Frequency of Different Duration Ratios

Just as composers use some intervals more than others, they employ some duration ratios (the length of the first note divided into the length of the second note) frequently and some hardly at all.  The following figure shows visually how frequently-used duration ratios stack up against infrequently-used duration ratios in the Skiptune database when it had 82,000 tunes and a total of 486 different duration ratios for two-note patterns:

Figure 1  plots the accumulated percent of the number of times duration ratios are used in all tunes (counting each duration ratio instance as many times as it’s used in a tune).  The sharply increasing blue line reaches around 99 percent by the time we’ve plotted the 25 most frequently used duration ratios.  It is rather clear from this chart that composers rely heavily on a couple dozen duration ratios, spicing it up a bit with less frequently used duration ratios.  The dashed line and “Rarely Used Patterns” is discussed on our Surprisingly Rare Patterns page.

Now let’s examine those 25 most common duration ratios.  Following is a table of all the duration ratios used in all the tunes in the database.  Each row in the following table shows the duration ratio in musical notation, the number of tunes in which it’s found, the percent of tunes in which it’s found, the number of instances of that duration ratio (including repeated uses within the same tune), those repeated instances as a percent of all repeated instances, and finally the accumulated percent of repeated instances.

When the table first loads on your screen, it is ranked by the column labeled “# Instances” in descending order, but you can change the ranking using the arrows in the column headers.  Only 25 duration ratios are shown at a time but you can click “Next” at the bottom-right of the table to see subsequent duration ratios, though without the musical notation.  You can also search for a particular duration ratio to see where it’s ranked (as an example, type “16.0” without the quotes in the search bar to see how many times the second note is 16 times longer in duration than the note that precedes it).

Table of Duration Ratios, Most Common to Least

Rank	durR	#Tunes	Tunes%	#Instances	Instances%	%Accum
1	1.0	81082	98.9	2740156	57.58	57.58
2	2.0	74718	91.1	507195	10.66	68.23
3	0.5	72783	88.8	454536	9.55	77.79
