1ed88c: Difference between revisions

Latest revision as of 03:18, 28 September 2025

88-cent equal temperament (88cET, also known as 1ed88¢ or APS88¢) uses equal steps of 88 cents each. It is equivalent to 13.6364edo, and is a subset of 150edo (every eleventh step).

Theory

88-cent equal temperament uses 88 cents, or 11\150 of an octave, to generate a nonoctave rank-1 scale. Since the 88-cent step is an excellent generator for the octacot temperament, it can be viewed as the generator chain of octacot, stripped of octaves. However viewed, octacot and 88-cent equal temperament are very closely related, and the chords of 88-cent equal temperament are listed on the page Chords of octacot. From this it may be seen that octacot, and hence 88 cent equal temperament , share an abundance of essentially tempered chords.

Eight steps of 88 cents gives 704 cents, two cents sharp of 3/2, and eighteen gives 1584 cents, two cents flat of 5/2. Taken together this tells us that (5/2)⁴/(3/2)⁹ = 20000/19683, the minimal diesis or tetracot comma, must be being tempered out. Eleven steps of 88 cents gives 968 cents, less than a cent flat of 7/4, and this tells us that (7/4)⁸/(3/2)¹¹ = 5764801/5668704 must be tempered out also. Taking this, multiplying it by the tetracot comma and taking the fourth root yields 245/243, which therefore must be tempered out also. The tetracot comma and 245/243 taken together define 7-limit octacot.

Continuing on, twenty steps of 88 cents gives 1760 cents, which we may compare to the 1751.3 cents of 11/4 and suggests 100/99 being tempered out, and four steps gives 352 cents, which may be compared to the 359.5 cents of 16/13, and suggests 325/324 being tempered out. These would give an extended octacot, for which 88 cents would be an excellent generator tuning.

Harmonics

Approximation of harmonics in 1ed88c
Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+32.0	+34.0	-24.0	+29.7	-22.0	-24.8	+8.0	-19.9	-26.3	-15.3	+10.0
Error	Relative (%)	+36.4	+38.7	-27.3	+33.7	-24.9	-28.2	+9.1	-22.6	-29.9	-17.4	+11.4
Step		14	22	27	32	35	38	41	43	45	47	49

The 88cET family

Gary Morrison originally conceived of 88-cent equal temperament as composed of steps of exactly 88¢. Nonetheless, composers have recognized a kinship between strict 88cET and some other scales – in particular, the 41ed8 (equivalent to taking three steps of 41edo as a generator with no octaves), the 68ed32 (taking every 5 steps of 68edo), the 109ed256 (taking every 8 steps of 109edo), the 150ed2048 (taking every 11 steps of 150edo i.e. the strict 88cET), the 8edf, and the 11ed7/4, the latter being a preferred variant of composer and software designer X. J. Scott. These cousins of strict 88cET have single steps of approximately 87.805¢, 88.235¢, 88.073¢, 88¢, 87.744¢, and 88.075¢, respectively. These small differences add up, as can be seen by examining the interval list below.

