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Just intonation subgroup/Mike's tips: Difference between revisions

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On Thu, Nov 1, 2012 at 9:10 PM, Chris Vaisvil &lt;[http://mailto.wikispaces.com/[email protected] [email protected]]&gt;
On Thu, Nov 1, 2012 at 9:10 PM, Chris Vaisvil &lt;[email protected]&gt;


wrote:
wrote:
<br>&gt;
<br>&gt; For certain, no. I could only guess that subgroups are actually harmonic
<br>&gt; series prime limits.


&gt;
Subgroups expand the concept of a prime limit. For instance, say you
 
<ul><li>For certain, no. I could only guess that subgroups are actually harmonic</li><li>series prime limits.</li></ul>Subgroups expand the concept of a prime limit. For instance, say you


want the 7-limit, but you don't care about prime 5; you just want
want the 7-limit, but you don't care about prime 5; you just want
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Chris Vaisvil said:
Chris Vaisvil said:


<ul><li>As someone pretty ignorant of tuning theory I wish there was a table that said</li><li>
<br>&gt; As someone pretty ignorant of tuning theory I wish there was a table that said
 
<br>&gt;
</li><li>If you play scale (tuning) steps 0:4:8:10 in 11 edo you will come close to</li><li>approximating a harmonic series chord of 0:3:6:7</li></ul>
<br>&gt; If you play scale (tuning) steps 0:4:8:10 in 11 edo you will come close to
<br>&gt; approximating a harmonic series chord of 0:3:6:7


There's an easy way to do that in Scala.  
There's an easy way to do that in Scala.  
Line 89: Line 91:
Super. Click "OK", and you'll see the following on your main Scala window:
Super. Click "OK", and you'll see the following on your main Scala window:


-----
Scale is equal tempered, only showing first degree.
Scale is equal tempered, only showing first degree.
0-4-12: BP Wide Triad 2nd inversion 7:9:15 diff. 1.280,-10.352
 
0-5-9: NM Subfocal Tritonic Seventh 8:11:14 diff. -5.863, 12.992
0-4-12: BP Wide Triad 2nd inversion 7:9:15 diff. 1.280,-10.352
0-1-3-4: Hüzzam 5-9-5 diff. -4.117, 10.292, 6.175
 
Total of 3 with 3 unique
0-5-9: NM Subfocal Tritonic Seventh 8:11:14 diff. -5.863, 12.992
 
0-1-3-4: Hüzzam 5-9-5 diff. -4.117, 10.292, 6.175
 
Total of 3 with 3 unique
 
-----


The first line shows that, because this is an ET, talking about starting on scale step 1-10 would be redundant. If you had a scale with different step sizes, it would run through each chord available on each step.
The first line shows that, because this is an ET, talking about starting on scale step 1-10 would be redundant. If you had a scale with different step sizes, it would run through each chord available on each step.
Line 114: Line 109:
Two chords isn't much, so let's loosen our constraints and see what chords are available that are less out-of-tune than a 7/4 in 12 EDO: 1000.0 - 968.8 = 31.2 cents. Change the constraints as above, get the following:
Two chords isn't much, so let's loosen our constraints and see what chords are available that are less out-of-tune than a 7/4 in 12 EDO: 1000.0 - 968.8 = 31.2 cents. Change the constraints as above, get the following:


-----
0-4-7: Isoharmonic Augmented Triad 7:9:11 diff. 1.280,-18.856
0-4-7: Isoharmonic Augmented Triad 7:9:11 diff. 1.280,-18.856
0-4-12: BP Wide Triad 2nd inversion 7:9:15 diff. 1.280,-10.352
 
0-5-9: NM Subfocal Tritonic Seventh 8:11:14 diff. -5.863, 12.992
0-4-12: BP Wide Triad 2nd inversion 7:9:15 diff. 1.280,-10.352
0-3-6: Isoharmonic Diminished Triad 9:11:13 diff. -20.135, 17.928
 
0-3-6-8: Isoharmonic Diminished Seventh 9:11:13:15 diff. -20.135, 17.928,-11.631
0-5-9: NM Subfocal Tritonic Seventh 8:11:14 diff. -5.863, 12.992
0-5-9: NM Trevicesimal Tritonic Seventh Triple 13:18:23 diff. -17.928,-5.929
 
0-3-6: Diminished 25:30:36 diff. 11.631, 23.263
0-3-6: Isoharmonic Diminished Triad 9:11:13 diff. -20.135, 17.928
0-2-4: Double Septimal Whole-Tone 49:56:64 diff. -12.992,-25.985
 
0-3-6: 7-Tone Neutral Triad 2-2 diff. -15.584,-31.169
0-3-6-8: Isoharmonic Diminished Seventh 9:11:13:15 diff. -20.135, 17.928,-11.631
0-1-2: Semitone Trichord 1-1 diff. 9.091, 18.182
 
