Kite's ups and downs notation: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-10-04 03:12:24 UTC</tt>.

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-10-04 04:13:45 UTC</tt>.

: The original revision id was <tt>~~593964730~~</tt>.

: The original revision id was <tt>593967506</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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The third special case is when the edo's 5th is narrower than 4\7, as in 16edo. There are two approaches. One preserves the harmonic (chain-of-fifths) meaning of sharp/flat, major/minor and aug/dim, and the other preserves the melodic meaning.

In the first approach, major is still fifthwards, which makes it narrower than minor. Aug is narrower than dim. This makes interval arithmetic and chord names unaffected. M2 + M2 is still M3, and a C minor chord is still C Eb G. Sharp is flatter than natural. ~~To describe~~ someone singing ~~below~~ pitch, instead of saying "you're singing ~~flat~~", you would say "you're singing ~~down~~".

In the first approach, major is still fifthwards, which makes it narrower than minor. Aug is narrower than dim. This makes interval arithmetic and chord names unaffected. M2 + M2 is still M3, and a C minor chord is still C Eb G. Sharp is flatter than natural. __**Up is still ascending in pitch**__. If someone's singing above pitch, instead of saying "you're singing sharp", you would say "you're singing up".

In the 2nd approach, major is still wider than minor, so major is not fifthwards but fourthwards. Sharp is still sharper than natural. The chain of fifths runs backwards:

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16edo: C - C#/Db - D - D#/Eb - E - E# - Fb - F - F#/Gb - G - G#/Ab - A - A#/Bb - B - B# - Cb - C

Interval arithmetic is done using a simple trick: first reverse everything, then perform normal arithmetic, then reverse everything again. Reversing means exchanging major for minor, aug for dim and sharp for flat. Perfect and natural are unaffected.

Interval arithmetic is done using a simple trick: first reverse everything, then perform normal arithmetic, then reverse everything again. Reversing means exchanging major for minor, aug for dim and sharp for flat. Perfect and natural are unaffected. Examples:

||= initial question ||= reverse everything ||= do the math ||= reverse again ||

||= M2 + M2 ||= m2 + m2 ||= dim3 ||= aug3 ||

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||= Eb + m3 ||= E# + M3 ||= G## ||= Gbb ||

||= Eb + P5 ||= E# + P5 ||= B# ||= Bb ||

||= ~~C major~~ ||= ~~C minor~~ ||= C ~~Eb G~~ ||= C E~~# G~~ ||

||= A minor ||= A major ||= A C# E ||= A Cb E ||

||= Eb major ||= E# minor ||= E# G# B# ||= Eb Gb Db ||

||= G7 = M3 + P5 + m7 ||= m3 + P5 + M7 ||= G Bb D F# ||= G B# D Fb ||

~~Whichever approach is used, __**up is always ascending**__.~~ Both approaches have their merit, but the first one will be used here.

Both approaches have their merit, but the first one will be used here.

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The third special case is when the edo's 5th is narrower than 4\7, as in 16edo. There are two approaches. One preserves the harmonic (chain-of-fifths) meaning of sharp/flat, major/minor and aug/dim, and the other preserves the melodic meaning.

In the first approach, major is still fifthwards, which makes it narrower than minor. Aug is narrower than dim. This makes interval arithmetic and chord names unaffected. M2 + M2 is still M3, and a C minor chord is still C Eb G. Sharp is flatter than natural. ~~To describe~~ someone singing ~~below~~ pitch, instead of saying &quot;you're singing ~~flat~~&quot;, you would say &quot;you're singing ~~down~~&quot;.

In the first approach, major is still fifthwards, which makes it narrower than minor. Aug is narrower than dim. This makes interval arithmetic and chord names unaffected. M2 + M2 is still M3, and a C minor chord is still C Eb G. Sharp is flatter than natural. Up is still ascending in pitch. If someone's singing above pitch, instead of saying &quot;you're singing sharp&quot;, you would say &quot;you're singing up&quot;.

In the 2nd approach, major is still wider than minor, so major is not fifthwards but fourthwards. Sharp is still sharper than natural. The chain of fifths runs backwards:

Line 1,459:

16edo: C - C#/Db - D - D#/Eb - E - E# - Fb - F - F#/Gb - G - G#/Ab - A - A#/Bb - B - B# - Cb - C

Interval arithmetic is done using a simple trick: first reverse everything, then perform normal arithmetic, then reverse everything again. Reversing means exchanging major for minor, aug for dim and sharp for flat. Perfect and natural are unaffected.

Interval arithmetic is done using a simple trick: first reverse everything, then perform normal arithmetic, then reverse everything again. Reversing means exchanging major for minor, aug for dim and sharp for flat. Perfect and natural are unaffected. Examples:

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</tr>

<tr>

<td style="text-align: center;">~~C major~~

<td style="text-align: center;">A minor

</td>

<td style="text-align: center;">~~C minor~~

<td style="text-align: center;">A major

</td>

<td style="text-align: center;">C ~~Eb G~~

<td style="text-align: center;">A C# E

</td>

<td style="text-align: center;">C E~~# G~~

<td style="text-align: center;">A Cb E

</td>

</tr>

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~~Whichever approach is used, up is always ascending.~~ Both approaches have their merit, but the first one will be used here.

Both approaches have their merit, but the first one will be used here.

