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Between
== Sandbox ==
0.0239167
and
{{Harmonics in cet|33.547|columns=13|intervals=prime}}
0.0239833


{| class="wikitable sortable"
{{Harmonics in cet|33.426|columns=13|intervals=prime}}
|+ style="font-size: 105%;" | List of Octave-Based Fine Measures (Logarithmic)
|-
! Unit Name (Symbol):
! Divisions of Octave
! Prime Factors
! Origin / Significance
|-
| [[Eka]]
| [[16edo|16]]
| 2<sup>4</sup>
| From Sanskrit ''eka'': one, unit; chromatic unit of Armodue 16edo Theory<ref>[http://www.armodue.com/risorse.htm Armodue: le risorse di un nuovo sistema musicale]</ref>.
|-
| [[Normal diesis]]
| [[31edo|31]]
| 31 (prime)
| See the dedicated page.
|-
| [[Méride]]
| [[43edo|43]]
| 43 (prime)
| Proposed by [[Joseph Sauveur]], as 7 heptaméride units<ref name="measure">[http://www.huygens-fokker.org/docs/measures.html Stichting Huygens-Fokker: Logarithmic Interval Measures]</ref><ref>[http://tonalsoft.com/enc/m/meride.aspx Tonalsoft | ''Méride / 43-ed2 / 43-edo / 43-ET / 43-tone equal-temperament'']</ref>.
|-
| [[Holdrian comma]]
| [[53edo|53]]
| 53 (prime)
| See the dedicated page.
|-
| [[Holdrian comma|Mercator’s old comma]]
| [[55edo|55]]
| 5 x 11
| Not to be confused with [[Mercator's comma]].
|-
| [[Decitone]]
| [[60edo|60]]
| 2<sup>2</sup> × 3 × 5
|
|-
| [[Morion]]
| [[72edo|72]]
| 2<sup>3</sup> × 3<sup>2</sup>
| See the dedicated page.
|-
| [[Farab]]
| [[144edo|144]]
| 2<sup>4</sup> × 3<sup>2</sup>
| 1/12 of [[12edo]] semitone; Proposed by [[al-Farabi]] in 10th century<ref name="measure"/><ref>[http://tonalsoft.com/enc/f/farab.aspx Tonalsoft | ''Farab''].</ref>.
|-
| [[Mem]]
| [[205edo|205]]
| 5 × 41
| Unit used by H-Pi Instruments<ref name="measure"/><ref>[http://musictheory.zentral.zone/huntsystem1.html H-Pi Instruments | Hunt Theoretical System]</ref><ref>[http://tonalsoft.com/enc/m/mem.aspx Tonalsoft | ''Mem, 205-edo'']</ref>.
|-
| [[Tredek]]
| [[270edo|270]]
| 2 × 3<sup>3</sup> × 5
| Proposed by [[Joseph Monzo]] (2013)<ref>[http://tonalsoft.com/enc/t/tredek.aspx Tonalsoft | ''Tredek, 270-edo'']</ref>.
|-
| [[Savart]]*
| [[300edo|300]]
| 2<sup>2</sup> × 3 × 5<sup>2</sup>
| [[Alexander Wood]]'s definition of the Savart<ref>''[https://books.google.com.au/books?id=NWZ8CgAAQBAJ&lpg=PT50&vq=savart&pg=PT51 The Physics of Music]'', Alexander Wood, 1944.</ref>, containing [[12edo]]. 
|-
| [[Heptaméride]] / [[eptaméride]] / [[savart]]*
| [[301edo|301]]
| 7 × 43
| 301 ≃ 1,000 × log<sub>10</sub>2; 1/7 of Méride unit; proposed by Joseph Sauveur (1701), advocated by [[Félix Savart]]<ref name="measure"/><ref>[http://tonalsoft.com/enc/h/heptameride.aspx Tonalsoft | ''Heptaméride'']</ref>.
|-
| [[Gene]]
| [[311edo|311]]
| 311 (prime)
| Proposed by Joseph Monzo (2007)<ref>[http://tonalsoft.com/enc/g/gene.aspx Tonalsoft | ''Gene, 311-edo'']</ref>.
|-
| [[Dröbisch Angle]]
| [[360edo|360]]
| 2<sup>3</sup> × 3<sup>2</sup> × 5
| Proposed as ''angle'' by [[Moritz Dröbisch]] in the 19th century, later by [[Andrew Pikler]] as the current name in ''Logarithmic Frequency Systems'' (1966)<ref name="measure"/>.
|-
| [[Squb]]
| [[494edo|494]]
| 2 × 13 × 19
| {{Citation needed}}
|-
| Great [[iring]] / [[centitone]]
| [[500edo|500]]
| 2<sup>2</sup> × 5<sup>3</sup>
