Revision as of 21:56, 3 April 2019

50edo divides the octave into 50 equal parts of precisely 24 cents each. In the 5-limit, it tempers out 81/80, making it a meantone system, and in that capacity has historically has drawn some notice. In "Harmonics or the Philosophy of Musical Sounds" (1759) by Robert Smith, a musical temperament is described where the octave is divided into 50 equal parts – 50edo, in one word. Later, W.S.B. Woolhouse noted it was fairly close to the least squares tuning for 5-limit meantone. 50edo, however, is especially interesting from a higher limit point of view. While 31edo extends meantone with a 7/4 which is nearly pure, 50 has a flat 7/4 but both 11/8 and 13/8 are nearly pure.

50 tempers out 126/125, 225/224 and 3136/3125 in the 7-limit, indicating it supports septimal meantone; 245/242, 385/384 and 540/539 in the 11-limit and 105/104, 144/143 and 196/195 in the 13-limit, and can be used for even higher limits. Aside from meantone and its extension meanpop, it can be used to advantage for the 15&50 temperament (Coblack), and provides the optimal patent val for 11 and 13 limit bimeantone. It is also the unique equal temperament tempering out both 81/80 and the vishnuzma, |23 6 -14>, so that in 50et seven chromatic semitones are a perfect fourth. In 12et by comparison this gives a fifth, in 31et a doubly diminished fifth, and in 19et a diminished fourth.

Relations

The 50edo system is related to 7edo, 12edo, 19edo, 31edo as the next approximation to the "Golden Tone System" (Das Goldene Tonsystem) of Thorvald Kornerup (and similarly as the next step from 31edo in Joseph Yasser's "A Theory of Evolving Tonality").

Intervals

Degrees of 50edo	Cents value	pions	7mus	Ratios*	Generator for*
0	0			1/1
1	24	25.44	30.72 (1E.B8₁₆)	45/44, 49/48, 56/55, 65/64, 66/65, 78/77, 91/90, 99/98, 100/99, 121/120, 169/168	Sengagen
2	48	50.88	61.44 (3D.71₁₆)	33/32, 36/35, 50/49, 55/54, 64/63
3	72	76.32	92.16 (5C.29₁₆)	21/20, 25/24, 26/25, 27/26, 28/27	Vishnu (2/oct), Coblack (5/oct)
4	96	101.76	122.88 (7A.E1₁₆)	22/21	Injera (50d val, 2/oct)
5	120	127.2	153.6 (99.9A₁₆)	16/15, 15/14, 14/13
6	144	152.64	184.32 (B8.52₁₆)	13/12, 12/11
7	168	178.08	215.04 (D7.0A₁₆)	11/10
8	192	203.52	245.76 (F5.C3₁₆)	9/8, 10/9
9	216	228.96	276.48 (114.7B₁₆)	25/22	Tremka, Machine (50b val)
10	240	254.4	307.2 (133.33₁₆)	8/7, 15/13
11	264	279.88	337.92 (151.EB8₁₆)	7/6	Septimin (13-limit)
12	288	305.28	368.64 (170.A4₁₆)	13/11
13	312	330.72	399.36 (18F.5C₁₆)	6/5
14	336	356.16	430.08 (1AE.148₁₆)	27/22, 39/32, 40/33, 49/40
15	360	381.6	460.8 (1CC.CD₁₆)	16/13, 11/9
16	384	407.04	491.52 (1EB.85₁₆)	5/4	Wizard (2/oct)
17	408	432.48	522.24 (20A.4₁₆)	14/11	Ditonic
18	432	457.92	552.96 (228.F6₁₆)	9/7	Hedgehog (50cc val, 2/oct)
19	456	483.36	583.68 (247.AE₁₆)	13/10	Bisemidim (2/oct)
20	480	508.8	614.4 (266.66₁₆)	33/25, 55/42, 64/49
21	504	534.24	645.12 (285.1F₁₆)	4/3	Meantone/Meanpop
22	528	559.68	675.84 (2A3.D7₁₆)	15/11
23	552	585.12	706.56 (2C2.8F₁₆)	11/8, 18/13	Barton, Emka
24	576	610.56	737.28 (2E1.48₁₆)	7/5
25	600	636	768 (300₁₆)	63/44, 88/63, 78/55, 55/39
26	624	661.44	798.72 (31E.B8₁₆)	10/7
27	648	686.88	829.44 (33D.71₁₆)	16/11, 13/9
28	672	712.32	860.16 (35C.29₁₆)	22/15
29	696	737.76	900.88 (37A.E1₁₆)	3/2
30	720	763.2	921.6 (399.9A₁₆)	50/33, 84/55, 49/32
31	744	788.64	952.32 (3B8.52₁₆)	20/13
32	768	814.08	983.04 (3D7.0A₁₆)	14/9
33	792	239.52	1013.76 (3F5.C3₁₆)	11/7
34	816	864.96	1044.48 (414.7B₁₆)	8/5
35	840	890.4	1095.2 (433.33₁₆)	13/8, 18/11
36	864	915.84	1105.92 (451.EB8₁₆)	44/27, 64/39, 33/20, 80/49
37	888	941.28	1136.64 (470.A4₁₆	5/3
38	912	966.72	1167.36 (48F.5C₁₆)	22/13
39	936	992.16	1198.08 (4AE.148₁₆)	12/7
40	960	1017.6	1228.8 (4CC.CD₁₆)	7/4
41	984	1043.04	1261.52 (4EB.85₁₆)	44/25
42	1008	1068.48	1290.24 (50A.4₁₆)	16/9, 9/5
43	1032	1093.92	1320.96 (528.F6₁₆)	20/11
44	1056	1119.36	1351.68 (547.AE₁₆)	24/13, 11/6
45	1080	1144.8	1382.4 (566.66₁₆)	15/8, 28/15, 13/7
46	1104	1170.24	1413.12 (585.1F₁₆)	21/11
47	1128	1195.68	1443.84 (5A3.D7₁₆)	40/21, 48/25, 25/13, 52/27, 27/14
48	1152	1221.12	1474.56 (5C2.8F₁₆)	64/33, 35/18, 49/25, 108/55, 63/32
49	1176	1246.56	1505.28 (5E1.48₁₆)	88/45, 96/49, 55/28, 128/65, 65/33, 77/39, 180/91, 196/99, 99/50, 240/121, 336/169
50	1200	1272	1536 (600₁₆)	2/1

