Porcupine/Chords: Difference between revisions
added more chord names, added C as the chord root |
added more chord names |
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Though we're used to thinking of 4:5:6 as the definitive "major chord", with all inversions coming from that, there is nothing definitive about calling these lists below "chord" or "inversion". That's just the way the generators came out. | Though we're used to thinking of 4:5:6 as the definitive "major chord", with all inversions coming from that, there is nothing definitive about calling these lists below "chord" or "inversion". That's just the way the generators came out. | ||
The '''bolded''' inversions are named using [[ups and downs]] as described on the [[Pergen|pergens]] page. The pergen is (P8, P4/3) third-of-a-4th, #7 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf notation guide for rank-2 pergens]. One up is -7 generators, octave-reduced, which is a third-sharp. The generator is vM2 = 167¢ - c/3, where c = the amount in cents the tempered fifth exceeds 700¢. ^1 = 33¢ + 2.33c. | The '''bolded''' inversions are named using [[ups and downs]] as described on the [[Pergen|pergens]] page. The pergen is (P8, P4/3) third-of-a-4th, #7 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf notation guide for rank-2 pergens]. One up is -7 generators, octave-reduced, which is a third-sharp. Thus ^<sup>3</sup>C = C# and the enharmonic interval is v<sup>3</sup>A1. The generator is vM2 = 167¢ - c/3, where c = the amount in cents the tempered fifth exceeds 700¢. ^1 = 33¢ + 2.33c. In 22edo, ^1 = 1\22 = 54.5¢. | ||
In Porcupine, 5/4 = vM3, 7/4 = m7 and 11/8 = ^4. Thus ^1 equals ~81/80 and ~33/32. This may not be true for other (P8, P4/3) temperaments. So the ratios in the table below are specific to Porcupine, but the chord names apply to any (P8, P4/3) temperament. | |||
{| class="wikitable" | {| class="wikitable" | ||
|+Porcupine's genchain | |+Porcupine's genchain | ||
| Line 437: | Line 439: | ||
| 1-14/11-7/5 | | 1-14/11-7/5 | ||
| utonal | | utonal | ||
| 1/1-14/11-7/5 | | '''1/1-14/11-7/5''' | ||
| 1/1-11/10-11/7 | | 1/1-11/10-11/7 | ||
| 1/1-10/7-20/11 | | 1/1-10/7-20/11 | ||
| | |Cv4(vv5) | ||
|- | |- | ||
| 0-1-12 | | 0-1-12 | ||
| Line 447: | Line 449: | ||
| 1/1-10/9-14/9 | | 1/1-10/9-14/9 | ||
| 1/1-7/5-9/5 | | 1/1-7/5-9/5 | ||
| 1/1-9/7-10/7 | | '''1/1-9/7-10/7''' | ||
| | |C,^^11no5 | ||
|- | |- | ||
| 0-2-12 | | 0-2-12 | ||
| Line 455: | Line 457: | ||
| 1/1-11/9-14/9 | | 1/1-11/9-14/9 | ||
| 1/1-14/11-18/11 | | 1/1-14/11-18/11 | ||
| 1/1-9/7-11/7 | | '''1/1-9/7-11/7''' | ||
| | |C(^5) | ||
|- | |- | ||
| 0-3-12 | | 0-3-12 | ||
| Line 471: | Line 473: | ||
| 1/1-16/11-14/9 | | 1/1-16/11-14/9 | ||
| 1/1-16/15-11/8 | | 1/1-16/15-11/8 | ||
| 1/1-9/7-15/8 | | '''1/1-9/7-15/8''' | ||
| | |C,vM7no5 | ||
|- | |- | ||
| 0-6-12 | | 0-6-12 | ||
| Line 487: | Line 489: | ||
