ED5: Difference between revisions
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The fifth harmonic is particularly wide as far as equivalences go.<span style=""> There are (at absolute most) ~4.8 pentaves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with pentave equivalence, </span>this fact shapes one's musical approach dramatically. Following this, the quintessential example of a pentave based tuning is hyperpyth (see [[17ed5|17ed5]]). However, perhaps the more common reason to use these scales is in approximation with lower harmonic factors than 5. This approach is highlighted by Hieronymus ([[20ed5|20ed5]]) which itself is a zeta peak tuning (not "no-fives", full on zeta). Other reasons for taking the nth root of 5 include finding temperaments like orwell, meantone, and thuja. This approach can of course be used indiscriminately. | The fifth harmonic is particularly wide as far as equivalences go.<span style=""> There are (at absolute most) ~4.8 pentaves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with pentave equivalence, </span>this fact shapes one's musical approach dramatically. Following this, the quintessential example of a pentave based tuning is hyperpyth (see [[17ed5|17ed5]]). However, perhaps the more common reason to use these scales is in approximation with lower harmonic factors than 5. This approach is highlighted by Hieronymus ([[20ed5|20ed5]]) which itself is a zeta peak tuning (not "no-fives", full on zeta). Other reasons for taking the nth root of 5 include finding temperaments like orwell, meantone, and thuja. This approach can of course be used indiscriminately. | ||
[[2ed5]] | |||
3ed5 [[Orwell|orwell]] generator (with octaves) | 3ed5 [[Orwell|orwell]] generator (with octaves) | ||
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4ed5 [[Meantone|meantone]] generator (with octaves) | 4ed5 [[Meantone|meantone]] generator (with octaves) | ||
[[ | [[5ed5]] [[2L_7s|thuja]] generator (with octaves) | ||
6ed5 [[Trienstonic_clan#Uncle|uncle]] generator (with octaves) | 6ed5 [[Trienstonic_clan#Uncle|uncle]] generator (with octaves) | ||
7ed5 | [[7ed5]] compare [[3edo]] | ||
[[8ed5]] | |||
[[ | [[9ed5]] | ||
[[ | [[10ed5]] | ||
[[ | [[11ed5]] | ||
12ed5 | [[12ed5]] | ||
[[ | [[13ed5]] | ||
14ed5 compare [[ | 14ed5 compare [[6edo]] | ||
[[ | [[15ed5]] | ||
16ed5 compare [[ | 16ed5 compare [[7edo]] | ||
[[ | [[17ed5]] | ||
[[ | [[18ed5]] | ||
19ed5 compare [[Bohlen-Pierce|Bohlen-Pierce]] | [[19ed5]] compare [[Bohlen-Pierce|Bohlen-Pierce]] | ||
[[ | [[20ed5]] (Hieronymus Tuning) | ||
21ed5 compare [[ | 21ed5 compare [[9edo]] | ||
[[22ed5]] | [[22ed5]] | ||
23ed5 compare [[ | 23ed5 compare [[10edo]] | ||
24ed5 | [[24ed5]] | ||
[[ | [[25ed5]] (Stockhausen, McLaren) | ||
26ed5 | [[26ed5]] | ||
[[27ed5]] | [[27ed5]] | ||
28ed5 compare [[12edo | [[28ed5]] compare [[12edo]] | ||
[[29ed5]] | |||
30ed5 compare [[13edo]] | |||
[[31ed5]] | |||
[[32ed5]] compare [[14edo]] | |||
[[33ed5]] | |||
[[34ed5]] | |||
[[ | [[35ed5]] compare [[15edo]] | ||
[[36ed5]] | |||
37ed5 compare [[16edo]] | |||
38ed5 compare [[26edt]] | |||
[[39ed5]] | |||
[[40ed5]] | |||
[[41ed5]] | |||
[[42ed5]] | |||
[[43ed5]] | |||
[[44ed5]] compare [[19edo]] | |||
[[ | [[45ed5]] | ||
[[Pentave_Reduced_Harmonics|Pentave Reduced Harmonics]] | [[Pentave_Reduced_Harmonics|Pentave Reduced Harmonics]] | ||