Using the 13-limit patent val, except as noted.

Selected just intervals by error

The following table shows how some prominent just intervals are represented in 50edo (ordered by absolute error).

Best direct mapping, even if inconsistent

Interval, complement	Error (abs., in cents)
16/13, 13/8	0.528
15/14, 28/15	0.557
11/8, 16/11	0.682
13/11, 22/13	1.210
13/10, 20/13	1.786
5/4, 8/5	2.314
7/6, 12/7	2.871
11/10, 20/11	2.996
9/7, 14/9	3.084
6/5, 5/3	3.641
13/12, 24/13	5.427
4/3, 3/2	5.955
7/5, 10/7	6.512
12/11, 11/6	6.637
15/13, 26/15	7.741
16/15, 15/8	8.269
14/13, 13/7	8.298
8/7, 7/4	8.826
15/11, 22/15	8.951
14/11, 11/7	9.508
10/9, 9/5	9.596
18/13, 13/9	11.382
11/9, 18/11	11.408
9/8, 16/9	11.910

Patent val mapping

Interval, complement	Error (abs., in cents)
16/13, 13/8	0.528
15/14, 28/15	0.557
11/8, 16/11	0.682
13/11, 22/13	1.210
13/10, 20/13	1.786
5/4, 8/5	2.314
7/6, 12/7	2.871
11/10, 20/11	2.996
9/7, 14/9	3.084
6/5, 5/3	3.641
13/12, 24/13	5.427
4/3, 3/2	5.955
7/5, 10/7	6.512
12/11, 11/6	6.637
15/13, 26/15	7.741
16/15, 15/8	8.269
14/13, 13/7	8.298
8/7, 7/4	8.826
15/11, 22/15	8.951
14/11, 11/7	9.508
10/9, 9/5	9.596
18/13, 13/9	11.382
9/8, 16/9	11.910
11/9, 18/11	12.592

Commas

50 EDO tempers out the following commas. (Note: This assumes the val < 50 79 116 140 173 185 204 212 226 |, comma values in cents rounded to 2 decimal places.) This list is not all-inclusive, and is based on the interval table from Scala version 2.2.