| {{Citation needed}}
|-
| Dexl
| [[540edo|540]]
| 2<sup>2</sup> × 3<sup>3</sup> × 5
| Proposed by Joseph Monzo (2023)<ref>[http://tonalsoft.com/enc/d/dexl.aspx Tonalsoft | ''Dexl, 540-edo'']</ref>.
|-
| [[Iring]] / [[centitone]]
| [[600edo|600]]
| 2<sup>3</sup> × 3 × 5<sup>2</sup>
| [[Relative cent]] of [[6edo]] ([[12edo]] tone); Proposed by [[Widogast Iring]] (1898), later by [[Joseph Yasser]] as a "centitone" (1932)<ref name="measure"/><ref>[http://www.tonalsoft.com/enc/c/centitone.aspx Tonalsoft | ''Centitone, iring'']</ref>.
|-
| [[Skisma]] (Sk)
| [[612edo|612]]
| 2<sup>2</sup> × 3<sup>2</sup> × 17
| Edo representation of [[Sagittal notation|Sagittal]]'s Ultra (Herculean) precision level JI notation (58eda), where it is known as an "ultrina"<ref name="measure"/><ref>[http://tonalsoft.com/enc/s/sk.aspx Tonalsoft | ''Sk, 612-edo'']</ref>.
|-
| [[Delfi]]
| [[665edo|665]]
| 5 × 7 × 19
| <ref name="measure"/>
|-
| Small [[iring]] / [[centitone]]
| [[700edo|700]]
| 2<sup>2</sup> × 5<sup>2</sup> x 7
| {{Citation needed}}
|-
| [[Woolhouse]]
| [[730edo|730]]
| 2 × 5 × 73
| Proposed by [[Wesley S.B. Woolhouse]] (1835)<ref>[https://archive.org/details/essayonmusicali00woolgoog/page/n34/mode/2up ''Essay on musical intervals, harmonics, and the temperament of the musical scale, &c''], Wesley S.B. Woolhouse. </ref>.
|-
| [[Millioctave]] (moct)
| [[1000edo|1000]]
| 2<sup>3</sup> × 5<sup>3</sup>
| See the dedicated page.
|-
| [[Cent]] (¢)
| 1200
| 2<sup>4</sup> × 3 × 5<sup>2</sup>
| See the dedicated page.
|-
| Greater muon
| [[1224edo|1224]]
| 2<sup>3</sup> × 3<sup>2</sup> × 17
| {{Citation needed}}
|-
| Triangular cent
| [[1260edo|1260]]
| 2<sup>2</sup> × 3<sup>2</sup> × 5 × 7
| {{Citation needed}}
|-
| Pion
| [[1272edo|1272]]
| 2<sup>3</sup> × 3 × 53
| {{Citation needed}}
|-
| Pound
| [[1344edo|1344]]
| 2<sup>6</sup> × 3 × 7
| {{Citation needed}}
|-
| Neutron
| [[1392edo|1392]]
| 2<sup>4</sup> × 3 × 29
| {{Citation needed}}
|-
| Lesser muon
| [[1428edo|1428]]
| 2<sup>2</sup> × 3 × 7 × 17
| {{Citation needed}}
|-
| Decifarab
| [[1440edo|1440]]
| 2<sup>5</sup> × 3<sup>2</sup> × 5
| 1/10 of [[Farab]] unit<ref name="measure"/>.
|-
| Quadratic cent
| [[1452edo|1452]]
| 2<sup>2</sup> × 3 × 11<sup>2</sup>
| {{Citation needed}}
|-
| Ksion
| [[1476edo|1476]]
| 2<sup>2</sup> × 3<sup>2</sup> × 41
| {{Citation needed}}
|-
| Cubic cent
| [[1500edo|1500]]
| 2<sup>2</sup> × 3 × 5<sup>3</sup>
| {{Citation needed}}
|-
| Heptamu (7mu)
| [[1536edo|1536]]
| 2<sup>9</sup> × 3
| Seventh MIDI-resolution unit, 1/128 (1/(2<sup>7</sup>)) of [[12edo]] semitone<ref>[http://tonalsoft.com/enc/number/7mu.aspx Tonalsoft | ''7mu / heptamu'']</ref>
|-
| Rhoon
| [[1560edo|1560]]
| 2<sup>3</sup> × 3 × 5 × 13
| {{Citation needed}}
|-
| śata
| [[1600edo|1600]]
| 2<sup>6</sup> × 5<sup>2</sup>
| From Sanskrit ''śatam'': hundred; [[Relative cent]] of Armodue 16edo Theory{{Citation needed}}
|-
| Tile
| [[1632edo|1632]]
| 2<sup>5</sup> × 3 × 17
| {{Citation needed}}
|-
| [[Iota]]
| [[1700edo|1700]]
| 2<sup>2</sup> × 5<sup>2</sup> × 17
| [[Relative cent]] of [[17edo]]; proposed by [[Margo Schulter]] (2002) and [[George Secor]]<ref name="measure"/>.
|-
| [[Harmos]]
| [[1728edo|1728]]
| 2<sup>6</sup> × 3<sup>3</sup>
