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'''218edo''', having a step size of 5.50458715596 [[cent]]s, contains very accurate ratios, such as [[7/4]], [[11/8]], [[9/7]], [[8/7]], [[9/8]], [[10/9]], [[11/10]] and [[17/16]] (sizes are approximated within 5.5 cents).
{{Infobox ET}}
{{ED intro}}


The following table shows the nearest matches for the interval, not the matches from the [[patent val]]. '''Bold''' numbers are off within less than 0.1 (10%) of the step size.
218edo is in[[consistent]] to the [[5-odd-limit]], with [[harmonic]] [[3/1|3]] falling about halfway between its steps. However, it contains very accurate ratios, such as [[7/4]], [[9/7]], [[9/8]], [[10/9]], [[11/10]], [[17/16]], and [[19/16]], which are approximated within 0.55-cent deviation (10% the step size). The suggested [[subgroup]]s are therefore 2.9.7.17.19 and 2.9.5.7.11.17.19.23.
 
{| class="wikitable"
|-
! Interval fraction
| [[3/2]]
| [[4/3]]
| [[5/4]]
| [[8/5]]
| [[5/3]]
| [[6/5]]
| '''[[7/4]]'''
| '''[[8/7]]'''
| [[10/9]]
| [[9/5]]
| '''[[9/8]]'''
| '''[[16/9]]'''
|-
! Steps in 218edo
| 128
| 90
| 70
| 148
| 161
| 57
| '''176'''
| '''42'''
| 33
| 185
| '''37'''
| '''181'''
|}
 
Suggested [[subgroup]]s: 2.9.7.17 and 2.9.5.7.11.17.
 
Also explore [[436edo]].


Commas using the [[13-limit]] patent val:
Commas using the [[13-limit]] patent val:


; [[3-limit]]: 1/1
; [[5-limit]]: 20000/19683, 1220703125/1207959552


; [[5-limit]]: 20000/19683
; [[7-limit]]: 4000/3969, 65625/65536, 245/243, 2401/2400 117649/116640


; [[7-limit]]: 4000/3969 65625/65536 245/243 2401/2400 60025/59049
; [[11-limit]]: 4000/3993, 12005/11979, 16384/16335, 4375/4356, 78125/77616, 896/891, 67228/66825, 1375/1372, 6875/6804, 5632/5625, 385/384, 94325/93312, 15488/15435, 75625/75264, 15488/15309, 3388/3375, 1331/1323, 6655/6561, 65219/64800, 43923/43904, 73205/72576,


; [[11-limit]]: 4000/3993 12005/11979 16384/16335 4375/4356 78125/77616 896/891 67228/66825 1375/1372 6875/6804 5632/5625 385/384 94325/93312 15488/15435 75625/75264 15488/15309 3388/3375 1331/1323 6655/6561 65219/64800 43923/43904 73205/72576
; [[13-limit]]: 28672/28561, 86240/85683, 20480/20449, 5600/5577, 16807/16731, 25000/24843, 6125/6084, 86625/86528, 68992/68445, 58080/57967, 96800/95823, 847/845, 41503/41067, 33275/33124, 65219/64896, 29575/29403, 4225/4224, 21632/21609, 676/675, 33124/32805, 9295/9261, 46475/45927, 13013/12960, 28561/28512


; [[13-limit]]: 28672/28561 86240/85683 20480/20449 5600/5577 16807/16731 25000/24843 6125/6084 86625/86528 68992/68445 58080/57967 96800/95823 847/845 41503/41067 33275/33124 65219/64896 29575/29403 4225/4224 21632/21609 676/675 33124/32805 9295/9261 46475/45927 13013/12960 28561/28512
=== Odd harmonics ===
{{Harmonics in equal|218}}


[[Category:Stub]]
=== Subsets and supersets ===
[[Category:Edo]]
Since 218 factors into {{factorization|218}}, 218edo contains [[2edo]] and [[109edo]] as its subsets. [[436edo]], which doubles it, is worth exploring.
Retrieved from "https://en.xen.wiki/w/218edo"