User:Userminusone/Proposed Polychromatic Notation for 311edo

Intro

Polychromatic notation is a system originally proposed by Dolores Catherino which represents small pitch deviations with deviations in color. This method of notation allows for a really efficient and clear depiction of specific interval sizes within a musical score, since colored note heads read very easily and don't require additional microtonal accidentals. Unlike Catherino, I don't think polychromatic notation should become the gold standard of microtonality, and I appreciate other notation systems that have different aesthetic characteristics and are suited for different use cases. However, I still think polychromatic notation is a very practical way of analyzing and understanding interval sizes in particularly large edos, which is why I've decided to develop one for 311edo, a particularly efficient system for working with excellently approximated high limit Just Intonation.

Diatonic Framework

My proposed polychromatic notation for 311edo works using an underlying diatonic framework for basic interval categories. All this means is that transposing a pitch by a series of fifths or fourths preserves its color, but changes its note name, accidental, or both. One consequence of this is that one could theoretically notate all of 311edo using only a single pitch color (since 311edo's circle of fifths reaches all of its notes), but this most likely won't happen in practice since most pitches would require way more than two sharps or flats to notate.

Pitch Colors and Single Step Modifiers

Since 311edo has so many notes, and to ensure that each pitch color is reasonably visually distinct from all others, I have decided that adjacent pitch colors should be separated by 3 steps of 311edo. A nice coincidence of this is that the syntonic comma, which is 6 steps in 311edo, can be represented by a separation of two pitch colors. In order to access all the pitches of 311edo, the "+" and "-" symbols are used to increase and decrease the pitch by 1 step of 311edo, respectively. With this system, only 11 different pitch colors are required to access all of 311edo's notes, which are as follows:

salmon (#FF6E71)

red (#FF4200)

orange (#FF9B24)

yellow (#F8E82D)

lime (#B4DF1A)

green (#34C300)

aqua (#17EBB8)

sky (#00C2EB)

blue (#226DFF)

purple (#B65DFF)

pink (#FF70FE)

Note Naming

In order to name a note in this system, just take the name of the note, the name of its single pitch offset, and the name of its pitch color. A pitch offset of 1 (using the "+" symbol) is named "acute", a pitch offset of 0 (using neither "+" nor "-") is named "mid", and a pitch offset of -1 (using the "-" symbol) is named "grave".

As an example, the note "G#+" has the name "G sharp acute aqua", the note "Eb-" has the name "E flat grave yellow", and the note "B" has the name "B natural mid salmon".

Example Table

Here is a table of 311edo intervals and associated note names, using Inthar's consistent patent val readings of 311edo:

