49edo: Difference between revisions

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== Theory ==

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 ~~and the {{w|e (mathematical constant)|e-based}} analog of [[Lucy tuning]]~~. It [[tempering out|tempers out]] [[64/63]], [[245/243]], and [[3125/3087]] in the 7-limit, and [[100/99]] and [[1375/1372]] in the 11-limit.

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 ===

=== Subsets and supersets ===

Since 49 factors into ~~{{factorization|49}}~~, 49edo contains [[7edo]] as its only nontrivial subset. 49edo is the first square edo with a [[enfactoring|non-enfactored]] diatonic fifth.

Since 49 factors into primes as 72, 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 ==

{| class="wikitable center-all right-2 left-3"

! #

|-

! #

! Cents

! Approximate ~~Ratios~~*

! Approximate ratios*

! [[Ups and downs notation~~|Ups and Downs Notation~~]]

! [[Ups and downs notation]]

|-

| 0

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| 9

| 220.408

| [[8/7]], ''[[9/8]]''

| [[8/7]], ''[[9/8]]'', [[25/22]]

| {{UDnote|step=9}}

|-

Line 220:

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| 40

| 979.592

| [[7/4]], ''[[16/9]]''

| [[7/4]], ''[[16/9]]'', [[44/25]]

| {{UDnote|step=40}}

|-

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| {{UDnote|step=49}}

|}

<nowiki>*~~</nowiki> based~~ on 49edo's 11-limit patent val {{val| 49 78 114 138 170 }} mapping

<nowiki />* Based on 49edo's 11-limit patent val {{val| 49 78 114 138 170 }} mapping

== Notation ==

=== Ups and downs notation ===

~~Using [[Helmholtz–Ellis notation|Helmholtz–Ellis]] accidentals,~~ 49edo can be notated using [[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.

Alternatively, sharps and flats with arrows borrowed from [[Helmholtz–Ellis notation]] can be used:

=== Sagittal notation ===

==== Evo flavor ====

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 ====

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 ==

=== Interval mappings ===

{{Q-odd-limit intervals|49.1|apx=val|header=none|tag=none|title=15-odd-limit intervals by 49f val mapping}}

=== Zeta peaks ===

Line 284:

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== Approximation to irrational intervals ==

=== Acoustic ϕ and ϕϕ-1 ===

=== Acoustic ϕ and ϕϕ−1 ===

49edo has a very close approximation of both [[acoustic phi]] and ϕϕ-1, a kind of logarithmic phi that divides [[acoustic phi]] logarithmically by phi ([[Logarithmic phi|instead of dividing 2/1]]).

49edo has a very close approximation of both [[acoustic phi]] and [[phith root of phi|ϕϕ-1]], a kind of logarithmic phi that divides [[acoustic phi]] logarithmically by phi ([[Logarithmic phi|instead of dividing 2/1]]).

ϕϕ-1 has interesting applications as [[Metallic MOS]], and in particular the fractal-like possibilities of self-similar subdivision of musical scales within [[acoustic phi]].

The [[phith root of phi|phith root of phi (ϕϕ-1)]] 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"

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! #\49

|-

| ϕ / ϕϕ-1 = ϕ(2-ϕ)

| {{nowrap|ϕ / ϕϕ−1 {{=}} ϕ(2 − ϕ)}}

| 0.155

| 13

|-

| ϕ

| -0.437

| −0.437

| 34

|-

| ϕϕ-1

| ϕϕ−1

| -0.592

| −0.592

| 21

|}

Line 312:

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=== Music ===

* [https://www.youtube.com/watch?v=vZyAm-D3nlk&ab_channel=Sevish Sevish - Star Nursery] uses a scale based on [[acoustic phi]] and ϕϕ-1. 49edo provides a suitable approximation for this scale with the mode: 5 3 5 5 3 5 3 5

* [https://www.youtube.com/watch?v=vZyAm-D3nlk&ab_channel=Sevish Sevish - Star Nursery] uses a scale based on [[acoustic phi]] and ϕϕ−1. 49edo provides a suitable approximation for this scale with the mode: 5 3 5 5 3 5 3 5

== Regular temperament properties ==

{| class="wikitable center-4 center-5 center-6"

|-

! rowspan="2" | [[Subgroup]]

! rowspan="2" | [[Comma list~~|Comma List~~]]

! rowspan="2" | [[Comma list]]

! rowspan="2" | [[Mapping]]

! rowspan="2" | Optimal 8ve ~~Sstretch~~ (¢)

! rowspan="2" | Optimal 8ve stretch (¢)

! colspan="2" | Tuning ~~Error~~

! colspan="2" | Tuning error

|-

! [[TE error|Absolute]] (¢)