Monzo	Cents	Ratio	Name 1	Name 2
\| -4 4 -1 >	21.51	81/80	Syntonic comma	Didymus comma
\| -27 -2 13 >	18.17		Ditonma
\| 23 6 -14 >	3.34		Vishnu comma
\| 1 2 -3 1 >	13.79	126/125	Starling comma	Small septimal comma
\| -5 2 2 -1 >	7.71	225/224	Septimal kleisma	Marvel comma
\| 6 0 -5 2 >	6.08	3136/3125	Hemimean	Middle second comma
\| -6 -8 2 5 >	1.12		Wizma
\|-11 2 7 -3 >	1.63		Meter
\| 11 -10 -10 10 >	5.57		Linus
\|-13 10 0 -1 >	50.72	59049/57344	Harrison's comma
\| 2 3 1 -2 -1 >	3.21	540/539	Swets' comma	Swetisma
\| -3 4 -2 -2 2 >	0.18	9801/9800	Kalisma	Gauss' comma
\| 5 -1 3 0 -3 >	3.03	4000/3993	Wizardharry	Undecimal schisma
\| -7 -1 1 1 1 >	4.50	385/384	Keenanisma	Undecimal kleisma
\| -1 0 1 2 -2 >	21.33	245/242	Cassacot
\| 2 -1 0 1 -2 1 >	4.76	364/363	Gentle comma
\| 2 -1 -1 2 0 -1 >	8.86	196/195	Mynucuma
\| 2 3 0 -1 1 -2 >	7.30	1188/1183	Kestrel Comma
\| 3 0 2 0 1 -3 >	2.36	2200/2197	Petrma	Parizek comma
\| -3 1 1 1 0 -1 >	16.57	105/104	Animist comma	Small tridecimal comma
\| 4 2 0 0 -1 -1 >	12.06	144/143	Grossma
\| 3 -2 0 1 -1 -1 0 0 1 >	1.34	1288/1287	Triaphonisma

