Comparison of mode notation systems: Difference between revisions

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=__How to name rank-2 scales__= 

Here's how to name MOS, MODMOS and even non-MOS rank-2 scales 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.

Conventionally, diatonic modes are named arbitrarily with individual names (2nd column). But to cover all possible xenharmonic possibilities, it's better to number them systematically (first column). Here are all the modes of Meantone[7], using ~3/2 as the generator:
|| new scale name || old scale name || Ls pattern || example on white keys || genchain ||
|| 1st Meantone[7] || Lydian || LLLs LLs || F G A B C D E F || **F** C G D A E B ||
|| 2nd Meantone[7] || Ionian (major) || LLsL LLs || C D E F G A B C || F **C** G D A E B ||
|| 3rd Meantone[7] || Mixolydian || LLsL LsL || G A B C D E F G || F C **G** D A E B ||
|| 4th Meantone[7] || Dorian || LsLL LsL || D E F G A B C D || F C G **D** A E B ||
|| 5th Meantone[7] || Aeolian (minor) || LsLL sLL || A B C D E F G A || F C G D **A** E B ||
|| 6th Meantone[7] || Phrygian || sLLL sLL || E F G A B C D E || F C G D A **E** B ||
|| 7th Meantone[7] || Locrian || sLLs LLL || B C D E F G A B || F C G D A E **B** ||
Scales are formed from a segment of the generator-chain, or genchain. The first note in the genchain is the tonic of mode #1, the 2nd note is the tonic of mode #2, etc. For example, Dorian is 4th Meantone[7], spoken as "fourth meantone heptatonic" or possibly "fourth meantone seven". If in D, as above, it would be "D 4th Meantone heptatonic". The same 7 modes, all with C as the tonic:
|| new scale name || old scale name || Ls pattern || example in C || ------------------- genchain --------------- ||
|| 1st Meantone[7] || Lydian || LLLs LLs || C D E F# G A B C ||> **C** G D A E B F# ||
|| 2nd Meantone[7] || Ionian (major) || LLsL LLs || C D E F G A B C ||> F **C** G D A E B ---- ||
|| 3rd Meantone[7] || Mixolydian || LLsL LsL || C D E F G A Bb C ||> Bb F **C** G D A E ------- ||
|| 4th Meantone[7] || Dorian || LsLL LsL || C D Eb F G A Bb C || ------------- Eb Bb F **C** G D A ||
|| 5th Meantone[7] || Aeolian (minor) || LsLL sLL || C D Eb F G Ab Bb C || --------- Ab Eb Bb F **C** G D ||
|| 6th Meantone[7] || Phrygian || sLLL sLL || C Db Eb F G Ab Bb C || ---- Db Ab Eb Bb F **C** G ||
|| 7th Meantone[7] || Locrian || sLLs LLL || C Db Eb F Gb Ab Bb C || Gb Db Ab Eb Bb F **C** ||
Similar modes are grouped together. The overall progression is from sharper to flatter. However for the 5 pentatonic modes, the overall progression is from flatter to sharper. Unlike UDP notation, the generator isn't always chroma-positive.
|| new scale name || old scale name || Ls pattern || example in C || --------- genchain ------- ||
|| 1st Meantone[5] || major pentatonic || ssL sL || C D E G A C ||> **C** G D A E ||
|| 2nd Meantone[5] ||= ??? || sLs sL || C D F G A C ||> F **C** G D A -- ||
|| 3rd Meantone[5] ||= ??? || sLs Ls || C D F G Bb C || -------- Bb F **C** G D ||
|| 4th Meantone[5] || minor pentatonic || Lss Ls || C Eb F G Bb C || ---- Eb Bb F **C** G ||
|| 5th Meantone[5] ||= ??? || LsL ss || C Eb F Ab Bb C || Ab Eb Bb F **C** ||
12-note meantone scales:
|| scale name || Ls pattern || example in C || genchain ||
|| 1st Meantone[12] || sLsLsLL sLsLL || C C# D D# E E# F# G G# A A# B C || **C** G D A E B F# C# G# D# A# E# ||
|| 2nd Meantone[12] || sLsLLsL sLsLL || C C# D D# E F F# G G# A A# B C || F **C** G D A E B F# C# G# D# A# ||
|| 3rd Meantone[12] || sLsLLsL sLLsL || C C# D D# E F F# G G# A Bb B C || Bb F **C** G D A E B F# C# G# D# ||
|| 4th Meantone[12] || sLLsLsL sLLsL || C C# D Eb E F F# G G# A Bb B C || Eb Bb F **C** G D A E B F# C# G# ||
|| 5th Meantone[12] || sLLsLsL LsLsL || C C# D Eb E F F# G Ab A Bb B C || Ab Eb Bb F **C** G D A E B F# C# ||
|| 6th Meantone[12] || LsLsLsL LsLsL || C Db D Eb E F F# G Ab A Bb B C || Db Ab Eb Bb F **C** G D A E B F# ||
|| 7th Meantone[12] || LsLsLLs LsLsL || C Db D Eb E F Gb G Ab A Bb B C || Gb Db Ab Eb Bb F **C** G D A E B ||
||= etc. ||   ||   ||   ||
If the fifth were larger than 700¢, which would be the case for Superpyth[12], L and s would be interchanged in this table.


==[[#How to name rank-2 scales-Generator choice]]**__Generator choice__**== 
The octave inverse of a generator is also a generator. To avoid ambiguity, the smaller of the two options is chosen. An exception is made for 3/2, which is preferred over 4/3 for historical reasons. More examples:

