Kite's Genchain mode numbering: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-09-24 20:06:52 UTC</tt>.

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-09-24 23:02:33 UTC</tt>.

: The original revision id was <tt>~~593219786~~</tt>.

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|| Locrian || 7th Meantone [7] || sLLs LLL || C Db Eb F Gb Ab Bb C || Gb Db Ab Eb Bb F __**C**__ ||

The octave inverse of a generator is also a generator. To avoid ambiguity in mode numbers, the smaller of the two generators is chosen. An exception is made for 3/2, which is preferred over 4/3 for historical reasons (see below). **__Unlike modal UDP notation, the generator isn't always chroma-positive__.** There are several disadvantages of only using chroma-positive generators, see [[Naming Rank-2 Scales using Mode Numbers#Why%20not%20just%20use%20UDP%20notation?|Why not just use UDP notation?]] ~~below~~.

The octave inverse of a generator is also a generator. To avoid ambiguity in mode numbers, the smaller of the two generators is chosen. An exception is made for 3/2, which is preferred over 4/3 for historical reasons (see below). **__Unlike modal UDP notation, the generator isn't always chroma-positive__.** There are several disadvantages of only using chroma-positive generators, see [[Naming Rank-2 Scales using Mode Numbers#Why%20not%20just%20use%20UDP%20notation?|Why not just use UDP notation?]] at the bottom of this page.

Pentatonic meantone scales:

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Chromatic meantone scales.

|| scale name || sL pattern

|| scale name || sL pattern (assumes

(assumes 3/2 < 700¢) || example in C || genchain ||

~3/2 < 700¢) || example in C || genchain ||

|| 1st Meantone [12] || sLsL sLL 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] || sLsL LsL 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# ||

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=[[#How to name rank-2 scales-MODMOS scales]]**__MODMOS scales__**=

[[MODMOS Scales|MODMOS]] scales are named as chromatic alterations of a MOS scale, similar to UDP notation. The ascending melodic minor scale is 5th Meantone [7] #6 #7. The "#" symbol means moved N steps forwards on the genchain, whether the generator is chroma-positive or not. This scale has the same name in 16edo, even though in 16edo, G# is actually flat of G. An alternative, especially for non-heptatonic scales, is to use + and - for forwards and backwards, as in 5th Meantone [7] +6 +7.

[[MODMOS Scales|MODMOS]] scales are named as chromatic alterations of a MOS scale, similar to UDP notation. The ascending melodic minor scale is 5th Meantone [7] #6 #7. The "#" symbol means moved N steps forwards on the genchain, whether the generator is chroma-positive or not. This scale has the same name in 16edo, even though in 16edo, G# is actually flat of G. A good alternative, especially for non-heptatonic and non-fifth-based scales, is to use + and - for forwards and backwards, as in 5th Meantone [7] +6 +7.

MODMOS names are ambiguous. ~~This~~ scale could also be written as 2nd Meantone [7] b3 (major scale with a minor 3rd), or as 4th Meantone [7] #7 (dorian with a major 7th).

MODMOS names are ambiguous. The ascending melodic minor scale could also be written as 2nd Meantone [7] b3 (major scale with a minor 3rd), or as 4th Meantone [7] #7 (dorian with a major 7th).

|| old scale name || example in A || genchain || new scale name || sML pattern ||

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|| Hungarian gypsy minor || A B C D# E F G A || F C G * __**A**__ E B * * * D# || 5th Meantone [7] #4 || MsLs sMM ||

|| Phrygian dominant || A Bb C# D E F G A || Bb F * G D __**A**__ E * * C# || 6th Meantone [7] #3 || sLsM sMM ||

As can be seen from the genchains or from the sML patterns, the harmonic minor and the phrygian dominant are modes of each other, as are the double harmonic minor and the double harmonic major. Unfortunately the scale names do not indicate this.

As can be seen from the genchains, or from the sML patterns, the harmonic minor and the phrygian dominant are modes of each other, as are the double harmonic minor and the double harmonic major. Unfortunately the scale names do not indicate this.

