49edo: Difference between revisions
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{{ED intro}} | |||
== Theory == | == Theory == | ||
49edo is very much on the sharp side of things, with sharp tunings of | 49edo is very much on the sharp side of things, with sharp tunings of [[harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]], and [[11/1|11]]. It is the [[optimal patent val]] for [[superpyth]] temperament in the 7- and 11-limit, [[Archytas family #Archytas|archytas]] ([[7-limit]]), and [[Archytas family #Ares|ares]] ([[11-limit]]) planar temperaments, being almost exactly equal to {{frac|3|10}}-comma superpyth. It [[tempering out|tempers out]] [[64/63]], [[245/243]], and [[3125/3087]] in the 7-limit, and [[100/99]], [[540/539]], and [[1375/1372]] in the 11-limit. In the 13-limit, its [[patent val]] {{val| 49 78 114 138 170 181 }}, has a rather flat (by relative error) harmonic [[13/1|13]], which leads to inconsistent mappings; but using the 49f val {{val| 49 78 114 138 170 182 }} improves 13-limit consistency, and in this val it tempers out [[364/363]] and [[847/845]]. | ||
=== | === Harmonics === | ||
{{ | {{Harmonics in equal|49}} | ||
=== Subsets and supersets === | |||
Since 49 factors into primes as 7<sup>2</sup>, 49edo contains [[7edo]] as its only nontrivial subset. 49edo is the first square edo with a [[enfactoring|non-enfactored]] diatonic fifth. Doubling it produces [[98edo]], a respectable (if overly complex) [[meantone]] tuning. | |||
== Intervals == | == Intervals == | ||
{| class="wikitable center-all right-2 left-3" | {| class="wikitable center-all right-2 left-3" | ||
! # | |- | ||
! # | |||
! Cents | ! Cents | ||
! Approximate | ! Approximate ratios* | ||
! | ! [[Ups and downs notation]] | ||
|- | |- | ||
| 0 | | 0 | ||
| 0.000 | | 0.000 | ||
| [[1/1]] | | [[1/1]] | ||
| | | {{UDnote|step=0}} | ||
|- | |- | ||
| 1 | | 1 | ||
| 24.490 | | 24.490 | ||
| [[50/49]] | | [[50/49]] | ||
| | | {{UDnote|step=1}} | ||
|- | |- | ||
| 2 | | 2 | ||
| 48.980 | | 48.980 | ||
| ''[[ | | ''[[28/27]]'', [[36/35]], ''[[49/48]]'', ''[[81/80]]'' | ||
| | | {{UDnote|step=2}} | ||
|- | |- | ||
| 3 | | 3 | ||
| 73.469 | | 73.469 | ||
| [[ | | [[22/21]], [[25/24]], ''[[33/32]]'' | ||
| | | {{UDnote|step=3}} | ||
|- | |- | ||
| 4 | | 4 | ||
| 97.959 | | 97.959 | ||
| ''[[16/15]]'', [[21/20]] | | ''[[16/15]]'', [[21/20]] | ||
| | | {{UDnote|step=4}} | ||
|- | |- | ||
| 5 | | 5 | ||
| 122.449 | | 122.449 | ||
| [[15/14]] | | [[15/14]] | ||
| | | {{UDnote|step=5}} | ||
|- | |- | ||
| 6 | | 6 | ||
| 146.939 | | 146.939 | ||
| [[12/11]] | | [[12/11]] | ||
| | | {{UDnote|step=6}} | ||
|- | |- | ||
| 7 | | 7 | ||