Sensi[8] modes in 19edo (generator = 3rd = ~9/7 = 7\19, L = 3\19, s = 2\19)
|| scale name || Ls pattern || example in C || genchain ||
|| 1st Sensi[8] || ssL ssL sL || C Db D# E# F# G A Bb C || **C** E# A Db F# Bb D# G ||
|| 2nd Sensi[8] || ssL sL ssL || C Db D# E# F# G# A Bb C || G# **C** E# A Db F# Bb D# ||
|| 3rd Sensi[8] || sL ssL ssL || C Db Eb E# F# G# A Bb C || Eb G# **C** E# A Db F# Bb ||
|| 4th Sensi[8] || sL ssL sL s || C Db Eb E# F# G# A B C || B Eb G# **C** E# A Db F# ||
|| 5th Sensi[8] || sL sL ssL s || C Db Eb E# Gb G# A B C || Gb B Eb G# **C** E# A Db ||
|| 6th Sensi[8] || Lss Lss Ls || C D Eb E# Gb G# A B C || D Gb B Eb G# **C** E# A ||
|| 7th Sensi[8] || Lss Ls Lss || C D Eb E# Gb G# A# B C || A# D Gb B Eb G# **C** E# ||
|| 8th Sensi[8] || Ls Lss Lss || C D Eb F Gb G# A# B C || F A# D Gb B Eb G# **C** ||
Porcupine[7] modes in 22edo (generator = 2nd = ~10/9 = 3\22, L = 4\22, s = 3\22), using [[xenharmonic/ups and downs notation|ups and downs notation]].
Because the generator is a 2nd, the genchain looks like the scale.
|| scale name || Ls pattern || example in C || genchain ||
|| 1st Porcupine[7] || ssss ssL || C Dv Eb^ F Gv Ab^ Bb C || **C** Dv Eb^ F Gv Ab^ Bb ||
|| 2nd Porcupine[7] || ssss sLs || C Dv Eb^ F Gv Ab^ Bb^ C || Bb^ **C** Dv Eb^ F Gv Ab^ ||
|| 3rd Porcupine[7] || ssss Lss || C Dv Eb^ F Gv Av Bb^ C || Av Bb^ **C** Dv Eb^ F Gv ||
|| 4th Porcupine[7] || sssL sss || C Dv Eb^ F G Av Bb^ C || G Av Bb^ **C** Dv Eb^ F ||
|| 5th Porcupine[7] || ssLs sss || C Dv Eb^ F^ G Av Bb^ C ||= F^ G Av Bb^ **C** Dv Eb^ ||
|| 6th Porcupine[7] || sLss sss || C Dv Ev F^ G Av Bb^ C || Ev F^ G Av Bb^ **C** Dv ||
|| 7th Porcupine[7] || Lsss sss || C D Ev F^ G Av Bb^ C || D Ev F^ G Av Bb^ **C** ||


==[[#How to name rank-2 scales-MODMOS scales]]**__MODMOS scales__**== 
These are written as MOS scales with chromatic alterations. To find the scale's name, first write out the genchain for the scale, which will always have gaps. Then compact it into 7 contiguous notes by altering one or more notes. There may be more than one way to do this, usually choose the method that alters as few notes as possible. Then find the name of the mode, then add the appropriate alterations.
|| old scale name || example in A || genchain (* marks a gap) || compacted genchain || new scale name ||
|| Harmonic minor || A B C D E F G# A || F C * D **A** E B * * G# || F C G D **A** E B || 5th Meantone[7] #7 ||
|| Melodic minor || A B C D E F# G# A || C * D **A** E B F# * G# || F C G D **A** E B || 5th Meantone[7] #6 #7 ||
||= " ||= " ||= " || D **A** E B F# C# G# || 2nd Meantone[2] b3 ||
|| Japanese pentatonic || A B C E F A || F C * * **A** E B || **A** E B F# C# || 1st Meantone[5] b3 b5 ||
|| (a mode of the above) || F A B C E F || **F** C * * A E B || Ab Eb Bb **F** C || 4th Meantone[5] #2 #3 #5 ||
Unfortunately there is some ambiguity, as the two names for melodic minor show. The Japanese pentatonic is b5, not b6, because we use pentatonic scale degrees. The mode of Japanese pentatonic alters three notes, not two, to avoid "b1 b5". Unfortunately, it's not apparent by the scale names that the last two examples are modes of each other.


==[[#How to name rank-2 scales-Fractional-octave periods]]**__Fractional-octave periods__**== 
Fractional-period rank-2 temperaments have multiple genchains running in parallel. For example, shrutal[10] might look like this:
Eb -- Bb -- F --- C --- G
A --- E --- B --- F# -- C#

Or alternatively, using 16/15 not 3/2 as the generator:
Eb -- E --- F --- F# -- G
A --- Bb -- B --- C --- C#

Multiple genchains occur because rank-2 really is 2 dimensional, with a "genweb" running in octaves (or whatever the period is) vertically and fifths (or whatever the generator is) horizontally. When the period is an octave, this octave-reduces to a single horizontal genchain. But shrutal has a genweb with vertical half-octaves, which octave-reduces to two parallel genchains. Temperaments with third-octave periods reduce to a triple-genchain, and so forth.

In order to be a MOS scale, the genchains must of course be the right length, and without any gaps. But they must also line up exactly, so that each note has a neighbor immediately above and/or below. In other words, every column of the genweb must be complete.

If the period is a fraction of an octave, 3/2 is still preferred over all other generators, even though that makes the generator larger than the period. Shrutal's generator is 3/2, not 16/15. However, 16/15 would still create the same mode numbers and thus the same scale names.

All five Shrutal[10] modes:
|| scale name || Ls pattern || example in C || 1st genchain || 2nd genchain ||
|| 1st Shrutal[10] || ssssL-ssssL || C C# D D# E F# G G# A A# C || **C** G D A E || F# C# G# D# A# ||
|| 2nd Shrutal[10] || sssLs-sssLs || C C# D D# F F# G G# A B C || F **C** G D A || B F# C# G# D# ||
|| 3rd Shrutal[10] || ssLss-ssLss || C C# D E F F# G G# Bb B C || Bb F **C** G D || E B F# C# G# ||
|| 4th Shrutal[10] || sLsss-sLsss || C C# Eb E F F# G A Bb B C || Eb Bb F **C** G || A E B F# C# ||
|| 5th Shrutal[10] || Lssss-Lssss || C D Eb E F F# Ab A Bb B C || Ab Eb Bb F **C** || D A E B F# ||
Both Blackwood[10] modes:
|| scale name || Ls pattern || example in C || 1st genchain || 2nd chain || 3rd chain || 4th chain || 5th chain ||
|| 1st Blackwood[10] || LsLsLs LsLs || C C# D Ev E F# G G# A B C || **C** Ev || D F# || E G# || G B || A C# ||
|| 2nd Blackwood[10] || sLsLsL sLsL || C C^ D Eb E F G Ab A Bb C || Ab **C** || Bb D || C^ E || Eb G || F A ||
The period is a fifth-octave = 240¢. The generator is 5/4. Ups and downs are used to avoid having duplicate notes.


==[[#How to name rank-2 scales-Non-MOS scales]]**__Non-MOS non-MODMOS scales__**== 
These can be indicated with curly brackets {}, because regular brackets [] are reserved for MOS scales. The same naming methods apply. Examples:

C D E F F# G A B C, which has a genchain F **C** G D A E B F#, and is named C 2nd Meantone{8}.

C D E F F# G A Bb C, with genchain Bb F **C** G D A E * F#. Alter as few notes as possible to get if not a MOS, at least an unbroken genchain: F **C** G D A E B F#. The scale is C 2nd Meantone{8} b7.