| 1728 = 12<sup>3</sup>; 1/144 of [[12edo]] semitone; Proposed by [[Paul Beaver]]<ref name="measure"/><ref name="equal">[http://tonalsoft.com/enc/e/equal-temperament.aspx Tonalsoft | ''Equal temperaments'']</ref>.
|-
| Hind śat / Indian cent
| 2200
| 2<sup>3</sup> × 11 × 5<sup>2</sup>
| {{Citation needed}}
|-
| [[Mina]]
| [[2460edo|2460]]
| 2<sup>2</sup> × 3 × 5 × 41
| Abbreviation of "schismina", edo representation of [[Sagittal notation|Sagittal]]'s Extreme (Olympian) precision level JI notation (233eda)<ref name="measure"/><ref>[http://tonalsoft.com/enc/m/mina.aspx Tonalsoft | ''Mina'']</ref>.
|-
| Centidiesis
| 3100
| 2<sup>2</sup> × 5<sup>2</sup> x 31
| {{Citation needed}}
|-
| Centiméride
| 4300
| 2<sup>2</sup> × 5<sup>2</sup> x 43
| {{Citation needed}}
|-
| [[Major tina]]
| [[8269edo|8269]]
| 8269 (prime)
| Proposed by [[Flora Canou]] (2021)<ref>[https://forum.sagittal.org/viewtopic.php?f=4&t=515 The Sagittal Forum | ''Definition of the tina reviewed'']</ref>.
|-
| [[Tina]]
| [[8539edo|8539]]
| 8539 (prime)
| Provides good approximations for 41-limit primes except 37; named by [[Dave Keenan]] and [[George Secor]]; edo representation of [[Sagittal notation|Sagittal]]'s Insane (Magrathean) precision level JI notation (809eda)<ref name="measure"/><ref>[http://tonalsoft.com/enc/t/tina.aspx Tonalsoft | ''Tina'']</ref>.
|-
| [[Purdal]]
| [[9900edo|9900]]
| 2<sup>2</sup> × 3<sup>2</sup> × 5<sup>2</sup> × 11
| [[Relative cent]] of [[99edo]]; Suggested by [[Osmiorisbendi]], advocated by [[Tútim Dennsuul Wafiil]]. See the dedicated page.
|-
| [[Türk sent]] / [[Turkish cent]]
| [[10600edo|10600]]
| 2<sup>3</sup> × 5<sup>2</sup> × 53
| [[Relative cent]] of [[106edo]], 1/200 of [[53edo]]; invented by [[M. Ekrem Karadeniz]] (1965), influenced by [[Abdülkadir Töre]]<ref name="measure"/><ref>[http://www.tonalsoft.com/enc/t/turk-sent.aspx Tonalsoft | ''Türk-sent'']</ref><ref>[http://www.ozanyarman.com/files/doctorate_thesis.pdf ''79-Tone Tuning & Theory for Turkish Maqam Music''], Ozan Yarman. </ref>.
|-
| [[Prima]]
| [[12276edo|12276]]
| 2<sup>2</sup> × 3<sup>2</sup> × 11 × 31
| Proposed by [[Erv Wilson]], [[Gene Ward Smith]] and [[Gavin Putland]]<ref name="measure"/>.
|-
| [[Jinn]]
| [[16808edo|16808]]
| 2<sup>3</sup> × 11 × 191
| See the dedicated page.
|-
| [[Jot]]
| [[30103edo|30103]]
| 30103 (prime)
| 30103 ≃ 100,000 × log<sub>10</sub>2; Proposed by [[Augustus de Morgan]] (1864)<ref name="measure"/><ref>[http://www.tonalsoft.com/enc/j/jot.aspx Tonalsoft | ''Jot'']</ref><ref name="equal"/>.
|-
| [[Imp]]
| [[31920edo|31920]]
| 2<sup>4</sup> × 3 × 5 × 7 × 19
| <ref name="measure"/>
|-
| [[Flu]]
| [[46032edo|46032]]
| 2<sup>4</sup> × 3 × 7 × 137
| Proposed by Gene Ward Smith (2005)<ref name="measure"/><ref>[http://tonalsoft.com/enc/f/flu.aspx Tonalsoft | ''Flu'']</ref>.
|-
| [[Normal atom]]
| [[78005edo|78005]]
| 5 × 15601
| Name proposed by Tristan Bay in 2023; 78005edo consistently maps Kirnberger's atom to 1 edostep and is a very strong 5-limit system. {{Citation needed}}
|-
| [[MIDI Tuning Standard unit]] (14mu)
| [[196608edo|196608]]
| 2<sup>16</sup> × 3
| Fourteenth MIDI-resolution unit, 1/16384 (1/(2<sup>14</sup>)) of [[12edo]] semitone<ref name="measure"/>.
|}


