Xenharmonic Wiki

Peppermint-24: Difference between revisions

← Older editNewer edit →
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,280 edits
Add plain easy to copy lists of intervals
Sintel (talk | contribs)
autopatrolled, emailconfirmed
1,636 edits
Formatting (a numbered list of numbers is kind of confusing!)
Line 10: Line 10:
Here is a 24-note keyboard arrangement, with an asterisk (*) showing a note on the upper keyboard:
Here is a 24-note keyboard arrangement, with an asterisk (*) showing a note on the upper keyboard:


<pre>     187.349  346.393              683.253    891.445 1050.488
<pre>
    187.349  346.393              683.253    891.445 1050.488
       C#*      Eb*                  F#*      G#*    Bb*
       C#*      Eb*                  F#*      G#*    Bb*
   C*        D*          E*      F*        G*        A*      B*    C*
   C*        D*          E*      F*        G*        A*      B*    C*
Line 20: Line 21:
   C        D          E      F          G        A        B    C
   C        D          E      F          G        A        B    C
   0      208.191    416.382 495.904    704.096  912.287 1120.478 1200
   0      208.191    416.382 495.904    704.096  912.287 1120.478 1200
 
</pre>
 </pre>


== Intervals ==
== Intervals ==
Line 27: Line 27:
=== Single chain ===
=== Single chain ===
Offset two of these by 58.680 cents.
Offset two of these by 58.680 cents.
# 128.669
<pre>
# 208.191
128.669
# 287.713
208.191
# 416.382
287.713
# 495.904
416.382
# 624.574
495.904
# 704.096
624.574
# 832.765
704.096
# 912.287
832.765
# 991.809
912.287
# 1120.478
991.809
# 1200.000
1120.478
1200.000
</pre>


=== Combined (both chains) ===
=== Combined (both chains) ===
# 58.680
<pre>
# 128.669
58.680
# 187.349
128.669
# 208.191
187.349
# 266.871
208.191
# 287.713
266.871
# 346.393
287.713
# 416.382
346.393
# 475.062
416.382
# 495.904
475.062
# 554.584
495.904
# 624.574
554.584
# 683.253
624.574
# 704.096
683.253
# 762.775
704.096
# 832.765
762.775
# 891.445
832.765
# 912.287
891.445
# 970.967
912.287
# 991.809
970.967
# 1050.488
991.809
# 1120.478
1050.488
# 1179.157
1120.478
# 1200.000
1179.157
1200.000
</pre>


==Catalogue of ratio equivalents==
==Catalogue of ratio equivalents==
Line 77: Line 81:
===Multiplex (n:1) and [[superparticular]] (n+1:n) intervals===
===Multiplex (n:1) and [[superparticular]] (n+1:n) intervals===


*1:2 (1200) -- This is the usual octave (e.g. F3-F4), at a pure 1:2.
* 1:2 (1200) -- This is the usual octave (e.g. F3-F4), at a pure 1:2.
*2:3 (701.96) -- This is the usual fifth (e.g. F3-C4, 704.10, +2.14).
* 2:3 (701.96) -- This is the usual fifth (e.g. F3-C4, 704.10, +2.14).
* 3:4 (498.04) -- Usual fourth (e.g. C4-F4, 495.90, -2.14).
* 3:4 (498.04) -- Usual fourth (e.g. C4-F4, 495.90, -2.14).
*6:7 (266.87) -- Major second + QD (e.g. D4-E*4), at a pure 6:7.
* 6:7 (266.87) -- Major second + QD (e.g. D4-E*4), at a pure 6:7.
*7:8 (231.17) -- Minor third - QD (e.g. C*4-Eb4, 229.03, -2.14)
* 7:8 (231.17) -- Minor third - QD (e.g. C*4-Eb4, 229.03, -2.14)
*8:9 (203.91) -- Usual major second (e.g. C4-D4, 208.19, +4.28)
* 8:9 (203.91) -- Usual major second (e.g. C4-D4, 208.19, +4.28)
*11:12 (150.64) -- Major second - QD (e.g. C*4-D4, 149.51, -1.13)
* 11:12 (150.64) -- Major second - QD (e.g. C*4-D4, 149.51, -1.13)
*12:13 (138.57) -- Minor second + QD (e.g. E4-F*4, 138.20, -0.37)
* 12:13 (138.57) -- Minor second + QD (e.g. E4-F*4, 138.20, -0.37)
* 13:14 (128.30) -- Usual apotome (e.g. C4-C#4, 128.67, +0.37)
* 13:14 (128.30) -- Usual apotome (e.g. C4-C#4, 128.67, +0.37)
*17:18 (98.95) -- Diminished third - QD (e.g. G#*4-Bb4, 100.36, -1.41)
* 17:18 (98.95) -- Diminished third - QD (e.g. G#*4-Bb4, 100.36, -1.41)
* 21:22 (80.54) -- Usual minor second (e.g. E4-F4, 79.52, -1.02)
* 21:22 (80.54) -- Usual minor second (e.g. E4-F4, 79.52, -1.02)
*24:25 (70.67) -- Apotome - QD (e.g. E*4-Eb4, 69.99, -0.68)
* 24:25 (70.67) -- Apotome - QD (e.g. E*4-Eb4, 69.99, -0.68)
*27:28 (62.96) -- QD (e.g. E4-E*4, 58.68, -4.28)
* 27:28 (62.96) -- QD (e.g. E4-E*4, 58.68, -4.28)


===Other ratios===
===Other ratios===
Many of these fall within the [[17-odd-limit]].
Many of these fall within the [[17-odd-limit]].