A B C D D# E F G G# A, with genchain F C G D **A** E B * * G# D#. Sharpen F and C to get an unbroken genchain: G D **A** E B F# C# G# D#, giving the name A 3rd Meantone{9} b3 b7.

F G A C F, with genchain **F** C G * A. No amount of altering will make an unbroken chain, so the name is F 1st Meantone[5] no 5.


==[[#How to name rank-2 scales-Color notation]]__Color notation__== 
This method of scale naming can be combined with [[xenharmonic/Kite's color notation|Kite's color notation]], as in "2nd green heptatonic" for 2nd Meantone[7].

Original HTML content:

<html><head><title>Naming Rank-2 Scales</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="How to name rank-2 scales"></a><!-- ws:end:WikiTextHeadingRule:0 --><u>How to name rank-2 scales</u></h1>
 <br />
Here's how to name MOS, MODMOS and even non-MOS rank-2 scales 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 />
Conventionally, diatonic modes are named arbitrarily with individual names (2nd column). But to cover all possible xenharmonic possibilities, it's better to number them systematically (first column). Here are all the modes of Meantone[7], using ~3/2 as the generator:<br />


<table class="wiki_table">
    <tr>
        <td>new scale name<br />
</td>
        <td>old scale name<br />
</td>
        <td>Ls pattern<br />
</td>
        <td>example on white keys<br />
</td>
        <td>genchain<br />
</td>
    </tr>
    <tr>
        <td>1st Meantone[7]<br />
</td>
        <td>Lydian<br />
</td>
        <td>LLLs LLs<br />
</td>
        <td>F G A B C D E F<br />
</td>
        <td><strong>F</strong> C G D A E B<br />
</td>
    </tr>
    <tr>
        <td>2nd Meantone[7]<br />
</td>
        <td>Ionian (major)<br />
</td>
        <td>LLsL LLs<br />
</td>
        <td>C D E F G A B C<br />
</td>
        <td>F <strong>C</strong> G D A E B<br />
</td>
    </tr>
    <tr>
        <td>3rd Meantone[7]<br />
</td>
        <td>Mixolydian<br />
</td>
        <td>LLsL LsL<br />
</td>
        <td>G A B C D E F G<br />
</td>
        <td>F C <strong>G</strong> D A E B<br />
</td>
    </tr>
    <tr>
        <td>4th Meantone[7]<br />
</td>
        <td>Dorian<br />
</td>
        <td>LsLL LsL<br />
</td>
        <td>D E F G A B C D<br />
</td>
        <td>F C G <strong>D</strong> A E B<br />
</td>
    </tr>
    <tr>
        <td>5th Meantone[7]<br />
</td>
        <td>Aeolian (minor)<br />
</td>
        <td>LsLL sLL<br />
</td>
        <td>A B C D E F G A<br />
</td>
        <td>F C G D <strong>A</strong> E B<br />
</td>
    </tr>
    <tr>
        <td>6th Meantone[7]<br />
</td>
        <td>Phrygian<br />
</td>
        <td>sLLL sLL<br />
</td>
        <td>E F G A B C D E<br />
</td>
        <td>F C G D A <strong>E</strong> B<br />
</td>
    </tr>
    <tr>
        <td>7th Meantone[7]<br />
</td>
        <td>Locrian<br />
</td>
        <td>sLLs LLL<br />
</td>
        <td>B C D E F G A B<br />
</td>
        <td>F C G D A E <strong>B</strong><br />
</td>
    </tr>
</table>

Scales are formed from a segment of the generator-chain, or genchain. The first note in the genchain is the tonic of mode #1, the 2nd note is the tonic of mode #2, etc. For example, Dorian is 4th Meantone[7], spoken as &quot;fourth meantone heptatonic&quot; or possibly &quot;fourth meantone seven&quot;. If in D, as above, it would be &quot;D 4th Meantone heptatonic&quot;. The same 7 modes, all with C as the tonic:<br />


<table class="wiki_table">
    <tr>
        <td>new scale name<br />
</td>
        <td>old scale name<br />
</td>
        <td>Ls pattern<br />
</td>
        <td>example in C<br />
</td>
        <td>------------------- genchain ---------------<br />
</td>
    </tr>
    <tr>
        <td>1st Meantone[7]<br />
</td>
        <td>Lydian<br />
</td>
        <td>LLLs LLs<br />
</td>
        <td>C D E F# G A B C<br />
</td>
        <td style="text-align: right;"><strong>C</strong> G D A E B F#<br />
</td>
    </tr>
    <tr>
        <td>2nd Meantone[7]<br />
</td>
        <td>Ionian (major)<br />
</td>
        <td>LLsL LLs<br />
</td>
        <td>C D E F G A B C<br />
</td>
        <td style="text-align: right;">F <strong>C</strong> G D A E B ----<br />
</td>
    </tr>
    <tr>
        <td>3rd Meantone[7]<br />
</td>
        <td>Mixolydian<br />
</td>
        <td>LLsL LsL<br />
</td>
        <td>C D E F G A Bb C<br />
</td>
        <td style="text-align: right;">Bb F <strong>C</strong> G D A E -------<br />
</td>
    </tr>
    <tr>
        <td>4th Meantone[7]<br />
</td>
        <td>Dorian<br />
</td>
        <td>LsLL LsL<br />
</td>
        <td>C D Eb F G A Bb C<br />
</td>
        <td>------------- Eb Bb F <strong>C</strong> G D A<br />
</td>
    </tr>
    <tr>
        <td>5th Meantone[7]<br />
</td>
        <td>Aeolian (minor)<br />
</td>
        <td>LsLL sLL<br />
</td>
        <td>C D Eb F G Ab Bb C<br />
</td>
        <td>--------- Ab Eb Bb F <strong>C</strong> G D<br />
</td>
    </tr>
    <tr>
        <td>6th Meantone[7]<br />
</td>
        <td>Phrygian<br />
</td>
        <td>sLLL sLL<br />
</td>
        <td>C Db Eb F G Ab Bb C<br />
</td>
        <td>---- Db Ab Eb Bb F <strong>C</strong> G<br />
</td>
    </tr>
    <tr>
        <td>7th Meantone[7]<br />
</td>
        <td>Locrian<br />
</td>
        <td>sLLs LLL<br />
</td>
        <td>C Db Eb F Gb Ab Bb C<br />
</td>
        <td>Gb Db Ab Eb Bb F <strong>C</strong><br />
</td>
    </tr>
</table>

Similar modes are grouped together. The overall progression is from sharper to flatter. However for the 5 pentatonic modes, the overall progression is from flatter to sharper. Unlike UDP notation, the generator isn't always chroma-positive.<br />