| 171.429 | | 171.429 | ||
| [[10/9]], [[11/10]] | | [[10/9]], [[11/10]] | ||
| | | {{UDnote|step=7}} | ||
|- | |- | ||
| 8 | | 8 | ||
| 195.918 | | 195.918 | ||
| [[28/25]] | | [[28/25]] | ||
| | | {{UDnote|step=8}} | ||
|- | |- | ||
| 9 | | 9 | ||
| 220.408 | | 220.408 | ||
| ''[[9/8]]'', [[ | | [[8/7]], ''[[9/8]]'', [[25/22]] | ||
| | | {{UDnote|step=9}} | ||
|- | |- | ||
| 10 | | 10 | ||
| 244.898 | | 244.898 | ||
| 125/108, 144/125 | | 125/108, 144/125 | ||
| | | {{UDnote|step=10}} | ||
|- | |- | ||
| 11 | | 11 | ||
| 269.388 | | 269.388 | ||
| [[7/6]] | | [[7/6]] | ||
| | | {{UDnote|step=11}} | ||
|- | |- | ||
| 12 | | 12 | ||
| 293.878 | | 293.878 | ||
| [[25/21]], [[33/28]] | | [[25/21]], [[33/28]] | ||
| | | {{UDnote|step=12}} | ||
|- | |- | ||
| 13 | | 13 | ||
| 318.367 | | 318.367 | ||
| [[6/5]] | | [[6/5]] | ||
| | | {{UDnote|step=13}} | ||
|- | |- | ||
| 14 | | 14 | ||
| 342.857 | | 342.857 | ||
| [[11/9]] | | [[11/9]] | ||
| | | {{UDnote|step=14}} | ||
|- | |- | ||
| 15 | | 15 | ||
| 367.347 | | 367.347 | ||
| [[27/22]] | | [[27/22]] | ||
| | | {{UDnote|step=15}} | ||
|- | |- | ||
| 16 | | 16 | ||
| 391.837 | | 391.837 | ||
| [[5/4]] | | [[5/4]] | ||
| | | {{UDnote|step=16}} | ||
|- | |- | ||
| 17 | | 17 | ||
| 416.327 | | 416.327 | ||
| [[14/11]] | | [[14/11]] | ||
| | | {{UDnote|step=17}} | ||
|- | |- | ||
| 18 | | 18 | ||
| 440.816 | | 440.816 | ||
| [[9/7]] | | [[9/7]] | ||
| | | {{UDnote|step=18}} | ||
|- | |- | ||
| 19 | | 19 | ||
| 465.306 | | 465.306 | ||
| 125/96, ''162/125'' | | 125/96, ''162/125'' | ||
| | | {{UDnote|step=19}} | ||
|- | |- | ||
| 20 | | 20 | ||
| 489.796 | | 489.796 | ||
| [[4/3]], ''[[21/16]]'' | | [[4/3]], ''[[21/16]]'' | ||
| | | {{UDnote|step=20}} | ||
|- | |- | ||
| 21 | | 21 | ||
| 514.286 | | 514.286 | ||
| [[75/56]] | | [[75/56]] | ||
| | | {{UDnote|step=21}} | ||
|- | |- | ||
| 22 | | 22 | ||
| 538.776 | | 538.776 | ||
| | | [[15/11]], ''[[27/20]]'' | ||
| | | {{UDnote|step=22}} | ||
|- | |- | ||
| 23 | | 23 | ||
| 563.265 | | 563.265 | ||
| [[11/8]] | | [[11/8]] | ||
| | | {{UDnote|step=23}} | ||
|- | |- | ||
| 24 | | 24 | ||
| 587.755 | | 587.755 | ||
| [[7/5]] | | [[7/5]] | ||
| | | {{UDnote|step=24}} | ||
|- | |- | ||
| 25 | | 25 | ||
| 612.245 | | 612.245 | ||
| [[10/7]] | | [[10/7]] | ||
| | | {{UDnote|step=25}} | ||
|- | |- | ||
| 26 | | 26 | ||
| 636.735 | | 636.735 | ||
| [[16/11]] | | [[16/11]] | ||
| | | {{UDnote|step=26}} | ||
|- | |- | ||
| 27 | | 27 | ||
| 661.244 | | 661.244 | ||
| | | [[22/15]], ''[[40/27]]'' | ||
| | | {{UDnote|step=27}} | ||
|- | |- | ||
| 28 | | 28 | ||
| 685.714 | | 685.714 | ||
| [[112/75]] | | [[112/75]] | ||
