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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<span style="color: #004d25; font-family: 'Times New Roman',Times,serif; font-size: 20px;">'''41 Tone Equal Temperament'''</span>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-11 21:04:30 UTC</tt>.<br>
: The original revision id was <tt>621464371</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">&lt;span style="color: #004d25; font-family: 'Times New Roman',Times,serif; font-size: 20px;"&gt;**41 Tone Equal Temperament**&lt;/span&gt;
&lt;span style="display: block; text-align: right;"&gt;[[xenharmonie/41edo|Deutsch]]
&lt;/span&gt;
[[toc|flat]]
----
=Introduction=
The 41-tET, 41-EDO, or 41-ET, is the scale derived by dividing the octave into 41 equally-sized steps. Each step represents a frequency ratio of 29.268 [[cent]]s, an [[interval]] close in size to [[64_63|64/63]], the [[Septimal comma|septimal comma]]. 41-ET can be seen as a tuning of the //[[Schismatic family#Garibaldi|Garibaldi temperament]]// &lt;ref&gt;[[http://x31eq.com/schismic.htm|"Schismic Temperaments"]] at x31eq.com the website of [[Graham Breed]]&lt;/ref&gt; , &lt;ref&gt;[[http://x31eq.com/decimal_lattice.htm|"Lattices with Decimal Notation"]] at x31eq.com&lt;/ref&gt; , &lt;ref&gt;[[http://en.wikipedia.org/wiki/Schismatic_temperament|Schismatic temperament]]&lt;/ref&gt; the //[[Magic family|Magic temperament]]// &lt;ref&gt;[[http://en.wikipedia.org/wiki/Magic_temperament|Magic temperament]]&lt;/ref&gt; and the superkleismic (41&amp;26) temperament. It is the second smallest equal temperament (after [[29edo]]) whose perfect fifth is closer to just intonation than that of [[12edo|12-ET]], and is the seventh [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta integral edo]] after 31; it is not, however, a [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta gap edo]]. This has to do with the fact that it can deal with the [[11-limit]] fairly well, and the [[13-limit]] perhaps close enough for government work, though its [[13_10|13/10]] is 14 cents sharp. Various 13-limit [[magic extensions]] are supported by 41: 13-limit magic, and less successfully necromancy and witchcraft, all merge into one in 41edo tuning. The 41f val provides a superb tuning for sorcery, giving a less-complex version of the 13-limit, and the 41ef val likewise works well for telepathy; telepathy and sorcery merging into one however not in 41edo but in 22edo.


41edo is consistent in the 15 odd limit. In fact, //all// of its intervals between 100 and 1100 cents in size are 15-odd-limit consonances. (In comparison, [[31edo]] is only consistent up to the 11-limit, and the intervals 12/31 and 19/31 have no 11-limit approximations).
<span style="display: block; text-align: right;">[[:de:41edo Deutsch]]</span>
__FORCETOC__
-----


41-ET forms the foundation of the [[http://www.h-pi.com/theory/huntsystem1.html|H-System]], which uses the scale degrees of 41-ET as the basic [[13-limit]] intervals requiring fine tuning +/- 1 [[http://www.h-pi.com/theory/huntsystem2.html|average JND]] from the 41-ET circle in [[205edo]].
=Introduction=
The 41-tET, 41-EDO, or 41-ET, is the scale derived by dividing the octave into 41 equally-sized steps. Each step represents a frequency ratio of 29.268 [[cent|cent]]s, an [[interval|interval]] close in size to [[64/63|64/63]], the [[Septimal_comma|septimal comma]]. 41-ET can be seen as a tuning of the ''[[Schismatic_family#Garibaldi|Garibaldi temperament]]'' </sup>[[#cite_note-1|[1]]]</sup> , </sup>[[#cite_note-2|[2]]]</sup> , </sup>[[#cite_note-3|[3]]]</sup> the ''[[Magic_family|Magic temperament]]'' </sup>[[#cite_note-4|[4]]]</sup> and the superkleismic (41&amp;26) temperament. It is the second smallest equal temperament (after [[29edo|29edo]]) whose perfect fifth is closer to just intonation than that of [[12edo|12-ET]], and is the seventh [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta integral edo]] after 31; it is not, however, a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta gap edo]]. This has to do with the fact that it can deal with the [[11-limit|11-limit]] fairly well, and the [[13-limit|13-limit]] perhaps close enough for government work, though its [[13/10|13/10]] is 14 cents sharp. Various 13-limit [[Magic_extensions|magic extensions]] are supported by 41: 13-limit magic, and less successfully necromancy and witchcraft, all merge into one in 41edo tuning. The 41f val provides a superb tuning for sorcery, giving a less-complex version of the 13-limit, and the 41ef val likewise works well for telepathy; telepathy and sorcery merging into one however not in 41edo but in 22edo.


