User:Eufalesio/Good scales: Difference between revisions

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Here's a data dump of scales I use. Some of them with funny names because they are in conlangs. I will provide the scales and all their modes, apart from other properties. Note however that for chiral scales I am NOT pairing them up. The first mode of a scale is one that I deem the most useful to me. This is why chiral scales are all messed up in order.   
Here's a data dump of scales I use. Some of them with funny names because they are in conlangs. I will provide the scales and all their modes, apart from other properties. Note however that for chiral scales I am NOT pairing them up. The first mode of a scale is one that I deem the most useful to me. This is why chiral scales are all messed up in order.   


Notice, NONE of them are essentially tempered scales, det scales, whatever. If I happen to be using one (like for instance minthmic scales), it's pure coincidence. My mind thinks only in JI, and the det scale pops up not because I want to use det scales, but because I want to reach the primes with the least amount of commas.   
Notice, NONE of them are tempered scales, det scales, whatever. If I happen to be using one (like for instance minthmic scales), it's pure coincidence. My mind thinks only in JI, and the det scale pops up not because I want to use det scales, but because I want to reach the primes with the least amount of commas.   


Right next to the name, you will see the following descriptors on each scale:   
Right next to the name, you will see the following descriptors on each scale:   
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* MVn: [[Maximum variety]], often 4 or more.
* MVn: [[Maximum variety]], often 4 or more.
* CS: [[Constant structure]]. All my scales are CS, coincidentally.
* CS: [[Constant structure]]. All my scales are CS, coincidentally.
* SP: [[Strictly proper]]
* SP: [[Strictly proper]]. Because I'm cataloging JI scales, they can only be strictly proper or not proper.
* MOS: [[MOS scale]], which implies SV2 and CS.
* SYM: Symmetric. That is, not [[chiral]].
* MOS: [[MOS scale]], which implies SYM, SV2 and CS.


One pattern you'll see in all my scale prime modes is that they '''always''' have 3/2, and extremely frequently, 9/8 too. This is one hill I will die on, the perfect fifth 3/2 is obligatory! I need not have 4/3 (and in many cases I use other types of fourths such as 21/16, 27/20, 65/48, 11/8).
One pattern you'll see in all my scale prime modes is that they '''always''' have 3/2, and extremely frequently, 9/8 too. This is one hill I will die on, the perfect fifth 3/2 is obligatory! I need not have 4/3 (and in many cases I use other types of fourths such as 21/16, 27/20, 65/48, 11/8).
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|}
|}


=== A general Skirmish ===
=== A general Skirmish [SV3, MVn ===
Any scale of this form for any cent value 0 < C <  4/3. I declare to be a Skirmish. RH Skirmish have sqrt(4/3) < C < 4/3, and LH 1 < C < sqrt(4/3). This also means that the above scales, Nicepent, Pyth pentic modes, and semiquartal scales are Skirmishes, though... the term is better for C ≈ 13/12, you know, "minor second-ish" intervals.  
Any scale of this form for any cent value 0 < C <  4/3. I declare to be a Skirmish. RH Skirmish have sqrt(4/3) < C < 4/3, and LH 1 < C < sqrt(4/3). This also means that the above scales, Nicepent, Pyth pentic modes, and semiquartal scales are Skirmishes, though... the term is better for C ≈ 13/12, you know, "minor second-ish" intervals.  
{| class="wikitable"
{| class="wikitable"
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The reason to use this mode and no others is that it provides an easy set of dodecatonic nominals to alter outwards from, also the numerically simplest mode of p-chromatic. Despite how bad it may seem to have a spine that is not symmetric across the octave, working with a MOS is wayyy better than whatever amalgamation I'd end up with were I to have √2 stuck in the middle.
The reason to use this mode and no others is that it provides an easy set of dodecatonic nominals to alter outwards from, also the numerically simplest mode of p-chromatic. Despite how bad it may seem to have a spine that is not symmetric across the octave, working with a MOS is wayyy better than whatever amalgamation I'd end up with were I to have √2 stuck in the middle.