Between
{{Harmonics in cet|33.368|columns=13|intervals=prime}}
0.0239167
 
and
{{Harmonics in cet|33.361|columns=13|intervals=prime}}
0.0239833
 
 
.
 
 
.
 
 
{{Harmonics in cet|33.333|columns=13|intervals=prime}}
 
 
.
 
 
.
 
 
{{Harmonics in cet|33.302|columns=13|intervals=prime}}
 
{{Harmonics in cet|33.286|columns=13|intervals=prime}}
 
{{Harmonics in cet|33.152|columns=13|intervals=prime}}
 
 
.
 
 
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{{Harmonics in equal|1|8|7 |columns=18}}
{{Harmonics in equal|1|9|8 |columns=18}}
 
 
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{{Harmonics in equal|1|10|9 |columns=18}}
{{Harmonics in equal|1|11|10 |columns=18}}
{{Harmonics in equal|1|12|11 |columns=18}}
{{Harmonics in equal|1|13|12 |columns=18}}
{{Harmonics in equal|1|14|13 |columns=18}}
{{Harmonics in equal|1|15|14 |columns=18}}
{{Harmonics in equal|1|16|15 |columns=18}}
{{Harmonics in equal|1|17|16 |columns=18}}
{{Harmonics in equal|1|18|17 |columns=18}}
{{Harmonics in equal|1|19|18 |columns=18}}
 
 
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{{Harmonics in equal|1|20|19 |columns=18}}
{{Harmonics in equal|1|21|20 |columns=18}}
{{Harmonics in equal|1|22|21 |columns=18}}
{{Harmonics in equal|1|23|22 |columns=18}}
{{Harmonics in equal|1|24|23 |columns=18}}
{{Harmonics in equal|1|25|24 |columns=18}}
{{Harmonics in equal|1|26|25 |columns=18}}
{{Harmonics in equal|1|27|26 |columns=18}}
{{Harmonics in equal|1|28|27 |columns=18}}
{{Harmonics in equal|1|29|28 |columns=18}}
 
 
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{{Harmonics in equal|1|30|29 |columns=18}}
{{Harmonics in equal|1|31|30 |columns=18}}
{{Harmonics in equal|1|32|31 |columns=18}}
{{Harmonics in equal|1|33|32 |columns=18}}
{{Harmonics in equal|1|34|33 |columns=18}}
{{Harmonics in equal|1|35|34 |columns=18}}
{{Harmonics in equal|1|36|35 |columns=18}}
{{Harmonics in equal|1|37|36 |columns=18}}
{{Harmonics in equal|1|38|37 |columns=18}}
{{Harmonics in equal|1|39|38 |columns=18}}
 
<br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br>
<br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br>
<br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br>
<br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br> <br>
Page end.

Latest revision as of 09:31, 17 August 2025

This is a working out sandbox page, not a content page.


Sandbox

Approximation of prime harmonics in 1ed33.547c
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41
Error Absolute (¢) +7.7 +10.2 -1.9 -14.1 +8.5 -12.3 -7.1 +1.6 +6.3 +7.6 -7.2 -11.6 +12.0
Relative (%) +22.9 +30.5 -5.7 -42.1 +25.4 -36.7 -21.1 +4.9 +18.9 +22.7 -21.5 -34.6 +35.7
Step 36 57 83 100 124 132 146 152 162 174 177 186 192


Approximation of prime harmonics in 1ed33.426c
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41
Error Absolute (¢) +3.3 +3.3 -12.0 +7.2 -6.5 +5.1 +8.7 +16.7 -13.3 -13.5 +4.8 -0.7 -11.3
Relative (%) +10.0 +10.0 -35.8 +21.5 -19.4 +15.3 +25.9 +49.9 -39.7 -40.2 +14.3 -2.0 -33.7
Step 36 57 83 101 124 133 147 153 162 174 178 187 192


Approximation of prime harmonics in 1ed33.368c
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41
Error Absolute (¢) +1.2 +0.0 +16.6 +1.3 -13.7 -2.6 +0.1 +7.8 +10.7 +9.8 -5.5 -11.5 +11.0
Relative (%) +3.7 +0.1 +49.7 +4.0 -41.0 -7.7 +0.4 +23.3 +32.1 +29.4 -16.6 -34.5 +32.9
Step 36 57 84 101 124 133 147 153 163 175 178 187 193


Approximation of prime harmonics in 1ed33.361c
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41
Error Absolute (¢) +1.0 -0.4 +16.0 +0.6 -14.6 -3.5 -0.9 +6.7 +9.6 +8.6 -6.8 -12.8 +9.6
Relative (%) +3.0 -1.1 +48.0 +1.9 -43.6 -10.5 -2.7 +20.1 +28.7 +25.8 -20.3 -38.5 +28.8
Step 36 57 84 101 124 133 147 153 163 175 178 187 193


.


.


Approximation of prime harmonics in 1ed33.333c
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41
Error Absolute (¢) -0.0 -2.0 +13.7 -2.2 +15.3 -7.2 -5.0 +2.4 +5.0 +3.7 -11.8 +15.3 +4.2
Relative (%) -0.0 -5.9 +41.0 -6.6 +45.9 -21.7 -15.0 +7.3 +15.0 +11.1 -35.3 +45.8 +12.6
Step 36 57 84 101 125 133 147 153 163 175 178 188 193


.


.