41edo is the 13th [[prime numbers|prime]] edo, following [[37edo]] and coming before [[43edo]].
41edo is consistent in the 15 odd limit. In fact, ''all'' of its intervals between 100 and 1100 cents in size are 15-odd-limit consonances. (In comparison, [[31edo|31edo]] is only consistent up to the 11-limit, and the intervals 12/31 and 19/31 have no 11-limit approximations).


=Commas=  
41-ET forms the foundation of the [http://www.h-pi.com/theory/huntsystem1.html H-System], which uses the scale degrees of 41-ET as the basic [[13-limit|13-limit]] intervals requiring fine tuning +/- 1 [http://www.h-pi.com/theory/huntsystem2.html average JND] from the 41-ET circle in [[205edo|205edo]].
 
41edo is the 13th [[prime_numbers|prime]] edo, following [[37edo|37edo]] and coming before [[43edo|43edo]].
 
=Commas=
41 EDO tempers out the following commas using its patent val, &lt; 41 65 95 115 142 152 168 174 185 199 203 |.
41 EDO tempers out the following commas using its patent val, &lt; 41 65 95 115 142 152 168 174 185 199 203 |.
||~ Name ||~ Monzo ||~ Ratio ||~ Cents ||
|| odiheim || | -1 2 -4 5 -2 &gt; ||=  || 0.15 ||
|| harmonisma || | 3 -2 0 -1 3 -2 &gt; ||= 10648/10647 || 0.16 ||
|| tridecimal schisma, Sagittal schismina || | 12 -2 -1 -1 0 -1/1 &gt; ||= 4096/4095 || 0.42 ||
|| Lehmerisma || | -4 -3 2 -1 2 &gt; ||= 3025/3024 || 0.57 ||
|| Breedsma || | -5 -1 -2 4 &gt; ||= 2401/2400 || 0.72 ||
|| Eratosthenes' comma || | 6 -5 -1 0 0 0 0 1 &gt; ||= 1216/1215 || 1.42 ||
|| schisma || | -15 8 1 &gt; ||= 32805/32768 || 1.95 ||
|| squbema || | -3 6 0 -1 0 -1 &gt; ||= 729/728 || 2.38 ||
|| septendecimal bridge comma || | -1 -1 1 -1 1 1 -1 &gt; ||= 715/714 || 2.42 ||
|| Swets' comma, swetisma || | 2 3 1 -2 -1 &gt; ||= 540/539 || 3.21 ||
|| undevicesimal comma, Boethius' comma || | -9 3 0 0 0 0 0 1 &gt; ||= 513/512 || 3.38 ||
|| moctdel || | -2 0 3 -3 1 &gt; ||= 1375/1372 || 3.78 ||
|| Beta 2, septimal schisma, garischisma || | 25 -14 0 -1 &gt; ||=  || 3.80 ||
|| Werckmeister's undecimal septenarian schisma, werckisma || | -3 2 -1 2 -1 &gt; ||= 441/440 || 3.93 ||
|| cuthbert || | 0 0 -1 1 2 -2 &gt; ||= 847/845 || 4.09 ||
|| undecimal kleisma, keenanisma || | -7 -1 1 1 1 &gt; ||= 385/384 || 4.50 ||
|| gentle comma || | 2 -1 0 1 -2 1 &gt; ||= 364/363 || 4.76 ||
|| minthma || | 5 -3 0 0 1 -1 &gt; ||= 352/351 || 4.93 ||
|| marveltwin || | -2 -4 2 0 0 1 &gt; ||= 325/324 || 5.34 ||
|| Beta 5, Garibaldi comma, hemifamity || | 10 -6 1 -1 &gt; ||= 5120/5103 || 5.76 ||