4	0.333	57525	70.2	294927	6.2	83.98
5	3.0	47952	58.5	174654	3.67	87.65
6	4.0	39740	48.5	103730	2.18	89.83
7	1.5	36266	44.2	98959	2.08	91.91
8	0.25	29099	35.5	64762	1.36	93.27
9	0.75	15968	19.5	38906	0.82	94.09
10	0.667	15905	19.4	34786	0.73	94.82
11	6.0	18752	22.9	34356	0.72	95.54
12	0.167	16351	19.9	30856	0.65	96.19
13	0.2	14747	18.0	28237	0.59	96.78
14	5.0	10392	12.7	19994	0.42	97.2
15	8.0	10646	13.0	17240	0.36	97.57
16	0.143	6948	8.5	11082	0.23	97.8
17	1.333	4811	5.9	9309	0.2	98.0
18	2.5	4096	5.0	6683	0.14	98.14
19	0.125	4397	5.4	6545	0.14	98.27
20	0.375	3624	4.4	6427	0.14	98.41
21	7.0	3657	4.5	6061	0.13	98.54
22	12.0	3553	4.3	5038	0.11	98.64
23	0.1	3010	3.7	4290	0.09	98.73
24	0.111	2411	2.9	3850	0.08	98.81
25	0.4	2416	2.9	3835	0.08	98.89
26	4.5	2084	2.5	3195	0.07	98.96
27	9.0	1974	2.4	3028	0.06	99.02
28	10.0	2069	2.5	2930	0.06	99.09
29	2.25	1291	1.6	2687	0.06	99.14
30	1.667	1399	1.7	2421	0.05	99.19
31	3.5	1679	2.0	2245	0.05	99.24
32	0.6	1578	1.9	2014	0.04	99.28
33	0.091	1244	1.5	2002	0.04	99.32
34	16.0	1518	1.9	1929	0.04	99.37
35	0.083	1190	1.5	1665	0.04	99.4
36	2.667	979	1.2	1375	0.03	99.43
37	1.25	945	1.2	1348	0.03	99.46
38	0.286	1005	1.2	1330	0.03	99.49
39	1.75	745	0.9	1267	0.03	99.51
40	0.222	781	1.0	1154	0.02	99.54
41	11.0	657	0.8	1037	0.02	99.56
42	0.071	777	0.9	979	0.02	99.58
43	14.0	684	0.8	838	0.02	99.6
44	0.8	613	0.7	825	0.02	99.61
45	0.067	533	0.7	663	0.01	99.63
46	7.5	456	0.6	584	0.01	99.64
47	0.077	399	0.5	537	0.01	99.65
48	0.3	377	0.5	534	0.01	99.66
49	2.333	371	0.5	525	0.01	99.67
50	5.5	376	0.5	503	0.01	99.68
51	0.188	366	0.4	503	0.01	99.69
52	13.0	372	0.5	469	0.01	99.7
53	15.0	345	0.4	446	0.01	99.71
54	0.062	353	0.4	422	0.01	99.72
55	0.833	287	0.3	415	0.01	99.73
56	0.875	229	0.3	403	0.01	99.74
57	0.571	277	0.3	392	0.01	99.75
58	0.444	294	0.4	384	0.01	99.76
59	24.0	289	0.4	367	0.01	99.76
60	0.133	265	0.3	361	0.01	99.77
61	0.182	239	0.3	346	0.01	99.78
62	6.5	245	0.3	319	0.01	99.79
63	2.75	224	0.3	303	0.01	99.79
64	0.429	216	0.3	291	0.01	99.8
65	0.15	200	0.2	263	0.01	99.8
66	20.0	204	0.2	259	0.01	99.81
67	18.0	212	0.3	254	0.01	99.81
68	3.333	193	0.2	254	0.01	99.82
69	0.231	203	0.2	231	0.0	99.82
70	1.2	178	0.2	227	0.0	99.83
71	0.154	180	0.2	222	0.0	99.83
72	0.625	164	0.2	222	0.0	99.84
73	5.333	167	0.2	210	0.0	99.84
74	0.214	160	0.2	208	0.0	99.85
75	4.667	158	0.2	198	0.0	99.85
76	10.5	176	0.2	200	0.0	99.86
77	1.167	136	0.2	172	0.0	99.86