Approximation of prime harmonics in 1ed33.302c
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41
Error Absolute (¢) -1.1 -3.7 +11.1 -5.3 +11.4 -11.4 -9.6 -2.3 -0.0 -1.7 +16.0 +9.4 -1.8
Relative (%) -3.4 -11.2 +33.2 -16.0 +34.3 -34.1 -28.7 -6.9 -0.1 -5.2 +48.1 +28.3 -5.3
Step 36 57 84 101 125 133 147 153 163 175 179 188 193


Approximation of prime harmonics in 1ed33.286c
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41
Error Absolute (¢) -1.7 -4.7 +9.7 -6.9 +9.4 -13.5 -11.9 -4.8 -2.7 -4.5 +13.2 +6.4 -4.9
Relative (%) -5.1 -14.0 +29.2 -20.8 +28.3 -40.5 -35.8 -14.3 -8.0 -13.6 +39.5 +19.3 -14.6
Step 36 57 84 101 125 133 147 153 163 175 179 188 193


Approximation of prime harmonics in 1ed33.152c
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41
Error Absolute (¢) -6.5 -12.3 -1.5 +12.7 -7.3 +1.8 +1.5 +7.9 +8.7 +5.2 -10.8 +14.4 +2.4
Relative (%) -19.7 -37.1 -4.7 +38.2 -22.1 +5.6 +4.6 +23.8 +26.1 +15.6 -32.7 +43.4 +7.3
Step 36 57 84 102 125 134 148 154 164 176 179 189 194


.


.


Approximation of harmonics in 1ed8/7
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) -44 -53 -88 -12 -97 +99 +99 -105 -56 +10 +90 -48 +55 -65 +55 -50 +82 -12
Relative (%) -19.1 -22.7 -38.2 -5.3 -41.8 +42.7 +42.7 -45.5 -24.4 +4.2 +39.1 -20.9 +23.6 -28.0 +23.6 -21.8 +35.4 -5.1
Step 5 8 10 12 13 15 16 16 17 18 19 19 20 20 21 21 22 22
Approximation of harmonics in 1ed9/8
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) +23.5 -66.8 +46.9 +68.4 -43.3 +97.6 +70.4 +70.4 +91.9 -73.1 -19.8 +45.5 -82.8 +1.7 +93.8 -11.1 +93.8 +0.2
Relative (%) +11.5 -32.7 +23.0 +33.6 -21.2 +47.9 +34.5 +34.5 +45.1 -35.9 -9.7 +22.3 -40.6 +0.8 +46.0 -5.5 +46.0 +0.1
Step 6 9 12 14 15 17 18 19 20 20 21 22 22 23 24 24 25 25


.


.