| | | {{UDnote|step=28}} | ||
|- | |- | ||
| 29 | | 29 | ||
| 710.204 | | 710.204 | ||
| [[3/2]], ''[[32/21]]'' | | [[3/2]], ''[[32/21]]'' | ||
| | | {{UDnote|step=29}} | ||
|- | |- | ||
| 30 | | 30 | ||
| 734.694 | | 734.694 | ||
| ''125/81'', 192/125 | | ''125/81'', 192/125 | ||
| | | {{UDnote|step=30}} | ||
|- | |- | ||
| 31 | | 31 | ||
| 759.184 | | 759.184 | ||
| [[14/9]] | | [[14/9]] | ||
| | | {{UDnote|step=31}} | ||
|- | |- | ||
| 32 | | 32 | ||
| 783.673 | | 783.673 | ||
| [[11/7]] | | [[11/7]] | ||
| | | {{UDnote|step=32}} | ||
|- | |- | ||
| 33 | | 33 | ||
| 808.163 | | 808.163 | ||
| [[8/5]] | | [[8/5]] | ||
| | | {{UDnote|step=33}} | ||
|- | |- | ||
| 34 | | 34 | ||
| 832.653 | | 832.653 | ||
| [[44/27]] | | [[44/27]] | ||
| | | {{UDnote|step=34}} | ||
|- | |- | ||
| 35 | | 35 | ||
| 857.143 | | 857.143 | ||
| [[18/11]] | | [[18/11]] | ||
| | | {{UDnote|step=35}} | ||
|- | |- | ||
| 36 | | 36 | ||
| 881.633 | | 881.633 | ||
| [[5/3]] | | [[5/3]] | ||
| | | {{UDnote|step=36}} | ||
|- | |- | ||
| 37 | | 37 | ||
| 906.122 | | 906.122 | ||
| [[42/25]], [[56/33]] | | [[42/25]], [[56/33]] | ||
| | | {{UDnote|step=37}} | ||
|- | |- | ||
| 38 | | 38 | ||
| 930.612 | | 930.612 | ||
| [[12/7]] | | [[12/7]] | ||
| | | {{UDnote|step=38}} | ||
|- | |- | ||
| 39 | | 39 | ||
| 955.102 | | 955.102 | ||
| 125/72, 216/125 | | 125/72, 216/125 | ||
| | | {{UDnote|step=39}} | ||
|- | |- | ||
| 40 | | 40 | ||
| 979.592 | | 979.592 | ||
| ''[[16/9]]'', [[ | | [[7/4]], ''[[16/9]]'', [[44/25]] | ||
| | | {{UDnote|step=40}} | ||
|- | |- | ||
| 41 | | 41 | ||
| 1004.082 | | 1004.082 | ||
| [[25/14]] | | [[25/14]] | ||
| | | {{UDnote|step=41}} | ||
|- | |- | ||
| 42 | | 42 | ||
| 1028.571 | | 1028.571 | ||
| [[9/5]], [[20/11]] | | [[9/5]], [[20/11]] | ||
| | | {{UDnote|step=42}} | ||
|- | |- | ||
| 43 | | 43 | ||
| 1053.061 | | 1053.061 | ||
| [[11/6]] | | [[11/6]] | ||
| | | {{UDnote|step=43}} | ||
|- | |- | ||
| 44 | | 44 | ||
| 1077.551 | | 1077.551 | ||
| [[28/15]] | | [[28/15]] | ||
| | | {{UDnote|step=44}} | ||
|- | |- | ||
| 45 | | 45 | ||
| 1102.041 | | 1102.041 | ||
| ''[[15/8]]'', [[40/21]] | | ''[[15/8]]'', [[40/21]] | ||
| | | {{UDnote|step=45}} | ||
|- | |- | ||
| 46 | | 46 | ||
| 1126.531 | | 1126.531 | ||
| [[ | | [[21/11]], [[48/25]], ''[[64/33]]'' | ||
| | | {{UDnote|step=46}} | ||
|- | |- | ||
| 47 | | 47 | ||
| 1151.020 | | 1151.020 | ||
| ''[[ | | ''[[27/14]]'', [[35/18]], ''[[96/49]]'', ''[[160/81]]'' | ||
| | | {{UDnote|step=47}} | ||
|- | |- | ||
| 48 | | 48 | ||
| 1175.510 | | 1175.510 | ||
| [[49/25]] | | [[49/25]] | ||
| | | {{UDnote|step=48}} | ||
|- | |- | ||
| 49 | | 49 | ||
| 1200.000 | | 1200.000 | ||
