Kite's Genchain mode numbering: Difference between revisions
Wikispaces>TallKite **Imported revision 593267764 - Original comment: ** |
Wikispaces>TallKite **Imported revision 593268444 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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>2016-09-25 21: | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-09-25 21:53:18 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>593268444</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> | ||
| Line 9: | Line 9: | ||
[[toc]] | [[toc]] | ||
**Mode | **Mode Numbers** provide a way to name MOS, MODMOS and even non-MOS rank-2 scales and modes systematically. Like [[xenharmonic/Modal UDP notation|Modal UDP notation]], it starts with the convention of using //some-temperament-name// [//some-number//] to create a generator-chain, and adds a way to number each mode uniquely. | ||
[[xenharmonic/MOSScales|MOS scales]] are formed from a segment of the [[xenharmonic/periods and generators|generator-chain]], or genchain. The first note in the genchain is the tonic of the 1st mode, the 2nd note is the tonic of the 2nd mode, etc., somewhat analogous to harmonica positions. | [[xenharmonic/MOSScales|MOS scales]] are formed from a segment of the [[xenharmonic/periods and generators|generator-chain]], or genchain. The first note in the genchain is the tonic of the 1st mode, the 2nd note is the tonic of the 2nd mode, etc., somewhat analogous to harmonica positions. | ||
| Line 122: | Line 122: | ||
Ascending melodic minor modes: | Ascending melodic minor modes: | ||
1st Meantone [7] #5: C D E F# G# A B C | 1st Meantone [7] #5: C D E F# G# A B C | ||
7th Meantone [7] b4: C Db Eb Fb Gb Ab Bb C (avoid "2nd Meantone [7] #1") | |||
3rd Meantone [7] # | 3rd Meantone [7] #4: C D E F# G A Bb C | ||
4th Meantone [7] | 4th Meantone [7] #7: C D Eb F G A B C | ||
5th Meantone [7] # | 5th Meantone [7] #3: C D E F G Ab Bb C | ||
6th Meantone [7] #6 | 6th Meantone [7] #6: C Db Eb F G A Bb C | ||
7th Meantone [7] # | 7th Meantone [7] #2: C D Eb F Gb Ab Bb C | ||
| Line 255: | Line 255: | ||
|| octotonic: || || || (assumes 3/2 < 700¢) || | || octotonic: || || || (assumes 3/2 < 700¢) || | ||
|| C D E F F# G A B C || F __**C**__ G D A E B F# || C 2nd Meantone {8} || LLMs MLLM || | || C D E F F# G A B C || F __**C**__ G D A E B F# || C 2nd Meantone {8} || LLMs MLLM || | ||
|| " || " || C 2nd Meantone [7] add #4 || | ||= " ||= " || C 2nd Meantone [7] add #4 || " || | ||
||= " ||= " || C 1st Meantone [7] add b4 * || | ||= " ||= " || C 1st Meantone [7] add b4 * || " || | ||
|| C D E F F# G A Bb C || Bb F __**C**__ G D A E * F# || C 3rd Meantone [7] add #4 || LLMs MLML || | || C D E F F# G A Bb C || Bb F __**C**__ G D A E * F# || C 3rd Meantone [7] add #4 || LLMs MLML || | ||
|| A B C D D# E F G# A || F C * D __**A**__ E B * * G# D# || A 5th Meantone [7] #7 add #4 || LMLs MMXM || | || A B C D D# E F G# A || F C * D __**A**__ E B * * G# D# || A 5th Meantone [7] #7 add #4 || LMLs MMXM || | ||
| Line 262: | Line 262: | ||
|| nonotonic: || || || || | || nonotonic: || || || || | ||
|| A B C# D D# E F# G G# A || G D __**A**__ E B F# C# G# D# || A 3rd Meantone {9} || LLMsM LMsM || | || A B C# D D# E F# G G# A || G D __**A**__ E B F# C# G# D# || A 3rd Meantone {9} || LLMsM LMsM || | ||
|| " || " || A 3rd Meantone [7] add #4, #7 || | || " || " || A 3rd Meantone [7] add #4, #7 || " || | ||
||= " ||= " || A 2nd Meantone [7] add #4, b7 || | ||= " ||= " || A 2nd Meantone [7] add #4, b7 || " || | ||
||= " ||= " || A 1st Meantone [7] add b4, b7 || | ||= " ||= " || A 1st Meantone [7] add b4, b7 || " || | ||
|| A B C D D# E F G G# A || F C G D __**A**__ E B * * G# D# || A 5th Meantone [7] add #4, #7 || LMLsM MLsM || | || A B C D D# E F G G# A || F C G D __**A**__ E B * * G# D# || A 5th Meantone [7] add #4, #7 || LMLsM MLsM || | ||
|| hexatonic: || || || || | || hexatonic: || || || || | ||
