@@ Line 1: / Line 1: @@
-Peppermint 24 is a scale first documented by Margo Schulter on the Yahoo tuning forum:
+'''Peppermint 24''' is a [[scale]] first documented by [[Margo Schulter]] on the Yahoo tuning forum: [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_38440.html#38440 M. Schulter (7/3/2002 3:51:43 AM)]
-https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_38440.html#38440
+==Concept==
+Peppermint 24 aims to map [[superparticular]] and other ratios within [[wikipedia:Harry_Partch|Harry Partch's]] larger [[17-limit]] set, to two conventional piano keyboards.
-==Premise==
-Peppermint 24 aims to map superparticular and other ratios within [[wikipedia:Harry_Partch|Harry Partch's]] larger 17-limit set, to two conventional piano keyboards.
 It takes as its basis a [[Regular_Temperaments|regular temperament]] mentioned in [[Erv_Wilson|Ervin Wilson]]'s Scale Tree and described on the Tuning List by [[Keenan Pepper]], with a fifth of about 704.096 [[Cent|cents]], and a precise ratio of [[wikipedia:Golden_ratio|Phi]], the Golden Section (~1.618) between the larger chromatic semitone (e.g. C-C#) at about 128.669 cents and the smaller diatonic semitone (e.g. C#-D) at about 79.522 cents. Said fifth has a precise value of (67 + √5)/118 octaves, which is (40200 + 600 √5)/59 cents.
@@ Line 13: / Line 11: @@
 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>
+.349  346.393              683.253    891.445 1050.488
         C#*      Eb*                   F#*       G#*     Bb*
    C*        D*          E*      F*        G*        A*       B*     C*
@@ Line 23: / Line 22: @@
    C         D           E       F          G         A        B     C
        208.191    416.382 495.904    704.096   912.287 1120.478 1200
+</pre>
- </pre>
+== Intervals ==
+=== Single chain ===
+Offset two of these by 58.680 cents.
+<pre>
+.669
+.191
+.713
+.382
+.904
+.574
+.096
+.765
+.287
+.809
+.478
+.000
+</pre>
+=== Combined (both chains) ===
+<pre>
+.680
+.669
+.349
+.191
+.871
+.713
+.393
+.382
+.062
+.904
+.584
+.574
+.253
+.096
+.775
+.765
+.445
+.287
+.967
+.809
+.488
+.478
+.157
+.000
+</pre>
 ==Catalogue of ratio equivalents==
@@ Line 37: / Line 82: @@
 ===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).
-*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)
-*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)
-*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 (many within 17-odd limit===
+===Other ratios===
 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)
-*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)
-*13:22 (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)
-*16:23 (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)
-*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)
-*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)
+== Subsets ==
+=== Diatonic and related scales ===
+C Major
+* 208.191
+* 416.382
+* 495.904
+* 704.096
+* 912.287
+* 1120.478
+* 1200.000
+=== Salt and pepper scale and its subsets ===
+Salt and pepper{{idiosyncratic}}
+''A 12-tone subset of Peppermint-24 designed by [[Budjarn Lambeth]] to concentrate the most frequently used intervals on just one keyboard.''
+* 128.669
+* 187.349
+* 208.191
+* 266.871
+* 287.713
+* 495.904
+* 704.096
+* 832.765
+* 891.445
+* 970.967
+* 1050.488
+* 1200.000
+<small>
+Evacuated planet{{idiosyncratic}} (approximated from [[66afdo|66]][[afdo]])
+* 128.669
+* 495.904
+* 704.096
+* 1050.488
+* 1200.000
+Flattened pseudo-[[equiheptatonic]]
+* 128.669
+* 266.871
+* 495.904
+* 704.096
+* 832.765
+* 1050.488
+* 1200.000
+Geode{{idiosyncratic}} (approximated from [[6afdo]])
+* 266.871
+* 495.904
+* 704.096
+* 1050.488
+* 1200.000
+Minor hexatonic (approximated from [[12edo]])
+* 187.349
+* 287.713
+* 495.904
+* 704.096
+* 970.967
+* 1200.000
+Pepperbass{{idiosyncratic}} (original/default tuning)
+(''works well with jungle- or trap-style sub bass'')
+* 208.191
+* 704.096
+* 891.445
+* 1050.488
+* 1200.000
+Pseudo-[[6afdo]]
+* 266.871
+* 495.904
+* 704.096
+* 891.445
+* 1050.488
+* 1200.000
+Pseudo-akebono I (approximated from [[12edo]])
+* 208.191
+* 287.713
+* 704.096
+* 891.445
+* 1200.000
+Pseudo-akebono II (approximated from [[12edo]])
+* 128.669
+* 495.904
+* 704.096
+* 832.765
+* 1200.000
+Pseudo-[[equipentatonic]]
+* 266.871
+* 495.904
+* 704.096
+* 970.967
+* 1200.000
+Pseudo-hirajoshi (approximated from [[12edo]])
+* 208.191
+* 287.713
+* 704.096
+* 832.765
+* 1200.000
+Sharpened pseudo-[[pelog]]
+* 128.669
+* 287.713
+* 704.096
+* 832.765
+* 1200.000
+</small>
+=== Ketchup and mustard scale and its subsets ===
+Ketchup and mustard{{idiosyncratic}}
+''A 12-tone subset of Peppermint-24 designed by [[Budjarn Lambeth]] to map intervals which sound nice with an inharmonic [[gamelan]]-like timbre to a 12-key keyboard (e.g. [https://scaleworkshop.plainsound.org/scale/h2qwnm0-l this timbre in Scale Workshop]).''