| [[2/1]] | | [[2/1]] | ||
| | | {{UDnote|step=49}} | ||
|} | |} | ||
<nowiki />* Based on 49edo's 11-limit patent val {{val| 49 78 114 138 170 }} mapping | |||
== Notation == | |||
=== Ups and downs notation === | |||
49edo can be notated using [[ups and downs notation|ups and downs]]. Trup is equivalent to quudsharp, trudsharp is equivalent to quup, etc. | |||
{{Ups and downs sharpness}} | |||
Alternatively, sharps and flats with arrows borrowed from [[Helmholtz–Ellis notation]] can be used: | |||
{{Sharpness-sharp7}} | |||
=== Sagittal notation === | |||
==== Evo flavor ==== | |||
<imagemap> | |||
File:49-EDO_Evo_Sagittal.svg | |||
desc none | |||
rect 80 0 300 50 [[Sagittal_notation]] | |||
rect 300 0 589 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] | |||
rect 20 80 140 106 [[513/512]] | |||
rect 140 80 240 106 [[81/80]] | |||
rect 240 80 360 106 [[33/32]] | |||
default [[File:49-EDO_Evo_Sagittal.svg]] | |||
</imagemap> | |||
==== Revo flavor ==== | |||
<imagemap> | |||
File:49-EDO_Revo_Sagittal.svg | |||
desc none | |||
rect 80 0 300 50 [[Sagittal_notation]] | |||
rect 300 0 534 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] | |||
rect 20 80 140 106 [[513/512]] | |||
rect 140 80 240 106 [[81/80]] | |||
rect 240 80 360 106 [[33/32]] | |||
default [[File:49-EDO_Revo_Sagittal.svg]] | |||
</imagemap> | |||
== Approximation to JI == | |||
[[File:49ed2.svg|250px|thumb|right|alt=alt : Your browser has no SVG support.|Selected 19-limit intervals approximated in 49edo]] | |||
=== Interval mappings === | |||
{{Q-odd-limit intervals|49}} | |||
{{Q-odd-limit intervals|49.1|apx=val|header=none|tag=none|title=15-odd-limit intervals by 49f val mapping}} | |||
=== Zeta peaks === | |||
The strongest [[The Riemann zeta function and tuning|local zeta peak]] around 49edo is its second closest, 49.141 edo. One step is 24.419 cents, and two steps, 48.839 cents, is a good generator for [[Triple BP]]. | |||
== Approximation to irrational intervals == | |||
=== Acoustic ϕ and ϕ<sup>ϕ<sup>−1</sup></sup> === | |||
49edo has a very close approximation of both [[acoustic phi]] and [[phith root of phi|ϕ<sup>ϕ<sup>-1</sup></sup>]], a kind of logarithmic phi that divides [[acoustic phi]] logarithmically by phi ([[Logarithmic phi|instead of dividing 2/1]]). | |||
== | The [[phith root of phi|phith root of phi (ϕ<sup>ϕ<sup>-1</sup></sup>)]] has interesting applications as [[Metallic MOS]], and in particular the fractal-like possibilities of self-similar subdivision of musical scales within [[acoustic phi]]. | ||
{| class="wikitable center-all" | |||
|+ style="font-size: 105%;" | Direct approximation | |||
|- | |||
