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A '''substitute harmonic'''{{idiosyncratic}} is a more complex [[harmonic]] which is used to substitute for a simpler one.  
A '''substitute harmonic'''{{idiosyncratic}} is a more complex [[harmonic]] which is used to substitute for a simpler one.  


For example, you could substitute the 3rd harmonic for the very similar 769th harmonic. By doing this, you could convert a 2.3.5 [[subgroup temperament]] into a 2.769.5 subgroup temperament. Or, you could convert a 3.5.7 [[combination product set]] into a 769.5.7 combination product set. This could allow for a whole array of subtly different harmonic flavours of existing tunings, while preserving their basic melodic and harmonic structure.
For example, you could substitute the 3rd harmonic out for the 769th harmonic, whose [[octave reduction]] is very close to the 3rd harmonic's. By doing this, you could convert a 2.3.5 [[subgroup temperament]] into a 2.5.769 subgroup temperament. Or, you could convert a 3.5.7 [[combination product set]] into a 5.7.769 combination product set.


You could also substitute a simpler harmonic ''n'' for two more complex harmonics, to make a dual-substitute-n temperament{{idiosyncratic}}, with similar aims (but different tactics) to a [[dual-fifth]] temperament.
You could also substitute a simpler harmonic ''n'' in a dual-n temperament for two more complex harmonics, to make a '''dual-substitute-n temperament'''{{idiosyncratic}}. For example, you could convert a [[Dual-fifth temperaments|2.3-.3+.5 subgroup temperament]] into a 2.5.767.769 subgroup temperament.


= List of substitute harmonics =
The use of substitute harmonics is one kind of [[fudging]].


== Substitutes for the 2nd harmonic (1200) ==
== List of substitute harmonics ==
This list is not exhaustive.
Each harmonic is given in octave-reduced [[cent]]s. This list is not exhaustive.
* 255th harmonic
 
* 2041st harmonic
=== Substitutes for the 2nd harmonic (1200) ===
* 1021st harmonic
* the 1017th harmonic (~1188)
* 2043rd harmonic
* the 509th harmonic (~1190)
* 511th harmonic
* the 1019th harmonic (~1192)
* 2045th harmonic
* the 255th harmonic (~1193)
* 1023rd harmonic
* the 1021st harmonic (~1195)
* 2047th harmonic
* the 511th harmonic (~1197)
* 1025th harmonic
* the 1023rd harmonic (~1198)
* 513th harmonic
* the 1025th harmonic (~2)
* 1027th harmonic
* the 513th harmonic (~3)
* 257th harmonic
* the 1027th harmonic (~5)
* 1029th harmonic
* the 257th harmonic (~7)
* 515th harmonic
* the 1029th harmonic (~8)
* 1031st harmonic
* the 515th harmonic (~10)
* 129th harmonic
* the 1031st harmonic (~12)
 
=== Substitutes for the 3rd harmonic (~702) ===
* the 381st harmonic (~688)
* the 763rd harmonic (~691)
* the 191st harmonic (~693)
* the 765th harmonic (~695)
* the 383rd harmonic (~697)
* the 767th harmonic (~700)
* the 769th harmonic (~704)
* the 385th harmonic (~706)
* the 771st harmonic (~709)
* the 193rd harmonic (~711)
* the 773rd harmonic (~713)
* the 387th harmonic (~715)
 
=== Substitutes for the 5th harmonic (~386) ===
* the 317th harmonic (~370)
* the 635th harmonic (~373)
* the 159th harmonic (~375)
* the 637th harmonic (~378)
* the 319th harmonic (~381)
* the 639th harmonic (~384)
* the 641st harmonic (~389)
* the 321st harmonic (~392)
* the 643rd harmonic (~394)
* the 161st harmonic (~397)
* the 645th harmonic (~400)
* the 323rd harmonic (~402)
 
=== Substitutes for the 7th harmonic (~969) ===
* the 111th harmonic (~953)
* the 889th harmonic (~955)
* the 445th harmonic (~957)
* the 891st harmonic (~959)
* the 223rd harmonic (~961)
* the 893rd harmonic (~963)
* the 447th harmonic (~965)
* the 895th harmonic (~967)
* the 897th harmonic (~971)
* the 449th harmonic (~973)
* the 899th harmonic (~975)
* the 225th harmonic (~977)
* the 901st harmonic (~978)
* the 451st harmonic (~980)
* the 903rd harmonic (~982)
* the 113th harmonic (~984)
 