Music

Twinkle canon – 50 edo by Claudi Meneghin

Fantasia Catalana by Claudi Meneghin

Fugue on the Dragnet theme by Claudi Meneghin

the late little xmas album by Cam Taylor

Harpsichord meantone improvisation 1 in 50EDO by Cam Taylor

Long improvisation 2 in 50EDO by Cam Taylor

Chord sequence for Difference tones in 50EDO by Cam Taylor

Enharmonic Modulations in 50EDO by Cam Taylor

Harmonic Clusters on 50EDO Harpsichord by Cam Taylor

Fragment in Fifty by Cam Taylor

Additional reading

Robert Smith's book online

More information about Robert Smith's temperament

50EDO Theory - Intervals, Chords and Scales in 50EDO by Cam Taylor

iamcamtaylor - Blog on 50EDO and extended meantone theory by Cam Taylor

50edo: Difference between revisions

Revision as of 21:56, 3 April 2019

Contents

Relations

Intervals

Selected just intervals by error

Best direct mapping, even if inconsistent

Patent val mapping

Commas

Music

Additional reading

Navigation menu

@@ Line 1: / Line 1: @@
 __FORCETOC__
 '''50edo''' divides the [[Octave|octave]] into 50 equal parts of precisely 24 [[cent|cent]]s each. In the [[5-limit|5-limit]], it tempers out 81/80, making it a [[Meantone|meantone]] system, and in that capacity has historically has drawn some notice. In [http://lit.gfax.ch/Harmonics%202nd%20Edition%20%28Robert%20Smith%29.pdf "Harmonics or the Philosophy of Musical Sounds"] (1759) by Robert Smith, a musical temperament is described where the octave is divided into 50 equal parts &ndash; 50edo, in one word. Later, W.S.B. Woolhouse noted it was fairly close to the [[Target_tunings|least squares]] tuning for 5-limit meantone. 50edo, however, is especially interesting from a higher limit point of view. While [[31edo|31edo]] extends meantone with a [[7/4|7/4]] which is nearly pure, 50 has a flat 7/4 but both [[11/8|11/8]] and [[13/8|13/8]] are nearly pure.
@@ Line 13: / Line 14: @@
 ! | Degrees of 50edo
 ! | Cents value
+!pions
+!7mus
 ! | Ratios*
 ! | Generator for*
 |-
 | | 0
-| | 0
+|  colspan="3"| 0
 | | 1/1
 | |
@@ Line 23: / Line 26: @@
 | | 1
 | | 24
+|25.44
+|30.72 (1E.B8<sub>16</sub>)
 | | 45/44, 49/48, 56/55, 65/64, 66/65, 78/77, 91/90, 99/98, 100/99, 121/120, 169/168
 | | [[Hemimean_clan#Sengagen|Sengagen]]
@@ Line 28: / Line 33: @@
 | | 2
 | | 48
+|50.88
+|61.44 (3D.71<sub>16</sub>)
 | | 33/32, 36/35, 50/49, 55/54, 64/63
 | |
@@ Line 33: / Line 40: @@
 | | 3
 | | 72
+|76.32
+|92.16 (5C.29<sub>16</sub>)
 | | 21/20, 25/24, 26/25, 27/26, 28/27
 | | [[Vishnuzmic_family#Vishnu|Vishnu]] (2/oct), [http://x31eq.com/cgi-bin/rt.cgi?ets=15%2650&limit=11 Coblack] (5/oct)
@@ Line 38: / Line 47: @@
 | | 4
 | | 96
+|101.76
+|122.88 (7A.E1<sub>16</sub>)
 | | 22/21
 | | [[Meantone_family#Injera|Injera]] (50d val, 2/oct)
@@ Line 43: / Line 54: @@
 | | 5
 | | 120
+|127.2
+|153.6 (99.9A<sub>16</sub>)
 | | 16/15, 15/14, 14/13
 | |
@@ Line 48: / Line 61: @@
 | | 6
 | | 144
+|152.64
+|184.32 (B8.52<sub>16</sub>)
 | | 13/12, 12/11
 | |
@@ Line 53: / Line 68: @@
 | | 7
 | | 168
+|178.08
+|215.04 (D7.0A<sub>16</sub>)
 | | 11/10
 | |
@@ Line 58: / Line 75: @@
 | | 8
 | | 192
+|203.52
+|245.76 (F5.C3<sub>16</sub>)
 | | 9/8, 10/9
 | |
@@ Line 63: / Line 82: @@
 | | 9
 | | 216
+|228.96
+|276.48 (114.7B<sub>16</sub>)
