaps J K L M #N, it would be 1st Meantone [5] #5. If discussing scales in the abstract without reference to any note names, one need to specify which type of numbering is bering used. | If the scale is written using heptatonically using 7 /note names, the degree numbers are heptatonic. C D E G A# is written 1st Meantone [5] #6. If the scale were written pentatonically using 5 note names, perhaps J K L M #N, it would be 1st Meantone [5] #5. If discussing scales in the abstract without reference to any note names, one need to specify which type of numbering is bering used. | ||
The scale of 8\13 fifths A C B D F E G A mentioned above can't be notated with fifth-based heptatonic and requires pentatonic notation. Using the numbers 1-5 both as note names and as scale degrees, we get this genchain: | The scale of 8\13 fifths A C B D F E G A mentioned above can't be notated with fifth-based heptatonic and requires pentatonic notation. Because the pentatonic fifth is chroma-negative, the fifthward side of the genchain is flat and the fourthwards side is sharp (assuming a fifth < 720¢). Use "+" for fifthwards and "-" for fourthwards. Using the numbers 1-5 both as note names and as scale degrees, we get this genchain: | ||
...5# 3# 1# 4# 2# 5 3 1 4 2 5b 3b 1b 4b 2b... | ...5# 3# 1# 4# 2# 5 3 1 4 2 5b 3b 1b 4b 2b bb5... | ||
...-5 -3 -1 -4 -2 5 3 1 4 2 +5 +3 +1 +4 +2 ++5... | |||
and these standard modes: | and these standard modes: | ||
1 1st Meantone [5] = 1 2 | 1 1st Meantone [5] = 1 2 +3 4 +5 1 | ||
1 2nd Meantone [5] = 1 2 3 4 | 1 2nd Meantone [5] = 1 2 3 4 +5 1 | ||
1 3rd Meantone [5] = 1 2 3 4 5 1 | 1 3rd Meantone [5] = 1 2 3 4 5 1 | ||
1 4th Meantone [5] = 1 | 1 4th Meantone [5] = 1 -2 3 4 5 1 | ||
1 5th Meantone [5] = 1 | 1 5th Meantone [5] = 1 -2 3 -4 5 1 | ||
The initial "1" is the tonic of the scale. | The initial "1" is the tonic of the scale. | ||
The A C B D F E G A scale becomes 1 2 2 | The A C B D F E G A scale becomes 1 2 -2 3 4 +5 5 1, which has 3 possible names: | ||
1 3rd Meantone [5] add | 1 3rd Meantone [5] add -2, +5 | ||
1 2nd Meantone [5] add | 1 2nd Meantone [5] add -2, -5 | ||
1 4th Meantone [5] add | 1 4th Meantone [5] add +2, +5 | ||
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If the scale is written using heptatonically using 7 /note names, the degree numbers are heptatonic. C D E G A# is written 1st Meantone [5] #6. If the scale were written pentatonically using 5 note names, perhaps J K L M #N, it would be 1st Meantone [5] #5. If discussing scales in the abstract without reference to any note names, one need to specify which type of numbering is bering used.<br /> | If the scale is written using heptatonically using 7 /note names, the degree numbers are heptatonic. C D E G A# is written 1st Meantone [5] #6. If the scale were written pentatonically using 5 note names, perhaps J K L M #N, it would be 1st Meantone [5] #5. If discussing scales in the abstract without reference to any note names, one need to specify which type of numbering is bering used.<br /> | ||
<br /> | <br /> | ||
The scale of 8\13 fifths A C B D F E G A mentioned above can't be notated with fifth-based heptatonic and requires pentatonic notation. Using the numbers 1-5 both as note names and as scale degrees, we get this genchain:<br /> | The scale of 8\13 fifths A C B D F E G A mentioned above can't be notated with fifth-based heptatonic and requires pentatonic notation. Because the pentatonic fifth is chroma-negative, the fifthward side of the genchain is flat and the fourthwards side is sharp (assuming a fifth &lt; 720¢). Use &quot;+&quot; for fifthwards and &quot;-&quot; for fourthwards. Using the numbers 1-5 both as note names and as scale degrees, we get this genchain:<br /> | ||
...5# 3# 1# 4# 2# 5 3 1 4 2 5b 3b 1b 4b 2b...<br /> | ...5# 3# 1# 4# 2# 5 3 1 4 2 5b 3b 1b 4b 2b bb5...<br /> | ||
...-5 -3 -1 -4 -2 5 3 1 4 2 +5 +3 +1 +4 +2 ++5...<br /> | |||
and these standard modes:<br /> | and these standard modes:<br /> | ||
1 1st Meantone [5] = 1 2 | 1 1st Meantone [5] = 1 2 +3 4 +5 1<br /> | ||
1 2nd Meantone [5] = 1 2 3 4 | 1 2nd Meantone [5] = 1 2 3 4 +5 1<br /> | ||
1 3rd Meantone [5] = 1 2 3 4 5 1<br /> | 1 3rd Meantone [5] = 1 2 3 4 5 1<br /> | ||
1 4th Meantone [5] = 1 | 1 4th Meantone [5] = 1 -2 3 4 5 1<br /> | ||
1 5th Meantone [5] = 1 | 1 5th Meantone [5] = 1 -2 3 -4 5 1<br /> | ||
The initial &quot;1&quot; is the tonic of the scale.<br /> | The initial &quot;1&quot; is the tonic of the scale.<br /> | ||
<br /> | <br /> | ||
The A C B D F E G A scale becomes 1 2 2 | The A C B D F E G A scale becomes 1 2 -2 3 4 +5 5 1, which has 3 possible names:<br /> | ||
1 3rd Meantone [5] add | 1 3rd Meantone [5] add -2, +5<br /> | ||
1 2nd Meantone [5] add | 1 2nd Meantone [5] add -2, -5<br /> | ||
1 4th Meantone [5] add | 1 4th Meantone [5] add +2, +5<br /> | ||
<br /> | <br /> | ||
<br /> | <br /> | ||