184edo: Difference between revisions

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'''184edo''' is the [[EDO|equal division of the octave]] into 184 parts of 6.5217 [[cent]]s each. It is closely related to [[46edo]], but the patent vals differ on the mapping for 5. It is inconsistent to the 5-limit and higher limit, with five mappings possible for the 11-limit: <184 292 427 517 637| (optimal patent val), <184 291 427 516 636| (184bde), <184 292 428 517 637| (184c), <184 292 427 516 636| (184de), and <184 292 427 517 636| (184e). Using the optimal patent val, it tempers out the [[Tetracot family|tetracot comma]], 20000/19683 and 286102294921875/281474976710656 in the 5-limit; 3125/3087, 10976/10935, and 65536/64827 in the 7-limit; 540/539, 896/891, 6875/6804, and 12005/11979 in the 11-limit. Using the 184bde val, it tempers out 129140163/125000000 and 553584375/536870912 in the 5-limit; 225/224, 50421/50000, and 38263752/37515625 in the 7-limit; 385/384, 540/539, 15309/15125, and 43923/43750 in the 11-limit. Using the 184c val, it tempers out the [[Diaschismic family|diaschisma]], 2048/2025 and the [[Sensipent family|sensipent comma]], 78732/78125 in the 5-limit; 2401/2400 and 65536/64827 in the 7-limit; 176/175, 896/891, 3773/3750, and 14641/14580 in the 11-limit. Using the 184de val, it tempers out 1029/1024, 153664/151875, and 214375/209952 in the 7-limit; 896/891, 1331/1323, 2401/2376, and 3773/3750 in the 11-limit. Using the 184e val, it tempers out 385/384, 3388/3375, 9801/9800, and 12100/11907 in the 11-limit.

[[~~Category~~:~~Edo~~]]

184edo is closely related to [[46edo]], but the [[patent val]]s differ on the mapping for [[5/1|5]]. It is in[[consistent]] to the [[5-odd-limit]] and higher limits, with five mappings possible for the 11-limit: {{val| 184 292 427 517 637 }} ([[patent val]]), {{val| 184 '''291''' 427 '''516''' '''636''' }} (184bde), {{val| 184 292 '''428''' 517 637 }} (184c), {{val| 184 292 427 '''516''' '''636''' }} (184de), and {{val| 184 292 427 517 '''636''' }} (184e).

Using the patent val, it tempers out the [[tetracot comma]], 20000/19683 and 286102294921875/281474976710656 in the 5-limit; [[3125/3087]], [[10976/10935]], and 65536/64827 in the 7-limit; [[540/539]], [[896/891]], 6875/6804, and 12005/11979 in the 11-limit; [[352/351]], [[364/363]], [[640/637]], and [[676/675]] in the 13-limit.

Using the 184bde val, it tempers out 129140163/125000000 and 553584375/536870912 in the 5-limit; [[225/224]], [[50421/50000]], and 38263752/37515625 in the 7-limit; [[385/384]], [[540/539]], 15309/15125, and 43923/43750 in the 11-limit; [[351/350]], [[625/624]], [[1001/1000]], 4455/4394, and 7203/7150 in the 13-limit. Using the 184bdef val, [[1573/1568]], [[1575/1573]], 1701/1690, [[1716/1715]], and 3042/3025 are tempered out in the 13-limit.

Using the 184c val, it tempers out the [[diaschisma]], 2048/2025 and the [[sensipent comma]], 78732/78125 in the 5-limit; [[2401/2400]] and 65536/64827 in the 7-limit; [[176/175]], 896/891, 3773/3750, and [[14641/14580]] in the 11-limit; 351/350, 352/351, 364/363, and 9295/9261 in the 13-limit.

Using the 184de val, it tempers out [[1029/1024]], 153664/151875, and 214375/209952 in the 7-limit; 896/891, 1331/1323, 2401/2376, and 3773/3750 in the 11-limit; 196/195, 676/675, 1001/1000, 3185/3168 in the 13-limit.

Using the 184e val, it tempers out 385/384, 3388/3375, [[9801/9800]], and 12100/11907 in the 11-limit; [[275/273]], 572/567, 640/637, and [[847/845]] in the 13-limit.

=== Odd harmonics ===

=== Subsets and supersets ===

Since 184 factors into {{factorization|184}}, 184edo has subset edos {{EDOs| 2, 4, 8, 23, 46, and 92 }}.