The advantage of ambiguous names is that one can choose the mode number. If a piece changes from a MOS scale to a MODMOS scale, one can describe both scales with the same mode number. For example, a piece might change from A dorian to A melodic minor. In this context, melodic minor might better be described as an altered dorian scale.

The advantage of ambiguous names is that one can choose the mode number. If a piece changes from a MOS scale to a MODMOS scale, one can describe both scales with the same mode number. For example, a piece might change from D dorian to D melodic minor. In this context, melodic minor might better be described as an altered dorian scale.

Unlike MOS scales, adjacent MODMOS modes differ by more than one note. Harmonic minor modes:

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6th Meantone [7] #3: C Db E F G Ab Bb C (phrygian dominant)

7th Meantone [7] #6: C Db Eb F Gb A Bb C

The 3rd scale breaks the pattern to avoid an altered tonic ("3rd Meantone [7] #1").

The 3rd scale breaks the pattern to avoid an altered tonic ("3rd Meantone [7] #1"). The Bbb is "b7" not "bb7" because the 7th mode is Locrian, and Bbb is only one semitone flat of the Locrian mode's minor 7th Bb.

Ascending melodic minor modes:

1st Meantone [7] #~~6 #7~~: C D E F# G# A B C

1st Meantone [7] #5: C D E F# G# A B C

2nd Meantone [7] #6 #7: C Db Eb Fb Gb Ab Bb C

3rd Meantone [7] #6 #7: C D E F# G A Bb C

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The octave inverse of a generator is also a generator. To avoid ambiguity in mode numbers, the smaller of the two generators is chosen. An exception is made for 3/2, which is preferred over 4/3 for historical reasons (see below). Unlike modal UDP notation, the generator isn't always chroma-positive. There are several disadvantages of only using chroma-positive generators, see <a class="wiki_link" href="/Naming%20Rank-2%20Scales%20using%20Mode%20Numbers#Why%20not%20just%20use%20UDP%20notation?">Why not just use UDP notation?</a> ~~below~~.

The octave inverse of a generator is also a generator. To avoid ambiguity in mode numbers, the smaller of the two generators is chosen. An exception is made for 3/2, which is preferred over 4/3 for historical reasons (see below). Unlike modal UDP notation, the generator isn't always chroma-positive. There are several disadvantages of only using chroma-positive generators, see <a class="wiki_link" href="/Naming%20Rank-2%20Scales%20using%20Mode%20Numbers#Why%20not%20just%20use%20UDP%20notation?">Why not just use UDP notation?</a> at the bottom of this page.

Pentatonic meantone scales:

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<td>scale name

</td>

<td>sL pattern

<td>sL pattern (assumes

~~(assumes~~ 3/2 &lt; 700¢)

~3/2 &lt; 700¢)

</td>

<td>example in C

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<h1 id="toc1"><a name="MODMOS scales"></a><a name="How to name rank-2 scales-MODMOS scales"></a>MODMOS scales</h1>

<a class="wiki_link" href="/MODMOS%20Scales">MODMOS</a> scales are named as chromatic alterations of a MOS scale, similar to UDP notation. The ascending melodic minor scale is 5th Meantone [7] #6 #7. The &quot;#&quot; symbol means moved N steps forwards on the genchain, whether the generator is chroma-positive or not. This scale has the same name in 16edo, even though in 16edo, G# is actually flat of G. An alternative, especially for non-heptatonic scales, is to use + and - for forwards and backwards, as in 5th Meantone [7] +6 +7.

<a class="wiki_link" href="/MODMOS%20Scales">MODMOS</a> scales are named as chromatic alterations of a MOS scale, similar to UDP notation. The ascending melodic minor scale is 5th Meantone [7] #6 #7. The &quot;#&quot; symbol means moved N steps forwards on the genchain, whether the generator is chroma-positive or not. This scale has the same name in 16edo, even though in 16edo, G# is actually flat of G. A good alternative, especially for non-heptatonic and non-fifth-based scales, is to use + and - for forwards and backwards, as in 5th Meantone [7] +6 +7.