Intervals

Todo: cleanup

Degree	11ed7/4	88cET	41ed8	8edf	Solfege syllable	Some Nearby JI Intervals
first octave
0	0	0	0	0	do	1/1=0
1	88.075	88	87.805	87.744	rih	22/21=80.537, 21/20=84.467, 20/19=88.801, 19/18=93.603
2	176.15	176	175.610	175.489	reh	11/10=165.004, 21/19=173.268, 10/9=182.404
3	264.225	264	263.415	263.233	ma	7/6=266.871
4	352.3	352	351.220	350.978	mu	11/9=347.408, 27/22=354.547, 16/13=359.472
5	440.375	440	439.024	438.722	mo	32/25=427.373, 9/7=435.084, 22/17=446.363
6	528.45	528	526.829	526.466	fih	19/14=528.687, 49/36=533.742, 15/11=536.95
7	616.526	616	614.634	614.211	se	10/7=617.488
8	704.601	704	702.439	701.955	sol	3/2=701.955
9	792.676	792	790.244	789.699	leh	11/7=782.492, 30/19=790.756, 128/81=792.180, 19/12=795.558, 27/17=800.910, 8/5=813.686
10	880.751	880	878.049	877.444	la	5/3=884.359
11	968.826	968	965.854	965.188	ta	7/4=968.826
12	1056.901	1056	1053.659	1052.933	tu	11/6=1049.363, 35/19=1057.627, 24/13=1061.427
13	1144.976	1144	1141.463	1140.677	to	27/14=1137.039, 31/16=1145.036
second octave
14	33.051	32	29.268	28.421	di	65/64=26.841, 64/63=27.264, 63/62=27.700, 58/57=30.109
15	121.126	120	117.073	116.166	ra	16/15=111.731, 15/14=119.443, 14/13=128.298
16	209.201	208	204.878	203.910	re	9/8=203.910
17	297.276	296	292.683	291.654	meh	13/11=289.210, 32/27=294.135, 19/16=297.513
18	385.351	384	380.488	379.399	mi	5/4=386.314
19	473.427	472	468.293	467.143	fe	17/13=464.428, 21/16=470.781
20	561.502	560	556.098	554.888	fu	11/8=551.318, 18/13=563.382
21	649.577	648	643.902	642.632	su	16/11=648.682
22	737.652	736	731.707	730.376	si	32/21=729.219, 26/17=735.572, 49/32=737.652
23	825.727	824	819.512	818.121	le	8/5=813.686, 45/28=821.398, 21/13=830.253
24	913.802	912	907.317	905.865	laa	42/25=898.153, 32/19=902.487, 27/16=905.865, 22/13=910.790, 17/10=918.642
25	1001.877	1000	995.122	993.609	teh	39/22=991.165, 16/9=996.090, 25/14=1003.802, 34/19=1007.442
26	1089.952	1088	1082.927	1081.354	ti	28/15=1080.557, 15/8=1088.269
27	1178.027	1176	1170.732	1169.098	da	63/32=1172.736, 160/81=1178.494
third octave
28	66.102	64	58.537	56.843	ro	33/3253.273, 28/27=62.961, 80/77=66.170, 27/26=65.337
29	154.177	152	146.341	144.587	ru	49/45=147.428, 12/11=150.637, 35/32=155.140
30	242.252	240	234.146	232.331	ri	8/7=231.174, 23/20=241.961, 15/13=247.741
31	330.328	328	321.951	320.076	me	6/5=315.641, 23/19=330.761
32	418.403	416	409.756	407.820	maa	81/64=407.820, 33/26=412.745, 14/11=417.508
33	506.478	504	497.561	495.564	fa	85/64=491.269, 4/3=498.045, 75/56=505.757
34	594.553	592	585.366	583.309	fi	7/5=582.512, 45/32=590.224, 38/27=591.648
35	682.628	680	673.171	671.053	sih	28/19=671.313, 40/27=680.449
36	770.703	768	760.976	758.798	lo	17/11=753.637, 99/64=755.228, 14/9=764.916, 39/25=769.855, 25/16=772.627
37	858.778	856	848.780	846.542	lu	13/8=840.528, 18/11=852.592
38	946.853	944	936.585	934.286	li	12/7=933.129, 19/11=946.195
39	1034.928	1032	1024.390	1022.031	te	9/5=1017.596, 49/27=1031.787, 20/11=1034.996
40	1123.003	1120	1112.195	1109.775	taa	36/19=1106.397, 243/128=1109.775, 19/10=1111.199, 21/11=1119.463
fourth octave (near match)
41	11.078	8	0	1197.59	do	1/1=0, 2/1=1200

Scales

Symmetrical scales of 88cET

Music

Carlo Serafini

Chris Vaisvil

Mundoworld

"To Become Water" from Mundoworld III (2021) – Spotify | YouTube
"Mirage Passage" from Mirage Passage (2024) – Spotify | YouTube