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2016-10-04 03:12:24 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-10-04 04:13:45 UTC</tt>.<br>
-: The original revision id was <tt>593964730</tt>.<br>
+: The original revision id was <tt>593967506</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>
@@ Line 128: / Line 128: @@
 The third special case is when the edo's 5th is narrower than 4\7, as in 16edo. There are two approaches. One preserves the harmonic (chain-of-fifths) meaning of sharp/flat, major/minor and aug/dim, and the other preserves the melodic meaning.
-In the first approach, major is still fifthwards, which makes it narrower than minor. Aug is narrower than dim. This makes interval arithmetic and chord names unaffected. M2 + M2 is still M3, and a C minor chord is still C Eb G. Sharp is flatter than natural. To describe someone singing below pitch, instead of saying "you're singing flat", you would say "you're singing down".
+In the first approach, major is still fifthwards, which makes it narrower than minor. Aug is narrower than dim. This makes interval arithmetic and chord names unaffected. M2 + M2 is still M3, and a C minor chord is still C Eb G. Sharp is flatter than natural. __**Up is still ascending in pitch**__. If someone's singing above pitch, instead of saying "you're singing sharp", you would say "you're singing up".
 In the 2nd approach, major is still wider than minor, so major is not fifthwards but fourthwards. Sharp is still sharper than natural. The chain of fifths runs backwards:
@@ Line 136: / Line 136: @@
 edo: C - C#/Db - D - D#/Eb - E - E# - Fb - F - F#/Gb - G - G#/Ab - A - A#/Bb - B - B# - Cb - C
-Interval arithmetic is done using a simple trick: first reverse everything, then perform normal arithmetic, then reverse everything again. Reversing means exchanging major for minor, aug for dim and sharp for flat. Perfect and natural are unaffected.
+Interval arithmetic is done using a simple trick: first reverse everything, then perform normal arithmetic, then reverse everything again. Reversing means exchanging major for minor, aug for dim and sharp for flat. Perfect and natural are unaffected. Examples:
 ||= initial question ||= reverse everything ||= do the math ||= reverse again ||
 ||= M2 + M2 ||= m2 + m2 ||= dim3 ||= aug3 ||
@@ Line 143: / Line 143: @@
 ||= Eb + m3 ||= E# + M3 ||= G## ||= Gbb ||
 ||= Eb + P5 ||= E# + P5 ||= B# ||= Bb ||
-||= C major ||= C minor ||= C Eb G ||= C E# G ||
+||= A minor ||= A major ||= A C# E ||= A Cb E ||
 ||= Eb major ||= E# minor ||= E# G# B# ||= Eb Gb Db ||
 ||= G7 = M3 + P5 + m7 ||= m3 + P5 + M7 ||= G Bb D F# ||= G B# D Fb ||
-Whichever approach is used, __**up is always ascending**__. Both approaches have their merit, but the first one will be used here.
+Both approaches have their merit, but the first one will be used here.
@@ Line 1,451: / Line 1,451: @@
 The third special case is when the edo's 5th is narrower than 4\7, as in 16edo. There are two approaches. One preserves the harmonic (chain-of-fifths) meaning of sharp/flat, major/minor and aug/dim, and the other preserves the melodic meaning.&lt;br /&gt;
 &lt;br /&gt;
-In the first approach, major is still fifthwards, which makes it narrower than minor. Aug is narrower than dim. This makes interval arithmetic and chord names unaffected. M2 + M2 is still M3, and a C minor chord is still C Eb G. Sharp is flatter than natural. To describe someone singing below pitch, instead of saying &amp;quot;you're singing flat&amp;quot;, you would say &amp;quot;you're singing down&amp;quot;.&lt;br /&gt;
+In the first approach, major is still fifthwards, which makes it narrower than minor. Aug is narrower than dim. This makes interval arithmetic and chord names unaffected. M2 + M2 is still M3, and a C minor chord is still C Eb G. Sharp is flatter than natural. &lt;u&gt;&lt;strong&gt;Up is still ascending in pitch&lt;/strong&gt;&lt;/u&gt;. If someone's singing above pitch, instead of saying &amp;quot;you're singing sharp&amp;quot;, you would say &amp;quot;you're singing up&amp;quot;.&lt;br /&gt;
 &lt;br /&gt;
 In the 2nd approach, major is still wider than minor, so major is not fifthwards but fourthwards. Sharp is still sharper than natural. The chain of fifths runs backwards:&lt;br /&gt;
@@ Line 1,459: / Line 1,459: @@
 edo: C - C#/Db - D - D#/Eb - E - E# - Fb - F - F#/Gb - G - G#/Ab - A - A#/Bb - B - B# - Cb - C&lt;br /&gt;
 &lt;br /&gt;
-Interval arithmetic is done using a simple trick: first reverse everything, then perform normal arithmetic, then reverse everything again. Reversing means exchanging major for minor, aug for dim and sharp for flat. Perfect and natural are unaffected.&lt;br /&gt;
+Interval arithmetic is done using a simple trick: first reverse everything, then perform normal arithmetic, then reverse everything again. Reversing means exchanging major for minor, aug for dim and sharp for flat. Perfect and natural are unaffected. Examples:&lt;br /&gt;
@@ Line 1,524: / Line 1,524: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;C major&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;A minor&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;C minor&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;A major&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;C Eb G&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;A C# E&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;C E# G&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;A Cb E&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 1,556: / Line 1,556: @@
 &lt;br /&gt;
-Whichever approach is used, &lt;u&gt;&lt;strong&gt;up is always ascending&lt;/strong&gt;&lt;/u&gt;. Both approaches have their merit, but the first one will be used here.&lt;br /&gt;
+Both approaches have their merit, but the first one will be used here.&lt;br /&gt;
 &lt;br /&gt;
 &lt;br /&gt;