<table class="wiki_table">
    <tr>
        <td>new scale name<br />
</td>
        <td>old scale name<br />
</td>
        <td>Ls pattern<br />
</td>
        <td>example in C<br />
</td>
        <td>--------- genchain -------<br />
</td>
    </tr>
    <tr>
        <td>1st Meantone[5]<br />
</td>
        <td>major pentatonic<br />
</td>
        <td>ssL sL<br />
</td>
        <td>C D E G A C<br />
</td>
        <td style="text-align: right;"><strong>C</strong> G D A E<br />
</td>
    </tr>
    <tr>
        <td>2nd Meantone[5]<br />
</td>
        <td style="text-align: center;">???<br />
</td>
        <td>sLs sL<br />
</td>
        <td>C D F G A C<br />
</td>
        <td style="text-align: right;">F <strong>C</strong> G D A --<br />
</td>
    </tr>
    <tr>
        <td>3rd Meantone[5]<br />
</td>
        <td style="text-align: center;">???<br />
</td>
        <td>sLs Ls<br />
</td>
        <td>C D F G Bb C<br />
</td>
        <td>-------- Bb F <strong>C</strong> G D<br />
</td>
    </tr>
    <tr>
        <td>4th Meantone[5]<br />
</td>
        <td>minor pentatonic<br />
</td>
        <td>Lss Ls<br />
</td>
        <td>C Eb F G Bb C<br />
</td>
        <td>---- Eb Bb F <strong>C</strong> G<br />
</td>
    </tr>
    <tr>
        <td>5th Meantone[5]<br />
</td>
        <td style="text-align: center;">???<br />
</td>
        <td>LsL ss<br />
</td>
        <td>C Eb F Ab Bb C<br />
</td>
        <td>Ab Eb Bb F <strong>C</strong><br />
</td>
    </tr>
</table>

12-note meantone scales:<br />


<table class="wiki_table">
    <tr>
        <td>scale name<br />
</td>
        <td>Ls pattern<br />
</td>
        <td>example in C<br />
</td>
        <td>genchain<br />
</td>
    </tr>
    <tr>
        <td>1st Meantone[12]<br />
</td>
        <td>sLsLsLL sLsLL<br />
</td>
        <td>C C# D D# E E# F# G G# A A# B C<br />
</td>
        <td><strong>C</strong> G D A E B F# C# G# D# A# E#<br />
</td>
    </tr>
    <tr>
        <td>2nd Meantone[12]<br />
</td>
        <td>sLsLLsL sLsLL<br />
</td>
        <td>C C# D D# E F F# G G# A A# B C<br />
</td>
        <td>F <strong>C</strong> G D A E B F# C# G# D# A#<br />
</td>
    </tr>
    <tr>
        <td>3rd Meantone[12]<br />
</td>
        <td>sLsLLsL sLLsL<br />
</td>
        <td>C C# D D# E F F# G G# A Bb B C<br />
</td>
        <td>Bb F <strong>C</strong> G D A E B F# C# G# D#<br />
</td>
    </tr>
    <tr>
        <td>4th Meantone[12]<br />
</td>
        <td>sLLsLsL sLLsL<br />
</td>
        <td>C C# D Eb E F F# G G# A Bb B C<br />
</td>
        <td>Eb Bb F <strong>C</strong> G D A E B F# C# G#<br />
</td>
    </tr>
    <tr>
        <td>5th Meantone[12]<br />
</td>
        <td>sLLsLsL LsLsL<br />
</td>
        <td>C C# D Eb E F F# G Ab A Bb B C<br />
</td>
        <td>Ab Eb Bb F <strong>C</strong> G D A E B F# C#<br />
</td>
    </tr>
    <tr>
        <td>6th Meantone[12]<br />
</td>
        <td>LsLsLsL LsLsL<br />
</td>
        <td>C Db D Eb E F F# G Ab A Bb B C<br />
</td>
        <td>Db Ab Eb Bb F <strong>C</strong> G D A E B F#<br />
</td>
    </tr>
    <tr>
        <td>7th Meantone[12]<br />
</td>
        <td>LsLsLLs LsLsL<br />
</td>
        <td>C Db D Eb E F Gb G Ab A Bb B C<br />
</td>
        <td>Gb Db Ab Eb Bb F <strong>C</strong> G D A E B<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">etc.<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
</table>

If the fifth were larger than 700¢, which would be the case for Superpyth[12], L and s would be interchanged in this table.<br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="How to name rank-2 scales-Generator choice"></a><!-- ws:end:WikiTextHeadingRule:2 --><!-- ws:start:WikiTextAnchorRule:12:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@How to name rank-2 scales-Generator choice&quot; title=&quot;Anchor: How to name rank-2 scales-Generator choice&quot;/&gt; --><a name="How to name rank-2 scales-Generator choice"></a><!-- ws:end:WikiTextAnchorRule:12 --><strong><u>Generator choice</u></strong></h2>
 The octave inverse of a generator is also a generator. To avoid ambiguity, the smaller of the two options is chosen. An exception is made for 3/2, which is preferred over 4/3 for historical reasons. More examples:<br />
<br />
Sensi[8] modes in 19edo (generator = 3rd = ~9/7 = 7\19, L = 3\19, s = 2\19)<br />


<table class="wiki_table">
    <tr>
        <td>scale name<br />
</td>
        <td>Ls pattern<br />
</td>
        <td>example in C<br />
</td>
        <td>genchain<br />
</td>
    </tr>
    <tr>
        <td>1st Sensi[8]<br />
</td>
        <td>ssL ssL sL<br />
</td>
        <td>C Db D# E# F# G A Bb C<br />
</td>
        <td><strong>C</strong> E# A Db F# Bb D# G<br />
</td>
    </tr>
    <tr>
        <td>2nd Sensi[8]<br />
</td>
        <td>ssL sL ssL<br />
</td>
        <td>C Db D# E# F# G# A Bb C<br />
</td>
        <td>G# <strong>C</strong> E# A Db F# Bb D#<br />
</td>
    </tr>
    <tr>
        <td>3rd Sensi[8]<br />
</td>
        <td>sL ssL ssL<br />
</td>
        <td>C Db Eb E# F# G# A Bb C<br />
</td>
        <td>Eb G# <strong>C</strong> E# A Db F# Bb<br />
</td>
    </tr>
    <tr>
        <td>4th Sensi[8]<br />
</td>
        <td>sL ssL sL s<br />
</td>
        <td>C Db Eb E# F# G# A B C<br />
</td>
        <td>B Eb G# <strong>C</strong> E# A Db F#<br />
</td>
    </tr>
    <tr>
        <td>5th Sensi[8]<br />
</td>
        <td>sL sL ssL s<br />
</td>
        <td>C Db Eb E# Gb G# A B C<br />
</td>
        <td>Gb B Eb G# <strong>C</strong> E# A Db<br />
</td>
    </tr>
    <tr>
        <td>6th Sensi[8]<br />
</td>
        <td>Lss Lss Ls<br />
</td>
        <td>C D Eb E# Gb G# A B C<br />
</td>
        <td>D Gb B Eb G# <strong>C</strong> E# A<br />
</td>
    </tr>
    <tr>
        <td>7th Sensi[8]<br />
</td>
        <td>Lss Ls Lss<br />
</td>
        <td>C D Eb E# Gb G# A# B C<br />
</td>
        <td>A# D Gb B Eb G# <strong>C</strong> E#<br />
</td>
    </tr>
    <tr>
        <td>8th Sensi[8]<br />
</td>
        <td>Ls Lss Lss<br />
</td>
        <td>C D Eb F Gb G# A# B C<br />
</td>
        <td>F A# D Gb B Eb G# <strong>C</strong><br />
</td>
    </tr>
</table>