1ed88c: Difference between revisions

Latest revision as of 03:18, 28 September 2025

Contents

Theory

Harmonics

The 88cET family

Intervals

Scales

Music

Further reading

Navigation menu

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+'''88-cent equal temperament''' ('''88cET''', also known as '''1ed88¢''' or '''APS88¢''') uses equal steps of 88 [[cent]]s each. It is equivalent to 13.6364edo, and is a subset of [[150edo]] (every eleventh step).
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2010-09-28 02:46:41 UTC</tt>.<br>
-: The original revision id was <tt>165931725</tt>.<br>
-: The revision comment was: <tt>some typo for table, links added (a few only)</tt><br>
-The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
-<h4>Original Wikitext content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=88cET=
-==Theory==
+== Theory ==
+-cent [[Equal-step tuning|equal temperament]] uses 88 cents, or 11\150 of an octave, to generate a [[nonoctave]] rank-1 scale. Since the 88-cent step is an excellent generator for the [[octacot]] temperament, it can be viewed as the generator chain of octacot, stripped of octaves. However viewed, octacot and 88-cent equal temperament are very closely related, and the chords of 88-cent equal temperament are listed on the page [[Chords of octacot]]. From this it may be seen that octacot, and hence 88 cent equal temperament , share an abundance of [[essentially tempered chord]]s.
-cent equal temperament uses 88 cents, or 11/150 of an octave, to generate a nonoctave rank one scale. Since 88 cents is an excellent generator for [[Tetracot family|octacot temperament]], it can be viewed as the generator chain of octacot, stripped of octaves. However viewed, octacot and 88 cents equal temperament are very closely related.
+Eight steps of 88 cents gives 704 cents, two cents sharp of 3/2, and eighteen gives 1584 cents, two cents flat of 5/2. Taken together this tells us that (5/2)<sup>4</sup>/(3/2)<sup>9</sup> = [[20000/19683]], the minimal diesis or tetracot comma, must be being tempered out. Eleven steps of 88 cents gives 968 cents, less than a cent flat of 7/4, and this tells us that (7/4)<sup>8</sup>/(3/2)<sup>11</sup> = 5764801/5668704 must be tempered out also. Taking this, multiplying it by the tetracot comma and taking the fourth root yields [[245/243]], which therefore must be tempered out also. The tetracot comma and 245/243 taken together define 7-limit octacot.
-Eight steps of 88 cents gives 704 cents, two cents sharp of 3/2, and eighteen gives 1584 cents, two cents flat of 5/2. Taken together this tells us that (5/2)^4/(3/2)^9 = 20000/19683, the minimal diesis or tetracot comma, must be being tempered out. Eleven steps of 88 cents gives 968 cents, less than a cent flat of 7/4, and this tells us that (7/4)^8/(3/2)^11 = 5764801/5668704 must be tempered out also. Taking this, multiplying it by the tetracot comma and taking the fourth root yields 245/243, which therefore must be tempered out also. The tetracot comma and 245/243 taken together define 7-limit octacot.
+Continuing on, twenty steps of 88 cents gives 1760 cents, which we may compare to the 1751.3 cents of 11/4 and suggests [[100/99]] being tempered out, and four steps gives 352 cents, which may be compared to the 359.5 cents of 16/13, and suggests [[325/324]] being tempered out. These would give an extended octacot, for which 88 cents would be an excellent generator tuning.
-Continuing on, twenty steps of 88 cents gives 1760 cents, whioh we may compare to the 1751.3 cents of 11/4 and suggests 100/99 being tempered out, and four steps gives 352 cents, which may be compared to the 359.5 cents of 16/13, and suggestes 325/324 being tempered out. These would give an extended octacot, for which 88 cents would be an excellent generator tuning.
+=== Harmonics ===
+{{Harmonics in cet|88}}
-==Intervals==
+== The 88cET family ==
+[[Gary Morrison]] originally conceived of 88-cent equal temperament as composed of steps of exactly 88¢. Nonetheless, composers have recognized a kinship between strict 88cET and some other scales – in particular, the 41ed8 (equivalent to taking three steps of [[41edo]] as a generator with no octaves), the 68ed32 (taking every 5 steps of [[68edo]]), the 109ed256 (taking every 8 steps of [[109edo]]), the 150ed2048 (taking every 11 steps of [[150edo]] i.e. the strict 88cET), the [[8edf]], and the 11ed7/4, the latter being a preferred variant of composer and software designer [[X. J. Scott]]. These cousins of strict 88cET have single steps of approximately 87.805¢, 88.235¢, 88.073¢, 88¢, 87.744¢, and 88.075¢, respectively. These small differences add up, as can be seen by examining the interval list below.
-cET is considered a very consonant tuning, and you will find that many of its intervals fall very close to simple ratios in 7- and 11-limit just intonation. It is also extremely close to [[41edo]], which is itself extremely close to the 8th root of 3:2 (a perfect fifth divided into exactly 8 logarithmically equal steps). See chart:
+== Intervals ==