| 1/1-16/15-14/9 | | 1/1-16/15-14/9 | ||
| 1/1-16/11-15/8 | | 1/1-16/11-15/8 | ||
| 1/1-9/7-11/8 | | '''1/1-9/7-11/8''' | ||
| | |C,^11no5 | ||
|- | |- | ||
| 0-9-12 | | 0-9-12 | ||
| Line 503: | Line 505: | ||
| 1/1-14/11-14/9 | | 1/1-14/11-14/9 | ||
| 1/1-11/9-11/7 | | 1/1-11/9-11/7 | ||
| 1/1-9/7-18/11 | | '''1/1-9/7-18/11''' | ||
| | |C,v6no5 | ||
|- | |- | ||
| 0-11-12 | | 0-11-12 | ||
| Line 511: | Line 513: | ||
| 1/1-7/5-14/9 | | 1/1-7/5-14/9 | ||
| 1/1-10/9-10/7 | | 1/1-10/9-10/7 | ||
| 1/1-9/7-9/5 | | '''1/1-9/7-9/5''' | ||
| | |C,^7no5 | ||
|- | |- | ||
| 0-2-14 | | 0-2-14 | ||
| Line 606: | Line 608: | ||
! Second inversion | ! Second inversion | ||
! Third inversion | ! Third inversion | ||
! | !Name | ||
|- | |- | ||
| 0-1-2-3 | | 0-1-2-3 | ||
| Line 674: | Line 676: | ||
|1-6/5-16/11-8/5 | |1-6/5-16/11-8/5 | ||
| | | | ||
|1-6/5-16/11-8/5 | |1/1-6/5-16/11-8/5 | ||
| | | | ||
| | | | ||
|'''1/1-5/4-3/2-9/5''' | |||
|Cv^7 | |Cv^7 | ||
|- | |- | ||
| Line 685: | Line 687: | ||
| '''1/1-6/5-16/11-7/4''' | | '''1/1-6/5-16/11-7/4''' | ||
| 1/1-6/5-16/11-5/3 | | 1/1-6/5-16/11-5/3 | ||
| 1/1-6/5-11/8-5/3 | | '''1/1-6/5-11/8-5/3''' | ||
| 1/1-8/7-11/8-5/3 | | 1/1-8/7-11/8-5/3 | ||
|C^m,7(v5) | |C^m,7(v5) <u>or</u> | ||
C^mv6^11no5 | |||
|- | |- | ||
| 0-3-6-9 | | 0-3-6-9 | ||
| 1-4/3-7/4-7/6 | | 1-4/3-7/4-7/6 | ||
| archytas | | archytas | ||
| 1/1-7/6-4/3-7/4 | | 1/1/1-7/6-4/3-7/4 | ||
| 1/1-8/7-3/2-12/7 | | 1/1-8/7-3/2-12/7 | ||
| '''1/1-4/3-3/2-7/4''' | | '''1/1-4/3-3/2-7/4''' | ||
| Line 698: | Line 701: | ||
|C7sus4 | |C7sus4 | ||
|- | |- | ||
|0-3-9- | |0-3-9-12 | ||
| | |1-4/3-7/6-14/9 | ||
| | |archytas | ||
| | |1/1-7/6-4/3-14/9 | ||
| | |'''1/1-7/6-3/2-7/4''' | ||
| | |1/1-9/8-4/3-12/7 | ||
| | |1/1-9/7-3/2-12/7 | ||
|Cm7 | |Cm7 <u>or</u> C6 | ||
|- | |- | ||
| 0-4-8-12 | | 0-4-8-12 | ||
| Line 713: | Line 716: | ||
| 1/1-15/11-16/11-15/8 | | 1/1-15/11-16/11-15/8 | ||
| 1/1-16/15-11/8-22/15 | | 1/1-16/15-11/8-22/15 | ||
| 1/1-9/7- | | '''1/1-9/7-11/8-15/8''' | ||
|C,vM7^11no5 | |C,vM7^11no5 | ||
|} | |} | ||
| Line 725: | Line 728: | ||
! Transversal | ! Transversal | ||
! Type | ! Type | ||
!Name | |||
|- | |- | ||
| | | | ||
| | | | ||
| | | | ||
| | |||
|- | |- | ||
| 0-1-2-3-6 | | 0-1-2-3-6 | ||
| 1-10/9-11/9-4/3-16/9 | | 1-10/9-11/9-4/3-16/9 | ||
| otonal | | otonal | ||
|Cv,9^11 | |||
|- | |- | ||
| 0-2-3-4-6 | | 0-2-3-4-6 | ||
| | | | ||
| | | | ||
|C^m,7,11(v5) <u>or</u> | |||
C4^7v9 <u>or</u> C^4v6,9 | |||
|- | |- | ||
| 0-3-4-5-6 | | 0-3-4-5-6 | ||
| | | | ||
| | | | ||
|C^mv9,11 | |||
|- | |- | ||
| 0-2-4-6-8 | | 0-2-4-6-8 | ||
| 1-6/5-16/11-7/4-16/15 | | 1-6/5-16/11-7/4-16/15 | ||
| porcupine | | porcupine | ||
|C^m,7(v5) <u>or</u> | |||
C^mv6^11no5 | |||
|- | |- | ||
| 0-3-6-9-12 | | 0-3-6-9-12 | ||
| 1-4/3-7/4-7/6-14/9 | | 1-4/3-7/4-7/6-14/9 | ||
| archytas | | archytas | ||
|C9(4) <u>or</u> C6,9 <u>or</u> Cm7,11 | |||
|} | |} | ||