|| F G A C D E F || __**F**__ C G D A E || F 1st Meantone {6} || MML MMs || | || F G A C D E F || __**F**__ C G D A E || F 1st Meantone {6} || MML MMs || | ||
|| " || " || F 2nd Meantone [7] no4 || | || " || " || F 2nd Meantone [7] no4 || " || | ||
||= " ||= " || F 1st Meantone [7] no4 || | ||= " ||= " || F 1st Meantone [7] no4 || " || | ||
|| G A C D E F# G || C __**G**__ D A E * F# || G 2nd Meantone [7] no3 || MLM MMs || | || G A C D E F# G || C __**G**__ D A E * F# || G 2nd Meantone [7] no3 || MLM MMs || | ||
|| pentatonic: || || || || | || pentatonic: || || || || | ||
|| F G A C E F || __**F**__ C G * A E || F 2nd Meantone [7] no4 no6 || MML Xs || | || F G A C E F || __**F**__ C G * A E || F 2nd Meantone [7] no4 no6 || MML Xs || | ||
||= " ||= " || F 1st Meantone [7] no4 no6 || | ||= " ||= " || F 1st Meantone [7] no4 no6 || " || | ||
|| A B C E F A || F C * * __**A**__ E B || A 5th Meantone [7] no4 no7 || MsL sL || | || A B C E F A || F C * * __**A**__ E B || A 5th Meantone [7] no4 no7 || MsL sL || | ||
* In the 3rd row, "add b4" means add a 4th flattened relative to the Lydian mode's 4th, not the perfect 4th. | * In the 3rd row, "add b4" means add a 4th flattened relative to the Lydian mode's 4th, not the perfect 4th. | ||
| Line 310: | Line 310: | ||
|| notation || scale name || sL pattern || example in C || genchain || | || notation || scale name || sL pattern || example in C || genchain || | ||
|| heptatonic || 5th Sensi [8] || sL sL ssLs || C Db Eb E# Gb G# A B C || Gb B Eb G# __**C**__ E# A Db || | || heptatonic || 5th Sensi [8] || sL sL ssLs || C Db Eb E# Gb G# A B C || Gb B Eb G# __**C**__ E# A Db || | ||
|| octotonic || 5th Sensi [8] || | || octotonic || 5th Sensi [8] ||= " || C D E# F G# H A B# C || G# B# E# H __**C**__ F A D || | ||
|| heptatonic || 5th Sensi [8] +7 || sL sL sssL || C Db Eb E# Gb G# A Bb C || Gb * Eb G# __**C**__ E# A Db * Bb || | || heptatonic || 5th Sensi [8] +7 || sL sL sssL || C Db Eb E# Gb G# A Bb C || Gb * Eb G# __**C**__ E# A Db * Bb || | ||
|| octotonic || 5th Sensi [8] +8 || | || octotonic || 5th Sensi [8] +8 ||= " || C D E# F G# H A B C || G# * E# H __**C**__ F A D * B || | ||
Heptatonic fifth-based notation: | Heptatonic fifth-based notation: | ||
C - C# - Db - D - D# - Eb - E - E#/Fb - F - F# - Gb - G - G# - Ab - A - A# - Bb - B - B#/Cb - C | C - C# - Db - D - D# - Eb - E - E#/Fb - F - F# - Gb - G - G# - Ab - A - A# - Bb - B - B#/Cb - C | ||
| Line 318: | Line 318: | ||
C - C#/Db - D - D#/Eb - E - E# - Fb - F - F#/Gb - G - G# - Hb - H - H#/Ab - A - A#/Bb - B - B# - Cb -C | C - C#/Db - D - D#/Eb - E - E# - Fb - F - F#/Gb - G - G# - Hb - H - H#/Ab - A - A#/Bb - B - B# - Cb -C | ||
The heptatonic-notated MODMOS has "+7" because B is the 7th letter from C. Likewise octotonic has "+8" because with H, B is the 8th letter. | |||
| Line 407: | Line 407: | ||
<!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --><div style="margin-left: 1em;"><a href="#Rationale">Rationale</a></div> | <!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --><div style="margin-left: 1em;"><a href="#Rationale">Rationale</a></div> | ||
<!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --></div> | <!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --></div> | ||
<!-- ws:end:WikiTextTocRule:19 --><strong>Mode | <!-- ws:end:WikiTextTocRule:19 --><strong>Mode Numbers</strong> provide a way to name MOS, MODMOS and even non-MOS rank-2 scales and modes systematically. Like <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Modal%20UDP%20notation">Modal UDP notation</a>, it starts with the convention of using <em>some-temperament-name</em> [<em>some-number</em>] to create a generator-chain, and adds a way to number each mode uniquely.<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS scales</a> are formed from a segment of the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/periods%20and%20generators">generator-chain</a>, or genchain. The first note in the genchain is the tonic of the 1st mode, the 2nd note is the tonic of the 2nd mode, etc., somewhat analogous to harmonica positions.<br /> | <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS scales</a> are formed from a segment of the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/periods%20and%20generators">generator-chain</a>, or genchain. The first note in the genchain is the tonic of the 1st mode, the 2nd note is the tonic of the 2nd mode, etc., somewhat analogous to harmonica positions.<br /> | ||