|| hemimage || | 5 -7 -1 3 &gt; ||= 10976/10935 || 6.48 ||
|| septendecimal kleisma || | 8 -1 -1 0 0 0 -1 &gt; ||= 256/255 || 6.78 ||
|| small BP diesis, mirkwai || | 0 3 4 -5 &gt; ||= 16875/16807 || 6.99 ||
|| neutral third comma, rastma || | -1 5 0 0 -2 &gt; ||= 243/242 || 7.14 ||
|| kestrel comma || | 2 3 0 -1 1 -2 &gt; ||= 1188/1183 || 7.30 ||
|| septimal kleisma, marvel comma || | -5 2 2 -1 &gt; ||= 225/224 || 7.71 ||
|| huntma || | 7 0 1 -2 0 -1 &gt; ||= 640/637 || 8.13 ||
|| spleen comma || | 1 1 1 1 -1 0 0 -1 &gt; ||= 210/209 || 8.26 ||
|| orgonisma || | 16 0 0 -2 -3 &gt; ||= 65536/65219 || 8.39 ||
|| gamelan residue, gamelisma || | -10 1 0 3 &gt; ||= 1029/1024 || 8.43 ||
|| septendecimal comma || | -7 7 0 0 0 0 -1 &gt; ||= 2187/2176 || 8.73 ||
|| mynucuma || | 2 -1 -1 2 0 -1 &gt; ||= 196/195 || 8.86 ||
|| quince || | -15 0 -2 7 &gt; ||=  || 9.15 ||
|| undecimal semicomma, pentacircle (minthma * gentle) || | 7 -4 0 1 -1 &gt; ||= 896/891 || 9.69 ||
|| 29th-partial chroma || | -4 -2 1 0 0 0 0 0 0 1 &gt; ||= 145/144 || 11.98 ||
|| grossma || | 4 2 0 0 -1 -1 &gt; ||= 144/143 || 12.06 ||
|| gassorma || | 0 -1 2 -1 1 -1 &gt; ||= 275/273 || 12.64 ||
|| septimal semicomma, octagar || | 5 -4 3 -2 &gt; ||= 4000/3969 || 13.47 ||
|| minor BP diesis, sensamagic || | 0 -5 1 2 &gt; ||= 245/243 || 14.19 ||
|| secorian || | 12 -7 0 1 0 -1/1 &gt; ||= 28672/28431 || 14.61 ||
|| mirwomo comma || | -15 3 2 2 &gt; ||= 33075/32768 || 16.14 ||
|| vicesimotertial comma || | 5 -6 0 0 0 0 0 0 1 &gt; ||= 736/729 || 16.54 ||
|| small tridecimal comma, animist || | -3 1 1 1 0 -1 &gt; ||= 105/104 || 16.57 ||
|| hemimin || | 6 1 0 1 -3 &gt; ||= 1344/1331 || 16.83 ||
|| Ptolemy's comma, ptolemisma || | 2 -2 2 0 -1 &gt; ||= 100/99 || 17.40 ||
|| '41-tone' comma || | 65 -41 &gt; ||=  || 19.84 ||
|| tolerma || | 10 -11 2 1 &gt; ||=  || 19.95 ||
|| major BP diesis, gariboh || | 0 -2 5 -3 &gt; ||= 3125/3087 || 21.18 ||
|| cassacot || | -1 0 1 2 -2 &gt; ||= 245/242 || 21.33 ||
|| keema || | -5 -3 3 1 &gt; ||= 875/864 || 21.90 ||
|| blackjackisma || | -10 7 8 -7 &gt; ||=  || 22.41 ||
|| roda || | 20 -17 3 &gt; ||=  || 25.71 ||
|| minimal diesis, tetracot comma || | 5 -9 4 &gt; ||= 20000/19683 || 27.66 ||
|| small diesis, magic comma || | -10 -1 5 &gt; ||= 3125/3072 || 29.61 ||
|| thuja comma || | 15 0 1 0 -5 &gt; ||=  || 29.72 ||
|| Ampersand's comma || | -25 7 6 &gt; ||=  || 31.57 ||
|| great BP diesis || | 0 -7 6 -1 &gt; ||= 15625/15309 || 35.37 ||
|| shibboleth || | -5 -10 9 &gt; ||=  || 57.27 ||