 | | 25/22
 | | [http://x31eq.com/cgi-bin/rt.cgi?ets=50%2661p&limit=2.3.5.11.13 Tremka], [[Subgroup_temperaments#x2.9.7.11-Machine|Machine]] (50b val)
@@ Line 68: / Line 89: @@
 | | 10
 | | 240
+|254.4
+|307.2 (133.33<sub>16</sub>)
 | | 8/7, 15/13
 | |
@@ Line 73: / Line 96: @@
 | | 11
 | | 264
+|279.88
+|337.92 (151.EB8<sub>16</sub>)
 | | 7/6
 | | [[Marvel_temperaments#Septimin-13-limit|Septimin (13-limit)]]
@@ Line 78: / Line 103: @@
 | | 12
 | | 288
+|305.28
+|368.64 (170.A4<sub>16</sub>)
 | | 13/11
 | |
@@ Line 83: / Line 110: @@
 | | 13
 | | 312
+|330.72
+|399.36 (18F.5C<sub>16</sub>)
 | | 6/5
 | |
@@ Line 88: / Line 117: @@
 | | 14
 | | 336
+|356.16
+|430.08 (1AE.148<sub>16</sub>)
 | | 27/22, 39/32, 40/33, 49/40
 | |
@@ Line 93: / Line 124: @@
 | | 15
 | | 360
+|381.6
+|460.8 (1CC.CD<sub>16</sub>)
 | | 16/13, 11/9
 | |
@@ Line 98: / Line 131: @@
 | | 16
 | | 384
+|407.04
+|491.52 (1EB.85<sub>16</sub>)
 | | 5/4
 | | [[Marvel_temperaments#Wizard-11-limit|Wizard]] (2/oct)
@@ Line 103: / Line 138: @@
 | | 17
 | | 408
+|432.48
+|522.24 (20A.4<sub>16</sub>)
 | | 14/11
 | | [[Ditonmic_family|Ditonic]]
@@ Line 108: / Line 145: @@
 | | 18
 | | 432
+|457.92
+|552.96 (228.F6<sub>16</sub>)
 | | 9/7
 | | [[Porcupine_family#Hedgehog|Hedgehog]] (50cc val, 2/oct)
@@ Line 113: / Line 152: @@
 | | 19
 | | 456
+|483.36
+|583.68 (247.AE<sub>16</sub>)
 | | 13/10
 | | [[Starling_temperaments#Bisemidim|Bisemidim]] (2/oct)
@@ Line 118: / Line 159: @@
 | | 20
 | | 480
+|508.8
+|614.4 (266.66<sub>16</sub>)
 | | 33/25, 55/42, 64/49
 | |
@@ Line 123: / Line 166: @@
 | | 21
 | | 504
+|534.24
+|645.12 (285.1F<sub>16</sub>)
 | | 4/3
 | | [[Meantone|Meantone]]/[[Meanpop|Meanpop]]
@@ Line 128: / Line 173: @@
 | | 22
 | | 528
+|559.68
+|675.84 (2A3.D7<sub>16</sub>)
 | | 15/11
 | |
@@ Line 133: / Line 180: @@
 | | 23
 | | 552
+|585.12
+|706.56 (2C2.8F<sub>16</sub>)
 | | 11/8, 18/13
 | | [[Chromatic_pairs#Barton|Barton]], [[Hemimean_clan#Emka|Emka]]
@@ Line 138: / Line 187: @@
 | | 24
 | | 576
+|610.56
+|737.28 (2E1.48<sub>16</sub>)
 | | 7/5
 | |
@@ Line 143: / Line 194: @@
 | | 25
 | | 600
+|636
+|768 (300<sub>16</sub>)
 | | 63/44, 88/63, 78/55, 55/39
 | |
@@ Line 148: / Line 201: @@
 | | 26
 | | 624
+|661.44
+|798.72 (31E.B8<sub>16</sub>)
 | | 10/7
 | |
@@ Line 153: / Line 208: @@
 | | 27
 | | 648
+|686.88
+|829.44 (33D.71<sub>16</sub>)
 | | 16/11, 13/9
 | |
@@ Line 158: / Line 215: @@
 | | 28
 | | 672
+|712.32
+|860.16 (35C.29<sub>16</sub>)
 | | 22/15
 | |
@@ Line 163: / Line 222: @@
 | | 29
 | | 696
+|737.76
+|900.88 (37A.E1<sub>16</sub>)
 | | 3/2
 | |
@@ Line 168: / Line 229: @@
 | | 30
 | | 720
+|763.2
+|921.6 (399.9A<sub>16</sub>)
 | | 50/33, 84/55, 49/32
 | |
@@ Line 173: / Line 236: @@
 | | 31
 | | 744
+|788.64
+|952.32 (3B8.52<sub>16</sub>)
 | | 20/13
 | |
@@ Line 178: / Line 243: @@
 | | 32
 | | 768
+|814.08
+|983.04 (3D7.0A<sub>16</sub>)
 | | 14/9
 | |
@@ Line 183: / Line 250: @@
 | | 33
 | | 792
+|239.52
+|1013.76 (3F5.C3<sub>16</sub>)
 | | 11/7
 | |
@@ Line 188: / Line 257: @@
 | | 34
 | | 816
+|864.96
+|1044.48 (414.7B<sub>16</sub>)
 | | 8/5
 | |
@@ Line 193: / Line 264: @@
 | | 35
 | | 840
+|890.4
+|1095.2 (433.33<sub>16</sub>)
 | | 13/8, 18/11
 | |
@@ Line 198: / Line 271: @@
 | | 36