Approximation of harmonics in 1ed10/9
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) +76.8 -77.9 -28.8 -50.3 -1.1 -85.6 +48.1 +26.6 +26.6 +44.0 +75.7 -62.8 -8.7 +54.2 -57.5 +19.9 -79.0 +9.8
Relative (%) +42.1 -42.7 -15.8 -27.6 -0.6 -46.9 +26.4 +14.6 +14.6 +24.1 +41.5 -34.5 -4.8 +29.7 -31.5 +10.9 -43.3 +5.4
Step 7 10 13 15 17 18 20 21 22 23 24 24 25 26 26 27 27 28
Approximation of harmonics in 1ed11/10
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) -45.0 +78.1 +75.1 +18.8 +33.1 -68.7 +30.1 -8.8 -26.2 -26.2 -11.8 +14.6 +51.3 -68.2 -14.9 +45.2 -53.8 +17.6
Relative (%) -27.3 +47.3 +45.5 +11.4 +20.1 -41.7 +18.2 -5.3 -15.9 -15.9 -7.2 +8.8 +31.1 -41.3 -9.0 +27.4 -32.6 +10.7
Step 7 12 15 17 19 20 22 23 24 25 26 27 28 28 29 30 30 31
Approximation of harmonics in 1ed12/11
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) +5.1 +56.3 +10.2 -74.8 +61.4 -54.8 +15.3 -38.0 -69.8 +66.5 +66.5 -72.1 -49.7 -18.5 +20.4 +66.1 -32.9 +24.1
Relative (%) +3.4 +37.4 +6.8 -49.7 +40.8 -36.4 +10.1 -25.2 -46.3 +44.2 +44.2 -47.8 -33.0 -12.3 +13.5 +43.9 -21.8 +16.0
Step 8 13 16 18 21 22 24 25 26 28 29 29 30 31 32 33 33 34
Approximation of harmonics in 1ed13/12
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) +47.2 +38.1 -44.3 -14.9 -53.4 -43.1 +2.9 -62.4 +32.3 +5.9 -6.2 -6.2 +4.1 +23.2 +50.0 -54.9 -15.3 +29.7
Relative (%) +34.0 +27.5 -31.9 -10.7 -38.5 -31.1 +2.1 -45.1 +23.3 +4.2 -4.5 -4.5 +2.9 +16.7 +36.1 -39.6 -11.0 +21.4
Step 9 14 17 20 22 24 26 27 29 30 31 32 33 34 35 35 36 37
Approximation of harmonics in 1ed14/13
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) -45.3 +22.5 +37.7 +36.2 -22.8 -33.1 -7.6 +45.0 -9.1 -45.8 +60.2 +49.9 +49.9 +58.8 -53.0 -29.6 -0.3 +34.4
Relative (%) -35.3 +17.6 +29.4 +28.3 -17.8 -25.8 -6.0 +35.1 -7.1 -35.7 +46.9 +38.9 +38.9 +45.8 -41.3 -23.1 -0.2 +26.8
Step 9 15 19 22 24 26 28 30 31 32 34 35 36 37 37 38 39 40
Approximation of harmonics in 1ed15/14
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) -5.6 +9.1 -11.1 -39.1 +3.6 -24.4 -16.7 +18.3 -44.7 +29.2 -2.0 -21.1 -30.0 -30.0 -22.3 -7.8 +12.7 +38.5
Relative (%) -4.7 +7.6 -9.3 -32.8 +3.0 -20.5 -14.0 +15.3 -37.4 +24.4 -1.7 -17.7 -25.1 -25.1 -18.7 -6.5 +10.6 +32.3
Step 10 16 20 23 26 28 30 32 33 35 36 37 38 39 40 41 42 43
Approximation of harmonics in 1ed16/15
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) +29.0 -2.5 -53.6 +7.0 +26.5 -16.9 -24.6 -5.0 +36.0 -17.3 +55.6 +28.7 +12.2 +4.4 +4.4 +11.2 +24.0 +42.1
Relative (%) +26.0 -2.3 -48.0 +6.2 +23.7 -15.1 -22.0 -4.5 +32.2 -15.4 +49.7 +25.7 +10.9 +4.0 +4.0 +10.0 +21.5 +37.7
Step 11 17 21 25 28 30 32 34 36 37 39 40 41 42 43 44 45 46
Approximation of harmonics in 1ed17/16
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) -45.5 -12.8 +14.0 +47.5 +46.7 -10.3 -31.5 -25.5 +2.0 +46.9 +1.2 -32.4 +49.2 +34.7 +27.9 +27.9 +33.9 +45.3
Relative (%) -43.3 -12.2 +13.3 +45.2 +44.5 -9.8 -30.0 -24.3 +1.9 +44.7 +1.2 -30.9 +46.9 +33.1 +26.6 +26.6 +32.3 +43.2
Step 11 18 23 27 30 32 34 36 38 40 41 42 44 45 46 47 48 49
Approximation of harmonics in 1ed18/17
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) -12.5 -21.8 -25.1 -15.6 -34.4 -4.4 -37.6 -43.6 -28.1 +4.8 -46.9 +12.4 -16.9 -37.4 +48.8 +42.8 +42.8 +48.1
Relative (%) -12.7 -22.0 -25.4 -15.7 -34.7 -4.4 -38.0 -44.1 -28.4 +4.8 -47.4 +12.6 -17.1 -37.8 +49.3 +43.2 +43.2 +48.6
Step 12 19 24 28 31 34 36 38 40 42 43 45 46 47 49 50 51 52
Approximation of harmonics in 1ed19/18
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) +16.8 -29.9 +33.7 +21.8 -13.1 +0.9 -43.1 +33.8 +38.6 -32.8 +3.8 -41.2 +17.7 -8.1 -26.2 -37.6 -43.0 -43.0
Relative (%) +18.0 -31.9 +36.0 +23.3 -13.9 +0.9 -46.0 +36.1 +41.3 -35.0 +4.0 -44.0 +18.9 -8.7 -28.0 -40.2 -45.9 -45.9
Step 13 20 26 30 33 36 38 41 43 44 46 47 49 50 51 52 53 54


.


.