*4:7 (968.83) -- Major sixth + QD (e.g. G3-E*4, 970.97, +2.14)
* 4:7 (968.83) -- Major sixth + QD (e.g. G3-E*4, 970.97, +2.14)
*7:9 (435.08) -- Fourth - QD (e.g. G*4-C5, 437.22, +2.14)
* 7:9 (435.08) -- Fourth - QD (e.g. G*4-C5, 437.22, +2.14)
*7:12 (933.13) -- Minor seventh - QD (e.g. G*3-F4), at a pure 7:12.
* 7:12 (933.13) -- Minor seventh - QD (e.g. G*3-F4), at a pure 7:12.
*9:14 (764.92) -- Fifth + QD (e.g. G4-D*5, 762.78, -2.14)
* 9:14 (764.92) -- Fifth + QD (e.g. G4-D*5, 762.78, -2.14)
*9:16 (996.09) -- Usual minor seventh (e.g. G4-F4, 991.81, -4.28)
* 9:16 (996.09) -- Usual minor seventh (e.g. G4-F4, 991.81, -4.28)
*6:11 (1049.36) -- Minor seventh + QD (e.g. G3-F*4, 1050.49, +1.13)
* 6:11 (1049.36) -- Minor seventh + QD (e.g. G3-F*4, 1050.49, +1.13)
*7:11 (782.49) -- Usual minor sixth (e.g. A3-F4, 783.62, +1.13)
* 7:11 (782.49) -- Usual minor sixth (e.g. A3-F4, 783.62, +1.13)
*8:11 (551.32) -- Fourth + QD (e.g. G3-C*4, 554.58, +3.27)
* 8:11 (551.32) -- Fourth + QD (e.g. G3-C*4, 554.58, +3.27)
*9:11 (347.41) -- Minor third + QD (e.g. G3-Bb*3, 346.39, -1.02)
* 9:11 (347.41) -- Minor third + QD (e.g. G3-Bb*3, 346.39, -1.02)
*8:13 (840.53) -- Minor sixth + QD (e.g. G3-Eb*3, 842.30, +1.77)
* 8:13 (840.53) -- Minor sixth + QD (e.g. G3-Eb*3, 842.30, +1.77)
* 9:13 (636.62) -- Diminished fifth + QD (e.g. A3-Eb*4, 634.11, -2.51)
* 9:13 (636.62) -- Diminished fifth + QD (e.g. A3-Eb*4, 634.11, -2.51)
*11:13 (289.21) -- Usual minor third (e.g. D3-F3, 287.71, -1.50)
* 11:13 (289.21) -- Usual minor third (e.g. D3-F3, 287.71, -1.50)
*11:14 (417.51) -- Usual major third (e.g. D3-F#3, 416.38, -1.13)
* 11:14 (417.51) -- Usual major third (e.g. D3-F#3, 416.38, -1.13)
*11:16 (648.68) -- Fifth - QD (e.g. F*3-C4, 645.42, -3.27)
* 11:16 (648.68) -- Fifth - QD (e.g. F*3-C4, 645.42, -3.27)
*11:18 (852.59) -- Major sixth - QD (e.g. G*4-E5, 853.61, +1.02)
* 11:18 (852.59) -- Major sixth - QD (e.g. G*4-E5, 853.61, +1.02)
*11:21 (1119.46) -- Usual major seventh (e.g. F3-E4, 1120.48, +1.02)
* 11:21 (1119.46) -- Usual major seventh (e.g. F3-E4, 1120.48, +1.02)
*12:17 (603.00) -- Augmented third + QD (e.g. Eb4-G#*4, 603.73, +0.73)
* 12:17 (603.00) -- Augmented third + QD (e.g. Eb4-G#*4, 603.73, +0.73)
*13:16 (359.47) -- Major third - QD (e.g. C*4-E4, 357.70, -1.77)
* 13:16 (359.47) -- Major third - QD (e.g. C*4-E4, 357.70, -1.77)
*13:18 (563.38) -- Augmented fourth - QD (e.g. C*4-F#4, 565.89, +2.51)
* 13:18 (563.38) -- Augmented fourth - QD (e.g. C*4-F#4, 565.89, +2.51)
* 13:21 (830.25) -- Usual augmented fifth (e.g. C4-G#4, 832.76, +2.51)
* 13:21 (830.25) -- Usual augmented fifth (e.g. C4-G#4, 832.76, +2.51)
*13:22 (910.79) -- Usual major sixth (e.g. G3-E4, 912.29, +1.50)
* 13:22 (910.79) -- Usual major sixth (e.g. G3-E4, 912.29, +1.50)
*13:23 (987.75) -- Usual minor seventh (e.g. D4-C5, 991.81, +4.06)
* 13:23 (987.75) -- Usual minor seventh (e.g. D4-C5, 991.81, +4.06)
