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| ''[[User:Dummy index]] posted this on Discord overnight (Sydney time), but I decided to move it here because I would rather discuss it on a talk page:''
| | == Moved post == |
| | | (I made a post here but moved it to a Discord thread.) --[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 21:58, 7 January 2025 (UTC) |
| “Hello,
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| '''> 16edo: 2 • 5 • 7 • 13 • 27 • 45'''
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| is dual-3. (and 14edo is dual-5 maybe.)
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| * In the first place, it is too much to have four basis elements within the 5-limit.
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| * 27 * 5 / 45 = 3 (76 + 37 - 88 = 25 steps) is same to nearest approximation of 3rd harmonic. Hence, it is inconsistent between 27 (76 steps) and 3 (25 steps). So we need to differentiate between 3^3 and 27 in some way, to regain regularity.
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| * One way, 27 = 9+ * 3- = 3++ * 3- * 3- (76 = 51 + 25 = 26 + 25 + 25). it means 2.5.7.13.27.45+ or 2.3-.3++.5.7.13 subgroup.
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| * Another way, 27+ = 9+ * 3 = 3+ * 3 * 3 for nearest approximation of 27th harmonic and 27 for 3^3. it means 2.5.7.13.27+.45+ or 2.3.3+.5.7.13 subgroup.”
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| ''I plan to re-read Index’s post carefully and write a reply here later today (Sydney time). It may be several hours before I can do that due to irl commitments.''
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| ''--[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 18:18, 7 January 2025 (UTC)''
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