Approximation of harmonics in 1ed20/19
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) +43.2 -37.1 -2.4 -33.5 +6.1 +5.6 +40.8 +14.5 +9.7 +22.3 -39.5 -0.5 -40.0 +18.2 -4.8 -20.9 -31.1 -35.9
Relative (%) +48.7 -41.8 -2.7 -37.7 +6.8 +6.3 +46.0 +16.4 +10.9 +25.1 -44.5 -0.6 -45.0 +20.5 -5.4 -23.6 -35.0 -40.4
Step 14 21 27 31 35 38 41 43 45 47 48 50 51 53 54 55 56 57
Approximation of harmonics in 1ed21/20
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) -17.5 +40.8 -34.9 +1.1 +23.3 +9.9 +32.1 -2.9 -16.4 -12.4 +5.9 +36.2 -7.6 +41.9 +14.6 -5.9 -20.3 -29.5
Relative (%) -20.7 +48.3 -41.3 +1.3 +27.6 +11.7 +38.0 -3.4 -19.4 -14.7 +7.0 +42.9 -9.0 +49.6 +17.3 -6.9 -24.1 -34.9
Step 14 23 28 33 37 40 43 45 47 49 51 53 54 56 57 58 59 60
Approximation of harmonics in 1ed22/21
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) +8.1 +30.9 +16.1 +32.5 +39.0 +13.7 +24.2 -18.7 -40.0 +36.6 -33.5 -11.0 +21.8 -17.1 +32.2 +7.8 -10.6 -23.7
Relative (%) +10.0 +38.4 +20.0 +40.3 +48.4 +17.0 +30.0 -23.2 -49.7 +45.5 -41.6 -13.6 +27.0 -21.3 +40.0 +9.7 -13.2 -29.4
Step 15 24 30 35 39 42 45 47 49 52 53 55 57 58 60 61 62 63
Approximation of harmonics in 1ed23/22
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) +31.3 +22.0 -14.4 -15.9 -23.7 +17.3 +17.0 -33.0 +15.4 +4.3 +7.6 +22.9 -28.4 +6.1 -28.7 +20.3 -1.7 -18.4
Relative (%) +40.7 +28.5 -18.6 -20.6 -30.8 +22.4 +22.0 -42.9 +20.0 +5.6 +9.9 +29.8 -36.9 +7.9 -37.3 +26.3 -2.3 -23.9
Step 16 25 31 36 40 44 47 49 52 54 56 58 59 61 62 64 65 66
Approximation of harmonics in 1ed24/23
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) -21.1 +13.7 +31.5 +13.6 -7.4 +20.5 +10.4 +27.5 -7.6 -25.2 -28.5 -19.7 -0.6 +27.3 -10.8 +31.6 +6.4 -13.5
Relative (%) -28.7 +18.7 +42.7 +18.4 -10.0 +27.8 +14.0 +37.3 -10.3 -34.2 -38.6 -26.7 -0.8 +37.0 -14.6 +43.0 +8.7 -18.4
Step 16 26 33 38 42 46 49 52 54 56 58 60 62 64 65 67 68 69
Approximation of harmonics in 1ed25/24
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) +1.4 +6.2 +2.9 -30.1 +7.6 +23.5 +4.3 +12.4 -28.7 +18.4 +9.1 +11.8 +24.9 -23.9 +5.7 -28.6 +13.8 -9.1
Relative (%) +2.0 +8.8 +4.1 -42.6 +10.8 +33.2 +6.1 +17.5 -40.6 +26.0 +12.8 +16.7 +35.2 -33.8 +8.1 -40.4 +19.6 -12.9
Step 17 27 34 39 44 48 51 54 56 59 61 63 65 66 68 69 71 72
Approximation of harmonics in 1ed26/25
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) +22.2 -0.7 -23.5 -2.4 +21.5 +26.2 -1.3 -1.5 +19.8 -9.4 -24.2 -27.0 -19.5 -3.2 +20.9 -16.1 +20.7 -5.0
Relative (%) +32.7 -1.1 -34.6 -3.5 +31.6 +38.6 -1.9 -2.2 +29.2 -13.8 -35.7 -39.8 -28.7 -4.6 +30.8 -23.8 +30.5 -7.4
Step 18 28 35 41 46 50 53 56 59 61 63 65 67 69 71 72 74 75
Approximation of harmonics in 1ed27/26
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) -23.9 -7.2 +17.5 +23.2 -31.1 +28.7 -6.4 -14.3 -0.7 +30.3 +10.3 +2.4 +4.8 +16.0 -30.4 -4.7 +27.1 -1.2
Relative (%) -36.6 -11.0 +26.8 +35.5 -47.6 +44.0 -9.9 -22.0 -1.1 +46.3 +15.8 +3.7 +7.3 +24.5 -46.5 -7.1 +41.4 -1.8
Step 18 29 37 43 47 52 55 58 61 64 66 68 70 72 73 75 77 78
Approximation of harmonics in 1ed28/27
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) -3.7 -13.1 -7.5 -16.0 -16.9 +31.1 -11.2 -26.3 -19.8 +4.1 -20.6 +29.7 +27.3 -29.2 -15.0 +6.0 -30.0 +2.3
Relative (%) -5.9 -20.9 -11.9 -25.5 -26.8 +49.3 -17.8 -41.7 -31.4 +6.5 -32.7 +47.2 +43.4 -46.3 -23.8 +9.5 -47.6 +3.7
Step 19 30 38 44 49 54 57 60 63 66 68 71 73 74 76 78 79 81
Approximation of harmonics in 1ed29/28
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) +15.0 -18.7 +30.1 +8.2 -3.6 -27.5 -15.7 +23.4 +23.3 -20.2 +11.4 -5.7 -12.5 -10.4 -0.6 +15.9 -22.3 +5.6
Relative (%) +24.7 -30.7 +49.5 +13.6 -6.0 -45.3 -25.8 +38.6 +38.3 -33.3 +18.7 -9.4 -20.5 -17.2 -1.1 +26.2 -36.7 +9.2
Step 20 31 40 46 51 55 59 63 66 68 71 73 75 77 79 81 82 84


.


.