=== Substitutes for the 11th harmonic (~551) ===
* the 349th harmonic (~537)
* the 699th harmonic (~539)
* the 175th harmonic (~541)
* the 701st harmonic (~544)
* the 351st harmonic (~546)
* the 703rd harmonic (~549)
* the 705th harmonic (~554)
* the 353rd harmonic (~556)
* the 707th harmonic (~559)
* the 177th harmonic (~561)
* the 709th harmonic (~564)
* the 355th harmonic (~566)
 
== Temperaments using substitute harmonics ==
 
===...with mostly sharp substitutes===
Name these after sharp weapons. If they closely resemble another temperament, reference that temperament in the name.
 
==== Daggerminished ====
Same melodic shape as [[diminished]]. Uses sharper substitutes for prime 3, 5, 7 and 11.
 
 
Subgroup
 
 
2.113.161.177.193
 
 
Equal Temperament Mappings
 
2 113 161 177 193
[ ⟨ 8 55 59 60 61 ]
⟨ 12 82 88 90 91 ] ⟩
 
 
Reduced Mapping
 
2 113 161 177 193
[ ⟨ 4 28 30 30 31 ]
⟨ 0 -1 -1 0 -1 ] ⟩
 
 
POTE Generator Tunings (cents)
 
⟨300.0000, 185.4640]
 
 
POTE Step Tunings (cents)
 
⟨43.60795, 70.92803]
 
 
POTE Tuning Map (cents)
 
⟨1200.000, 8214.536, 8814.536, 9000.000, 9114.536]
 
 
POTE Mistunings (cents)
 
⟨0.000, 30.321, 17.436, 38.873, 3.588]
 
 
Unison Vectors
 
*[7, -1, 1, -1, 0⟩ (20608:20001)
*[-1, -2, 2, 0, 0⟩ (25921:25538)
*[8, 1, -1, -1, 0⟩ (28928:28497)
*[15, 0, 0, -2, 0⟩ (32768:31329)
*[-1, -1, -1, 0, 2⟩ (37249:36386)
*[6, -2, 0, -1, 2⟩ (2383936:2260113)
 
 
==== Pajaraxe ====
Same melodic shape as [[pajara]]. Uses sharper substitutes for prime 3, 5, 7 and 11.
 
 
Subgroup
 
2.113.161.177.193
 
 
Equal Temperament Mappings
 
2 113 161 177 193
[ ⟨ 22 150 161 164 167 ]
⟨ 12 82 88 90 91 ] ⟩
 
 
Reduced Mapping
 
2 113 161 177 193
[ ⟨ 2 14 15 16 15 ]
⟨ 0 -2 -2 -6 1 ] ⟩
 
 
POTE Generator Tunings (cents)
 
⟨600.0000, 106.8797]
 
 
POTE Step Tunings (cents)
 
⟨41.27832, 24.32309]
 
 
POTE Tuning Map (cents)
 
⟨1200.000, 8186.241, 8786.241, 8958.722, 9106.880]
 
 
POTE Mistunings (cents)
 
⟨0.000, 2.026, -10.860, -2.405, -4.069]
 
 
Unison Vectors
 
*[-1, -2, 2, 0, 0⟩ (25921:25538)
*[13, -3, 0, 1, 0⟩ (1449984:1442897)
*[-14, 1, 2, -1, 0⟩ (2929073:2899968)
*[-22, 1, 0, 0, 2⟩ (4209137:4194304)
*[-9, -2, 0, 1, 2⟩ (6593073:6537728)
*[8, 0, 2, -1, -2⟩ (6635776:6593073)
 
 
==== Narrowed compton ====
These temperaments are like [[compton]] but with a smaller generator. They reduce the incidence of [[Wolf interval|wolf]] fifths, especially in the smaller 24- and 36-tone [[MOS scale]]s, and allow the melodic shape of [[compton]] to be used in tunings (especially [[edo]]s) that might not otherwise support it.
 
These temperaments work by replacing the 5th harmonic with a slightly sharper substitute harmonic. These temperaments do not follow the naming conventions of other sharp-substitute temperaments. Instead these should be named using words that end with “com” or “come”.
 