! Interval | |||
! Error (abs, [[Cent|¢]]) | |||
! #\49 | |||
|- | |||
| {{nowrap|ϕ / ϕ<sup>ϕ<sup>−1</sup></sup> {{=}} ϕ<sup>(2 − ϕ)</sup>}} | |||
| 0.155 | |||
| 13 | |||
|- | |||
| ϕ | |||
| −0.437 | |||
| 34 | |||
|- | |||
| ϕ<sup>ϕ<sup>−1</sup></sup> | |||
| −0.592 | |||
| 21 | |||
|} | |||
Not until [[592edo|592]] do we find a better edo in terms of relative error on these two intervals (but whose edo-steps upon which these intervals are mapped are not based on the Fibonacci sequence, unlike 49edo). | |||
=== Music === | |||
* [https://www.youtube.com/watch?v=vZyAm-D3nlk&ab_channel=Sevish Sevish - Star Nursery] uses a scale based on [[acoustic phi]] and ϕ<sup>ϕ<sup>−1</sup></sup>. 49edo provides a suitable approximation for this scale with the mode: 5 3 5 5 3 5 3 5 | |||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
! rowspan="2" | Subgroup | |- | ||
! rowspan="2" | [[Subgroup]] | |||
! rowspan="2" | [[Comma list]] | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
| Line 283: | Line 359: | ||
| 2.3 | | 2.3 | ||
| {{monzo| 78 -49 }} | | {{monzo| 78 -49 }} | ||
| | | {{mapping| 49 78 }} | ||
| | | −2.60 | ||
| 2.60 | | 2.60 | ||
| 10.62 | | 10.62 | ||
| Line 290: | Line 366: | ||
| 2.3.5 | | 2.3.5 | ||
| 15625/15552, 20480/19683 | | 15625/15552, 20480/19683 | ||
| | | {{mapping| 49 78 114 }} | ||
| | | −2.53 | ||
| 2.12 | | 2.12 | ||
| 8.69 | | 8.69 | ||
| Line 297: | Line 373: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 64/63, 245/243, 3125/3087 | | 64/63, 245/243, 3125/3087 | ||
| | | {{mapping| 49 78 114 138 }} | ||
| | | −2.85 | ||
| 1.92 | | 1.92 | ||
| 7.87 | | 7.87 | ||
| Line 304: | Line 380: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 64/63, 100/99, 245/243, 1331/1323 | | 64/63, 100/99, 245/243, 1331/1323 | ||
| | | {{mapping| 49 78 114 138 170 }} | ||
| | | −2.97 | ||
| 1.74 | | 1.74 | ||
| 7.11 | | 7.11 | ||
| Line 311: | Line 387: | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left- | {| class="wikitable center-all left-5" | ||
|+ | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
! Periods<br>per | |- | ||
! Generator | ! Periods<br>per 8ve | ||
! | ! Generator* | ||
! Cents* | |||
! Associated<br>ratio* | |||
! Temperament | |||
|- | |- | ||
| 1 | | 1 | ||
| 1\49 | | 1\49 | ||
| 24.5 | |||
| 99/98 | |||
| [[Sengagen]] | | [[Sengagen]] | ||
|- | |- | ||
| 1 | | 1 | ||
| 4\49 | | 4\49 | ||
| 98.0 | |||
| 16/15 | |||
| [[Passion]] | | [[Passion]] | ||
|- | |- | ||
| 1 | | 1 | ||
| 6\49 | | 6\49 | ||
| 146.9 | |||
| 12/11 | |||
| [[Bohpier]] | | [[Bohpier]] | ||
|- | |- | ||
| 1 | | 1 | ||
| 8\49 | | 8\49 | ||
| 195.9 | |||
| 28/25 | |||
| [[Didacus]] | | [[Didacus]] | ||