+{{todo|cleanup|inline=true}}
+{| class="wikitable"
+|-
+! Degree
+! 11ed7/4
+! 88cET
+! 41ed8
+! 8edf
+! Solfege <br>syllable
+! Some Nearby <br>JI Intervals
+|-
+! colspan="6" | first octave
+!
+|-
+| 0
+| 0
+| 0
+| 0
+| 0
+| do
+| 1/1=0
+|-
+| 1
+| 88.075
+| 88
+| 87.805
+| 87.744
+| rih
+| 22/21=80.537, 21/20=84.467, 20/19=88.801, 19/18=93.603
+|-
+| 2
+| 176.15
+| 176
+| 175.610
+| 175.489
+| reh
+| [[11/10]]=165.004, 21/19=173.268, [[10/9]]=182.404
+|-
+| 3
+| 264.225
+| 264
+| 263.415
+| 263.233
+| ma
+| [[7/6]]=266.871
+|-
+| 4
+| 352.3
+| 352
+| 351.220
+| 350.978
+| mu
+| [[11/9]]=347.408, 27/22=354.547, 16/13=359.472
+|-
+| 5
+| 440.375
+| 440
+| 439.024
+| 438.722
+| mo
+| 32/25=427.373, [[9/7]]=435.084, [[22/17]]=446.363
+|-
+| 6
+| 528.45
+| 528
+| 526.829
+| 526.466
+| fih
+| [[19/14]]=528.687, 49/36=533.742, [[15/11]]=536.95
+|-
+| 7
+| 616.526
+| 616
+| 614.634
+| 614.211
+| se
+| [[10/7]]=617.488
+|-
+| 8
+| 704.601
+| 704
+| 702.439
+| 701.955
+| sol
+| [[3/2]]=701.955
+|-
+| 9
+| 792.676
+| 792
+| 790.244
+| 789.699
+| leh
+| [[11/7]]=782.492, 30/19=790.756, 128/81=792.180, [[19/12]]=795.558, 27/17=800.910, [[8/5]]=813.686
+|-
+| 10
+| 880.751
+| 880
+| 878.049
+| 877.444
+| la
+| [[5/3]]=884.359
+|-
+| 11
+| 968.826
+| 968
+| 965.854
+| 965.188
+| ta
+| [[7/4]]=968.826
+|-
+| 12
+| 1056.901
+| 1056
+| 1053.659
+| 1052.933
+| tu
+| [[11/6]]=1049.363, 35/19=1057.627, 24/13=1061.427
+|-
+| 13
+| 1144.976
+| 1144
+| 1141.463
+| 1140.677
+| to
+| 27/14=1137.039, 31/16=1145.036
+|-
+! colspan="6" | second octave
+!
+|-
+| 14
+| 33.051
+| 32
+| 29.268
+| 28.421
+| di
+| 65/64=26.841, 64/63=27.264, 63/62=27.700, 58/57=30.109
+|-
+| 15
+| 121.126
+| 120
+| 117.073
+| 116.166
+| ra
+| 16/15=111.731, 15/14=119.443, 14/13=128.298
+|-
+| 16
+| 209.201
+| 208
+| 204.878
+| 203.910
+| re
+| 9/8=203.910
+|-
+| 17
+| 297.276
+| 296
+| 292.683
+| 291.654
+| meh
+| 13/11=289.210, 32/27=294.135, 19/16=297.513
+|-
+| 18
+| 385.351
+| 384
+| 380.488
+| 379.399
+| mi
+| 5/4=386.314
+|-
+| 19
+| 473.427
+| 472
+| 468.293
+| 467.143
+| fe
+| 17/13=464.428, 21/16=470.781
+|-
+| 20
+| 561.502
+| 560
+| 556.098
+| 554.888
+| fu
+| 11/8=551.318, 18/13=563.382
+|-
+| 21
+| 649.577
+| 648
+| 643.902
+| 642.632
+| su
+| 16/11=648.682
+|-
+| 22
+| 737.652
+| 736
+| 731.707
+| 730.376
+| si
+| 32/21=729.219, 26/17=735.572, 49/32=737.652
+|-
+| 23
+| 825.727
+| 824
+| 819.512
+| 818.121
+| le
+| 8/5=813.686, 45/28=821.398, 21/13=830.253
+|-
+| 24
+| 913.802
+| 912
+| 907.317
+| 905.865
+| laa
+| 42/25=898.153, 32/19=902.487, 27/16=905.865, 22/13=910.790, 17/10=918.642
+|-
+| 25
+| 1001.877
+| 1000
+| 995.122
+| 993.609
+| teh
+| 39/22=991.165, 16/9=996.090, 25/14=1003.802, 34/19=1007.442
+|-
+| 26
+| 1089.952
+| 1088
+| 1082.927
+| 1081.354
+| ti
+| 28/15=1080.557, 15/8=1088.269
+|-
+| 27
+| 1178.027
+| 1176
+| 1170.732
+| 1169.098
+| da
+| 63/32=1172.736, 160/81=1178.494
+|-
+! colspan="6" | third octave
+!
+|-
+| 28
+| 66.102
+| 64
+| 58.537
+| 56.843
+| ro
+| 33/3253.273, 28/27=62.961, 80/77=66.170, 27/26=65.337
+|-
+| 29
+| 154.177
+| 152
+| 146.341
+| 144.587
+| ru
+| 49/45=147.428, 12/11=150.637, 35/32=155.140
+|-
+| 30
+| 242.252
+| 240
+| 234.146
+| 232.331
+| ri
+| 8/7=231.174, 23/20=241.961, 15/13=247.741
+|-
+| 31
+| 330.328
+| 328
+| 321.951
+| 320.076
+| me
+| 6/5=315.641, 23/19=330.761
+|-
+| 32
+| 418.403
+| 416
+| 409.756
+| 407.820
+| maa
+| 81/64=407.820, 33/26=412.745, 14/11=417.508
+|-
+| 33
+| 506.478
+| 504
+| 497.561
+| 495.564
+| fa
+| 85/64=491.269, 4/3=498.045, 75/56=505.757
+|-
+| 34
+| 594.553
+| 592
+| 585.366
+| 583.309
+| fi
+| 7/5=582.512, 45/32=590.224, 38/27=591.648
+|-
+| 35
+| 682.628
+| 680
+| 673.171
+| 671.053
+| sih
+| 28/19=671.313, 40/27=680.449
+|-
+| 36
+| 770.703
+| 768
+| 760.976
+| 758.798
+| lo
+| 17/11=753.637, 99/64=755.228, 14/9=764.916, 39/25=769.855, 25/16=772.627
+|-
+| 37
+| 858.778
+| 856
+| 848.780
+| 846.542
+| lu
+| 13/8=840.528, 18/11=852.592
+|-
+| 38
+| 946.853
+| 944
+| 936.585
+| 934.286
+| li
+| 12/7=933.129, 19/11=946.195
+|-
+| 39
+| 1034.928
+| 1032
+| 1024.390
+| 1022.031
+| te
+| 9/5=1017.596, 49/27=1031.787, 20/11=1034.996
+|-
+| 40
+| 1123.003
+| 1120
+| 1112.195
+| 1109.775
+| taa
+| 36/19=1106.397, 243/128=1109.775, 19/10=1111.199, 21/11=1119.463
+|-
+! colspan="6" | fourth octave (near match)
+!
+|-
+| 41
+| 11.078
+| 8
+| 0
+| 1197.59
+| do
+| 1/1=0, 2/1=1200
+|}
-||~ Degree ||~ 88cET ||~ 41edo  ||~ 8th Root ||~ Some Nearby  ||
+== Scales ==
-||~        ||~        ||~ 3-steps ||~ of 3:2 ||~ JI Intervals ||
+* [[Symmetrical scales of 88cET]]
-||||||||||= **//first octave//** ||
-|| 0 || 0 || 0 || 0 || 1/1=0 ||
-|| 1 || 88 || 87.805 || 87.744 || 22/21=80.537, 21/20=84.467, 20/19=88.801, 19/18=93.603 ||
-|| 2 || 176 || 175.610 || 175.489 || [[11_10|11/10]]=165.004, 21/19=173.268, [[10_9|10/9]]=182.404  ||
-|| 3 || 264 || 263.415 || 263.233 || [[7_6|7/6]]=266.871  ||
-|| 4 || 352 || 351.220 || 350.978 || [[11_9|11/9]]= 347.408, 27/22=354.547, 16/13=359.472  ||
-|| 5 || 440 || 439.024 || 438.722 || 32/25=427.373, [[9_7|9/7]]=435.084, 22/17	446.363  ||