=Temperaments=  
{| class="wikitable"
[[List of edo-distinct 41et rank two temperaments]]
|-
! | Name
! | Monzo
! | Ratio
! | Cents
|-
| | odiheim
| | | -1 2 -4 5 -2 &gt;
| style="text-align:center;" |
| | 0.15
|-
| | harmonisma
| | | 3 -2 0 -1 3 -2 &gt;
| style="text-align:center;" | 10648/10647
| | 0.16
|-
| | tridecimal schisma, Sagittal schismina
| | | 12 -2 -1 -1 0 -1/1 &gt;
| style="text-align:center;" | 4096/4095
| | 0.42
|-
| | Lehmerisma
| | | -4 -3 2 -1 2 &gt;
| style="text-align:center;" | 3025/3024
| | 0.57
|-
| | Breedsma
| | | -5 -1 -2 4 &gt;
| style="text-align:center;" | 2401/2400
| | 0.72
|-
| | Eratosthenes' comma
| | | 6 -5 -1 0 0 0 0 1 &gt;
| style="text-align:center;" | 1216/1215
| | 1.42
|-
| | schisma
| | | -15 8 1 &gt;
| style="text-align:center;" | 32805/32768
| | 1.95
|-
| | squbema
| | | -3 6 0 -1 0 -1 &gt;
| style="text-align:center;" | 729/728
| | 2.38
|-
| | septendecimal bridge comma
| | | -1 -1 1 -1 1 1 -1 &gt;
| style="text-align:center;" | 715/714
| | 2.42
|-
| | Swets' comma, swetisma
| | | 2 3 1 -2 -1 &gt;
| style="text-align:center;" | 540/539
| | 3.21
|-
| | undevicesimal comma, Boethius' comma
| | | -9 3 0 0 0 0 0 1 &gt;
| style="text-align:center;" | 513/512
| | 3.38
|-
| | moctdel
| | | -2 0 3 -3 1 &gt;
| style="text-align:center;" | 1375/1372
| | 3.78
|-
| | Beta 2, septimal schisma, garischisma
| | | 25 -14 0 -1 &gt;
| style="text-align:center;" |
| | 3.80
|-
| | Werckmeister's undecimal septenarian schisma, werckisma
| | | -3 2 -1 2 -1 &gt;
| style="text-align:center;" | 441/440
| | 3.93
|-
| | cuthbert
| | | 0 0 -1 1 2 -2 &gt;
| style="text-align:center;" | 847/845
| | 4.09
|-
| | undecimal kleisma, keenanisma
| | | -7 -1 1 1 1 &gt;
| style="text-align:center;" | 385/384
| | 4.50
|-
| | gentle comma
| | | 2 -1 0 1 -2 1 &gt;
| style="text-align:center;" | 364/363
| | 4.76
|-
| | minthma
| | | 5 -3 0 0 1 -1 &gt;
| style="text-align:center;" | 352/351
| | 4.93
|-
| | marveltwin
| | | -2 -4 2 0 0 1 &gt;
| style="text-align:center;" | 325/324
| | 5.34
|-
| | Beta 5, Garibaldi comma, hemifamity
| | | 10 -6 1 -1 &gt;
| style="text-align:center;" | 5120/5103
| | 5.76
|-
| | hemimage
| | | 5 -7 -1 3 &gt;
| style="text-align:center;" | 10976/10935
| | 6.48
|-
| | septendecimal kleisma
| | | 8 -1 -1 0 0 0 -1 &gt;
| style="text-align:center;" | 256/255
| | 6.78
|-
| | small BP diesis, mirkwai
| | | 0 3 4 -5 &gt;
| style="text-align:center;" | 16875/16807
| | 6.99
|-
| | neutral third comma, rastma
| | | -1 5 0 0 -2 &gt;
| style="text-align:center;" | 243/242
| | 7.14
|-
| | kestrel comma
| | | 2 3 0 -1 1 -2 &gt;
| style="text-align:center;" | 1188/1183
| | 7.30
|-
| | septimal kleisma, marvel comma
| | | -5 2 2 -1 &gt;
| style="text-align:center;" | 225/224
| | 7.71
|-
| | huntma
| | | 7 0 1 -2 0 -1 &gt;
| style="text-align:center;" | 640/637
| | 8.13
|-
| | spleen comma
| | | 1 1 1 1 -1 0 0 -1 &gt;