 
===== Dotcom =====
Subgroup: 2.3.43
 
Recommended ETs: '''[[144edo]]''', [[156edo]], [[168edo]]
 
 
Equal Temperament Mappings
 
2 3 43
[ ⟨ 12 19 65 ]
⟨ 48 76 261 ] ⟩
 
Reduced Mapping
 
2 3 43
[ ⟨ 12 19 65 ]
⟨ 0 0 1 ] ⟩
 
POTE Generator Tunings (cents)
 
⟨100.0000, 8.1729]
 
POTE Step Tunings (cents)
 
⟨67.30854, 8.17286]
 
POTE Tuning Map (cents)
 
⟨1200.000, 1900.000, 6508.173]
 
POTE Mistunings (cents)
 
⟨0.000, -1.955, -3.345]
 
 
Complexity 1.041959
 
Adjusted Error 2.733862 cents
 
TE Error 0.503820 cents/octave
 
Unison Vector
 
[-19, 12, 0⟩ (531441:524288)
 
 
===== Sitcom =====
Subgroup: 2.3.85
 
Recommended ETs: '''[[96edo]]'''
 
 
Equal Temperament Mappings
 
2 3 85
[ ⟨ 12 19 77 ]
⟨ 48 76 307 ] ⟩
 
Reduced Mapping
 
2 3 85
[ ⟨ 12 19 77 ]
⟨ 0 0 -1 ] ⟩
 
POTE Generator Tunings (cents)
 
⟨100.0000, 12.6817]
 
POTE Step Tunings (cents)
 
⟨49.27306, 12.68173]
 
POTE Tuning Map (cents)
 
⟨1200.000, 1900.000, 7687.318]
 
POTE Mistunings (cents)
 
⟨0.000, -1.955, -3.951]
 
 
Complexity 0.882135
 
Adjusted Error 3.229180 cents
 
TE Error 0.503820 cents/octave
 
Unison Vector
 
[-19, 12, 0⟩ (531441:524288)
 
 
===== Romcom =====
Subgroup: 2.3.91
 
Recommended ETs: '''[[228edo]]''', [[216edo]], [[240edo]]
 
 
Equal Temperament Mappings
 
2 3 91
[ ⟨ 12 19 78 ]
⟨ 36 57 235 ] ⟩
 
Reduced Mapping
 
2 3 91
[ ⟨ 12 19 78 ]
⟨ 0 0 1 ] ⟩
 
POTE Generator Tunings (cents)
 
⟨100.0000, 5.3421]
 
POTE Step Tunings (cents)
 
⟨83.97384, 5.34205]
 
POTE Tuning Map (cents)
 
⟨1200.000, 1900.000, 7805.342]
 
POTE Mistunings (cents)
 
⟨0.000, -1.955, -4.012]
 
 
Complexity 0.868796
 
Adjusted Error 3.278758 cents
 
TE Error 0.503820 cents/octave
 
Unison Vector
 
[-19, 12, 0⟩ (531441:524288)
 
 
===== Income =====
Subgroup: 2.3.135
 
Recommended ETs: '''[[96edo]]'''
 
 
Equal Temperament Mappings
 
2 3 135
[ ⟨ 12 19 85 ]
⟨ 48 76 339 ] ⟩
 
Reduced Mapping
 
2 3 135
[ ⟨ 12 19 85 ]
⟨ 0 0 -1 ] ⟩
 
POTE Generator Tunings (cents)
 
⟨100.0000, 12.1836]
 
POTE Step Tunings (cents)
 
⟨51.26579, 12.18355]
 
POTE Tuning Map (cents)
 
⟨1200.000, 1900.000, 8487.816]
 
POTE Mistunings (cents)
 
⟨0.000, -1.955, -4.362]
 
 
Complexity 0.798940
 
Adjusted Error 3.565442 cents
 
TE Error 0.503820 cents/octave
 
Unison Vector
 
[-19, 12, 0⟩ (531441:524288)
 
 
===== Outcome =====
Subgroup: 2.3.143
 
Recommended ETs: '''[[96edo]]'''
 
 
Equal Temperament Mappings
 
2 3 143
[ ⟨ 12 19 86 ]
⟨ 48 76 343 ] ⟩
 
Reduced Mapping
 
2 3 143
[ ⟨ 12 19 86 ]
⟨ 0 0 -1 ] ⟩
 
POTE Generator Tunings (cents)
 