78	3.75	125	0.2	156	0.0	99.86
79	3.25	111	0.1	152	0.0	99.87
80	1.6	112	0.1	151	0.0	99.87
81	4.333	116	0.1	150	0.0	99.87
82	32.0	133	0.2	146	0.0	99.88
83	3.667	109	0.1	143	0.0	99.88
84	0.056	109	0.1	137	0.0	99.88
85	0.273	98	0.1	126	0.0	99.88
86	0.267	91	0.1	124	0.0	99.89
87	0.059	103	0.1	117	0.0	99.89
88	0.048	89	0.1	118	0.0	99.89
89	1.4	88	0.1	115	0.0	99.89
90	0.714	92	0.1	113	0.0	99.9
91	0.053	73	0.1	112	0.0	99.9
92	0.857	87	0.1	112	0.0	99.9
93	0.778	92	0.1	112	0.0	99.9
94	8.5	90	0.1	108	0.0	99.91
95	17.0	96	0.1	109	0.0	99.91
96	0.889	87	0.1	108	0.0	99.91
97	28.0	87	0.1	105	0.0	99.91
98	1.125	81	0.1	100	0.0	99.91
99	0.308	81	0.1	93	0.0	99.92
100	1.375	69	0.1	91	0.0	99.92
101	0.05	77	0.1	86	0.0	99.92
102	21.0	64	0.1	84	0.0	99.92
103	0.118	60	0.1	84	0.0	99.92
104	0.045	70	0.1	87	0.0	99.93
105	0.583	63	0.1	76	0.0	99.93
106	0.438	32	0.0	75	0.0	99.93
107	5.25	58	0.1	78	0.0	99.93
108	22.0	64	0.1	76	0.0	99.93
109	0.107	68	0.1	71	0.0	99.93
110	0.042	49	0.1	67	0.0	99.93
111	5.667	48	0.1	67	0.0	99.94
112	1.143	51	0.1	68	0.0	99.94
113	0.095	48	0.1	62	0.0	99.94
114	2.4	52	0.1	64	0.0	99.94
115	19.0	43	0.1	55	0.0	99.94
116	0.556	52	0.1	58	0.0	99.94
117	1.8	50	0.1	58	0.0	99.94
118	30.0	44	0.1	51	0.0	99.95
119	0.033	34	0.0	51	0.0	99.95
120	0.545	52	0.1	54	0.0	99.95
121	0.036	40	0.0	50	0.0	99.95
122	9.333	41	0.1	51	0.0	99.95
123	0.917	29	0.0	53	0.0	99.95
124	0.148	34	0.0	52	0.0	99.95
125	8.25	35	0.0	43	0.0	99.95
126	0.364	38	0.0	45	0.0	99.95
127	1.833	33	0.0	45	0.0	99.95
128	6.75	36	0.0	45	0.0	99.96
129	0.043	30	0.0	39	0.0	99.96
130	4.75	25	0.0	38	0.0	99.96
131	6.667	33	0.0	37	0.0	99.96
132	1.875	19	0.0	33	0.0	99.96
133	0.037	29	0.0	31	0.0	99.96
134	26.0	32	0.0	34	0.0	99.96
135	0.19	26	0.0	34	0.0	99.96
136	13.5	30	0.0	35	0.0	99.96
137	9.5	25	0.0	31	0.0	99.96
138	0.176	27	0.0	31	0.0	99.96
139	27.0	26	0.0	29	0.0	99.96
140	0.031	14	0.0	28	0.0	99.96
141	0.417	25	0.0	29	0.0	99.96
142	2.2	28	0.0	30	0.0	99.96
143	23.0	21	0.0	29	0.0	99.97
144	0.103	16	0.0	27	0.0	99.97
145	36.0	22	0.0	23	0.0	99.97
146	0.105	14	0.0	22	0.0	99.97
147	40.0	18	0.0	22	0.0	99.97
148	2.625	14	0.0	17	0.0	99.97
149	0.038	16	0.0	17	0.0	99.97
150	1.625	16	0.0	20	0.0	99.97
151	0.235	16	0.0	19	0.0	99.97
152	7.333	15	0.0	17	0.0	99.97
153	0.029	16	0.0	21	0.0	99.97
154	12.5	19	0.0	21	0.0	99.97
155	4.25	19	0.0	20	0.0	99.97
156	0.115	14	0.0	17	0.0	99.97
157	0.211	18	0.0	21	0.0	99.97
158	1.111	18	0.0	18	0.0	99.97