Steps	Cents	Note names				Intervals
0	0.000		C	B#-		1/1
1	3.859		C+	B#		449/448
2	7.717		C-	B#+		224/223, 225/224
3	11.576		C	B#-		150/149
4	15.434		C+	B#		338/335
5	19.293		C-	B#+		90/89
6	23.151		C	B#-		70/69, 78/77, 77/76, 76/75, 75/74, 74/73, 73/72
7	27.010	Db-	C+	B#		63/62, 64/63, 65/64, 66/65, 69/68
8	30.868	Db	C-	B#+		55/54, 56/55, 57/56, 58/57
9	34.727	Db+	C	B#-		49/48, 50/49, 51/50, 52/51
10	38.585	Db-	C+	B#		45/44, 46/45
11	42.444	Db	C-	B#+		40/39, 41/40, 42/41
12	46.302	Db+	C	B#-		37/36, 38/37, 39/38
13	50.161	Db-	C+	B#		34/33, 35/34, 36/35
14	54.019	Db	C-	C#-	B#+	32/31, 33/32
15	57.878	Db+	C	C#	B#-	30/29, 31/30
16	61.736	Db-	C+	C#+	B#	28/27, 29/28
17	65.595	Db		C#-	B#+	27/26
18	69.453	Db+		C#	B#-	25/24, 26/25
19	73.312	Db-		C#+	B#	24/23
20	77.170	Db		C#-	B#+	23/22
21	81.029	Db+		C#	B#-	22/21
22	84.887	Db-		C#+	B#	21/20
23	88.746	Db		C#-	B#+	20/19
24	92.605	Db+		C#		19/18, 39/37
25	96.463	Db-		C#+		37/35
26	100.322	Db		C#-		18/17, 35/33
27	104.180	Db+		C#		17/16
28	108.039	Db-		C#+		33/31
29	111.897	Db		C#-		16/15
30	115.756	Db+		C#		31/29
31	119.614	Db-		C#+		15/14
32	123.473	Db		C#-		29/27
33	127.331	Db+		C#		14/13
34	131.190	Db-		C#+		69/64
35	135.048	Db		C#-		27/25, 40/37
36	138.907	Db+		C#		13/12
37	142.765	Db-	D-	C#+		25/23
38	146.624	Db	D	C#-		37/34
39	150.482	Db+	D+	C#		12/11
40	154.341		D-	C#+		35/32
41	158.199		D	C#-		23/21, 34/31
42	162.058		D+	C#		45/41, 56/51
43	165.916		D-	C#+		11/10
44	169.775		D	C#-		32/29
45	173.633		D+	C#		21/19
46	177.492		D-	C#+		31/28
47	181.350		D			10/9
48	185.209		D+			49/44
49	189.068		D-			29/26, 39/35
50	192.926		D			19/17
51	196.785		D+			28/25
52	200.643		D-			55/49
53	204.502		D			9/8
54	208.360		D+			35/31
55	212.219		D-			26/23
56	216.077		D			17/15
57	219.936		D+			25/22, 42/37
58	223.794		D-			33/29
59	227.653		D			73/64
60	231.511	Eb-	D+			8/7
61	235.370	Eb	D-			55/48
62	239.228	Eb+	D			31/27, 39/34
63	243.087	Eb-	D+			23/20
64	246.945	Eb	D-			15/13, 128/111
65	250.804	Eb+	D			37/32
66	254.662	Eb-	D+			22/19
67	258.521	Eb	D-	D#-		29/25, 36/31
68	262.379	Eb+	D	D#		64/55
69	266.238	Eb-	D+	D#+		7/6
70	270.096	Eb		D#-		90/77
71	273.955	Eb+		D#		34/29, 41/35, 48/41, 75/64
72	277.814	Eb-		D#+		27/23
73	281.672	Eb		D#-		20/17
74	285.531	Eb+		D#		33/28, 46/39
75	289.389	Eb-		D#+		13/11
76	293.248	Eb		D#-		32/27
77	297.106	Eb+		D#		19/16
78	300.965	Eb-		D#+		25/21
79	304.823	Eb		D#-		31/26, 37/31
80	308.682	Eb+		D#		49/41, 55/46
81	312.540	Eb-		D#+		109/91
82	316.399	Eb		D#-		6/5
83	320.257	Fb-		D#	Eb+	77/64
84	324.116	Fb		D#+	Eb-	35/29
85	327.974	Fb+		D#-	Eb	29/24
86	331.833	Fb-		D#	Eb+	23/19, 40/33
87	335.691	Fb		D#+	Eb-	17/14
88	339.550	Fb+		D#-	Eb	28/23, 73/60
89	343.408	Fb-		D#	Eb+	39/32, 50/41, 128/105
90	347.267	Fb	E-	D#+	Eb-	11/9
91	351.125	Fb+	E	D#-	Eb	38/31
92	354.984	Fb-	E+	D#	Eb+	27/22
93	358.842	Fb	E-	D#+		16/13
94	362.701	Fb+	E	D#-		37/30
95	366.559	Fb-	E+	D#		21/17
96	370.418	Fb	E-	D#+		26/21
97	374.277	Fb+	E	D#-		36/29, 41/33
98	378.135	Fb-	E+	D#		46/37, 51/41, 56/45
99	381.994	Fb	E-	D#+		96/77
100	385.852	Fb+	E			5/4
101	389.711	Fb-	E+			124/99
102	393.569	Fb	E-			49/39, 64/51
103	397.428	Fb+	E			39/31, 44/35
104	401.286	Fb-	E+			29/23