Porcupine[7] modes in 22edo (generator = 2nd = ~10/9 = 3\22, L = 4\22, s = 3\22), using <a class="wiki_link" href="http://xenharmonic.wikispaces.com/ups%20and%20downs%20notation">ups and downs notation</a>.<br />
Because the generator is a 2nd, the genchain looks like the scale.<br />


<table class="wiki_table">
    <tr>
        <td>scale name<br />
</td>
        <td>Ls pattern<br />
</td>
        <td>example in C<br />
</td>
        <td>genchain<br />
</td>
    </tr>
    <tr>
        <td>1st Porcupine[7]<br />
</td>
        <td>ssss ssL<br />
</td>
        <td>C Dv Eb^ F Gv Ab^ Bb C<br />
</td>
        <td><strong>C</strong> Dv Eb^ F Gv Ab^ Bb<br />
</td>
    </tr>
    <tr>
        <td>2nd Porcupine[7]<br />
</td>
        <td>ssss sLs<br />
</td>
        <td>C Dv Eb^ F Gv Ab^ Bb^ C<br />
</td>
        <td>Bb^ <strong>C</strong> Dv Eb^ F Gv Ab^<br />
</td>
    </tr>
    <tr>
        <td>3rd Porcupine[7]<br />
</td>
        <td>ssss Lss<br />
</td>
        <td>C Dv Eb^ F Gv Av Bb^ C<br />
</td>
        <td>Av Bb^ <strong>C</strong> Dv Eb^ F Gv<br />
</td>
    </tr>
    <tr>
        <td>4th Porcupine[7]<br />
</td>
        <td>sssL sss<br />
</td>
        <td>C Dv Eb^ F G Av Bb^ C<br />
</td>
        <td>G Av Bb^ <strong>C</strong> Dv Eb^ F<br />
</td>
    </tr>
    <tr>
        <td>5th Porcupine[7]<br />
</td>
        <td>ssLs sss<br />
</td>
        <td>C Dv Eb^ F^ G Av Bb^ C<br />
</td>
        <td style="text-align: center;">F^ G Av Bb^ <strong>C</strong> Dv Eb^<br />
</td>
    </tr>
    <tr>
        <td>6th Porcupine[7]<br />
</td>
        <td>sLss sss<br />
</td>
        <td>C Dv Ev F^ G Av Bb^ C<br />
</td>
        <td>Ev F^ G Av Bb^ <strong>C</strong> Dv<br />
</td>
    </tr>
    <tr>
        <td>7th Porcupine[7]<br />
</td>
        <td>Lsss sss<br />
</td>
        <td>C D Ev F^ G Av Bb^ C<br />
</td>
        <td>D Ev F^ G Av Bb^ <strong>C</strong><br />
</td>
    </tr>
</table>

<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="How to name rank-2 scales-MODMOS scales"></a><!-- ws:end:WikiTextHeadingRule:4 --><!-- ws:start:WikiTextAnchorRule:13:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@How to name rank-2 scales-MODMOS scales&quot; title=&quot;Anchor: How to name rank-2 scales-MODMOS scales&quot;/&gt; --><a name="How to name rank-2 scales-MODMOS scales"></a><!-- ws:end:WikiTextAnchorRule:13 --><strong><u>MODMOS scales</u></strong></h2>
 These are written as MOS scales with chromatic alterations. To find the scale's name, first write out the genchain for the scale, which will always have gaps. Then compact it into 7 contiguous notes by altering one or more notes. There may be more than one way to do this, usually choose the method that alters as few notes as possible. Then find the name of the mode, then add the appropriate alterations.<br />


<table class="wiki_table">
    <tr>
        <td>old scale name<br />
</td>
        <td>example in A<br />
</td>
        <td>genchain (* marks a gap)<br />
</td>
        <td>compacted genchain<br />
</td>
        <td>new scale name<br />
</td>
    </tr>
    <tr>
        <td>Harmonic minor<br />
</td>
        <td>A B C D E F G# A<br />
</td>
        <td>F C * D <strong>A</strong> E B * * G#<br />
</td>
        <td>F C G D <strong>A</strong> E B<br />
</td>
        <td>5th Meantone[7] #7<br />
</td>
    </tr>
    <tr>
        <td>Melodic minor<br />
</td>
        <td>A B C D E F# G# A<br />
</td>
        <td>C * D <strong>A</strong> E B F# * G#<br />
</td>
        <td>F C G D <strong>A</strong> E B<br />
</td>
        <td>5th Meantone[7] #6 #7<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">&quot;<br />
</td>
        <td style="text-align: center;">&quot;<br />
</td>
        <td style="text-align: center;">&quot;<br />
</td>
        <td>D <strong>A</strong> E B F# C# G#<br />
</td>
        <td>2nd Meantone[2] b3<br />
</td>
    </tr>
    <tr>
        <td>Japanese pentatonic<br />
</td>
        <td>A B C E F A<br />
</td>
        <td>F C * * <strong>A</strong> E B<br />
</td>
        <td><strong>A</strong> E B F# C#<br />
</td>
        <td>1st Meantone[5] b3 b5<br />
</td>
    </tr>
    <tr>
        <td>(a mode of the above)<br />
</td>
        <td>F A B C E F<br />
</td>
        <td><strong>F</strong> C * * A E B<br />
</td>
        <td>Ab Eb Bb <strong>F</strong> C<br />
</td>
        <td>4th Meantone[5] #2 #3 #5<br />
</td>
    </tr>
</table>