159	0.455	18	0.0	20	0.0	99.97
160	6.333	15	0.0	18	0.0	99.97
161	0.263	18	0.0	18	0.0	99.97
162	0.136	10	0.0	19	0.0	99.97
163	25.0	10	0.0	12	0.0	99.97
164	1.286	13	0.0	13	0.0	99.97
165	2.167	14	0.0	15	0.0	99.97
166	3.167	13	0.0	14	0.0	99.97
167	0.312	12	0.0	15	0.0	99.98
168	16.5	13	0.0	14	0.0	99.98
169	0.12	12	0.0	15	0.0	99.98
170	0.03	10	0.0	12	0.0	99.98
171	0.04	15	0.0	16	0.0	99.98
172	3.375	6	0.0	12	0.0	99.98
173	2.8	12	0.0	13	0.0	99.98
174	0.7	12	0.0	14	0.0	99.98
175	0.129	9	0.0	12	0.0	99.98
176	0.094	13	0.0	15	0.0	99.98
177	0.321	11	0.0	14	0.0	99.98
178	0.643	10	0.0	14	0.0	99.98
179	6.25	12	0.0	14	0.0	99.98
180	0.533	12	0.0	14	0.0	99.98
181	9.75	11	0.0	14	0.0	99.98
182	29.0	12	0.0	14	0.0	99.98
183	0.688	11	0.0	13	0.0	99.98
184	8.333	9	0.0	15	0.0	99.98
185	0.385	12	0.0	12	0.0	99.98
186	48.0	15	0.0	15	0.0	99.98
187	0.412	10	0.0	10	0.0	99.98
188	35.0	6	0.0	9	0.0	99.98
189	11.5	8	0.0	9	0.0	99.98
190	0.026	8	0.0	8	0.0	99.98
191	64.0	11	0.0	11	0.0	99.98
192	8.667	10	0.0	10	0.0	99.98
193	0.357	10	0.0	10	0.0	99.98
194	1.556	7	0.0	8	0.0	99.98
195	0.9	8	0.0	9	0.0	99.98
196	4.125	8	0.0	8	0.0	99.98
197	0.45	8	0.0	9	0.0	99.98
198	1.571	8	0.0	8	0.0	99.98
199	0.28	11	0.0	11	0.0	99.98
200	0.381	9	0.0	11	0.0	99.98
201	19.5	10	0.0	10	0.0	99.98
202	0.563	7	0.0	10	0.0	99.98
203	0.087	8	0.0	10	0.0	99.98
204	0.35	5	0.0	8	0.0	99.98
205	45.0	5	0.0	10	0.0	99.98
206	0.462	7	0.0	9	0.0	99.98
207	0.061	8	0.0	11	0.0	99.98
208	1.429	9	0.0	9	0.0	99.99
209	0.121	6	0.0	8	0.0	99.99
210	31.0	9	0.0	9	0.0	99.99
211	0.727	6	0.0	8	0.0	99.99
212	0.722	1	0.0	8	0.0	99.99
213	1.714	7	0.0	8	0.0	99.99
214	0.16	4	0.0	8	0.0	99.99
215	0.173	8	0.0	10	0.0	99.99
216	38.0	8	0.0	8	0.0	99.99
217	13.333	8	0.0	11	0.0	99.99
218	0.562	9	0.0	10	0.0	99.99
219	14.667	4	0.0	9	0.0	99.99
220	3.2	8	0.0	8	0.0	99.99
221	1.778	8	0.0	9	0.0	99.99
222	5.75	3	0.0	3	0.0	99.99
223	0.021	6	0.0	7	0.0	99.99
224	0.017	3	0.0	4	0.0	99.99
225	0.019	3	0.0	3	0.0	99.99
226	0.018	4	0.0	4	0.0	99.99
227	56.0	6	0.0	6	0.0	99.99
228	60.0	6	0.0	7	0.0	99.99
229	1.222	7	0.0	7	0.0	99.99
230	2.429	3	0.0	3	0.0	99.99
231	2.6	6	0.0	6	0.0	99.99
232	22.667	1	0.0	3	0.0	99.99
233	2.286	3	0.0	4	0.0	99.99
234	2.125	3	0.0	3	0.0	99.99
235	34.0	4	0.0	4	0.0	99.99
236	10.333	5	0.0	6	0.0	99.99
237	0.636	4	0.0	4	0.0	99.99
238	1.857	3	0.0	3	0.0	99.99
239	17.5	5	0.0	5	0.0	99.99
240	0.458	3	0.0	3	0.0	99.99
241	7.667	3	0.0	4	0.0	99.99
242	1.1	5	0.0	7	0.0	99.99
