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]] | ||
Revision as of 11:10, 15 November 2018
Division of the Fifth Harmonic (5/1) into n equal parts
The fifth harmonic is particularly wide as far as equivalences go. 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, this fact shapes one's musical approach dramatically. Following this, the quintessential example of a pentave based tuning is hyperpyth (see 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) 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.
3ed5 orwell generator (with octaves)
4ed5 meantone generator (with octaves)
5ed5 thuja generator (with octaves)
6ed5 uncle generator (with octaves)
14ed5 compare 6edo
16ed5 compare 7edo
19ed5 compare Bohlen-Pierce
20ed5 (Hieronymus Tuning)
21ed5 compare 9edo
23ed5 compare 10edo
25ed5 (Stockhausen, McLaren)
30ed5 compare 13edo
37ed5 compare 16edo
38ed5 compare 26edt