| Line 1,152: | Line 1,152: | ||
Ascending melodic minor modes:<br /> | Ascending melodic minor modes:<br /> | ||
1st Meantone [7] #5: C D E F# G# A B C<br /> | 1st Meantone [7] #5: C D E F# G# A B C<br /> | ||
7th Meantone [7] b4: C Db Eb Fb Gb Ab Bb C (avoid &quot;2nd Meantone [7] #1&quot;)<br /> | |||
3rd Meantone [7] # | 3rd Meantone [7] #4: C D E F# G A Bb C<br /> | ||
4th Meantone [7] | 4th Meantone [7] #7: C D Eb F G A B C<br /> | ||
5th Meantone [7] # | 5th Meantone [7] #3: C D E F G Ab Bb C<br /> | ||
6th Meantone [7] #6 | 6th Meantone [7] #6: C Db Eb F G A Bb C<br /> | ||
7th Meantone [7] # | 7th Meantone [7] #2: C D Eb F Gb Ab Bb C<br /> | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
| Line 1,469: | Line 1,469: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>&quot;<br /> | <td style="text-align: center;">&quot;<br /> | ||
</td> | </td> | ||
<td>&quot;<br /> | <td style="text-align: center;">&quot;<br /> | ||
</td> | </td> | ||
<td>C 2nd Meantone [7] add #4<br /> | <td>C 2nd Meantone [7] add #4<br /> | ||
</td> | </td> | ||
<td><br /> | <td>&quot;<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,485: | Line 1,485: | ||
<td>C 1st Meantone [7] add b4 *<br /> | <td>C 1st Meantone [7] add b4 *<br /> | ||
</td> | </td> | ||
<td><br /> | <td>&quot;<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,545: | Line 1,545: | ||
<td>A 3rd Meantone [7] add #4, #7<br /> | <td>A 3rd Meantone [7] add #4, #7<br /> | ||
</td> | </td> | ||
<td><br /> | <td>&quot;<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,555: | Line 1,555: | ||
<td>A 2nd Meantone [7] add #4, b7<br /> | <td>A 2nd Meantone [7] add #4, b7<br /> | ||
</td> | </td> | ||
<td><br /> | <td>&quot;<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,565: | Line 1,565: | ||
<td>A 1st Meantone [7] add b4, b7<br /> | <td>A 1st Meantone [7] add b4, b7<br /> | ||
</td> | </td> | ||
<td><br /> | <td>&quot;<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,605: | Line 1,605: | ||
<td>F 2nd Meantone [7] no4<br /> | <td>F 2nd Meantone [7] no4<br /> | ||
</td> | </td> | ||
<td><br /> | <td>&quot;<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,615: | Line 1,615: | ||
<td>F 1st Meantone [7] no4<br /> | <td>F 1st Meantone [7] no4<br /> | ||
</td> | </td> | ||
<td><br /> | <td>&quot;<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,655: | Line 1,655: | ||
<td>F 1st Meantone [7] no4 no6<br /> | <td>F 1st Meantone [7] no4 no6<br /> | ||
</td> | </td> | ||
<td><br /> | <td>&quot;<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,734: | Line 1,734: | ||
<td>5th Sensi [8]<br /> | <td>5th Sensi [8]<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">&quot;<br /> | ||
</td> | </td> | ||
<td>C D E# F G# H A B# C<br /> | <td>C D E# F G# H A B# C<br /> | ||
| Line 1,758: | Line 1,758: | ||
<td>5th Sensi [8] +8<br /> | <td>5th Sensi [8] +8<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: center;">&quot;<br /> | ||
</td> | </td> | ||
<td>C D E# F G# H A B C<br /> | <td>C D E# F G# H A B C<br /> | ||
| Line 1,772: | Line 1,772: | ||
C - C#/Db - D - D#/Eb - E - E# - Fb - F - F#/Gb - G - G# - Hb - H - H#/Ab - A - A#/Bb - B - B# - Cb -C<br /> | C - C#/Db - D - D#/Eb - E - E# - Fb - F - F#/Gb - G - G# - Hb - H - H#/Ab - A - A#/Bb - B - B# - Cb -C<br /> | ||
<br /> | <br /> | ||
<br /> | The heptatonic-notated MODMOS has &quot;+7&quot; because B is the 7th letter from C. Likewise octotonic has &quot;+8&quot; because with H, B is the 8th letter.<br /> | ||
<br /> | <br /> | ||
<br /> | <br /> | ||