| style="text-align:center;" | 210/209
| | 8.26
|-
| | orgonisma
| | | 16 0 0 -2 -3 &gt;
| style="text-align:center;" | 65536/65219
| | 8.39
|-
| | gamelan residue, gamelisma
| | | -10 1 0 3 &gt;
| style="text-align:center;" | 1029/1024
| | 8.43
|-
| | septendecimal comma
| | | -7 7 0 0 0 0 -1 &gt;
| style="text-align:center;" | 2187/2176
| | 8.73
|-
| | mynucuma
| | | 2 -1 -1 2 0 -1 &gt;
| style="text-align:center;" | 196/195
| | 8.86
|-
| | quince
| | | -15 0 -2 7 &gt;
| style="text-align:center;" |
| | 9.15
|-
| | undecimal semicomma, pentacircle (minthma * gentle)
| | | 7 -4 0 1 -1 &gt;
| style="text-align:center;" | 896/891
| | 9.69
|-
| | 29th-partial chroma
| | | -4 -2 1 0 0 0 0 0 0 1 &gt;
| style="text-align:center;" | 145/144
| | 11.98
|-
| | grossma
| | | 4 2 0 0 -1 -1 &gt;
| style="text-align:center;" | 144/143
| | 12.06
|-
| | gassorma
| | | 0 -1 2 -1 1 -1 &gt;
| style="text-align:center;" | 275/273
| | 12.64
|-
| | septimal semicomma, octagar
| | | 5 -4 3 -2 &gt;
| style="text-align:center;" | 4000/3969
| | 13.47
|-
| | minor BP diesis, sensamagic
| | | 0 -5 1 2 &gt;
| style="text-align:center;" | 245/243
| | 14.19
|-
| | secorian
| | | 12 -7 0 1 0 -1/1 &gt;
| style="text-align:center;" | 28672/28431
| | 14.61
|-
| | mirwomo comma
| | | -15 3 2 2 &gt;
| style="text-align:center;" | 33075/32768
| | 16.14
|-
| | vicesimotertial comma
| | | 5 -6 0 0 0 0 0 0 1 &gt;
| style="text-align:center;" | 736/729
| | 16.54
|-
| | small tridecimal comma, animist
| | | -3 1 1 1 0 -1 &gt;
| style="text-align:center;" | 105/104
| | 16.57
|-
| | hemimin
| | | 6 1 0 1 -3 &gt;
| style="text-align:center;" | 1344/1331
| | 16.83
|-
| | Ptolemy's comma, ptolemisma
| | | 2 -2 2 0 -1 &gt;
| style="text-align:center;" | 100/99
| | 17.40
|-
| | '41-tone' comma
| | | 65 -41 &gt;
| style="text-align:center;" |
| | 19.84
|-
| | tolerma
| | | 10 -11 2 1 &gt;
| style="text-align:center;" |
| | 19.95
|-
| | major BP diesis, gariboh
| | | 0 -2 5 -3 &gt;
| style="text-align:center;" | 3125/3087
| | 21.18
|-
| | cassacot
| | | -1 0 1 2 -2 &gt;
| style="text-align:center;" | 245/242
| | 21.33
|-
| | keema
| | | -5 -3 3 1 &gt;
| style="text-align:center;" | 875/864
| | 21.90
|-
| | blackjackisma
| | | -10 7 8 -7 &gt;
| style="text-align:center;" |
| | 22.41
|-
| | roda
| | | 20 -17 3 &gt;
| style="text-align:center;" |
| | 25.71
|-
| | minimal diesis, tetracot comma
| | | 5 -9 4 &gt;
| style="text-align:center;" | 20000/19683
| | 27.66
|-
| | small diesis, magic comma
| | | -10 -1 5 &gt;
| style="text-align:center;" | 3125/3072
| | 29.61
|-
| | thuja comma
| | | 15 0 1 0 -5 &gt;
| style="text-align:center;" |
| | 29.72
|-
| | Ampersand's comma
| | | -25 7 6 &gt;
| style="text-align:center;" |
| | 31.57
|-
| | great BP diesis
| | | 0 -7 6 -1 &gt;
| style="text-align:center;" | 15625/15309
| | 35.37
|-
| | shibboleth
| | | -5 -10 9 &gt;
| style="text-align:center;" |
| | 57.27
|}
 