 | | 864
+|915.84
+|1105.92 (451.EB8<sub>16</sub>)
 | | 44/27, 64/39, 33/20, 80/49
 | |
@@ Line 203: / Line 278: @@
 | | 37
 | | 888
+|941.28
+|1136.64 (470.A4<sub>16</sub>
 | | 5/3
 | |
@@ Line 208: / Line 285: @@
 | | 38
 | | 912
+|966.72
+|1167.36 (48F.5C<sub>16</sub>)
 | | 22/13
 | |
@@ Line 213: / Line 292: @@
 | | 39
 | | 936
+|992.16
+|1198.08 (4AE.148<sub>16</sub>)
 | | 12/7
 | |
@@ Line 218: / Line 299: @@
 | | 40
 | | 960
+|1017.6
+|1228.8 (4CC.CD<sub>16</sub>)
 | | 7/4
 | |
@@ Line 223: / Line 306: @@
 | | 41
 | | 984
+|1043.04
+|1261.52 (4EB.85<sub>16</sub>)
 | | 44/25
 | |
@@ Line 228: / Line 313: @@
 | | 42
 | | 1008
+|1068.48
+|1290.24 (50A.4<sub>16</sub>)
 | | 16/9, 9/5
 | |
@@ Line 233: / Line 320: @@
 | | 43
 | | 1032
+|1093.92
+|1320.96 (528.F6<sub>16</sub>)
 | | 20/11
 | |
@@ Line 238: / Line 327: @@
 | | 44
 | | 1056
+|1119.36
+|1351.68 (547.AE<sub>16</sub>)
 | | 24/13, 11/6
 | |
@@ Line 243: / Line 334: @@
 | | 45
 | | 1080
+|1144.8
+|1382.4 (566.66<sub>16</sub>)
 | | 15/8, 28/15, 13/7
 | |
@@ Line 248: / Line 341: @@
 | | 46
 | | 1104
+|1170.24
+|1413.12 (585.1F<sub>16</sub>)
 | | 21/11
 | |
@@ Line 253: / Line 348: @@
 | | 47
 | | 1128
+|1195.68
+|1443.84 (5A3.D7<sub>16</sub>)
 | | 40/21, 48/25, 25/13, 52/27, 27/14
 | |
@@ Line 258: / Line 355: @@
 | | 48
 | | 1152
+|1221.12
+|1474.56 (5C2.8F<sub>16</sub>)
 | | 64/33, 35/18, 49/25, 108/55, 63/32
 | |
@@ Line 263: / Line 362: @@
 | | 49
 | | 1176
+|1246.56
+|1505.28 (5E1.48<sub>16</sub>)
+| | 88/45, 96/49, 55/28, 128/65, 65/33, 77/39, 180/91, 196/99, 99/50, 240/121, 336/169
 | |
-| |
+|-
+|50
+|1200
+|1272
+|1536 (600<sub>16</sub>)
+|2/1
+|
 |}
 *Using the 13-limit patent val, except as noted.
@@ Line 442: / Line 550: @@
 ! | Name 2
 |-
-| | | -4 4 -1 &gt;
+| |<nowiki> | -4 4 -1 </nowiki>&gt;
 | style="text-align:right;" | 21.51
 | style="text-align:center;" | 81/80
@@ Line 448: / Line 556: @@
 | | Didymus comma
 |-
-| | | -27 -2 13 &gt;
+| |<nowiki> | -27 -2 13 </nowiki>&gt;
 | style="text-align:right;" | 18.17
 | style="text-align:center;" |
@@ Line 454: / Line 562: @@
 | |
 |-
-| | | 23 6 -14 &gt;
+| |<nowiki> | 23 6 -14 </nowiki>&gt;
 | style="text-align:right;" | 3.34
 | style="text-align:center;" |
@@ Line 460: / Line 568: @@
 | |
 |-
-| | | 1 2 -3 1 &gt;
+| |<nowiki> | 1 2 -3 1 </nowiki>&gt;
 | style="text-align:right;" | 13.79
 | style="text-align:center;" | 126/125
@@ Line 466: / Line 574: @@
 | | Small septimal comma
 |-
-| | | -5 2 2 -1 &gt;
+| |<nowiki> | -5 2 2 -1 </nowiki>&gt;
 | style="text-align:right;" | 7.71
 | style="text-align:center;" | 225/224
@@ Line 472: / Line 580: @@
 | | Marvel comma
 |-
-| | | 6 0 -5 2 &gt;
+| |<nowiki> | 6 0 -5 2 </nowiki>&gt;
 | style="text-align:right;" | 6.08
 | style="text-align:center;" | 3136/3125
@@ Line 478: / Line 586: @@
 | | Middle second comma
 |-
-| | | -6 -8 2 5 &gt;
+| |<nowiki> | -6 -8 2 5 </nowiki>&gt;
 | style="text-align:right;" | 1.12
 | style="text-align:center;" |
@@ Line 484: / Line 592: @@
 | |
 |-
-| | |-11 2 7 -3 &gt;
+| |<nowiki> |-11 2 7 -3 </nowiki>&gt;
 | style="text-align:right;" | 1.63
 | style="text-align:center;" |
@@ Line 490: / Line 598: @@
 | |
 |-
-| | | 11 -10 -10 10 &gt;
+| |<nowiki> | 11 -10 -10 10 </nowiki>&gt;