-|| 6 || 528 || 526.829 || 526.466 || 19/14=528.687, 49/36=533.742, [[15_11|15/11]]=536.95  ||
-|| 7 || 616 || 614.634 || 614.211 ||  [[10_7|10/7]]=617.488 ||
-|| 8 || 704 || 702.439 || 701.955 || [[3_2|3/2]]=701.955  ||
-|| 9 || 792 || 790.244 || 789.699 ||  [[11_7|11/7]]=782.492, 30/19=790.756, 128/81=792.180, 19/12=795.558, 27/17=800.910, [[8_5|8/5]]=813.686 ||
-|| 10 || 880 || 878.049 || 878.444 || [[5_3|5/3]]=884.359  ||
-|| 11 || 968 || 965.854 || 965.188 || [[7_4|7/4]]=968.826 ||
-|| 12 || 1056 || 1053.659 || 1052.933 || [[11_6|11/6]]=1049.363, 35/19=1057.627, 24/13=1061.427  ||
-|| 13 || 1144 || 1141.463 || 1140.677 || 27/14=1137.039, 31/16=1145.036  ||
-||||||||||= **//second octave//** ||
-|| 14 || 32 || 29.268 || 28.421 ||   ||
-|| 15 || 120 || 117.073 || 116.166 ||   ||
-|| 16 || 208 || 204.878 || 203.910 ||   ||
-|| 17 || 296 || 292.683 || 291.654 ||   ||
-|| 18 || 384 || 380.488 || 379.399 ||   ||
-|| 19 || 472 || 468.293 || 467.143 ||   ||
-|| 20 || 560 || 556.098 || 554.888 ||   ||
-|| 21 || 648 || 643.902 || 642.632 ||   ||
-|| 22 || 736 || 731.707 || 730.376 ||   ||
-|| 23 || 824 || 819.512 || 818.121 ||   ||
-|| 24 || 912 || 907.317 || 905.865 ||   ||
-|| 25 || 1000 || 995.122 || 993.609 ||   ||
-|| 26 || 1088 || 1082.927 || 1081.354 ||   ||
-|| 27 || 1176 || 1170.732 || 1169.098 ||   ||
-||||||||||= **//third octave//** ||
-|| 28 || 64 || 58.537 || 56.843 ||   ||
-|| 29 || 152 || 146.341 || 144.587 ||   ||
-|| 30 || 240 || 234.146 || 232.331 ||   ||
-|| 31 || 328 || 321.951 || 320.076 ||   ||
-|| 32 || 416 || 409.756 || 407.820 ||   ||
-|| 33 || 504 || 497.561 || 495.564 ||   ||
-|| 34 || 592 || 585.366 || 583.309 ||   ||
-|| 35 || 680 || 673.171 || 671.053 ||   ||
-|| 36 || 768 || 760.976 || 758.798 ||   ||
-|| 37 || 856 || 848.780 || 846.542 ||   ||
-|| 38 || 944 || 936.585 || 934.286 ||   ||
-|| 39 || 1032 || 1024.390 || 1022.031 ||   ||
-|| 40 || 1120 || 1112.195 || 1109.775 ||   ||
-||||||||||= **//fourth octave//** (near match) ||
-|| 41 || 8 || 0 || 1197.59 ||   ||
-==Compositions==
+== Music ==
-[[http://www.seraph.it/dep/det/88east.mp3|88 East]] by [[Carlo Serafini]]
+; [[Carlo Serafini]]
-[[http://www.seraph.it/dep/det/88vocoeast.mp3|88 VocoEast]] by [[Carlo Serafini]]
+* [http://www.seraph.it/dep/det/88east.mp3 88 East]
-[[http://www.seraph.it/dep/det/88Bulgarians.mp3|88 Bulgarians]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/9660ca3450a996ea8b55713cbf36151f-15.html|blog entry]])
+* [http://www.seraph.it/dep/det/88vocoeast.mp3 88 VocoEast]
-[[http://www.seraph.it/dep/int/88jinglebells.mp3|88 Jingle Bells]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/495ec175ce56cf38cb399d1cd24db164-17.html|blog entry]])</pre></div>
+* [http://www.seraph.it/dep/det/88Bulgarians.mp3 88 Bulgarians] ([http://www.seraph.it/blog_files/9660ca3450a996ea8b55713cbf36151f-15.html blog entry])
-<h4>Original HTML content:</h4>
+* [http://www.seraph.it/dep/int/88jinglebells.mp3 88 Jingle Bells] ([http://www.seraph.it/blog_files/495ec175ce56cf38cb399d1cd24db164-17.html blog entry])
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;88cET&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x88cET"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;88cET&lt;/h1&gt;
+* [http://www.seraph.it/dep/det/The88thDoor.mp3 The 88th Door] ([http://www.seraph.it/blog_files/927f59ac10125056bcf7871636f246a6-302.html blog entry])
- &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x88cET-Theory"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Theory&lt;/h2&gt;
- &lt;br /&gt;
-cent equal temperament uses 88 cents, or 11/150 of an octave, to generate a nonoctave rank one scale. Since 88 cents is an excellent generator for &lt;a class="wiki_link" href="/Tetracot%20family"&gt;octacot temperament&lt;/a&gt;, it can be viewed as the generator chain of octacot, stripped of octaves. However viewed, octacot and 88 cents equal temperament are very closely related.&lt;br /&gt;
-&lt;br /&gt;
-Eight steps of 88 cents gives 704 cents, two cents sharp of 3/2, and eighteen gives 1584 cents, two cents flat of 5/2. Taken together this tells us that (5/2)^4/(3/2)^9 = 20000/19683, the minimal diesis or tetracot comma, must be being tempered out. Eleven steps of 88 cents gives 968 cents, less than a cent flat of 7/4, and this tells us that (7/4)^8/(3/2)^11 = 5764801/5668704 must be tempered out also. Taking this, multiplying it by the tetracot comma and taking the fourth root yields 245/243, which therefore must be tempered out also. The tetracot comma and 245/243 taken together define 7-limit octacot. &lt;br /&gt;
-&lt;br /&gt;
-Continuing on, twenty steps of 88 cents gives 1760 cents, whioh we may compare to the 1751.3 cents of 11/4 and suggests 100/99 being tempered out, and four steps gives 352 cents, which may be compared to the 359.5 cents of 16/13, and suggestes 325/324 being tempered out. These would give an extended octacot, for which 88 cents would be an excellent generator tuning.&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x88cET-Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Intervals&lt;/h2&gt;