=Temperaments=
[[List_of_edo-distinct_41et_rank_two_temperaments|List of edo-distinct 41et rank two temperaments]]
 
=Intervals=
 
{| class="wikitable"
|-
! |
! | cents value
! | Approximate
 
Ratios in the [[11-limit|11-limit]]
! colspan="2" | [[Ups_and_Downs_Notation|ups and]]
 
[[Ups_and_Downs_Notation|downs]]
 
[[Ups_and_Downs_Notation|notation]]
! | Proposed names
! | Andrew's


=Intervals=
||~  ||~ cents value ||~ Approximate
Ratios in the [[11-limit]] ||||~ [[xenharmonic/Ups and Downs Notation|ups and]]
[[xenharmonic/Ups and Downs Notation|downs]]
[[xenharmonic/Ups and Downs Notation|notation]] ||~ Proposed names ||~ Andrew's
solfege
solfege
syllable ||~ generator for ||~ some MOS and MODMOS Scales available ||
||= 0 ||= 0.00 ||&lt; [[1_1|1/1]] ||= P1 ||= D || Unison || do ||  ||  ||
||= 1 ||= 29.27 ||&lt; [[81_80|81/80]] ||= ^1 ||= D^ || Red unison || di ||  ||  ||
||= 2 ||= 58.54 ||&lt; [[25_24|25/24]], [[28_27|28/27]],
[[33_32|33/32]] ||= vm2 ||= Ebv || Blue minor second || ro || [[Hemimiracle]] ||  ||
||= 3 ||= 87.80 ||&lt; [[21_20|21/20]], [[22_21|22/21]] ||= m2 ||= Eb || Gray minor second || rih || 88cET (approx),
[[octacot]] ||  ||
||= 4 ||= 117.07 ||&lt; [[16_15|16/15]], [[15_14|15/14]] ||= ^m2 ||= Eb^ || Red minor second || ra || [[Miracle]] ||  ||
||= 5 ||= 146.34 ||&lt; [[12_11|12/11]] ||= ~2 ||= Evv || Neutral second || ru || [[Bohlen-Pierce]]/[[bohpier]] ||  ||
||= 6 ||= 175.61 ||&lt; [[10_9|10/9]], [[11_10|11/10]] ||= vM2 ||= Ev || Blue major second || reh || [[Tetracot]]/[[bunya]]/[[monkey]] || 13-tone MOS: 1 5 1 5 1 5 1 5 5 1 5 1 5 ||
||= 7 ||= 204.88 ||&lt; [[9_8|9/8]] ||= M2 ||= E || Gray major second || re || [[Baldy]] || 11-tone MOS: 6 1 6 6 1 6 1 6 1 6 1 ||
||= 8 ||= 234.15 ||&lt; [[8_7|8/7]] ||= ^M2 ||= E^ || Red major second || ri || [[Rodan]]/[[guiron]] || 11-tone MOS: 7 1 7 1 7 1 7 1 1 7 1 ||
||= 9 ||= 263.41 ||&lt; [[7_6|7/6]], [[32_25|32/25]] ||= vm3 ||= Fv || Blue minor third || ma || [[Septimin]] || 9-tone MOS: 5 4 5 5 4 5 4 5 4 ||
||= 10 ||= 292.68 ||&lt; [[32_27|32/27]] ||= m3 ||= F || Gray minor third || meh || [[Quasitemp]] ||  ||
||= 11 ||= 321.95 ||&lt; [[6_5|6/5]] ||= ^m3 ||= F^ || Red minor third || me || [[Superkleismic]] || 11-tone MOS: 5 3 5 3 3 5 3 3 5 3 3 ||
||= 12 ||= 351.22 ||&lt; [[11_9|11/9]],[[27_22|27/22]] ||= ~3 ||= F^^ || Neutral third || mu || [[Hemififths]]/[[karadeniz]] || 10-tone MOS: 5 2 5 5 2 5 5 5 2 5 ||
||= 13 ||= 380.49 ||&lt; [[5_4|5/4]] ||= vM3 ||= F#v || Blue major third || mi || [[Magic]]/[[witchcraft]] || 10-tone MOS: 2 9 2 2 9 2 2 9 2 2 ||
||= 14 ||= 409.76 ||&lt; [[14_11|14/11]], [[81_64|81/64]] ||= M3 ||= F# || Gray major third || maa || [[Hocus]] ||  ||