243	2.111	3	0.0	4	0.0	99.99
244	0.316	3	0.0	3	0.0	99.99
245	3.444	3	0.0	5	0.0	99.99
246	0.187	3	0.0	3	0.0	99.99
247	0.022	4	0.0	4	0.0	99.99
248	4.571	3	0.0	5	0.0	99.99
249	0.175	3	0.0	3	0.0	99.99
250	0.068	4	0.0	4	0.0	99.99
251	2.833	6	0.0	6	0.0	99.99
252	0.278	6	0.0	6	0.0	99.99
253	0.769	2	0.0	3	0.0	99.99
254	9.667	2	0.0	3	0.0	99.99
255	0.065	4	0.0	4	0.0	99.99
256	0.08	4	0.0	6	0.0	99.99
257	37.0	5	0.0	5	0.0	99.99
258	0.027	4	0.0	5	0.0	99.99
259	0.158	5	0.0	5	0.0	99.99
260	2.375	6	0.0	6	0.0	99.99
261	0.615	5	0.0	6	0.0	99.99
262	10.667	6	0.0	6	0.0	99.99
263	1.444	3	0.0	3	0.0	99.99
264	1.067	3	0.0	3	0.0	99.99
265	0.079	4	0.0	4	0.0	99.99
266	0.034	4	0.0	5	0.0	99.99
267	7.25	4	0.0	5	0.0	99.99
268	0.069	3	0.0	4	0.0	99.99
269	1.071	2	0.0	7	0.0	99.99
270	2.222	4	0.0	4	0.0	99.99
271	12.25	5	0.0	5	0.0	99.99
272	22.5	6	0.0	6	0.0	99.99
273	0.032	4	0.0	6	0.0	99.99
274	0.353	5	0.0	5	0.0	99.99
275	4.2	4	0.0	7	0.0	99.99
276	14.5	3	0.0	3	0.0	99.99
277	0.389	3	0.0	3	0.0	99.99
278	3.6	6	0.0	7	0.0	99.99
279	4.375	3	0.0	3	0.0	99.99
280	11.25	3	0.0	4	0.0	99.99
281	0.318	3	0.0	3	0.0	99.99
282	0.238	3	0.0	3	0.0	99.99
283	0.074	6	0.0	7	0.0	99.99
284	33.0	6	0.0	6	0.0	99.99
285	0.227	4	0.0	5	0.0	99.99
286	1.188	5	0.0	5	0.0	99.99
287	3.111	4	0.0	4	0.0	99.99
288	42.0	6	0.0	7	0.0	99.99
289	0.292	5	0.0	5	0.0	99.99
290	0.692	2	0.0	3	0.0	99.99
291	0.088	3	0.0	3	0.0	99.99
292	0.938	3	0.0	3	0.0	99.99
293	0.075	3	0.0	4	0.0	100.0
294	0.086	3	0.0	3	0.0	100.0
295	4.167	3	0.0	3	0.0	100.0
296	0.538	5	0.0	6	0.0	100.0
297	1.091	5	0.0	5	0.0	100.0
298	41.0	3	0.0	3	0.0	100.0
299	44.0	3	0.0	3	0.0	100.0
300	17.667	2	0.0	7	0.0	100.0
301	0.151	2	0.0	7	0.0	100.0
302	0.208	4	0.0	4	0.0	100.0
303	2.875	4	0.0	5	0.0	100.0
304	11.333	4	0.0	5	0.0	100.0
305	6.8	5	0.0	5	0.0	100.0
306	0.229	3	0.0	6	0.0	100.0
307	0.051	3	0.0	3	0.0	100.0
308	1.154	4	0.0	4	0.0	100.0
309	6.923	1	0.0	1	0.0	100.0
310	13.458	1	0.0	1	0.0	100.0
311	3.8	1	0.0	2	0.0	100.0
312	0.382	1	0.0	1	0.0	100.0
313	1.136	1	0.0	1	0.0	100.0
314	0.016	2	0.0	2	0.0	100.0
315	0.242	2	0.0	2	0.0	100.0
316	1.417	1	0.0	1	0.0	100.0
317	16.333	1	0.0	1	0.0	100.0
318	1.7	1	0.0	1	0.0	100.0
319	21.333	1	0.0	1	0.0	100.0
320	18.036	1	0.0	1	0.0	100.0
321	18.667	2	0.0	2	0.0	100.0
322	0.941	2	0.0	2	0.0	100.0
323	0.192	1	0.0	1	0.0	100.0
324	0.257	1	0.0	1	0.0	100.0
325	0.025	2	0.0	2	0.0	100.0
326	2.438	1	0.0	1	0.0	100.0
327	0.296	1	0.0	1	0.0	100.0
