User:BudjarnLambeth/Above octave

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Return to gallery lobby: Gallery of just intervals

The following is an exhibit featuring a sampling of [[just intonation] intervals larger than 1200 cents (so, larger than the just octave, 2/1). It is neither comprehensive nor systematic.

Criteria for inclusion

The criteria for an interval's inclusion are:

• It is a just interval larger than 2/1
• Someone cared enough to write about it
• Its ratio uses fairly simple numbers (there are no hard and fast rules, but generally the numerator should have 1 or 2 digits, and the denominator should have 1 or 2 digits)

If it meets those criteria, it is welcome to be added.

Dedicated interval pages

This page lists links to dedicated pages for each interval, under the heading "frequency ratio".

Said dedicated pages may include: descriptions of common usage, technical notes, poetry, links, reservations, complaints, chords or compositions that feature it, edos that approximate it, intervals that are functionally (or emotionally) related to it, nicknames, fan art, etc. Readers are encouraged to add such things to the interval pages. If your contribution is unconventional, add your name or pseudonym so future readers know where the idea originated.

The collection

See also List of intervals (Huygens-Fokker foundation)

If any FJS names are missing, please add them.

In the color names, "co" or "c" stands for compound, a conventional music term.

Frequency Ratio	Cents Value (three decimal places)	Color Name		FJS Name	Some common names
27/13	1265.337	3u8	thu8ve	A813	Luxembourg eighth
23/11	1276.956	23o1u9	twetholu 9th	A82311	vicesimotertial minor ninth
19/9	1293.603	19o9	ino 9th	m919	undevicesimal minor ninth
17/8	1304.955	17o9	iso 9th	m917	septendecimal minor ninth
32/15	1311.731	g9	gu 9th	m95	classic minor ninth
15/7	1319.443	ry8	ruyo 8ve	A857	septimal minor ninth
13/6	1338.573	3o9	tho 9th	m913	tridecimal minor ninth, tridecimal neutral ninth
11/5	1365.004	1o9	ilo 9th	m9115	neutral ninth
20/9	1382.404	y9	yo 9th	M95	Ptolemaic ninth
9/4	1403.910	w9	wa 9th	M9	major ninth
16/7	1431.174	r9	ru 9th	M97	septimal major ninth
7/3	1466.871	z10	zo 10th	m107	septimal minor tenth
19/8	1497.513				undevicesimal minor tenth
12/5	1515.641	g10	gu 10th	m105	classic minor tenth
17/7	1536.130	17or10	soru 10tg	m10177	septendecimal minor tenth
27/11	1554.547	c1u3	colu 3rd	M1011	rastmic neutral tenth
5/2	1586.314	y10	yo 10th	M105	classic major tenth
18/7	1635.084				septimal supermajor tenth
13/5	1654.214	3og11	thogu 11th	d11135	tridecimal eleventh
21/8	1670.781				septimal subeleventh
8/3	1698.045	w11, cw4	wa 11th, cowa 4th	P11	perfect eleventh
19/7	1728.687				undevicesimal supereleventh
11/4	1751.318	1o11, c1o4	ilo 11th, colo 4th	P1111	undecimal semi-augmented eleventh
14/5	1782.512	zg12, czg5	zogu 12th, cozogu 5th	d1275	short septimal navatone
17/6	1803.000	17o12	iso 12th	d1217	septendecimal navatone
20/7	1817.488	ry11	ruyo 11th	A1157	tall septimal navatone
23/8	1828.274	23o12	twetho 12th	A1123	trivigintal navatone
35/12	1853.185				septimal semi-diminished twelfth
3/1	1901.955	w12, cw5	wa 12th, cowa 5th	P12	3rd harmonic, perfect twelfth, tritave
28/9	1964.916				septimal subminor thirteenth
19/6	1995.558				undevicesimal minor thirteenth
16/5	2013.686	g13, cg6	gu 13th, cogu 6th	m135	classic minor thirteenth
13/4	2040.528	3o13, c3o6	tho 13th, cotho 6th	m1313	tridecimal neutral thirteenth
23/7	2059.448				trivigintal neutral/submajor thirteenth
10/3	2084.359	y13, cy6	yo 13th, coyo 6th	M135	just/classic(al)/ptolemaic major thirteenth
17/5	2118.642	c17og7	cosogu 7th	d14175	septendecimal major thirteenth
24/7	2133.129				septimal supermajor thirteenth
7/2	2168.826	cz7	cozo 7th	m147	harmonic fourteenth
32/9	2196.090				3-limit minor fourteenth
18/5	2217.596			m145	5-limit minor fourteenth
11/3	2249.363	c1o7	colo 7th	m1411	undecimal neutral fourteenth