- &lt;br /&gt;
-cET is considered a very consonant tuning, and you will find that many of its intervals fall very close to simple ratios in 7- and 11-limit just intonation. It is also extremely close to &lt;a class="wiki_link" href="/41edo"&gt;41edo&lt;/a&gt;, which is itself extremely close to the 8th root of 3:2 (a perfect fifth divided into exactly 8 logarithmically equal steps). See chart:&lt;br /&gt;
-&lt;br /&gt;
+; [[Chris Vaisvil]]
+* [http://micro.soonlabel.com/88cent_nonoctave/STE-004_88_cent_guitar.mp3 88 cent guitar improvisation]
+* [http://micro.soonlabel.com/88cent_nonoctave/Prelude_in_88_Cent_Tuning.mp3 A Simple Prelude for 88 Cent Piano] ([http://micro.soonlabel.com/88cent_nonoctave/A_Simple_Prelude_in_88_Cent_Tuning.pdf scordata])
-&lt;table class="wiki_table"&gt;
+; [[Mundoworld]]
-    &lt;tr&gt;
+* "To Become Water" from ''Mundoworld III'' (2021) – [https://open.spotify.com/track/39gEeGXprXGbAnbq0iyjMF Spotify] | [https://www.youtube.com/watch?v=RBv9c_qlFEk YouTube]
-        &lt;th&gt;Degree&lt;br /&gt;
+* "Mirage Passage" from ''Mirage Passage'' (2024) – [https://open.spotify.com/track/2hAyfHr9XPG96SZPvBNHPP Spotify] | [https://www.youtube.com/watch?v=dWgmmK80I9U YouTube]
-&lt;/th&gt;
-        &lt;th&gt;88cET&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;41edo&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;8th Root&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;Some Nearby&lt;br /&gt;
-&lt;/th&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;th&gt;&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;3-steps&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;of 3:2&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;JI Intervals&lt;br /&gt;
-&lt;/th&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td colspan="5" style="text-align: center;"&gt;&lt;strong&gt;&lt;em&gt;first octave&lt;/em&gt;&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;0&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;0&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;0&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;0&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1/1=0&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;1&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;88&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;87.805&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;87.744&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;22/21=80.537, 21/20=84.467, 20/19=88.801, 19/18=93.603&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;2&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;176&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;175.610&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;175.489&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/11_10"&gt;11/10&lt;/a&gt;=165.004, 21/19=173.268, &lt;a class="wiki_link" href="/10_9"&gt;10/9&lt;/a&gt;=182.404&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;3&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;264&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;263.415&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;263.233&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt;=266.871&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;4&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;352&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;351.220&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;350.978&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/11_9"&gt;11/9&lt;/a&gt;= 347.408, 27/22=354.547, 16/13=359.472&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;5&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;440&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;439.024&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;438.722&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;32/25=427.373, &lt;a class="wiki_link" href="/9_7"&gt;9/7&lt;/a&gt;=435.084, 22/17    446.363&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;6&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;528&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;526.829&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;526.466&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;19/14=528.687, 49/36=533.742, &lt;a class="wiki_link" href="/15_11"&gt;15/11&lt;/a&gt;=536.95&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;7&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;616&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;614.634&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;614.211&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/10_7"&gt;10/7&lt;/a&gt;=617.488&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;8&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;704&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;702.439&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;701.955&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt;=701.955&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;9&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;792&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;790.244&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;789.699&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/11_7"&gt;11/7&lt;/a&gt;=782.492, 