Unfortunately there is some ambiguity, as the two names for melodic minor show. The Japanese pentatonic is b5, not b6, because we use pentatonic scale degrees. The mode of Japanese pentatonic alters three notes, not two, to avoid &quot;b1 b5&quot;. Unfortunately, it's not apparent by the scale names that the last two examples are modes of each other.<br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="How to name rank-2 scales-Fractional-octave periods"></a><!-- ws:end:WikiTextHeadingRule:6 --><!-- ws:start:WikiTextAnchorRule:14:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@How to name rank-2 scales-Fractional-octave periods&quot; title=&quot;Anchor: How to name rank-2 scales-Fractional-octave periods&quot;/&gt; --><a name="How to name rank-2 scales-Fractional-octave periods"></a><!-- ws:end:WikiTextAnchorRule:14 --><strong><u>Fractional-octave periods</u></strong></h2>
 Fractional-period rank-2 temperaments have multiple genchains running in parallel. For example, shrutal[10] might look like this:<br />
Eb -- Bb -- F --- C --- G<br />
A --- E --- B --- F# -- C#<br />
<br />
Or alternatively, using 16/15 not 3/2 as the generator:<br />
Eb -- E --- F --- F# -- G<br />
A --- Bb -- B --- C --- C#<br />
<br />
Multiple genchains occur because rank-2 really is 2 dimensional, with a &quot;genweb&quot; running in octaves (or whatever the period is) vertically and fifths (or whatever the generator is) horizontally. When the period is an octave, this octave-reduces to a single horizontal genchain. But shrutal has a genweb with vertical half-octaves, which octave-reduces to two parallel genchains. Temperaments with third-octave periods reduce to a triple-genchain, and so forth.<br />
<br />
In order to be a MOS scale, the genchains must of course be the right length, and without any gaps. But they must also line up exactly, so that each note has a neighbor immediately above and/or below. In other words, every column of the genweb must be complete.<br />
<br />
If the period is a fraction of an octave, 3/2 is still preferred over all other generators, even though that makes the generator larger than the period. Shrutal's generator is 3/2, not 16/15. However, 16/15 would still create the same mode numbers and thus the same scale names.<br />
<br />
All five Shrutal[10] modes:<br />


<table class="wiki_table">
    <tr>
        <td>scale name<br />
</td>
        <td>Ls pattern<br />
</td>
        <td>example in C<br />
</td>
        <td>1st genchain<br />
</td>
        <td>2nd genchain<br />
</td>
    </tr>
    <tr>
        <td>1st Shrutal[10]<br />
</td>
        <td>ssssL-ssssL<br />
</td>
        <td>C C# D D# E F# G G# A A# C<br />
</td>
        <td><strong>C</strong> G D A E<br />
</td>
        <td>F# C# G# D# A#<br />
</td>
    </tr>
    <tr>
        <td>2nd Shrutal[10]<br />
</td>
        <td>sssLs-sssLs<br />
</td>
        <td>C C# D D# F F# G G# A B C<br />
</td>
        <td>F <strong>C</strong> G D A<br />
</td>
        <td>B F# C# G# D#<br />
</td>
    </tr>
    <tr>
        <td>3rd Shrutal[10]<br />
</td>
        <td>ssLss-ssLss<br />
</td>
        <td>C C# D E F F# G G# Bb B C<br />
</td>
        <td>Bb F <strong>C</strong> G D<br />
</td>
        <td>E B F# C# G#<br />
</td>
    </tr>
    <tr>
        <td>4th Shrutal[10]<br />
</td>
        <td>sLsss-sLsss<br />
</td>
        <td>C C# Eb E F F# G A Bb B C<br />
</td>
        <td>Eb Bb F <strong>C</strong> G<br />
</td>
        <td>A E B F# C#<br />
</td>
    </tr>
    <tr>
        <td>5th Shrutal[10]<br />
</td>
        <td>Lssss-Lssss<br />
</td>
        <td>C D Eb E F F# Ab A Bb B C<br />
</td>
        <td>Ab Eb Bb F <strong>C</strong><br />
</td>
        <td>D A E B F#<br />
</td>
    </tr>
</table>

Both Blackwood[10] modes:<br />


<table class="wiki_table">
    <tr>
        <td>scale name<br />
</td>
        <td>Ls pattern<br />
</td>
        <td>example in C<br />
</td>
        <td>1st genchain<br />
</td>
        <td>2nd chain<br />
</td>
        <td>3rd chain<br />
</td>
        <td>4th chain<br />
</td>
        <td>5th chain<br />
</td>
    </tr>
    <tr>
        <td>1st Blackwood[10]<br />
</td>
        <td>LsLsLs LsLs<br />
</td>
        <td>C C# D Ev E F# G G# A B C<br />
</td>
        <td><strong>C</strong> Ev<br />
</td>
        <td>D F#<br />
</td>
        <td>E G#<br />
</td>
        <td>G B<br />
</td>
        <td>A C#<br />
</td>
    </tr>
    <tr>
        <td>2nd Blackwood[10]<br />
</td>
        <td>sLsLsL sLsL<br />
</td>
        <td>C C^ D Eb E F G Ab A Bb C<br />
</td>
        <td>Ab <strong>C</strong><br />
</td>
        <td>Bb D<br />
</td>
        <td>C^ E<br />
</td>
        <td>Eb G<br />
</td>
        <td>F A<br />
</td>
    </tr>
</table>

The period is a fifth-octave = 240¢. The generator is 5/4. Ups and downs are used to avoid having duplicate notes.<br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="How to name rank-2 scales-Non-MOS non-MODMOS scales"></a><!-- ws:end:WikiTextHeadingRule:8 --><!-- ws:start:WikiTextAnchorRule:15:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@How to name rank-2 scales-Non-MOS scales&quot; title=&quot;Anchor: How to name rank-2 scales-Non-MOS scales&quot;/&gt; --><a name="How to name rank-2 scales-Non-MOS scales"></a><!-- ws:end:WikiTextAnchorRule:15 --><strong><u>Non-MOS non-MODMOS scales</u></strong></h2>
 These can be indicated with curly brackets {}, because regular brackets [] are reserved for MOS scales. The same naming methods apply. Examples:<br />
<br />
C D E F F# G A B C, which has a genchain F <strong>C</strong> G D A E B F#, and is named C 2nd Meantone{8}.<br />
<br />
C D E F F# G A Bb C, with genchain Bb F <strong>C</strong> G D A E * F#. Alter as few notes as possible to get if not a MOS, at least an unbroken genchain: F <strong>C</strong> G D A E B F#. The scale is C 2nd Meantone{8} b7.<br />
<br />
A B C D D# E F G G# A, with genchain F C G D <strong>A</strong> E B * * G# D#. Sharpen F and C to get an unbroken genchain: G D <strong>A</strong> E B F# C# G# D#, giving the name A 3rd Meantone{9} b3 b7.<br />
<br />
F G A C F, with genchain <strong>F</strong> C G * A. No amount of altering will make an unbroken chain, so the name is F 1st Meantone[5] no 5.<br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="How to name rank-2 scales-Color notation"></a><!-- ws:end:WikiTextHeadingRule:10 --><!-- ws:start:WikiTextAnchorRule:16:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@How to name rank-2 scales-Color notation&quot; title=&quot;Anchor: How to name rank-2 scales-Color notation&quot;/&gt; --><a name="How to name rank-2 scales-Color notation"></a><!-- ws:end:WikiTextAnchorRule:16 --><u>Color notation</u></h2>
 This method of scale naming can be combined with <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Kite%27s%20color%20notation">Kite's color notation</a>, as in &quot;2nd green heptatonic&quot; for 2nd Meantone[7].</body></html>