15/4	2288.269	cy7	coyo 7th	M145	just/classic(al)/ptolemaic major fourteenth
19/5	2311.199				undevicesimal major fourteenth
35/9	2351.230				septimal semi-augmented fourteenth
4/1	2400.000	cw8, ccw1	wa double 8ve	P15	4th harmonic, two octaves, just double octave
81/20	2421.506	g15	gu double 8ve	P155	syntonic double octave
25/6	2470.672				classic chromatic minor sixteenth
17/4	2504.955	cc17o2	cocoso 2nd	m1617	septendecimal minor sixteenth
64/15	2511.731	cc17o2	cocoso 2nd	m165	classic minor sixteenth
13/3	2538.573	c3o9, cc3o2	cotho 9th, cocotho 2nd	m1613	tridecimal minor sixteenth
22/5	2565.004				large undecimal neutral sixteenth
9/2	2603.910	cw9, ccw2	cowa 9th, cocoyo 2nd	M16	classic large major sixteenth
23/5	2641.961				trivigintal supermajor sixteenth
14/3	2666.871	cz10, ccz3	cozo 10th, cocozo 3rd	m177	septimal subminor seventeenth
19/4	2696.513				undevicesimal minor seventeenth
24/5	2715.641				classic minor seventeenth
44/9	2747.408				undecimal neutral seventeenth
5/1	2786.314	cy10, ccy3	coyo 10th, cocoyo 3rd	M175	5th harmonic, pentave
36/7	2835.084				septimal supermajor seventeenth
21/4	2870.781				septimal subeighteenth
16/3	2898.045	ccw4	cocowa 4th	P18	perfect eighteenth
27/5	2919.551				5-limit supereighteenth
11/2	2951.318	cc1o4	cocolo 4th	P1811	undecimal semi-augmented eighteenth
28/5	2982.512	cczg5	coco-zogu 5th	d1975	short septimal panchadashatone
45/8	2990.224	ccy4	cocoyo 4th	A185	quinquadragintimal panchadashatone
17/3	3003.000	cc17o5	cocoso 5th	d1917	septendecimal panchadasatone
40/7	3017.488	ccry4	coco-ruyo 4th	A1857	tall septimal panchadashatone
23/4	3028.274				vicesimotertial panchadashatone
35/6	3053.185				septimal semi-diminished nineteenth
6/1	3101.955	ccw5	cocowa 5th	P19	6th harmonic
55/9	3133.722				undecimal superninteenth
25/4	3172.627				5-limit subminor twentieth
19/3	3195.558				undevicesimal minor twentieth
32/5	3213.686				classic minor twentieth
13/2	3240.528	cc3o6	cocotho 6th	m2013	tridecimal neutral twentieth
20/3	3284.359				classic major twentieth
48/7	3333.129				septimal supermajor twentieth
7/1	3368.826	ccz7	cocozo 7th	m217	7th harmonic
36/5	3417.596				5-limit minor twentyfirst
22/3	3449.363				undecimal neutral twentyfirst
15/2	3488.269	ccy7	cocoyo 7th	M215	just/classic(al)/ptolemaic major twentyfirst
23/3	3526.319				vicesimotertial supermajor twentyfirst
31/4	3545.036				31-limit semi-augmented twentyfirst
8/1	3600.000	c3w1	wa triple 8ve	P22	8th harmonic, three octaves
33/4	3653.273				undecimal semi-diminished twentythird
25/3	3670.672				classic chromatic twentythird
17/2	3704.955				septendecimal minor twentythird
128/15	3711.731	c3g2	tricogu 2nd	m235	classic minor twenty-third
26/3	3738.573				tridecimal neutral twentythird
35/4	3755.140				septimal neutral twentythird
9/1	3803.910	c3w2	tricowa 2nd	M23	9th harmonic
10/1	3986.314	c3y3	tricoyo 3rd	M245	10th harmonic, decade
11/1	4151.318	c31o4	tricolo 4th	P2511	11th harmonic
12/1	4301.955	c3w5	tricowa 5th	P26	12th harmonic
13/1	4440.528	c33o6	tricotho 6th	m2713	13th harmonic
14/1	4568.826	c3z7	tricozo 7th	m287	14th harmonic
15/1	4688.269	c3y7	tricoyo 7th	M285	15th harmonic
16/1	4800.000	c4w1	wa quadruple 8ve	P29	16th harmonic, four octaves
17/1	4904.955	c^417o2	quadcoso 2nd	m3017	17th harmonic
256/15	4911.731	c4g2	quadcogu 2nd	m305	classic minor thirtieth
18/1	5004.910			M30	18th harmonic
19/1	5097.513	c419o3	quadcono 3rd	m3119	19th harmonic
20/1	5186.314			M315	20th harmonic
21/1	5270.781	c4z4	quadcozo 4th	P327	21st harmonic
22/1	5351.318			P3211	22nd harmonic
23/1	5428.274	c423o5	quadcotwetho	A3223	23rd harmonic
24/1	5501.955	c4w5	quadcowa 5th	P33	24th harmonic
25/1	5572.617	c4yy5	quadco-yoyo 5th	A335,5	25th harmonic
27/1	5705.865	c4w6	quadcowa 6th	M34	27th harmonic
29/1	5829.577	c429o7	quadcotweno 7th	m3529	29th harmonic
31/1	5945.036	c431o7	quadcothiwo 7th	M3531	31st harmonic
49/1	6737.652			M417,7	49th harmonic
1536/1	12701.955			P75	1536th harmonic