328	34.5	1	0.0	1	0.0	100.0
329	0.009	1	0.0	1	0.0	100.0
330	0.812	2	0.0	2	0.0	100.0
331	0.212	2	0.0	2	0.0	100.0
332	18.5	2	0.0	2	0.0	100.0
333	3.143	1	0.0	1	0.0	100.0
334	0.909	2	0.0	2	0.0	100.0
335	2.133	2	0.0	2	0.0	100.0
336	1.312	1	0.0	1	0.0	100.0
337	1.583	1	0.0	2	0.0	100.0
338	0.552	1	0.0	2	0.0	100.0
339	0.36	2	0.0	2	0.0	100.0
340	80.0	1	0.0	1	0.0	100.0
341	0.138	2	0.0	2	0.0	100.0
342	0.294	1	0.0	1	0.0	100.0
343	2.556	1	0.0	1	0.0	100.0
344	0.421	2	0.0	2	0.0	100.0
345	2.062	2	0.0	2	0.0	100.0
346	0.867	1	0.0	1	0.0	100.0
347	72.0	2	0.0	2	0.0	100.0
348	3.833	1	0.0	1	0.0	100.0
349	0.63	1	0.0	1	0.0	100.0
350	0.303	1	0.0	1	0.0	100.0
351	51.0	2	0.0	2	0.0	100.0
352	1.3	2	0.0	2	0.0	100.0
353	1.062	1	0.0	1	0.0	100.0
354	2.083	1	0.0	1	0.0	100.0
355	8.571	1	0.0	1	0.0	100.0
356	6.4	2	0.0	2	0.0	100.0
357	0.047	1	0.0	1	0.0	100.0
358	0.13	2	0.0	2	0.0	100.0
359	0.233	1	0.0	1	0.0	100.0
360	1.313	1	0.0	1	0.0	100.0
361	12.857	1	0.0	1	0.0	100.0
362	0.024	2	0.0	2	0.0	100.0
363	0.729	1	0.0	1	0.0	100.0
364	26.5	1	0.0	1	0.0	100.0
365	6.2	1	0.0	1	0.0	100.0
366	1.917	1	0.0	1	0.0	100.0
367	1.364	1	0.0	2	0.0	100.0
368	0.219	2	0.0	2	0.0	100.0
369	1.295	1	0.0	1	0.0	100.0
370	1.9	1	0.0	1	0.0	100.0
371	0.519	2	0.0	2	0.0	100.0
372	0.174	1	0.0	2	0.0	100.0
373	5.167	1	0.0	1	0.0	100.0
374	57.0	1	0.0	1	0.0	100.0
375	84.0	1	0.0	1	0.0	100.0
376	52.0	1	0.0	1	0.0	100.0
377	43.0	1	0.0	1	0.0	100.0
378	0.07	2	0.0	2	0.0	100.0
379	0.162	1	0.0	1	0.0	100.0
380	6.167	2	0.0	2	0.0	100.0
381	0.135	2	0.0	2	0.0	100.0
382	14.25	1	0.0	1	0.0	100.0
383	0.123	1	0.0	1	0.0	100.0
384	1.231	1	0.0	1	0.0	100.0
385	15.5	2	0.0	2	0.0	100.0
386	3.4	1	0.0	1	0.0	100.0
387	0.32	2	0.0	2	0.0	100.0
388	8.75	1	0.0	1	0.0	100.0
389	3.429	1	0.0	1	0.0	100.0
390	10.75	2	0.0	2	0.0	100.0
391	0.647	2	0.0	2	0.0	100.0
392	2.444	1	0.0	1	0.0	100.0
393	2.154	1	0.0	1	0.0	100.0
394	0.346	1	0.0	1	0.0	100.0
395	0.161	1	0.0	1	0.0	100.0
396	63.0	2	0.0	2	0.0	100.0
397	0.028	2	0.0	2	0.0	100.0
398	4.8	2	0.0	2	0.0	100.0
399	0.058	1	0.0	1	0.0	100.0
400	11.6	1	0.0	1	0.0	100.0
401	25.5	1	0.0	1	0.0	100.0
402	9.25	2	0.0	2	0.0	100.0
403	0.081	2	0.0	2	0.0	100.0
404	0.225	1	0.0	1	0.0	100.0
405	0.014	1	0.0	1	0.0	100.0
406	0.02	1	0.0	1	0.0	100.0
407	0.368	1	0.0	1	0.0	100.0
408	0.897	1	0.0	1	0.0	100.0
409	0.348	1	0.0	1	0.0	100.0
410	2.036	1	0.0	1	0.0	100.0
411	3.3	1	0.0	1	0.0	100.0
412	3.286	1	0.0	1	0.0	100.0
413	1.733	1	0.0	1	0.0	100.0
414	0.905	1	0.0	1	0.0	100.0