30/19=790.756, 128/81=792.180, 19/12=795.558, 27/17=800.910, &lt;a class="wiki_link" href="/8_5"&gt;8/5&lt;/a&gt;=813.686&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;10&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;880&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;878.049&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;878.444&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/5_3"&gt;5/3&lt;/a&gt;=884.359&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;11&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;968&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;965.854&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;965.188&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt;=968.826&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;12&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1056&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1053.659&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1052.933&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/11_6"&gt;11/6&lt;/a&gt;=1049.363, 35/19=1057.627, 24/13=1061.427&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;13&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1144&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1141.463&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1140.677&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;27/14=1137.039, 31/16=1145.036&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td colspan="5" style="text-align: center;"&gt;&lt;strong&gt;&lt;em&gt;second octave&lt;/em&gt;&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;14&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;32&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;29.268&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;28.421&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;15&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;120&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;117.073&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;116.166&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;16&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;208&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;204.878&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;203.910&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;17&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;296&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;292.683&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;291.654&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;18&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;384&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;380.488&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;379.399&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;19&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;472&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;468.293&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;467.143&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;20&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;560&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;556.098&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;554.888&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;21&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;648&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;643.902&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;642.632&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;22&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;736&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;731.707&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;730.376&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;23&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;824&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;819.512&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;818.121&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;24&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;912&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;907.317&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;905.865&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;25&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1000&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;995.122&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;993.609&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;26&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1088&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1082.927&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1081.354&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;27&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1176&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1170.732&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1169.098&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td