@@ 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>2016-04-21 04:47:21 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-04-21 04:55:24 UTC</tt>.<br>
-: The original revision id was <tt>580763689</tt>.<br>
+: The original revision id was <tt>580764023</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 35: / Line 35: @@
 || 4th Meantone[5] || minor pentatonic || Lss Ls || C Eb F G Bb C || ---- Eb Bb F **C** G ||
 || 5th Meantone[5] ||= ??? || LsL ss || C Eb F Ab Bb C || Ab Eb Bb F **C** ||
--note scales:
+-note meantone scales:
 || scale name || Ls pattern || example in C || genchain ||
 || 1st Meantone[12] || sLsLsLL sLsLL || C C# D D# E E# F# G G# A A# B C || **C** G D A E B F# C# G# D# A# E# ||
@@ Line 45: / Line 45: @@
 || 7th Meantone[12] || LsLsLLs LsLsL || C Db D Eb E F Gb G Ab A Bb B C || Gb Db Ab Eb Bb F **C** G D A E B ||
 ||= etc. ||   ||   ||   ||
-If the fifth is larger than 700¢, L and s would be reversed in the above table.
+If the fifth were larger than 700¢, which would be the case for Superpyth[12], L and s would be interchanged in this table.
 ==[[#How to name rank-2 scales-Generator choice]]**__Generator choice__**==
@@ Line 70: / Line 71: @@
 || 6th Porcupine[7] || sLss sss || C Dv Ev F^ G Av Bb^ C || Ev F^ G Av Bb^ **C** Dv ||
 || 7th Porcupine[7] || Lsss sss || C D Ev F^ G Av Bb^ C || D Ev F^ G Av Bb^ **C** ||
 ==[[#How to name rank-2 scales-MODMOS scales]]**__MODMOS scales__**==
@@ Line 80: / Line 82: @@
 || (a mode of the above) || F A B C E F || **F** C * * A E B || Ab Eb Bb **F** C || 4th Meantone[5] #2 #3 #5 ||
 Unfortunately there is some ambiguity, as the two names for melodic minor show. The Japanese pentatonic is b5, not b6, because we use pentatonic scale degrees. The mode of Japanese pentatonic alters three notes, not two, to avoid "b1 b5". Unfortunately, it's not apparent by the scale names that the last two examples are modes of each other.
 ==[[#How to name rank-2 scales-Fractional-octave periods]]**__Fractional-octave periods__**==
@@ Line 109: / Line 112: @@
 The period is a fifth-octave = 240¢. The generator is 5/4. Ups and downs are used to avoid having duplicate notes.
-==[[#How to name rank-2 scales-Non-MOS scales]]**__Non-MOS scales__**==
-These can be indicated with curly brackets {}, because regular brackets [] are reserved for MOS scales. The same naming methods apply:
-An ungapped example: C D E F F# G A B C, which has a genchain F **C** G D A E B F#, and is named 2nd Meantone{8}.
+==[[#How to name rank-2 scales-Non-MOS scales]]**__Non-MOS non-MODMOS scales__**==
+These can be indicated with curly brackets {}, because regular brackets [] are reserved for MOS scales. The same naming methods apply. Examples:
-A gapped example: C D E F F# G A Bb C, with genchain Bb F **C** G D A E * F#. Alter as few notes as possible to get if not a MOS, at least an unbroken genchain: F **C** G D A E B F#. The scale is 2nd Meantone[8] b7.
+C D E F F# G A B C, which has a genchain F **C** G D A E B F#, and is named C 2nd Meantone{8}.
-Sort of a Fur Elise scale: A B C D D# E F G G# A, with genchain F C G D **A** E B * * G# D#. Sharpen F and C to get an unbroken genchain: G D **A** E B F# C# G# D#, giving the name A 3rd Meantone[9] b3 b7.
+C D E F F# G A Bb C, with genchain Bb F **C** G D A E * F#. Alter as few notes as possible to get if not a MOS, at least an unbroken genchain: F **C** G D A E B F#. The scale is C 2nd Meantone{8} b7.
-Here's a tricky one: F G A C F, the genchain is F C G (gap) A, no way to make an unbroken chain. I would notate this Meantone[5] 1st mode, no 5.
+A B C D D# E F G G# A, with genchain F C G D **A** E B * * G# D#. Sharpen F and C to get an unbroken genchain: G D **A** E B F# C# G# D#, giving the name A 3rd Meantone{9} b3 b7.
+F G A C F, with genchain **F** C G * A. No amount of altering will make an unbroken chain, so the name is F 1st Meantone[5] no 5.
 ==[[#How to name rank-2 scales-Color notation]]__Color notation__==
-This method of scale naming can be combined with [[xenharmonic/Kite's color notation|Kite's color notation]], as is "2nd green heptatonic" for 2nd Meantone[7].</pre></div>
+This method of scale naming can be combined with [[xenharmonic/Kite's color notation|Kite's color notation]], as in "2nd green heptatonic" for 2nd Meantone[7].</pre></div>
 <h4>Original HTML content:</h4>
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Naming Rank-2 Scales&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="How to name rank-2 scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;u&gt;How to name rank-2 scales&lt;/u&gt;&lt;/h1&gt;
@@ Line 411: / Line 414: @@
 &lt;/table&gt;
--note scales:&lt;br /&gt;
+-note meantone scales:&lt;br /&gt;
@@ Line 507: / Line 510: @@
 &lt;/table&gt;
-If the fifth is larger than 700¢, L and s would be reversed in the above table.&lt;br /&gt;
+If the fifth were larger than 700¢, which would be the case for Superpyth[12], L and s would be interchanged in this table.&lt;br /&gt;
+&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="How to name rank-2 scales-Generator choice"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:12:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@How to name rank-2 scales-Generator choice&amp;quot; title=&amp;quot;Anchor: How to name rank-2 scales-Generator choice&amp;quot;/&amp;gt; --&gt;&lt;a name="How to name rank-2 scales-Generator choice"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:12 --&gt;&lt;strong&gt;&lt;u&gt;Generator choice&lt;/u&gt;&lt;/strong&gt;&lt;/h2&gt;
@@ Line 695: / Line 699: @@
 &lt;/table&gt;
