ED5: Difference between revisions
m todo cat via template |
m questionable table |
||
| Line 1: | Line 1: | ||
'''Ed5''' means '''Division of the Fifth Harmonic ([[5/1]]) into n equal parts'''. | '''Ed5''' means '''Division of the Fifth Harmonic ([[5/1]]) into n equal parts'''. | ||
= | == Theory == | ||
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 range restriction is a crucial consideration. Pentave equivalence itself may have a basis in Western music seeing as minor chords have an octave of 5 in their root (i.e. 10:12:15). | 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 range restriction is a crucial consideration. Pentave equivalence itself may have a basis in Western music seeing as minor chords have an octave of 5 in their root (i.e. 10:12:15). | ||
| Line 7: | Line 7: | ||
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. | 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. | ||
Some equal divisions of the pentave are known by alternate names or have special interest: | |||
*[[3ed5]] [[orwell]] generator (with octaves) | * [[3ed5]] [[orwell]] generator (with octaves) | ||
*[[4ed5]] [[meantone]] generator (with octaves) | * [[4ed5]] [[meantone]] generator (with octaves) | ||
*[[5ed5]] [[2L_7s|thuja]] generator (with octaves) | * [[5ed5]] [[2L_7s|thuja]] generator (with octaves) | ||
*[[6ed5]] [[ | * [[6ed5]] [[Trienstonic clan #Uncle|uncle]] generator (with octaves) | ||
*[[Hyperpyth | * [[Hyperpyth]] tuning (e.g. [[17ed5]]) | ||
*[[20ed5 | * [[20ed5]] Hieronymus Tuning | ||
*[[25ed5]] (Stockhausen, McLaren) | * [[25ed5]] (Stockhausen, McLaren) | ||
=Individual pages for ED5s= | == Individual pages for ED5s == | ||
* [[7ed5]] | * [[7ed5]] | ||
| Line 39: | Line 39: | ||
* [[95ed5]] | * [[95ed5]] | ||
=ED5-EDO correspondence= | == ED5-EDO correspondence == | ||
{{todo|cleanup|inline=1|comment=Who please will ever read through this table? Please see: ''[[{{TALKPAGENAME}} #Spam]]''}} | |||
{| class="wikitable" | {| class="wikitable" | ||
| Line 1,380: | Line 1,382: | ||
|} | |} | ||
=See also= | == See also == | ||
* [[Pentave Reduced Harmonics]] | * [[Pentave Reduced Harmonics]] | ||
* [[Pentave Reduced Subharmonics]] | * [[Pentave Reduced Subharmonics]] | ||