|- | |- | ||
| 1 | | 1 | ||
| 11\49 | | 11\49 | ||
| 269.4 | |||
| 7/6 | |||
| [[Infraorwell]] | | [[Infraorwell]] | ||
|- | |- | ||
| 1 | | 1 | ||
| 12\49 | | 12\49 | ||
| 293.9 | |||
| 25/21 | |||
| [[Kleiboh]] | | [[Kleiboh]] | ||
|- | |- | ||
| 1 | | 1 | ||
| 13\49 | | 13\49 | ||
| | | 318.4 | ||
| 6/5 | |||
| [[Catalan]] | |||
|- | |- | ||
| 1 | | 1 | ||
| 16\49 | | 16\49 | ||
| 391.8 | |||
| 5/4 | |||
| [[Magus]] | | [[Magus]] | ||
|- | |- | ||
| 1 | | 1 | ||
| 17\49 | | 17\49 | ||
| 416.3 | |||
| 14/11 | |||
| [[Sqrtphi]] | | [[Sqrtphi]] | ||
|- | |- | ||
| 1 | | 1 | ||
| 18\49 | | 18\49 | ||
| 440.8 | |||
| 9/7 | |||
| [[Clyde]] | | [[Clyde]] | ||
|- | |- | ||
| 1 | | 1 | ||
| 19\49 | | 19\49 | ||
| 465.3 | |||
| 55/36 | |||
| [[Semisept]] | | [[Semisept]] | ||
|- | |- | ||
| 1 | | 1 | ||
| 20\49 | | 20\49 | ||
| | | 489.8 | ||
| 4/3 | |||
| [[Superpyth]] | |||
|- | |- | ||
| 7 | | rowspan="2" | 7 | ||
| 20\49 | | rowspan="2" | 20\49<br />(1\49) | ||
| [[Sevond]]<br>[[Seville]] | | rowspan="2" | 489.8<br />(24.5) | ||
| 4/3<br />(250/243) | |||
| [[Sevond]] (49) | |||
|- | |||
| 4/3<br />(25/24) | |||
| style="text-align: left;" | [[Seville]] (49c) | |||
|} | |} | ||
<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | |||
== Octave stretch or compression == | |||
49edo's [[prime]]s 3, 5, 7 and 11 are all tuned sharp, so 49edo can benefit from [[octave shrinking]]. Some compressed-octave tunings of 49edo include (least to most compression): [[ed12|176ed12]], [[ed5|114ed5]], [[zpi|233zpi]], [[ed6|127ed6]], [[ed7|138ed7]] and [[78edt]]. | |||
=== Nonoctave temperament === | |||
The TE-optimized [[Triple BP|triple Bohlen–Pierce scale]] is obtained by taking every second degree of 49edo with the octave compressed by 3.861 cents to 1196.139 cents. It realizes the Tenney–Euclidean regular temperament on the 3.5.7.11.13 subgroup mapped as [⟨78 114 138 170 182]]. Under this compression, the primes map to the 49fgh val in the 23-limit. | |||
== Scales == | |||
=== MOS scales === | |||
{{main|List of MOS scales in 49edo}} | |||
* Bohpier[8]: 6 6 6 6 7 6 6 6 | |||
* Catalan[7]: 3 10 3 10 3 10 10 (vaugely diminished-like) | |||
* Catalan[11]: 3 7 3 3 7 3 3 7 3 3 7 | |||
* Catalan[19]: 3 3 1 3 3 3 3 1 3 3 3 1 3 3 3 3 1 3 3 | |||
* Clyde[5]: 5 13 5 13 13 (mysterious, adventurous) | |||
* Didacus[6]: 8 8 8 8 8 9 (like the whole tone scale) | |||
* Didacus[13]: 1 7 1 7 1 7 1 7 1 7 1 7 1 | |||
* Infraorwell[5]: 11 11 5 11 11 | |||
* Infraorwell[22]: 1 4 1 4 1 1 4 1 4 1 1 4 1 4 1 4 1 1 4 1 4 1 | |||
* Kleiboh[5]: 12 12 12 12 1 | |||
* Kleiboh[13]: 1 10 1 1 10 1 1 1 10 1 1 10 1 | |||