⟨100.0000, 12.5679]
 
POTE Step Tunings (cents)
 
⟨49.72855, 12.56786]
 
POTE Tuning Map (cents)
 
⟨1200.000, 1900.000, 8587.432]
 
POTE Mistunings (cents)
 
⟨-0.000, -1.955, -4.413]
 
 
Complexity 0.789672
 
Adjusted Error 3.607288 cents
 
TE Error 0.503820 cents/octave
 
Unison Vector
 
[-19, 12, 0⟩ (531441:524288)
 
 
===== Telecom =====
Subgroup: 2.3.191
 
Recommended ETs: '''[[108edo]]'''
 
 
Equal Temperament Mappings
 
2 3 191
[ ⟨ 12 19 91 ]
⟨ 48 76 363 ] ⟩
 
Reduced Mapping
 
2 3 191
[ ⟨ 12 19 91 ]
⟨ 0 0 -1 ] ⟩
 
POTE Generator Tunings (cents)
 
⟨100.0000, 11.7563]
 
POTE Step Tunings (cents)
 
⟨52.97495, 11.75626]
 
POTE Tuning Map (cents)
 
⟨1200.000, 1900.000, 9088.244]
 
POTE Mistunings (cents)
 
⟨0.000, -1.955, -4.671]
 
 
Complexity 0.746156
 
Adjusted Error 3.817661 cents
 
TE Error 0.503820 cents/octave
 
Unison Vector
 
[-19, 12, 0⟩ (531441:524288)
 
 
===== Intercom =====
Subgroup: 2.3.193
 
Recommended ETs: '''[[192edo]]''', [[180edo]], [[204edo]]
 
 
Equal Temperament Mappings
 
2 3 193
[ ⟨ 12 19 91 ]
⟨ 36 57 274 ] ⟩
 
Reduced Mapping
 
2 3 193
[ ⟨ 12 19 91 ]
⟨ 0 0 1 ] ⟩
 
POTE Generator Tunings (cents)
 
⟨100.0000, 6.2683]
 
POTE Step Tunings (cents)
 
⟨81.19502, 6.26833]
 
POTE Tuning Map (cents)
 
⟨1200.000, 1900.000, 9106.268]
 
POTE Mistunings (cents)
 
⟨-0.000, -1.955, -4.680]
 
 
Complexity 0.744680
 
Adjusted Error 3.825233 cents
 
TE Error 0.503820 cents/octave
 
Unison Vector
 
[-19, 12, 0⟩ (531441:524288)
 
 
===== Newcome =====
Subgroup: 2.3.217
 
Recommended ETs: '''[[132edo]]''', [[120edo]]
 
 
Equal Temperament Mappings
 
2 3 217
[ ⟨ 12 19 93 ]
⟨ 36 57 280 ] ⟩
 
Reduced Mapping
 
2 3 217
[ ⟨ 12 19 93 ]
⟨ 0 0 1 ] ⟩
 
POTE Generator Tunings (cents)
 
⟨100.0000, 9.0771]
 
POTE Step Tunings (cents)
 
⟨72.76862, 9.07713]
 
POTE Tuning Map (cents)
 
⟨1200.000, 1900.000, 9309.077]
 
POTE Mistunings (cents)
 
⟨0.000, -1.955, -4.784]
 
 
Complexity 0.728456
 
Adjusted Error 3.910426 cents
 
TE Error 0.503820 cents/octave
 
Unison Vector
 
[-19, 12, 0⟩ (531441:524288)
 
 
===== Satcom =====
Subgroup: 2.3.227
 
Recommended ETs: '''[[96edo]]'''
 
 
Equal Temperament Mappings
 
2 3 227
[ ⟨ 12 19 94 ]
⟨ 48 76 375 ] ⟩
 
Reduced Mapping
 
2 3 227
[ ⟨ 12 19 94 ]
⟨ 0 0 -1 ] ⟩
 
POTE Generator Tunings (cents)
 
⟨100.0000, 12.9662]
 
POTE Step Tunings (cents)
 
⟨48.13507, 12.96623]
 
POTE Tuning Map (cents)
 
⟨1200.000, 1900.000, 9387.034]
 
POTE Mistunings (cents)
 
⟨0.000, -1.955, -4.824]
 
