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Kite's Genchain mode numbering: Difference between revisions

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__FORCETOC__
__FORCETOC__
=MOS Scales=
=MOS scales=


'''Mode Numbers''' provide a way to name MOS, MODMOS and even non-MOS rank-2 scales and modes systematically. Like [[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.
'''Mode Numbers''' provide a way to name MOS, MODMOS and even non-MOS rank-2 scales and modes systematically. Like [[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.
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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 in "Rationale"). '''<u>Unlike modal UDP notation, the generator isn't always chroma-positive</u>.''' There are several disadvantages of only using chroma-positive generators. See the critique of UDP at the bottom of this page.
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 in "Rationale"). '''<u>Unlike modal UDP notation, the generator isn't always [[Chroma|chroma-positive]]</u>.''' There are several disadvantages of only using chroma-positive generators. See the critique of UDP at the bottom of this page.


Pentatonic meantone scales:
Pentatonic meantone scales:
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=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. 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 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 when the generator is chroma-positive, and N steps backwards when it isn't. This ensures a higher pitch. Note that Meantone[5] is chroma-negative. However, an exception is made for superflat edos like 16edo when the generator is a 3/2 fifth, because in those edos, G# is actually flat of G. Another exception is when the generator is close to the "tipping point" between chroma-positive and chroma-negative. A good alternative in these and other situations, including non-heptatonic and non-fifth-generated scales, is to use + for forwards in the genchain and - for backwards, as in 5th Meantone[7] +6 +7.


A MODMOS scale can have alternate names. The ascending melodic minor scale could also be called 2nd Meantone[7] b3 (major scale with a minor 3rd), or as 4th Meantone[7] #7 (dorian with a major 7th). Here are some '''Meantone''' MODMOS scales, with alternate names included only if they don't have more alterations than the original:
A MODMOS scale can have alternate names. The ascending melodic minor scale could also be called 2nd Meantone[7] b3 (major scale with a minor 3rd), or as 4th Meantone[7] #7 (dorian with a major 7th).  
 
'''Meantone''' MODMOS scales, with alternate names included only if they don't have more alterations than the original:


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[[Blackwood|'''Blackwood''']] '''aka 5-edo+ya''' has a fifth-octave period of 240¢. The generator is a just 5/4 = 386¢. There are only two [[Blackwood]][10] modes. The lattice can be expressed using a 3\5 period. Ups and downs indicate the generator, not the period:
[[Blackwood|'''Blackwood''']] '''aka 5-edo+ya''' has a fifth-octave period of 240¢. The generator is a just 5/4 = 386¢. There are only two [[Blackwood]][10] modes. Ups and downs indicate the generator, not the period. Both Blackwood modes, using ups and downs:
 
F ------ Av
 
D ------ F#v
 
C ------ Ev
 
A ------ C#v
 
G ------ Bv
 
Both Blackwood modes, using ups and downs:


{| class="wikitable"
{| class="wikitable"
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| | A 5th Meantone[7] #7 add #4
| | A 5th Meantone[7] #7 add #4
| | LMLs MMXM
| | LMLs MMXM
|-
| | A B C D D# E G# A
| | C * D <u>'''A'''</u> E B * * G# D#
| | A 5th Meantone[7] #7 add #4 no6
| | LMLs MXM
|-
|-
| | '''nonatonic:'''
| | '''nonatonic:'''
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Another possibility is a scale that would be MOS, but the generator is too sharp or flat. For example, a genchain F C G D A E B of 8\13 fifths makes an out-of-order scale A C B D F E G A. This scale is best named as Meantone[5] with added notes: Which brings us to...
Another possibility is a scale that would be MOS, but the generator is too sharp or flat. For example, a genchain F C G D A E B of 8\13 fifths makes an out-of-order scale A C B D F E G A. This scale is best named as Meantone[5] with added notes: Which brings us to...


=Non-heptatonic Scales=
=Non-heptatonic scales=


As long as we stick to MOS scales, terms like Meantone[5] or Meantone[6] are fine. But when we alter, add or drop notes, we need to define what something like "#5" means in a pentatonic or hexatonic context.
As long as we stick to MOS scales, terms like Meantone[5] or Meantone[6] are fine. But when we alter, add or drop notes, we need to define what something like "#5" means in a pentatonic or hexatonic context.
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