Approximation of harmonics in 1ed30/29
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) -26.2 -23.8 +6.4 -27.8 +8.7 -23.4 -19.8 +11.0 +4.7 +15.8 -17.5 +20.0 +9.1 +7.1 +12.7 +25.1 -15.1 +8.6
Relative (%) -44.6 -40.6 +10.8 -47.4 +14.8 -39.9 -33.8 +18.8 +8.0 +26.9 -29.8 +34.1 +15.5 +12.0 +21.6 +42.8 -25.8 +14.7
Step 20 32 41 47 53 57 61 65 68 71 73 76 78 80 82 84 85 87
Approximation of harmonics in 1ed31/30
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) -7.9 +28.1 -15.8 -4.7 +20.2 -19.6 -23.7 -0.5 -12.6 -7.3 +12.3 -12.7 -27.5 +23.4 +25.2 -23.0 -8.4 +11.5
Relative (%) -13.9 +49.5 -27.8 -8.3 +35.6 -34.5 -41.7 -0.9 -22.3 -12.9 +21.7 -22.4 -48.4 +41.2 +44.4 -40.5 -14.8 +20.3
Step 21 34 42 49 55 59 63 67 70 73 76 78 80 83 85 86 88 90
Approximation of harmonics in 1ed32/31
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) +9.2 +21.8 +18.4 +16.9 -23.9 -16.0 -27.3 -11.4 +26.1 +26.0 -14.7 +11.6 -6.8 -16.3 -18.1 -13.1 -2.1 +14.2
Relative (%) +16.8 +39.7 +33.5 +30.7 -43.6 -29.1 -49.7 -20.7 +47.5 +47.3 -26.8 +21.1 -12.3 -29.6 -32.9 -23.9 -3.9 +25.8
Step 22 35 44 51 56 61 65 69 73 76 78 81 83 85 87 89 91 93
Approximation of harmonics in 1ed33/32
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) +25.3 +15.9 -2.7 -16.1 -12.1 -12.6 +22.6 -21.5 +9.2 +4.0 +13.2 -18.9 +12.6 -0.2 -5.4 -3.8 +3.7 +16.7
Relative (%) +47.4 +29.8 -5.1 -30.3 -22.8 -23.7 +42.3 -40.4 +17.2 +7.5 +24.7 -35.4 +23.7 -0.5 -10.2 -7.2 +7.0 +31.3
Step 23 36 45 52 58 63 68 71 75 78 81 83 86 88 90 92 94 96
Approximation of harmonics in 1ed34/33
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) -11.3 +10.3 -22.6 +4.5 -1.0 -9.5 +17.8 +20.6 -6.8 -16.7 -12.3 +4.2 -20.8 +14.8 +6.5 +4.9 +9.3 +19.1
Relative (%) -21.9 +19.9 -43.7 +8.8 -1.9 -18.3 +34.4 +39.8 -13.1 -32.4 -23.8 +8.1 -40.2 +28.7 +12.5 +9.4 +18.0 +36.9
Step 23 37 46 54 60 65 70 74 77 80 83 86 88 91 93 95 97 99
Approximation of harmonics in 1ed35/34
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) +4.4 +5.0 +8.8 +24.0 +9.5 -6.5 +13.3 +10.1 -21.8 +14.0 +13.9 -24.3 -2.1 -21.1 +17.7 +13.1 +14.5 +21.3
Relative (%) +8.8 +10.1 +17.6 +47.8 +18.9 -12.9 +26.4 +20.1 -43.4 +27.8 +27.7 -48.5 -4.1 -42.1 +35.2 +26.1 +28.9 +42.4
Step 24 38 48 56 62 67 72 76 79 83 86 88 91 93 96 98 100 102
Approximation of harmonics in 1ed36/35
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) +19.3 +0.1 -10.3 -6.4 +19.3 -3.7 +9.0 +0.2 +12.9 -5.8 -10.2 -2.4 +15.6 -6.3 -20.5 +20.9 +19.4 +23.4
Relative (%) +39.5 +0.2 -21.0 -13.1 +39.7 -7.5 +18.5 +0.4 +26.4 -12.0 -20.8 -5.0 +32.0 -12.9 -42.0 +42.8 +39.9 +47.9
Step 25 39 49 57 64 69 74 78 82 85 88 91 94 96 98 101 103 105
Approximation of harmonics in 1ed37/36
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) -14.1 -4.6 +19.1 +12.3 -18.7 -1.0 +5.0 -9.2 -1.9 +22.9 +14.5 +18.3 -15.2 +7.7 -9.2 -19.2 -23.3 -22.1
Relative (%) -29.8 -9.7 +40.3 +25.9 -39.5 -2.1 +10.5 -19.4 -3.9 +48.2 +30.7 +38.5 -32.0 +16.2 -19.3 -40.6 -49.2 -46.5
Step 25 40 51 59 65 71 76 80 84 88 91 94 96 99 101 103 105 107
Approximation of harmonics in 1ed38/37
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) +0.4 -9.0 +0.8 -16.2 -8.6 +1.5 +1.2 -18.1 -15.8 +3.9 -8.2 -8.3 +1.9 +21.0 +1.6 -11.0 -17.7 -18.9
Relative (%) +0.9 -19.6 +1.7 -35.0 -18.7 +3.3 +2.6 -39.1 -34.2 +8.4 -17.8 -18.0 +4.1 +45.4 +3.4 -23.9 -38.3 -41.0
Step 26 41 52 60 67 73 78 82 86 90 93 96 99 102 104 106 108 110
Approximation of harmonics in 1ed39/38
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Error Absolute (¢) +14.2 -13.2 -16.6 +1.8 +1.0 +3.9 -2.4 +18.5 +16.0 -14.1 +15.1 +11.5 +18.1 -11.4 +11.8 -3.3 -12.3 -15.9
Relative (%) +31.5 -29.4 -36.9 +4.0 +2.1 +8.7 -5.4 +41.2 +35.5 -31.4 +33.6 +25.5 +40.2 -25.4 +26.1 -7.3 -27.3 -35.5
Step 27 42 53 62 69 75 80 85 89 92 96 99 102 104 107 109 111 113

































































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