415	31.5	1	0.0	1	0.0	100.0
416	10.8	1	0.0	1	0.0	100.0
417	13.75	1	0.0	1	0.0	100.0
418	0.842	1	0.0	1	0.0	100.0
419	0.157	1	0.0	1	0.0	100.0
420	18.75	2	0.0	2	0.0	100.0
421	0.044	1	0.0	1	0.0	100.0
422	0.471	1	0.0	1	0.0	100.0
423	12.667	1	0.0	1	0.0	100.0
424	0.171	1	0.0	1	0.0	100.0
425	37.5	1	0.0	1	0.0	100.0
426	7.75	1	0.0	2	0.0	100.0
427	0.567	1	0.0	1	0.0	100.0
428	1.438	2	0.0	2	0.0	100.0
429	68.0	1	0.0	1	0.0	100.0
430	1.909	2	0.0	2	0.0	100.0
431	3.875	1	0.0	1	0.0	100.0
432	0.706	1	0.0	1	0.0	100.0
433	0.391	1	0.0	1	0.0	100.0
434	0.097	1	0.0	1	0.0	100.0
435	12.333	1	0.0	1	0.0	100.0
436	0.054	2	0.0	2	0.0	100.0
437	1.818	2	0.0	2	0.0	100.0
438	1.615	1	0.0	1	0.0	100.0
439	0.923	1	0.0	1	0.0	100.0
440	2.571	1	0.0	1	0.0	100.0
441	0.093	1	0.0	1	0.0	100.0
442	0.098	1	0.0	1	0.0	100.0
443	1.037	1	0.0	1	0.0	100.0
444	2.889	2	0.0	2	0.0	100.0
445	0.128	1	0.0	1	0.0	100.0
446	0.259	1	0.0	1	0.0	100.0
447	0.933	2	0.0	2	0.0	100.0
448	11.429	1	0.0	1	0.0	100.0
449	96.0	1	0.0	1	0.0	100.0
450	3.857	1	0.0	1	0.0	100.0
451	20.25	1	0.0	1	0.0	100.0
452	5.625	1	0.0	1	0.0	100.0
453	0.536	1	0.0	1	0.0	100.0
454	4.875	1	0.0	1	0.0	100.0
455	2.462	1	0.0	1	0.0	100.0
456	50.0	1	0.0	1	0.0	100.0
457	0.24	1	0.0	1	0.0	100.0
458	10.143	1	0.0	1	0.0	100.0
459	1.35	2	0.0	2	0.0	100.0
460	2.857	2	0.0	2	0.0	100.0
461	0.588	1	0.0	2	0.0	100.0
462	13.167	1	0.0	1	0.0	100.0
463	46.0	1	0.0	1	0.0	100.0
464	5.375	1	0.0	1	0.0	100.0
465	10.125	1	0.0	1	0.0	100.0
466	7.167	1	0.0	1	0.0	100.0
467	0.955	1	0.0	1	0.0	100.0
468	0.542	1	0.0	1	0.0	100.0
469	0.437	1	0.0	1	0.0	100.0
470	3.556	1	0.0	1	0.0	100.0
471	1.083	2	0.0	2	0.0	100.0
472	0.846	1	0.0	2	0.0	100.0
473	39.0	1	0.0	1	0.0	100.0
474	1.467	1	0.0	1	0.0	100.0
475	27.5	1	0.0	1	0.0	100.0
476	0.718	1	0.0	2	0.0	100.0
477	0.049	1	0.0	1	0.0	100.0
478	0.524	2	0.0	2	0.0	100.0
479	0.476	1	0.0	1	0.0	100.0
480	1.308	1	0.0	1	0.0	100.0
481	3.889	1	0.0	1	0.0	100.0
482	11.667	1	0.0	1	0.0	100.0
483	16.667	1	0.0	1	0.0	100.0
484	0.06	1	0.0	1	0.0	100.0
485	7.2	2	0.0	2	0.0	100.0
486	4.444	1	0.0	1	0.0	100.0

Here’s how one reads this table.  The left column is the rank.  For instance, a duration ratio of 1.0 (any pair of notes with the same length or duration) is the most common duration ratio.  Moving left to right, we see that it appears in 80,082 tunes, which is 98.9 percent of the number of the 82,000 tunes in the database.  There are 2,740,156 instances of this duration ratio, making up 57.58 percent of all duration ratios instances The final column on the right is the accumulate percent of instances.