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| {{monzo| 78 -49 }}

| {{mapping| 49 78 }}

| ~~−2~~.60

| −2.60

| 2.60

| 10.62

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| 15625/15552, 20480/19683

| {{mapping| 49 78 114 }}

| ~~−2~~.53

| −2.53

| 2.12

| 8.69

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| 64/63, 245/243, 3125/3087

| {{mapping| 49 78 114 138 }}

| ~~−2~~.85

| −2.85

| 1.92

| 7.87

Line 349:

Line 381:

| 64/63, 100/99, 245/243, 1331/1323

| {{mapping| 49 78 114 138 170 }}

| ~~−2~~.97

| −2.97

| 1.74

| 7.11

Line 355:

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=== Rank-2 temperaments ===

{| class="wikitable center-all ~~right-3~~ left-5"

{| class="wikitable center-all left-5"

|+ ~~Rank~~-2 temperaments by ~~generators~~

|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator

|-

! Periods per 8ve

! Generator*

! Cents*

! Associated ~~Ratio~~*

! Associated ratio*

! ~~Temperaments~~

! Temperament

|-

| 1

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|-

| rowspan="2" | 7

| rowspan="2" | 20\49 (1\49)

| rowspan="2" | 20\49 (1\49)

| rowspan="2" | 489.8 (24.5)

| rowspan="2" | 489.8 (24.5)

| 4/3 (250/243)

| 4/3 (250/243)

| [[Sevond]] (49)

|-

| 4/3 (25/24)

| 4/3 (25/24)

| style="text-align: left" | [[Seville]] (49c)

| style="text-align: left;" | [[Seville]] (49c)

|}

<nowiki>*~~</nowiki>~~ [[Normal ~~lists~~|~~octave~~-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~|minimal form]] in parentheses if it is ~~distinct~~

<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 ===

* 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 ===

* [[Lumatone mapping for 49edo]]

~~See~~ [[~~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 ~~(Demo, January 2022)~~''] (~~2023~~)

* [https://www.youtube.com/watch?v=c_kzhcMMHWM&pp=ygUFNDllZG8%3D ''Wrong Generation''] (2022 demo version)

; [[~~Bryan Deister~~]]

; [[Cam Taylor]]

* [https://www.youtube.com/watch?v=~~7pK~~-~~JcIrd18 Deltarune~~ - ''~~Man'' (cover)~~] (2023)

* [https://www.youtube.com/watch?v=fns6688IRpg ''49-equal: 7-equal meets superpyth''] (2023)

~~[[Category:Superpyth]]~~

[[Category:Archytas]]

[[Category:Ares]]

[[Category:Listen]]