 
Complexity 0.722406
 
Adjusted Error 3.943173 cents
 
TE Error 0.503820 cents/octave
 
Unison Vector
 
[-19, 12, 0⟩ (531441:524288)
 
 
===== Minicom =====
Subgroup: 2.3.245
 
Recommended ETs: '''[[252edo]]''', [[264edo]], [[276edo]], [[288edo]], [[300edo]]
 
 
Equal Temperament Mappings
 
2 3 243
[ ⟨ 12 19 95 ]
⟨ 24 38 191 ] ⟩
 
Reduced Mapping
 
2 3 243
[ ⟨ 12 19 95 ]
⟨ 0 0 1 ] ⟩
 
POTE Generator Tunings (cents)
 
⟨100.0000, 4.8900]
 
POTE Step Tunings (cents)
 
⟨90.21997, 4.89002]
 
POTE Tuning Map (cents)
 
⟨1200.000, 1900.000, 9504.890]
 
POTE Mistunings (cents)
 
⟨0.000, -1.955, -4.885]
 
 
Complexity 0.713449
 
Adjusted Error 3.992680 cents
 
TE Error 0.503820 cents/octave
 
Unison Vector
 
[-19, 12, 0⟩ (531441:524288)
 
 
===== Glycome =====
Subgroup: 2.3.255
 
Recommended ETs: '''[[108edo]]'''
 
 
Equal Temperament Mappings
 
2 3 255
[ ⟨ 12 19 96 ]
⟨ 48 76 383 ] ⟩
 
Reduced Mapping
 
2 3 255
[ ⟨ 12 19 96 ]
⟨ 0 0 -1 ] ⟩
 
POTE Generator Tunings (cents)
 
⟨100.0000, 11.7037]
 
POTE Step Tunings (cents)
 
⟨53.18508, 11.70373]
 
POTE Tuning Map (cents)
 
⟨1200.000, 1900.000, 9588.296]
 
POTE Mistunings (cents)
 
⟨0.000, -1.955, -4.928]
 
 
Complexity 0.707243
 
Adjusted Error 4.027716 cents
 
TE Error 0.503820 cents/octave
 
Unison Vector
 
[-19, 12, 0⟩ (531441:524288)
 
===...with mostly flat substitutes===
Name these after flat regions like deserts. If they closely resemble another temperament, reference that temperament in the name.
 
 
====Sahara====
Uses flatter substitutes for prime 3, 5, 7 and 11.
 
 
Subgroup
 
2.111.159.175.191


== Substitutes for the 3rd harmonic (~702) ==
Each harmonic is given in octave-reduced [[cent]]s. This list is not exhaustive.
*the 381st harmonic (~688)
*the 763rd harmonic (~691)
*the 191st harmonic (~693)
*the 765th harmonic (~695)
*the 383rd harmonic (~697)
*the 767th harmonic (~700)
*the 769th harmonic (~704)
*the 385th harmonic (~706)
*the 771st harmonic (~709)
*the 193rd harmonic (~711)
*the 773rd harmonic (~713)
*the 387th harmonic (~715)


== Substitutes for the 5th harmonic (~386) ==
Equal Temperament Mappings
Each harmonic is given in octave-reduced cents. This list is not exhaustive.
*the 317th harmonic (~370)
*the 635th harmonic (~373)
*the 159th harmonic (~375)
*the 637th harmonic (~378)
*the 319th harmonic (~381)
*the 639th harmonic (~384)
*the 641st harmonic (~389)
*the 321st harmonic (~392)
*the 643rd harmonic (~394)
*the 161st harmonic (~397)
*the 645th harmonic (~400)
*the 323rd harmonic (~402)


== Substitutes for the 7th harmonic (~969) ==
2 111 159 175 191
Each harmonic is given in octave-reduced cents. This list is not exhaustive.
[ ⟨ 9 61 66 67 68 ]
*the 111th harmonic (~953)
⟨ 19 129 139 142 144 ] ⟩
*the 889th harmonic (~955)
*the 445th harmonic (~957)
*the 891st harmonic (~959)
*the 223rd harmonic (~961)
*the 893rd harmonic (~963)
*the 447th harmonic (~965)
*the 895th harmonic (~967)
*the 897th harmonic (~971)
*the 449th harmonic (~973)
*the 899th harmonic (~975)
*the 225th harmonic (~977)
*the 901st harmonic (~978)
*the 451st harmonic (~980)
*the 903rd harmonic (~982)
*the 113th harmonic (~984)