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-'''184edo''' is the [[EDO|equal division of the octave]] into 184 parts of 6.5217 [[cent]]s each. It is closely related to [[46edo]], but the patent vals differ on the mapping for 5. It is inconsistent to the 5-limit and higher limit, with five mappings possible for the 11-limit: &lt;184 292 427 517 637| (optimal patent val), &lt;184 291 427 516 636| (184bde), &lt;184 292 428 517 637| (184c), &lt;184 292 427 516 636| (184de), and &lt;184 292 427 517 636| (184e). Using the optimal patent val, it tempers out the [[Tetracot family|tetracot comma]], 20000/19683 and 286102294921875/281474976710656 in the 5-limit; 3125/3087, 10976/10935, and 65536/64827 in the 7-limit; 540/539, 896/891, 6875/6804, and 12005/11979 in the 11-limit. Using the 184bde val, it tempers out 129140163/125000000 and 553584375/536870912 in the 5-limit; 225/224, 50421/50000, and 38263752/37515625 in the 7-limit; 385/384, 540/539, 15309/15125, and 43923/43750 in the 11-limit. Using the 184c val, it tempers out the [[Diaschismic family|diaschisma]], 2048/2025 and the [[Sensipent family|sensipent comma]], 78732/78125 in the 5-limit; 2401/2400 and 65536/64827 in the 7-limit; 176/175, 896/891, 3773/3750, and 14641/14580 in the 11-limit. Using the 184de val, it tempers out 1029/1024, 153664/151875, and 214375/209952 in the 7-limit; 896/891, 1331/1323, 2401/2376, and 3773/3750 in the 11-limit. Using the 184e val, it tempers out 385/384, 3388/3375, 9801/9800, and 12100/11907 in the 11-limit.
+{{Infobox ET}}
+{{ED intro}}
-[[Category:Edo]]
+edo is closely related to [[46edo]], but the [[patent val]]s differ on the mapping for [[5/1|5]]. It is in[[consistent]] to the [[5-odd-limit]] and higher limits, with five mappings possible for the 11-limit: {{val| 184 292 427 517 637 }} ([[patent val]]), {{val| 184 '''291''' 427 '''516''' '''636''' }} (184bde), {{val| 184 292 '''428''' 517 637 }} (184c), {{val| 184 292 427 '''516''' '''636''' }} (184de), and {{val| 184 292 427 517 '''636''' }} (184e).
+Using the patent val, it tempers out the [[tetracot comma]], 20000/19683 and 286102294921875/281474976710656 in the 5-limit; [[3125/3087]], [[10976/10935]], and 65536/64827 in the 7-limit; [[540/539]], [[896/891]], 6875/6804, and 12005/11979 in the 11-limit; [[352/351]], [[364/363]], [[640/637]], and [[676/675]] in the 13-limit.
+Using the 184bde val, it tempers out 129140163/125000000 and 553584375/536870912 in the 5-limit; [[225/224]], [[50421/50000]], and 38263752/37515625 in the 7-limit; [[385/384]], [[540/539]], 15309/15125, and 43923/43750 in the 11-limit; [[351/350]], [[625/624]], [[1001/1000]], 4455/4394, and 7203/7150 in the 13-limit. Using the 184bdef val, [[1573/1568]], [[1575/1573]], 1701/1690, [[1716/1715]], and 3042/3025 are tempered out in the 13-limit.
+Using the 184c val, it tempers out the [[diaschisma]], 2048/2025 and the [[sensipent comma]], 78732/78125 in the 5-limit; [[2401/2400]] and 65536/64827 in the 7-limit; [[176/175]], 896/891, 3773/3750, and [[14641/14580]] in the 11-limit; 351/350, 352/351, 364/363, and 9295/9261 in the 13-limit.
+Using the 184de val, it tempers out [[1029/1024]], 153664/151875, and 214375/209952 in the 7-limit; 896/891, 1331/1323, 2401/2376, and 3773/3750 in the 11-limit; 196/195, 676/675, 1001/1000, 3185/3168 in the 13-limit.
+Using the 184e val, it tempers out 385/384, 3388/3375, [[9801/9800]], and 12100/11907 in the 11-limit; [[275/273]], 572/567, 640/637, and [[847/845]] in the 13-limit.
+=== Odd harmonics ===
+{{Harmonics in equal|184}}
+=== Subsets and supersets ===
+Since 184 factors into {{factorization|184}}, 184edo has subset edos {{EDOs| 2, 4, 8, 23, 46, and 92 }}.