105	405.145	Fb	E-			24/19
106	409.003	Fb+	E			19/15
107	412.862	Fb-	E+			33/26
108	416.720	Fb	E-			14/11
109	420.579	Fb+	E			39/29
110	424.437	Fb-	E+			23/18
111	428.296	Fb	E-			41/32, 32/25
112	432.154	Fb+	E			77/60
113	436.013	Fb-	F-		E+	9/7
114	439.871	Fb	F		E-	49/38
115	443.730	Fb+	F+		E	31/24
116	447.588		F-		E+	22/17
117	451.447		F		E-	83/64
118	455.305		F+		E	13/10
119	459.164		F-		E+	30/23
120	463.023		F	E#-	E-	17/13, 49/32
121	466.881		F+	E#	E	55/42, 38/29
122	470.740		F-	E#+	E+	21/16
123	474.598		F	E#-		25/19
124	478.457		F+	E#		29/22
125	482.315		F-	E#+		33/25
126	486.174		F	E#-		45/34, 49/37
127	490.032		F+	E#		85/64
128	493.891		F-	E#+		278/209
129	497.749		F	E#-		4/3
130	501.608		F+	E#		322/241, 163/122
131	505.466		F-	E#+		75/56
132	509.325		F	E#-		51/38
133	513.183		F+	E#		35/26, 39/29
134	517.042		F-	E#+		31/23
135	520.900		F	E#-		27/20
136	524.759	Gb-	F+	E#		23/17
137	528.617	Gb	F-	E#+		19/14
138	532.476	Gb+	F	E#-		34/25, 49/36, 87/64
139	536.334	Gb-	F+	E#		15/11
140	540.193	Gb	F-	E#+		41/30
141	544.051	Gb+	F	E#-		26/19, 37/27
142	547.910	Gb-	F+	E#		48/35
143	551.768	Gb	F-	F#-	E#+	11/8
144	555.627	Gb+	F	F#	E#-	29/21, 40/29, 51/37
145	559.486	Gb-	F+	F#+	E#	105/76
146	563.344	Gb		F#-	E#+	18/13
147	567.203	Gb+		F#	E#-	25/18, 68/49
148	571.061	Gb-		F#+	E#	89/64, 32/23
149	574.920	Gb		F#-	E#+	39/28, 46/33
150	578.778	Gb+		F#	E#-	88/63
151	582.637	Gb-		F#+	E#	7/5
152	586.495	Gb		F#-	E#+	87/62
153	590.354	Gb+		F#		45/32, 128/91
154	594.212	Gb-		F#+		31/22, 148/105
155	598.071	Gb		F#-		24/17, 41/29
156	601.929	Gb+		F#		17/12, 58/41
157	605.788	Gb-		F#+		44/31, 105/74
158	609.646	Gb		F#-		64/45, 91/64
159	613.505	Gb+		F#		124/87
160	617.363	Gb-		F#+		10/7
161	621.222	Gb		F#-		63/44
162	625.080	Gb+		F#		33/23, 56/39
163	628.939	Gb-		F#+		23/16, 128/89
164	632.797	Gb		F#-		36/25, 49/34
165	636.656	Gb+		F#		13/9
166	640.514	Gb-	G-	F#+		152/105
167	644.373	Gb	G	F#-		29/20, 42/29, 74/51
168	648.232	Gb+	G+	F#		16/11, 93/64
169	652.090		G-	F#+		35/24
170	655.949		G	F#-		19/13, 54/37
171	659.807		G+	F#		60/41
172	663.666		G-	F#+		22/15
173	667.524		G	F#-		25/17, 72/49, 128/87
174	671.383		G+	F#		28/19
175	675.241		G-	F#+		34/23
176	679.100		G			40/27
177	682.958		G+			46/31
178	686.817		G-			52/35, 58/39
179	690.675		G			76/51
180	694.534		G+			112/75
181	698.392		G-			241/161, 244/163
182	702.251		G			3/2
183	706.109		G+			209/139
184	709.968		G-			128/85
185	713.826		G			68/45, 74/49
186	717.685		G+			50/33
187	721.543		G-			97/64
188	725.402		G			38/25
189	729.260	Ab-	G+			32/21
190	733.119	Ab	G-			84/55
191	736.977	Ab+	G			49/32, 26/17
192	740.836	Ab-	G+			23/15
193	744.695	Ab	G-			20/13
194	748.553	Ab+	G			128/83
195	752.412	Ab-	G+			17/11
196	756.270	Ab	G-	G#-		99/64
197	760.129	Ab+	G	G#		48/31
198	763.987	Ab-	G+	G#+		14/9
199	767.846	Ab		G#-		120/77
200	771.704	Ab+		G#		25/16
201	775.563	Ab-		G#+		36/23
202	779.421	Ab		G#-		58/39
203	783.280	Ab+		G#		11/7
204	787.138	Ab-		G#+		52/33
205	790.997	Ab		G#-		30/19
206	794.855	Ab+		G#		19/12
207	798.714	Ab-		G#+		46/29
208	802.572	Ab		G#-		35/22, 62/39
209	806.431	Ab+		G#		51/32, 78/49
210	810.289	Ab-		G#+		99/62
211	814.148	Ab		G#-		8/5
212	818.006	Ab+		G#		77/48