colspan="5" style="text-align: center;"&gt;&lt;strong&gt;&lt;em&gt;third octave&lt;/em&gt;&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;28&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;64&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;58.537&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;56.843&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;29&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;152&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;146.341&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;144.587&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;30&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;240&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;234.146&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;232.331&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;31&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;328&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;321.951&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;320.076&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;32&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;416&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;409.756&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;407.820&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;33&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;504&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;497.561&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;495.564&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;34&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;592&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;585.366&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;583.309&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;35&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;680&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;673.171&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;671.053&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;36&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;768&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;760.976&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;758.798&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;37&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;856&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;848.780&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;846.542&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;38&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;944&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;936.585&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;934.286&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;39&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1032&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1024.390&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1022.031&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;40&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1120&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1112.195&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1109.775&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td colspan="5" style="text-align: center;"&gt;&lt;strong&gt;&lt;em&gt;fourth octave&lt;/em&gt;&lt;/strong&gt; (near match)&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;41&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;8&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;0&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1197.59&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-&lt;/table&gt;
-&lt;br /&gt;
+== Further reading ==
-&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x88cET-Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Compositions&lt;/h2&gt;
+* [[Gary Morrison]]’s 2001 [https://soundcloud.com/mr88cet/sets/88cet-lecture-demo-gary-morrison-june-2001 lecture about 88cET]
- &lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/88east.mp3" rel="nofollow"&gt;88 East&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/88vocoeast.mp3" rel="nofollow"&gt;88 VocoEast&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt;&lt;br /&gt;
+[[Category:Equal-step tuning]]
-&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/88Bulgarians.mp3" rel="nofollow"&gt;88 Bulgarians&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/9660ca3450a996ea8b55713cbf36151f-15.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/int/88jinglebells.mp3" rel="nofollow"&gt;88 Jingle Bells&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/495ec175ce56cf38cb399d1cd24db164-17.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;/body&gt;&lt;/html&gt;</pre></div>

1ed88c: Difference between revisions

Latest revision as of 03:18, 28 September 2025

Theory

Harmonics

The 88cET family

Intervals

Scales

Music

Further reading

Navigation menu

Search