Notice that the first six duration ratios make up 90 percent of all duration ratios in the entire database (see the rightmost column).  Ten duration ratios are used roughly 95 percent of the time.  That means that on average 95 percent of a random tune is made up entirely of a subset of these first ten duration ratios.  Adding another seven duration ratios for a total of 17 covers 98% of a random tune’s duration ratios.  At this point diminishing returns set in.  There are several hundred more duration ratios, each used with less and less frequency by composers.  By the time we reach 25 duration ratios, we have accounted for nearly 99 percent of all duration ratios used.

Observe that a duration ratio sometimes appears either before or after the reciprocal of that same duration ratio.  For instance, rows #2 and #3 contain duration ratios of 2.0 and 0.5, each a reciprocal of the other.  The same is true for rows #4 and #5 (0.333 and 3.0), and for rows #13 and #14 (0.2 and 5.0).  This observation is not too surprising, although one wonders why it doesn’t hold true more generally, and why the other duration ratios in the table do not share this feature.

Finally, notice that the ranking changes if you sort the table according to the number of tunes they’re found in.  You can see for yourself by clicking twice on the heading over the “# Tunes” column so that column is sorted in descending order.  Doing so will result in the left-most column being slightly different.  For instance, the 0.75 duration ratio, which was ranked ninth, moves down in the list (though the label still reads “9”).  This observation suggests that once composers decide to use the 0.75 duration ratio, they tend to use it multiple times in the same tune, and at a rate higher than that of other duration ratios.

Surprisingly Rare Duration Ratios

At the other end of the spectrum are duration ratios that are very rarely used, some only one time in the entire database.   But some rarely-used duration ratios just don’t look as though they should be used so infrequently, and these are the ones we are calling “surprisingly rare.”  The area of rare but common-looking duration ratios is so rich that we’ve devoted several pages to the topic, which you can access here.