+* 58.680
+* 128.669
+* 187.349
+* 266.871
+* 475.062
+* 683.253
+* 762.775
+* 832.765
+* 912.287
+* 970.967
+* 1050.488
+* 1200.000
+<small>
+Inharmonic geode{{idiosyncratic}}
+* 266.871
+* 475.062
+* 683.253
+* 1050.488
+* 1200.000
+Inharmonic minor hexatonic
+* 187.349
+* 266.871
+* 475.062
+* 683.253
+* 970.967
+* 1200.000
+Inharmonic pepperbass{{idiosyncratic}}
+* 187.349
+* 683.253
+* 762.775
+* 1050.488
+* 1200.000
+Inharmonic pseudo-[[6afdo]]
+* 266.871
+* 475.062
+* 683.253
+* 832.765
+* 1050.488
+* 1200.000
+Inharmonic pseudo-akebono I
+* 187.349
+* 266.871
+* 683.253
+* 912.287
+* 1200.000
+Inharmonic pseudo-akebono II
+* 58.680
+* 475.062
+* 683.253
+* 762.775
+* 1200.000
+Inharmonic pseudo-[[equipentatonic]]
+* 266.871
+* 475.062
+* 704.096
+* 970.967
+* 1200.000
+Inharmonic pseudo-hirajoshi
+* 187.349
+* 266.871
+* 683.253
+* 832.765
+* 1200.000
+Unsharpened pseudo-[[pelog]]
+* 128.669
+* 266.871
+* 683.253
+* 762.775
+* 1200.000
+</small>
+=== Miscellaneous ===
+Undecimal picardy hexatonic{{idiosyncratic}} (original/default tuning)
+* 58.680
+* 266.871
+* 346.393
+* 704.096
+* 970.967
+* 1200.000
+Unflattened pseudo-[[equiheptatonic]]
+* 187.349
+* 346.393
+* 495.904
+* 704.096
+* 832.765
+* 1050.488
+* 1200.000
+== Instruments ==
+=== Lumatone ===
+* [[:File:Peppermint-C62.ltn]] & [[:File:MillerPeppermintLumatone.jpeg]] — [[Herman Miller]]'s [[Lumatone]] mapping for peppermint-24.
+== Music ==
+=== Modern Renderings ===
+; {{W|John Bull (composer)|John Bull}}
+* [https://www.youtube.com/watch?v=Ku32F-zEtmU ''Fantasia «Ut Re Mi Fa Sol La»''] (late 1500s/early 1600s, from ''Fitzwilliam Virginal Book Vol.1 No.51'') – rendered by Claudi Meneghin (2020) in a 24 note per octave well-tempered tuning system that uses both [[golden meantone]] fifths and peppermint fifths (tuning specification in video description).
+; [[wikipedia:Wolfgang Amadeus Mozart|Wolfgang Amadeus Mozart]]
+* [https://www.youtube.com/watch?v=eRzdbzJah20 ''Mozart's Gigue KV 574, Arranged for Fortepiano (PEPPERMINT)''] (rendered in the 12 note subset by [[Claudi Meneghin]], 2025)
+* [https://www.youtube.com/watch?v=2-4oaNq7jwo ''2025-05-24 CHACONNE «LES REGRETS» - PEPPERMINT''] (rendered in a 46EDO-related subset by [[Claudi Meneghin]], (2025) ([https://www.youtube.com/shorts/I8NbVZFsIh0 short version])
+=== 21st Century ===
+; [[Budjarn Lambeth]]
+* [https://www.youtube.com/watch?v=g6e3zYlbsWc ''Microtonal Jungle-Inspired Track in the "Salt and Pepper Scale"''] (2025)
+; [[Claudi Meneghin]]
+* [https://www.youtube.com/watch?v=5vPvI6MXWFM ''ST LOUIS FUGUE (Fugue on St Louis Blues), for Baroque Ensemble - (Microtonal, PEPPERMINT)''] (2025)
+* [https://www.youtube.com/watch?v=iZlvKLg4CoM ''PEPPERMINT FUGUE in 5 parts «Les Regrets»''] (2025)
 [[Category:24-tone scales]]
+[[Category:Tempered scales]]
 [[Category:Todo:clarify]]

Peppermint-24: Difference between revisions