[[Category:Superpyth]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|49}}
+{{ED intro}}
 == Theory ==
-edo 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 and the {{w|e (mathematical constant)|e-based}} analog of [[Lucy tuning]]. It [[tempering out|tempers out]] [[64/63]], [[245/243]], and [[3125/3087]] in the 7-limit, and [[100/99]] and [[1375/1372]] in the 11-limit.
+edo 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|127|6|1|intervals=prime}}
+{{Harmonics in equal|49}}
 === Subsets and supersets ===
-Since 49 factors into {{factorization|49}}, 49edo contains [[7edo]] as its only nontrivial subset. 49edo is the first square edo with a [[enfactoring|non-enfactored]] diatonic fifth.
+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 ==
 {| class="wikitable center-all right-2 left-3"
-! #
+|-
+! &#35;
 ! Cents
-! Approximate Ratios*
+! Approximate ratios*
-! [[Ups and downs notation|Ups and Downs Notation]]
+! [[Ups and downs notation]]
 |-
 | 0
@@ Line 65: / Line 66: @@
 | 9
 | 220.408
-| [[8/7]], ''[[9/8]]''
+| [[8/7]], ''[[9/8]]'', [[25/22]]
 | {{UDnote|step=9}}
 |-
@@ Line 220: / Line 221: @@
 | 40
 | 979.592
-| [[7/4]], ''[[16/9]]''
+| [[7/4]], ''[[16/9]]'', [[44/25]]
 | {{UDnote|step=40}}
 |-
@@ Line 268: / Line 269: @@
 | {{UDnote|step=49}}
 |}
-<nowiki>*</nowiki> based on 49edo's 11-limit patent val {{val| 49 78 114 138 170 }} mapping
+<nowiki />* Based on 49edo's 11-limit patent val {{val| 49 78 114 138 170 }} mapping
 == Notation ==
 === Ups and downs notation ===
-Using [[Helmholtz–Ellis notation|Helmholtz&ndash;Ellis]] accidentals, 49edo can be notated using [[ups and downs notation]]:
+edo 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 ===
@@ Line 284: / Line 315: @@
 == Approximation to irrational intervals ==
-=== Acoustic ϕ and ϕ<sup>ϕ<sup>-1</sup></sup> ===
+=== Acoustic ϕ and ϕ<sup>ϕ<sup>−1</sup></sup> ===
-edo has a very close approximation of both [[acoustic phi]] and 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]]).
+edo 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]]).
-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]].
+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"
@@ Line 296: / Line 327: @@
 ! #\49
 |-
-| ϕ / ϕ<sup>ϕ<sup>-1</sup></sup> = ϕ<sup>(2-ϕ)</sup>
+| {{nowrap|ϕ / ϕ<sup>ϕ<sup>−1</sup></sup> {{=}} ϕ<sup>(2 − ϕ)</sup>}}
 | 0.155
 | 13
 |-
 | ϕ
-| -0.437
+| −0.437
 | 34
 |-
-| ϕ<sup>ϕ<sup>-1</sup></sup>
+| ϕ<sup>ϕ<sup>−1</sup></sup>
-| -0.592
+| −0.592
 | 21
 |}
@@ Line 312: / Line 343: @@
 === 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
+* [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 ==
 {| class="wikitable center-4 center-5 center-6"
+|-
 ! rowspan="2" | [[Subgroup]]
-! rowspan="2" | [[Comma list|Comma List]]
+! rowspan="2" | [[Comma list]]
 ! rowspan="2" | [[Mapping]]
-! rowspan="2" | Optimal<br>8ve Sstretch (¢)
+! rowspan="2" | Optimal<br>8ve stretch (¢)
-! colspan="2" | Tuning Error
+! colspan="2" | Tuning error
 |-
 ! [[TE error|Absolute]] (¢)
@@ Line 328: / Line 360: @@
 | {{monzo| 78 -49 }}
 | {{mapping| 49 78 }}
-| &minus;2.60
+| −2.60
 | 2.60
 | 10.62
@@ Line 335: / Line 367: @@
 | 15625/15552, 20480/19683
 | {{mapping| 49 78 114 }}
-| &minus;2.53
+| −2.53
 | 2.12
 | 8.69
@@ Line 342: / Line 374: @@
 | 64/63, 245/243, 3125/3087
 | {{mapping| 49 78 114 138 }}
-| &minus;2.85
+| −2.85
 | 1.92
 | 7.87
@@ Line 349: / Line 381: @@
 | 64/63, 100/99, 245/243, 1331/1323
 | {{mapping| 49 78 114 138 170 }}
-| &minus;2.97
+| −2.97
 | 1.74
 | 7.11
@@ Line 355: / Line 387: @@
 === Rank-2 temperaments ===
-{| class="wikitable center-all right-3 left-5"
+{| class="wikitable center-all left-5"
-|+ Rank-2 temperaments by generators
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
+|-
 ! Periods<br>per 8ve
 ! Generator*
 ! Cents*
-! Associated<br>Ratio*
+! Associated<br>ratio*
-! Temperaments
+! Temperament
 |-
 | 1
@@ Line 436: / Line 469: @@
 |-
 | rowspan="2" | 7
-| rowspan="2" | 20\49<br>(1\49)
+| rowspan="2" | 20\49<br />(1\49)
-| rowspan="2" | 489.8<br>(24.5)
+| rowspan="2" | 489.8<br />(24.5)
-| 4/3<br>(250/243)
+| 4/3<br />(250/243)
 | [[Sevond]] (49)
 |-
-| 4/3<br>(25/24)
+| 4/3<br />(25/24)
-| style="text-align: left" | [[Seville]] (49c)
+| style="text-align: left;" | [[Seville]] (49c)
 |}
-<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
+<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 ==
+edo'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 ===
+* [[Lumatone mapping for 49edo]]
-See [[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: string 2 open
+/1: not easily accessible
+/2: string 4 fret 5 and string 1 fret 12
+/4: string 3 fret 3
+/4: string 3 fret 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 (Demo, January 2022)''] (2023)
+* [https://www.youtube.com/watch?v=c_kzhcMMHWM&pp=ygUFNDllZG8%3D ''Wrong Generation''] (2022 demo version)
-; [[Bryan Deister]]
+; [[Cam Taylor]]
-* [https://www.youtube.com/watch?v=7pK-JcIrd18 Deltarune - ''Man'' (cover)] (2023)
+* [https://www.youtube.com/watch?v=fns6688IRpg ''49-equal: 7-equal meets superpyth''] (2023)
-[[Category:Superpyth]]
 [[Category:Archytas]]
 [[Category:Ares]]
 [[Category:Listen]]
+[[Category:Superpyth]]