||= 15 ||= 439.02 ||&lt; [[9_7|9/7]] ||= ^M3 ||= F#^ || Red major third || mo ||  || 11-tone MOS: 4 3 4 4 4 3 4 4 3 4 4 ||
||= 16 ||= 468.29 ||&lt; [[21_16|21/16]] ||= v4 ||= Gv || Blue fourth || fe || [[Barbad]] ||  ||
||= 17 ||= 497.56 ||&lt; [[4_3|4/3]] ||= P4 ||= G || Perfect fourth || fa || [[Schismatic]] ([[helmholtz]], [[Garibaldi temperament|garibaldi]], [[cassandra]]) ||  ||
||= 18 ||= 526.83 ||&lt; [[15_11|15/11]], [[27_20|27/20]] ||= ^4 ||= G^ || Red fourth || fih || [[Trismegistus]] || 9-tone MOS: 5 5 3 5 5 5 5 3 5 ||
||= 19 ||= 556.10 ||&lt; [[11_8|11/8]] ||= ^^4 ||= G^^ || Blue minor tritone || fu ||  ||  ||
||= 20 ||= 585.37 ||&lt; [[7_5|7/5]] ||= vA4, d5 ||= G#v,
Ab || Minor tritone / diminished fifth || fi || [[Pluto]] ||  ||
||= 21 ||= 614.63 ||&lt; [[10_7|10/7]] ||= A4, ^d5 ||= G#,
Ab^ || Major tritone / augmented fourth || se ||  ||  ||
||= 22 ||= 643.90 ||&lt; [[16_11|16/11]] ||= vv5 ||= Avv || Red major tritone || su ||  ||  ||
||= 23 ||= 673.17 ||&lt; [[22_15|22/15]], [[40_27|40/27]] ||= v5 ||= Av || Blue fifth || sih ||  ||  ||
||= 24 ||= 702.44 ||&lt; [[3_2|3/2]] ||= P5 ||= A || Perfect fifth || sol ||  ||  ||
||= 25 ||= 731.71 ||&lt; [[32_21|32/21]] ||= ^5 ||= A^ || Red fifth || si ||  ||  ||
||= 26 ||= 760.98 ||&lt; [[14_9|14/9]], [[25_16|25/16]] ||= vm6 ||= Bbv || Blue minor sixth || lo ||  ||  ||
||= 27 ||= 790.24 ||&lt; [[11_7|11/7]], [[128_81|128/81]] ||= m6 ||= Bb || Gray minor sixth || leh ||  ||  ||
||= 28 ||= 819.51 ||&lt; [[8_5|8/5]] ||= ^m6 ||= Bb^ || Red minor sixth || le ||  ||  ||
||= 29 ||= 848.78 ||&lt; [[18_11|18/11]], [[44_27|44/27]] ||= ~6 ||= Bvv || Neutral sixth || lu ||  ||  ||
||= 30 ||= 878.05 ||&lt; [[5_3|5/3]] ||= vM6 ||= Bv || Blue major sixth || la ||  ||  ||
||= 31 ||= 907.32 ||&lt; [[27_16|27/16]] ||= M6 ||= B || Gray major sixth || laa ||  ||  ||
||= 32 ||= 936.59 ||&lt; [[12_7|12/7]] ||= ^M6 ||= B^ || Red major sixth || li ||  ||  ||
||= 33 ||= 965.85 ||&lt; [[7_4|7/4]] ||= vm7 ||= Cv || Blue minor seventh || ta ||  ||  ||
||= 34 ||= 995.12 ||&lt; [[16_9|16/9]] ||= m7 ||= C || Gray minor seventh || teh ||  ||  ||
||= 35 ||= 1024.39 ||&lt; [[9_5|9/5]], [[20_11|20/11]] ||= ^m7 ||= C^ || Red minor seventh || te ||  ||  ||
||= 36 ||= 1053.66 ||&lt; [[11_6|11/6]] ||= ~7 ||= C^^ || Neutral seventh || tu ||  ||  ||
||= 37 ||= 1082.93 ||&lt; [[15_8|15/8]] ||= vM7 ||= C#v || Blue major seventh || ti ||  ||  ||
||= 38 ||= 1112.20 ||&lt; [[40_21|40/21]], [[21_11|21/11]] ||= M7 ||= C# || Gray major seventh || taa ||  ||  ||
||= 39 ||= 1141.46 ||&lt; [[48_25|48/25]], [[27_14|27/14]],
[[64_33|64/33]] ||= ^M7 ||= C#^ || Red major seventh || to ||  ||  ||
||= 40 ||= 1170.73 ||&lt; [[160_81|160/81]] ||= v8 ||= Dv || Blue octave || da ||  ||  ||
||= 41 ||= 1200 ||&lt; 2/1 ||= P8 ||= D ||  || do ||  ||  ||