*13:24 (1061.43) -- Major seventh - QD (e.g. F*3-E4), 1061.80, +0.37)
* 13:24 (1061.43) -- Major seventh - QD (e.g. F*3-E4), 1061.80, +0.37)
*14:17 (336.13) -- Usual augmented second (e.g. F4-G#4, 336.86, +0.73)
* 14:17 (336.13) -- Usual augmented second (e.g. F4-G#4, 336.86, +0.73)
*14:27 (1137.04) -- Octave - QD (e.g. F*4-F5, 1141.32, +4.28)
* 14:27 (1137.04) -- Octave - QD (e.g. F*4-F5, 1141.32, +4.28)
*15:17 (216.69) -- Diminished third + QD (e.g. C#4-Eb*4, 217.72, +1.04)
* 15:17 (216.69) -- Diminished third + QD (e.g. C#4-Eb*4, 217.72, +1.04)
* 16:21 (470.71) -- Major third + QD (e.g. C4-E*4, 475.06, +4.28)
* 16:21 (470.71) -- Major third + QD (e.g. C4-E*4, 475.06, +4.28)
*16:23 (628.27) -- Usual augmented fourth (e.g. C4-F#4, 624.57, -3.70)
* 16:23 (628.27) -- Usual augmented fourth (e.g. C4-F#4, 624.57, -3.70)
*18:23 (424.36) -- Diminished fourth + QD (e.g. B4-Eb*5, 425.91, +1.55)
* 18:23 (424.36) -- Diminished fourth + QD (e.g. B4-Eb*5, 425.91, +1.55)
* 16:25 (772.63) -- Diminished fourth + QD (e.g. F#4-Bb*4, 774.09, +1.46)
* 16:25 (772.63) -- Diminished fourth + QD (e.g. F#4-Bb*4, 774.09, +1.46)
*17:20 (281.36) -- Augmented second - QD (e.g. F*4-G#4, 278.18, -3.18)
* 17:20 (281.36) -- Augmented second - QD (e.g. F*4-G#4, 278.18, -3.18)
*17:21 (365.83) -- Usual diminished fourth (e.g. F#4-Bb4, 367.24, +1.41)
* 17:21 (365.83) -- Usual diminished fourth (e.g. F#4-Bb4, 367.24, +1.41)
* 17:28 (863.87) -- Usual diminished seventh (e.g. F#4-Eb4, 863.14, -0.73)
* 17:28 (863.87) -- Usual diminished seventh (e.g. F#4-Eb4, 863.14, -0.73)
*21:34 (834.17) -- Usual augmented fifth (e.g. F3-C#4, 832.76, +1.41)
* 21:34 (834.17) -- Usual augmented fifth (e.g. F3-C#4, 832.76, +1.41)
*28:51 (1038.08) -- Usual augmented sixth (e.g. Eb3-C#4, 1040.96, +2.87)
* 28:51 (1038.08) -- Usual augmented sixth (e.g. Eb3-C#4, 1040.96, +2.87)
*21:23 (157.49) -- Usual diminished third (e.g. C#4-Eb4, 159.04, +1.55)
* 21:23 (157.49) -- Usual diminished third (e.g. C#4-Eb4, 159.04, +1.55)
*21:26 (369.75) -- Usual diminished fourth (e.g. C#4-F4, 367.24, -1.51)
* 21:26 (369.75) -- Usual diminished fourth (e.g. C#4-F4, 367.24, -1.51)
*23:27 (277.59) -- Augmented second - QD (e.g. Eb*4-F#4, 278.18, +0.59)
* 23:27 (277.59) -- Augmented second - QD (e.g. Eb*4-F#4, 278.18, +0.59)
*26:33 (412.75) -- Usual major third (e.g. F4-A4, 416.38, +3.63)
* 26:33 (412.75) -- Usual major third (e.g. F4-A4, 416.38, +3.63)
*28:33 (284.45) -- Usual minor third (e.g. E4-G4, 287.71, +3.27)
* 28:33 (284.45) -- Usual minor third (e.g. E4-G4, 287.71, +3.27)
*33:56 (915.55) -- Usual major sixth (e.g. G4-E5, 912.29, -3.27)
* 33:56 (915.55) -- Usual major sixth (e.g. G4-E5, 912.29, -3.27)
[[Category:24-tone scales]]
[[Category:24-tone scales]]
[[Category:Tempered scales]]
[[Category:Tempered scales]]
[[Category:Todo:clarify]]
[[Category:Todo:clarify]]
Retrieved from "https://en.xen.wiki/w/Peppermint-24"