213	821.865	Ab-		G#+		37/23, 82/51, 45/28
214	825.723	Ab		G#-		29/18, 66/41
215	829.582	Ab+		G#		21/13
216	833.441	Ab-		G#+		34/21, 55/34, 89/55, 144/89
217	837.299	Ab		G#-		60/37
218	841.158	Ab+		G#		13/8
219	845.016	Ab-	A-	G#+		44/27
220	848.875	Ab	A	G#-		31/19
221	852.733	Ab+	A+	G#		18/11
222	856.592		A-	G#+		41/25, 64/39, 105/64
223	860.450		A	G#-		23/14, 120/73
224	864.309		A+	G#		28/17
225	868.167		A-	G#+		32/20, 38/23
226	872.026		A	G#-		48/29
227	875.884		A+	G#		58/35
228	879.743		A-	G#+		123/74, 128/77
229	883.601		A			5/3
230	887.460		A+			182/109
231	891.318		A-			82/49, 92/55
232	895.177		A			52/31, 62/37
233	899.035		A+			42/25
234	902.894		A-			32/19, 219/130
235	906.752		A			27/16
236	910.611		A+			22/13
237	914.469		A-			39/23, 56/33
238	918.328		A			17/10
239	922.186		A+			109/64
240	926.045		A-			29/17, 70/41, 41/24, 128/75
241	929.904		A			65/38, 77/45
242	933.762	Bb-	A+			12/7
243	937.621	Bb	A-			55/32
244	941.479	Bb+	A			50/29, 31/18
245	945.338	Bb-	A+			19/11
246	949.196	Bb	A-			64/37
247	953.055	Bb+	A			26/15, 111/64
248	956.913	Bb-	A+			40/23
249	960.772	Bb	A-	A#-		54/31, 68/39
250	964.630	Bb+	A	A#		96/55
251	968.489	Bb-	A+	A#+		7/4
252	972.347	Bb		A#-		128/73
253	976.206	Bb+		A#		58/33
254	980.064	Bb-		A#+		37/21, 44/25
255	983.923	Bb		A#-		30/17, 113/64
256	987.781	Bb+		A#		23/13
257	991.640	Bb-		A#+		62/35
258	995.498	Bb		A#-		16/9
259	999.357	Bb+		A#		98/55, 57/32
260	1003.215	Bb-		A#+		25/14
261	1007.074	Bb		A#-		34/19
262	1010.932	Bb+		A#		52/29, 70/39
263	1014.791	Bb-		A#+		88/49, 115/64
264	1018.650	Bb		A#-		9/5
265	1022.508	Cb-		A#	Bb+	56/31
266	1026.367	Cb		A#+	Bb-	38/21
267	1030.225	Cb+		A#-	Bb	29/16
268	1034.084	Cb-		A#	Bb+	20/11
269	1037.942	Cb		A#+	Bb-	51/28, 82/45
270	1041.801	Cb+		A#-	Bb	31/17, 42/23
271	1045.659	Cb-		A#	Bb+	64/35, 117/64
272	1049.518	Cb	B-	A#+	Bb-	11/6
273	1053.376	Cb+	B	A#-	Bb	68/37
274	1057.235	Cb-	B+	A#	Bb+	46/25
275	1061.093	Cb	B-	A#+		24/13
276	1064.952	Cb+	B	A#-		37/20, 50/27
277	1068.810	Cb-	B+	A#		128/69
278	1072.669	Cb	B-	A#+		13/7, 119/64
279	1076.527	Cb+	B	A#-		54/29
280	1080.386	Cb-	B+	A#		28/15
281	1084.244	Cb	B-	A#+		58/31
282	1088.103	Cb+	B			15/8
283	1091.961	Cb-	B+			62/33
284	1095.820	Cb	B-			32/17
285	1099.678	Cb+	B			17/9, 66/35
286	1103.537	Cb-	B+			70/37, 121/64
287	1107.395	Cb	B-			36/19, 74/39
288	1111.254	Cb+	B			19/10
289	1115.113	Cb-	B+			40/21
290	1118.971	Cb	B-			21/11
291	1122.830	Cb+	B			44/23
292	1126.688	Cb-	B+			23/13
293	1130.547	Cb	B-			48/25, 25/13, 123/64
294	1134.405	Cb+	B			52/27
295	1138.264	Cb-	C-		B+	27/14, 56/29
296	1142.122	Cb	C		B-	29/15, 60/31
297	1145.981	Cb+	C+		B	31/16, 64/33
298	1149.839		C-		B+	33/17, 68/35, 35/18
299	1153.698		C		B-	72/37, 37/19, 76/39
300	1157.556		C+		B	39/20, 80/41, 41/21, 125/64
301	1161.415		C-		B+	88/45, 45/23
302	1165.273		C	B#-	B-	96/49, 49/25, 100/51, 51/26
303	1169.132		C+	B#	B	108/55, 55/28, 112/57, 57/29
304	1172.990		C-	B#+	B+	124/63, 63/32, 128/65, 65/33
305	1176.849		C	B#-		148/75
306	1180.707		C+	B#		89/45
307	1184.566		C-	B#+		335/169
308	1188.424		C	B#-		149/75
309	1192.283		C+	B#		223/112, 448/225
310	1196.141		C-	B#+		896/449
311	1200.000		C	B#-		2/1