+&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="How to name rank-2 scales-MODMOS scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:13:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@How to name rank-2 scales-MODMOS scales&amp;quot; title=&amp;quot;Anchor: How to name rank-2 scales-MODMOS scales&amp;quot;/&amp;gt; --&gt;&lt;a name="How to name rank-2 scales-MODMOS scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:13 --&gt;&lt;strong&gt;&lt;u&gt;MODMOS scales&lt;/u&gt;&lt;/strong&gt;&lt;/h2&gt;
@@ Line 776: / Line 781: @@
 Unfortunately there is some ambiguity, as the two names for melodic minor show. The Japanese pentatonic is b5, not b6, because we use pentatonic scale degrees. The mode of Japanese pentatonic alters three notes, not two, to avoid &amp;quot;b1 b5&amp;quot;. Unfortunately, it's not apparent by the scale names that the last two examples are modes of each other.&lt;br /&gt;
+&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="How to name rank-2 scales-Fractional-octave periods"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:14:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@How to name rank-2 scales-Fractional-octave periods&amp;quot; title=&amp;quot;Anchor: How to name rank-2 scales-Fractional-octave periods&amp;quot;/&amp;gt; --&gt;&lt;a name="How to name rank-2 scales-Fractional-octave periods"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:14 --&gt;&lt;strong&gt;&lt;u&gt;Fractional-octave periods&lt;/u&gt;&lt;/strong&gt;&lt;/h2&gt;
@@ Line 932: / Line 938: @@
 The period is a fifth-octave = 240¢. The generator is 5/4. Ups and downs are used to avoid having duplicate notes.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="How to name rank-2 scales-Non-MOS scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:15:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@How to name rank-2 scales-Non-MOS scales&amp;quot; title=&amp;quot;Anchor: How to name rank-2 scales-Non-MOS scales&amp;quot;/&amp;gt; --&gt;&lt;a name="How to name rank-2 scales-Non-MOS scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:15 --&gt;&lt;strong&gt;&lt;u&gt;Non-MOS scales&lt;/u&gt;&lt;/strong&gt;&lt;/h2&gt;
- These can be indicated with curly brackets {}, because regular brackets [] are reserved for MOS scales. The same naming methods apply:&lt;br /&gt;
 &lt;br /&gt;
-An ungapped example: C D E F F# G A B C, which has a genchain F &lt;strong&gt;C&lt;/strong&gt; G D A E B F#, and is named 2nd Meantone{8}.&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="How to name rank-2 scales-Non-MOS non-MODMOS scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:15:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@How to name rank-2 scales-Non-MOS scales&amp;quot; title=&amp;quot;Anchor: How to name rank-2 scales-Non-MOS scales&amp;quot;/&amp;gt; --&gt;&lt;a name="How to name rank-2 scales-Non-MOS scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:15 --&gt;&lt;strong&gt;&lt;u&gt;Non-MOS non-MODMOS scales&lt;/u&gt;&lt;/strong&gt;&lt;/h2&gt;
+ These can be indicated with curly brackets {}, because regular brackets [] are reserved for MOS scales. The same naming methods apply. Examples:&lt;br /&gt;
 &lt;br /&gt;
-A gapped example: C D E F F# G A Bb C, with genchain Bb F &lt;strong&gt;C&lt;/strong&gt; G D A E * F#. Alter as few notes as possible to get if not a MOS, at least an unbroken genchain: F &lt;strong&gt;C&lt;/strong&gt; G D A E B F#. The scale is 2nd Meantone[8] b7.&lt;br /&gt;
+C D E F F# G A B C, which has a genchain F &lt;strong&gt;C&lt;/strong&gt; G D A E B F#, and is named C 2nd Meantone{8}.&lt;br /&gt;
 &lt;br /&gt;
-Sort of a Fur Elise scale: A B C D D# E F G G# A, with genchain F C G D &lt;strong&gt;A&lt;/strong&gt; E B * * G# D#. Sharpen F and C to get an unbroken genchain: G D &lt;strong&gt;A&lt;/strong&gt; E B F# C# G# D#, giving the name A 3rd Meantone[9] b3 b7.&lt;br /&gt;
+C D E F F# G A Bb C, with genchain Bb F &lt;strong&gt;C&lt;/strong&gt; G D A E * F#. Alter as few notes as possible to get if not a MOS, at least an unbroken genchain: F &lt;strong&gt;C&lt;/strong&gt; G D A E B F#. The scale is C 2nd Meantone{8} b7.&lt;br /&gt;
 &lt;br /&gt;
-Here's a tricky one: F G A C F, the genchain is F C G (gap) A, no way to make an unbroken chain. I would notate this Meantone[5] 1st mode, no 5.&lt;br /&gt;
+A B C D D# E F G G# A, with genchain F C G D &lt;strong&gt;A&lt;/strong&gt; E B * * G# D#. Sharpen F and C to get an unbroken genchain: G D &lt;strong&gt;A&lt;/strong&gt; E B F# C# G# D#, giving the name A 3rd Meantone{9} b3 b7.&lt;br /&gt;
 &lt;br /&gt;
+F G A C F, with genchain &lt;strong&gt;F&lt;/strong&gt; C G * A. No amount of altering will make an unbroken chain, so the name is F 1st Meantone[5] no 5.&lt;br /&gt;
 &lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="How to name rank-2 scales-Color notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:16:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@How to name rank-2 scales-Color notation&amp;quot; title=&amp;quot;Anchor: How to name rank-2 scales-Color notation&amp;quot;/&amp;gt; --&gt;&lt;a name="How to name rank-2 scales-Color notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:16 --&gt;&lt;u&gt;Color notation&lt;/u&gt;&lt;/h2&gt;
-  This method of scale naming can be combined with &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Kite%27s%20color%20notation"&gt;Kite's color notation&lt;/a&gt;, as is &amp;quot;2nd green heptatonic&amp;quot; for 2nd Meantone[7].&lt;/body&gt;&lt;/html&gt;</pre></div>
+  This method of scale naming can be combined with &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Kite%27s%20color%20notation"&gt;Kite's color notation&lt;/a&gt;, as in &amp;quot;2nd green heptatonic&amp;quot; for 2nd Meantone[7].&lt;/body&gt;&lt;/html&gt;</pre></div>

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