0-1-3: Phrygian Trichord 1-2 diff. 9.091, 27.273
0-5-9: NM Trevicesimal Tritonic Seventh Triple 13:18:23 diff. -17.928,-5.929
0-2-3: Minor Trichord 2-1 diff. 18.182, 27.273
 
0-3-8: Minor Trine 1st inversion 3-6 diff. 27.273,-27.273
0-3-6: Diminished 25:30:36 diff. 11.631, 23.263
0-3-8-11: Sixths Chord 3-6-3 diff. 27.273,-27.273, 0.000
 
0-3-9: Minor Quintal Triad 3-7 diff. 27.273,-18.182
0-2-4: Double Septimal Whole-Tone 49:56:64 diff. -12.992,-25.985
0-4-6: 13-Tone NM Crunchy Pepper Triple 5-2 diff. -25.175, 8.392
 
0-4-11: 13-Tone NM Converse Trine 5-8 diff. -25.175, 0.000
0-3-6: 7-Tone Neutral Triad 2-2 diff. -15.584,-31.169
0-7-11: 13-Tone NM Trine 8-5 diff. 25.175, 0.000
 
0-3-6-9: 16-Tone Diminished Seventh 4-5-4 diff. 27.273,-20.455, 6.818
0-1-2: Semitone Trichord 1-1 diff. 9.091, 18.182
0-5-9: 17-Tone NM Quasi-Trevicesimal Subfocal Tritonic Seventh 8-6 diff. -19.251,-6.417
 
0-2-9: 29-Tone NM Bivalent Ultra-Gothic Triple 6-17 diff. -30.094, 30.094
0-1-3: Phrygian Trichord 1-2 diff. 9.091, 27.273
0-5-9: 36-Tone NM Smaller Tritone Subfocal Seventh 17-12 diff. -21.212, 15.152
 
0-5-9: 36-Tone NM Larger Tritone Subfocal Seventh 17-13 diff. -21.212,-18.182
0-2-3: Minor Trichord 2-1 diff. 18.182, 27.273
0-5-9: 46-Tone NM Tritonic Subfocal Seventh 21-16 diff. -2.372, 16.601
 
0-1-3-4: Hüzzam 5-9-5 diff. -4.117, 10.292, 6.175
0-3-8: Minor Trine 1st inversion 3-6 diff. 27.273,-27.273
Total of 25 with 25 unique
 
0-3-8-11: Sixths Chord 3-6-3 diff. 27.273,-27.273, 0.000
 
0-3-9: Minor Quintal Triad 3-7 diff. 27.273,-18.182
 
0-4-6: 13-Tone NM Crunchy Pepper Triple 5-2 diff. -25.175, 8.392
 
0-4-11: 13-Tone NM Converse Trine 5-8 diff. -25.175, 0.000
 
0-7-11: 13-Tone NM Trine 8-5 diff. 25.175, 0.000
 
0-3-6-9: 16-Tone Diminished Seventh 4-5-4 diff. 27.273,-20.455, 6.818
 
0-5-9: 17-Tone NM Quasi-Trevicesimal Subfocal Tritonic Seventh 8-6 diff. -19.251,-6.417
 
0-2-9: 29-Tone NM Bivalent Ultra-Gothic Triple 6-17 diff. -30.094, 30.094
 
0-5-9: 36-Tone NM Smaller Tritone Subfocal Seventh 17-12 diff. -21.212, 15.152
 
0-5-9: 36-Tone NM Larger Tritone Subfocal Seventh 17-13 diff. -21.212,-18.182
 
0-5-9: 46-Tone NM Tritonic Subfocal Seventh 21-16 diff. -2.372, 16.601
 
0-1-3-4: Hüzzam 5-9-5 diff. -4.117, 10.292, 6.175
 
Total of 25 with 25 unique
 
-----


Notice that the first eight lines are the same kind of thing that we had talked about before. More chords are now available, but the additions are more damaged.
Notice that the first eight lines are the same kind of thing that we had talked about before. More chords are now available, but the additions are more damaged.
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One thing to remember is that these chords are those that Manuel has defined and loaded up into Scala. There may be other chords you want to consider, and this may not give you those. He has a lot of chords in there, though, so it could be your first stop for any scale you want to look at, and certainly makes sense for most ETs.  
One thing to remember is that these chords are those that Manuel has defined and loaded up into Scala. There may be other chords you want to consider, and this may not give you those. He has a lot of chords in there, though, so it could be your first stop for any scale you want to look at, and certainly makes sense for most ETs.  


<span style="font-family: arial,sans-serif;">Hope this helps,</span>
Hope this helps,


<span style="font-family: arial,sans-serif;">Jake</span>
Jake


<span style="color: #ffffff; display: block;"><u>._,_.</u>_</span>      [[Category:11edo]]
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