 | style="text-align:right;" | 5.57
 | style="text-align:center;" |
@@ Line 496: / Line 604: @@
 | |
 |-
-| | |-13 10 0 -1 &gt;
+| |<nowiki> |-13 10 0 -1 </nowiki>&gt;
 | style="text-align:right;" | 50.72
 | style="text-align:center;" | 59049/57344
@@ Line 502: / Line 610: @@
 | |
 |-
-| | | 2 3 1 -2 -1 &gt;
+| |<nowiki> | 2 3 1 -2 -1 </nowiki>&gt;
 | style="text-align:right;" | 3.21
 | style="text-align:center;" | 540/539
@@ Line 508: / Line 616: @@
 | | Swetisma
 |-
-| | | -3 4 -2 -2 2 &gt;
+| |<nowiki> | -3 4 -2 -2 2 </nowiki>&gt;
 | style="text-align:right;" | 0.18
 | style="text-align:center;" | 9801/9800
@@ Line 514: / Line 622: @@
 | | Gauss' comma
 |-
-| | | 5 -1 3 0 -3 &gt;
+| |<nowiki> | 5 -1 3 0 -3 </nowiki>&gt;
 | style="text-align:right;" | 3.03
 | style="text-align:center;" | 4000/3993
@@ Line 520: / Line 628: @@
 | | Undecimal schisma
 |-
-| | | -7 -1 1 1 1 &gt;
+| |<nowiki> | -7 -1 1 1 1 </nowiki>&gt;
 | style="text-align:right;" | 4.50
 | style="text-align:center;" | 385/384
@@ Line 526: / Line 634: @@
 | | Undecimal kleisma
 |-
-| | | -1 0 1 2 -2 &gt;
+| |<nowiki> | -1 0 1 2 -2 </nowiki>&gt;
 | style="text-align:right;" | 21.33
 | style="text-align:center;" | 245/242
@@ Line 532: / Line 640: @@
 | |
 |-
-| | | 2 -1 0 1 -2 1 &gt;
+| |<nowiki> | 2 -1 0 1 -2 1 </nowiki>&gt;
 | style="text-align:right;" | 4.76
 | style="text-align:center;" | 364/363
@@ Line 538: / Line 646: @@
 | |
 |-
-| | | 2 -1 -1 2 0 -1 &gt;
+| |<nowiki> | 2 -1 -1 2 0 -1 </nowiki>&gt;
 | style="text-align:right;" | 8.86
 | style="text-align:center;" | 196/195
@@ Line 544: / Line 652: @@
 | |
 |-
-| | | 2 3 0 -1 1 -2 &gt;
+| |<nowiki> | 2 3 0 -1 1 -2 </nowiki>&gt;
 | style="text-align:right;" | 7.30
 | style="text-align:center;" | 1188/1183
@@ Line 550: / Line 658: @@
 | |
 |-
-| | | 3 0 2 0 1 -3 &gt;
+| |<nowiki> | 3 0 2 0 1 -3 </nowiki>&gt;
 | style="text-align:right;" | 2.36
 | style="text-align:center;" | 2200/2197
@@ Line 556: / Line 664: @@
 | | Parizek comma
 |-
-| | | -3 1 1 1 0 -1 &gt;
+| |<nowiki> | -3 1 1 1 0 -1 </nowiki>&gt;
 | style="text-align:right;" | 16.57
 | style="text-align:center;" | 105/104
@@ Line 563: / Line 671: @@
 | |
 |-
-| | | 4 2 0 0 -1 -1 &gt;
+| |<nowiki> | 4 2 0 0 -1 -1 </nowiki>&gt;
 | style="text-align:right;" | 12.06
 | style="text-align:center;" | 144/143
@@ Line 569: / Line 677: @@
 | |
 |-
-| | | 3 -2 0 1 -1 -1 0 0 1 &gt;
+| |<nowiki> | 3 -2 0 1 -1 -1 0 0 1 </nowiki>&gt;
 | style="text-align:right;" | 1.34
 | style="text-align:center;" | 1288/1287
@@ Line 604: / Line 712: @@
 [https://www.dropbox.com/sh/4x81rzpkot32qzk/MQ3cJljjkh 50EDO Theory - Intervals, Chords and Scales in 50EDO by Cam Taylor]
-[http://iamcamtaylor.wordpress.com/ iamcamtaylor - Blog on 50EDO and extended meantone theory by Cam Taylor]      [[Category:50edo]]
+[http://iamcamtaylor.wordpress.com/ iamcamtaylor - Blog on 50EDO and extended meantone theory by Cam Taylor]
+[[Category:50edo]]
 [[Category:edo]]
 [[Category:golden]]

50edo: Difference between revisions

Revision as of 21:56, 3 April 2019

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Intervals

Selected just intervals by error

Best direct mapping, even if inconsistent

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