* Magus[7]: 1 15 1 15 1 15 1 (vaguely augmented-like) | |||
* Passion[12]: 4 4 4 4 4 4 5 4 4 4 4 4 (like [[12edo]]) | |||
* Passion[23]: 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 | |||
* Sevond[21]/Seville[21]: 1 5 1 1 5 1 1 5 1 1 5 1 1 5 1 1 5 1 1 5 1 | |||
* Superpyth[5]: 11 9 9 11 9 (in between minor pentatonic and [[equipentatonic]]) | |||
* Superpyth[7]: 9 2 9 9 9 2 9 (Dorian mode; rotate for other modes) | |||
* Superpyth[12]: 2 7 2 7 2 2 7 2 7 2 7 2 (same melodic shape as [[12edo]] but much more [[xenharmonic]] harmonies) | |||
* Superpyth[27]: 2 2 1 2 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 2 1 2 2 | |||
=== Other scales === | |||
* [[6ed7/3#6ed7/3+7edo scale|The 6ed7/3+7edo scale]] ''(non-octave-repeating)'' | |||
== Instruments == | |||
=== Lumatone === | |||
* [[Lumatone mapping for 49edo]] | |||
=== Skip fretting === | |||
'''Skip fretting system 49 3 7''' is a [[skip fretting]] system for [[49edo]]. All examples are for 5-string bass. | |||
; Harmonics | |||
1/1: string 2 open | |||
2/1: not easily accessible | |||
3/2: string 4 fret 5 and string 1 fret 12 | |||
5/4: string 3 fret 3 | |||
7/4: string 3 fret 11 | |||
11/8: string 3 fret 5 | |||
== Music == | |||
=== Modern renderings === | |||
; {{W|The Cure}} | |||
* [https://www.youtube.com/watch?v=GHslu-ZWspk ''Boys Don't Cry''] (1979) – Lumatone cover by [[YoVariable]] (2025) | |||
=== 21st century === | |||
; [[Bryan Deister]] | |||
* [https://www.youtube.com/watch?v=7pK-JcIrd18 Deltarune – ''Man'' (cover)] (2023) | |||
* [https://www.youtube.com/shorts/V8t7MyP2Nuo ''microtonal improv in 49edo''] (2024) | |||
* [https://www.youtube.com/shorts/zb1Z6o-Uvuw ''weathergirl - FLAVOR FOLEY (microtonal cover in 49edo)''] (2025) | |||
* [https://www.youtube.com/shorts/73PfAAWubVs ''I'm Your Captain Now (The Ancients) - The Recovery System (microtonal cover in 49edo)''] (2026) {{todo|research|comment=Identify the original composers.}} | |||
* [https://www.youtube.com/shorts/34w7euOF-Ss ''49edo improv''] (2026) | |||
* [https://www.youtube.com/shorts/_yNrDI6nS1I ''49edo riff''] (2026) | |||
* [https://www.youtube.com/shorts/BcBtD3nuEQs ''49edo groove''] (2026) | |||
* [https://www.youtube.com/shorts/VmUIxWb8NCY ''49edo prelude''] (2026) | |||
; [[Mercury Amalgam]] | |||
* [https://www.youtube.com/watch?v=c_kzhcMMHWM&pp=ygUFNDllZG8%3D ''Wrong Generation''] (2022 demo version) | |||
; [[Cam Taylor]] | |||
* [https://www.youtube.com/watch?v=fns6688IRpg ''49-equal: 7-equal meets superpyth''] (2023) | |||
[[Category:Archytas]] | [[Category:Archytas]] | ||
[[Category:Ares]] | [[Category:Ares]] | ||
[[Category:Listen]] | |||
[[Category:Superpyth]] | |||