Besides, this is the only scale for which I have proper, fully standardized names. You know them well: Unison, Minor second (or Limma), Major second (or Tone), Minor third, Major third, Perfect fourth, Tritone, Perfect Fifth, Minor sixth, Major Sixth, Minor seventh, Major seventh, Octave. Which Tritone? The big one. The one that's three stacked tones, for real.
Besides, this is the only scale for which I have proper, fully standardized names. You know them well: Unison, Minor second (or Limma), Major second (or Tone), Minor third, Major third, Perfect fourth, Tritone, Perfect Fifth, Minor sixth, Major Sixth, Minor seventh, Major seventh, Octave. Which Tritone? 729/512. The one that's three stacked tones one on top of each other, for real.
{| class="wikitable"
{| class="wikitable"
! colspan="12" |Scale degrees
! colspan="12" |Scale degrees
|-
|-
!256/243
!256/243
m2
!'''9/8'''
!'''9/8'''
M2
!32/27
!32/27
m3
!81/64
!81/64
M3
!'''4/3'''
!'''4/3'''
P4
!729/512
!729/512
TT
!'''3/2'''
!'''3/2'''
P5
!128/81
!128/81
m6
!27/16
!27/16
M6
!16/9
!16/9
m7
!'''15/8'''
!'''15/8'''
M7
!2
!2
P8
|}
|}
=== Duodene [MV4, CS, SP] ===
=== Duodene [MV4, CS, SP, SYM] ===
The best realization of the 12 notes of the piano, when played in a 5-limit fashion. Doing modal interchanges with these, you're pretty much set when it comes to 5-limit JI, with the benefit of being achiral, so you can set this on your MTS-ESP and just use the 12 modes of this without needing to contend with LH or RH.
{| class="wikitable"
{| class="wikitable"
! colspan="12" |Scale degrees
! colspan="12" |Scale degrees
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=== Nelaá - Jälg [MV4, CS, SP] ===
=== Nelaá - Jälg [MV4, CS, SP] ===
A closely related scale to Duodene that is almost the same, but this one IS chiral. I use RH more.
{| class="wikitable"
{| class="wikitable"
! colspan="12" |LH
|-
! colspan="12" |Scale degrees
|-
!16/15
!9/8
!6/5
!5/4
!4/3
!45/32
!3/2
!8/5
!5/3
!16/9
!15/8
! rowspan="12" |2
|-
|<small>135/128</small>
|<small>9/8</small>
|<small>75/64</small>
|<small>5/4</small>
|<small>675/512</small>
|<small>45/32</small>
|<small>3/2</small>
|<small>25/16</small>
|<small>5/3</small>
|<small>225/128</small>
|<small>15/8</small>
|-
|<small>16/15</small>
|<small>10/9</small>
|<small>32/27</small>
|<small>5/4</small>
|<small>4/3</small>
|<small>64/45</small>
|<small>40/27</small>
|<small>128/81</small>
|<small>5/3</small>
|<small>16/9</small>
|<small>256/135</small>
|-
|<small>25/24</small>
|<small>10/9</small>
|<small>75/64</small>
|<small>5/4</small>
|<small>4/3</small>
|<small>25/18</small>
|<small>40/27</small>
|<small>25/16</small>
|<small>5/3</small>
|<small>16/9</small>
|<small>15/8</small>
|-
|<small>16/15</small>
|<small>9/8</small>
|<small>6/5</small>
|<small>32/25</small>
|<small>4/3</small>
|<small>64/45</small>
|<small>3/2</small>
|<small>8/5</small>
|<small>128/75</small>
|<small>9/5</small>
|<small>48/25</small>
|-
|<small>135/128</small>
|<small>9/8</small>
|<small>6/5</small>
|<small>5/4</small>
|<small>4/3</small>
|<small>45/32</small>
|<small>3/2</small>
|<small>8/5</small>
|<small>27/16</small>
|<small>9/5</small>
|<small>15/8</small>
|-
|<small>16/15</small>
|<small>256/225</small>
|<small>32/27</small>
|<small>512/405</small>
|<small>4/3</small>
|<small>64/45</small>
|<small>1024/675</small>
|<small>8/5</small>
|<small>128/75</small>
|<small>16/9</small>
|<small>256/135</small>
|-
|<small>16/15</small>
|<small>10/9</small>
|<small>32/27</small>
|<small>5/4</small>
|<small>4/3</small>
|<small>64/45</small>
|<small>3/2</small>
|<small>8/5</small>
|<small>5/3</small>
|<small>16/9</small>
|<small>15/8</small>
|-
|<small>25/24</small>
|<small>10/9</small>
|<small>75/64</small>
|<small>5/4</small>
|<small>4/3</small>
|<small>45/32</small>
|<small>3/2</small>
|<small>25/16</small>
|<small>5/3</small>
|<small>225/128</small>
|<small>15/8</small>
|-
|<small>16/15</small>
|<small>9/8</small>
|<small>6/5</small>
|<small>32/25</small>
|<small>27/20</small>
|<small>36/25</small>
|<small>3/2</small>
|<small>8/5</small>
|<small>27/16</small>
|<small>9/5</small>
|<small>48/25</small>
|-
|<small>135/128</small>
|<small>9/8</small>
|<small>6/5</small>
|<small>81/64</small>
|<small>27/20</small>
|<small>45/32</small>
|<small>3/2</small>
|<small>405/256</small>
|<small>27/16</small>
|<small>9/5</small>
|<small>15/8</small>
|-
|<small>16/15</small>
|<small>256/225</small>
|<small>6/5</small>
|<small>32/25</small>
|<small>4/3</small>
|<small>64/45</small>
|<small>3/2</small>
|<small>8/5</small>
|<small>128/75</small>
|<small>16/9</small>
|<small>256/135</small>
|-
! colspan="12" |RH
|-
! colspan="12" |Scale degrees
! colspan="12" |Scale degrees
|-
|-
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This is still the base scale of what I call the "fudge workflow", when you want and can do JI stuff but you must play within the limitations of 12 keys per octave. I found that moving the fundamental of the scale along 48edo is good enough. Why move the fundamental of the scale along 48edo? Because that way you have the harmonic scale along all 48edo notes, which includes the 12edo chain of fifths, 25c steps close to 81/80 and 64/63, and 50c steps close to 33/32 and 1053/1024.  
This is still the base scale of what I call the "fudge workflow", when you want and can do JI stuff but you must play within the limitations of 12 keys per octave. I found that moving the fundamental of the scale along 48edo is good enough. Why move the fundamental of the scale along 48edo? Because that way you have the harmonic scale along all 48edo notes, which includes the 12edo chain of fifths, 25c steps close to 81/80 and 64/63, and 50c steps close to 33/32 and 1053/1024.  
The otonal version (LH) is the only one worth using. The utonal version (RH) really only has one use, to go down the subharmonic series in a progression, and for that a fudge workflow makes it useless. RH is horrible, so bad that I won't even write it.
{| class="wikitable"
{| class="wikitable"
! colspan="12" |Scale degrees
! colspan="12" |Scale degrees