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