== Substitutes for the 11th harmonic (~551) ==
Each harmonic is given in octave-reduced cents. This list is not exhaustive.
*the 349th harmonic (~537)
*the 699th harmonic (~539)
*the 175th harmonic (~541)
*the 701st harmonic (~544)
*the 351st harmonic (~546)
*the 703rd harmonic (~549)
*the 705th harmonic (~554)
*the 353rd harmonic (~556)
*the 707th harmonic (~559)
*the 177th harmonic (~561)
*the 709th harmonic (~564)
*the 355th harmonic (~566)


= Dual-substitute-n temperaments =
Reduced Mapping


== Dual-substitute-2 temperaments ==
2 111 159 175 191
[ ⟨ 1 7 7 8 8 ]
⟨ 0 -2 3 -5 -4 ] ⟩


== Dual-substitute-3 temperaments ==


=== 2.5.767.769 subgroup temperaments ===
POTE Generator Tunings (cents)


=== 2.5.383.385 subgroup temperaments ===
⟨1200.0000, 128.1188]


=== 2.5.765.771 subgroup temperaments ===


=== 2.5.191.193 subgroup temperaments ===
POTE Step Tunings (cents)


=== 2.5.7.767.769 subgroup temperaments ===
⟨34.25808, 46.93038]


=== 2.5.7.383.385 subgroup temperaments ===


=== 2.5.7.765.771 subgroup temperaments ===
POTE Tuning Map (cents)


=== 2.5.7.191.193 subgroup temperaments ===
⟨1200.000, 8143.762, 8784.357, 8959.406, 9087.525]


=== 2.5.7.11.767.769 subgroup temperaments ===


=== 2.5.7.11.383.385 subgroup temperaments ===
POTE Mistunings (cents)


=== 2.5.7.11.765.771 subgroup temperaments ===
⟨0.000, -9.537, 8.897, 17.952, -5.390]


=== 2.5.7.11.191.193 subgroup temperaments ===


=== 2.5.11.767.769 subgroup temperaments ===
Unison Vectors


=== 2.5.11.383.385 subgroup temperaments ===
*[-6, 2, 0, 0, -1⟩ (12321:12224)
*[8, 1, -1, -1, 0⟩ (9472:9275)
*[14, -1, -1, -1, 1⟩ (3129344:3088575)
*[-7, 1, 0, -2, 2⟩ (4049391:3920000)
*[2, 3, -1, -1, -1⟩ (1823508:1771525)
*[-15, 0, 1, -1, 2⟩ (5800479:5734400)


=== 2.5.11.765.771 subgroup temperaments ===


=== 2.5.11.191.193 subgroup temperaments ===
'''Sahara Septatonic scale''': A nice subset of Sahara[9]. Try noodling with it in Scale Workshop:


== Dual-substitute-5 temperaments ==
*256.237
*384.356
*512.475
*687.525
*943.762
*1071.881
*1200.


== Dual-substitute-7 temperaments ==


== Dual-substitute-11 temperaments ==
===...with an even mix of both===
Name these after dishes which involve mixing things (e.g. stirfry, salad). If they closely resemble another temperament, reference that temperament in the name.


== See also ==
== See also ==
Scales that make use of substitute harmonics:
* [[Ed255/128]] and [[Ed257/128]]
* [[Intercom scales]]
Other related concepts:
* [[Shadow]]
* [[Subgroup temperaments]]
** [[Equalizer subgroup]]s
** [[Dual-fifth temperaments]]
** [[Half-prime subgroup]]s
* [[List of octave-reduced harmonics]]
* [[List of octave-reduced harmonics]]
* [[Naughty and nice harmonics]]
* [[User:MasonGreen1/Naughty and nice harmonics]]


[[Category:Harmonic series]]
[[Category:Harmonic series]]
[[Category:Octave-reduced harmonics]]
[[Category:Octave-reduced harmonics]]
[[Category:Regular temperament theory]]
[[Category:Combination product sets]]
[[Category:Subgroup temperaments]]
[[Category:Subgroup temperaments]]
[[Category:Temperament collections]]
Retrieved from "https://en.xen.wiki/w/User:BudjarnLambeth/Substitute_harmonic"