Combining ups and downs notation with [[Kite's color notation|color notation]], qualities can be loosely associated with colors:
syllable
||~ quality ||~ color ||~ monzo format ||~ examples ||
! | generator for
||= downminor ||= blue ||= {a, b, 0, 1} ||= 7/6, 7/4 ||
! | some MOS and MODMOS Scales available
||= minor ||= fourthward white ||= {a, b}, b &lt; -1 ||= 32/27, 16/9 ||
|-
||= upminor ||= green ||= {a, b, -1} ||= 6/5, 9/5 ||
| style="text-align:center;" | 0
||= mid ||= jade ||= {a, b, 0, 0, 1} ||= 11/9, 11/6 ||
| style="text-align:center;" | 0.00
||= " ||= amber ||= {a, b, 0, 0, -1} ||= 12/11, 18/11 ||
| | [[1/1|1/1]]
||= downmajor ||= yellow ||= {a, b, 1} ||= 5/4, 5/3 ||
| style="text-align:center;" | P1
||= major ||= fifthward white ||= {a, b}, b &gt; 1 ||= 9/8, 27/16 ||
| style="text-align:center;" | D
||= upmajor ||= red ||= {a, b, 0, -1} ||= 9/7, 12/7 ||
| | Unison
| | do
| |
| |
|-
| style="text-align:center;" | 1
| style="text-align:center;" | 29.27
| | [[81/80|81/80]]
| style="text-align:center;" | ^1
| style="text-align:center;" | D^
| | Red unison
| | di
| |
| |
|-
| style="text-align:center;" | 2
| style="text-align:center;" | 58.54
| | [[25/24|25/24]], [[28/27|28/27]],
 
[[33/32|33/32]]
| style="text-align:center;" | vm2
| style="text-align:center;" | Ebv
| | Blue minor second
| | ro
| | [[Hemimiracle|Hemimiracle]]
| |
|-
| style="text-align:center;" | 3
| style="text-align:center;" | 87.80
| | [[21/20|21/20]], [[22/21|22/21]]
| style="text-align:center;" | m2
| style="text-align:center;" | Eb
| | Gray minor second
| | rih
| | 88cET (approx),
 
[[Octacot|octacot]]
| |
|-
| style="text-align:center;" | 4
| style="text-align:center;" | 117.07
| | [[16/15|16/15]], [[15/14|15/14]]
| style="text-align:center;" | ^m2
| style="text-align:center;" | Eb^
| | Red minor second
| | ra
| | [[Miracle|Miracle]]
| |
|-
| style="text-align:center;" | 5
| style="text-align:center;" | 146.34
| | [[12/11|12/11]]
| style="text-align:center;" | ~2
| style="text-align:center;" | Evv
| | Neutral second
| | ru
| | [[Bohlen-Pierce|Bohlen-Pierce]]/[[bohpier|bohpier]]
| |
|-
| style="text-align:center;" | 6
| style="text-align:center;" | 175.61
| | [[10/9|10/9]], [[11/10|11/10]]
| style="text-align:center;" | vM2
| style="text-align:center;" | Ev
| | Blue major second
| | reh
| | [[Tetracot|Tetracot]]/[[bunya|bunya]]/[[Monkey|monkey]]
| | 13-tone MOS: 1 5 1 5 1 5 1 5 5 1 5 1 5
|-
| style="text-align:center;" | 7
| style="text-align:center;" | 204.88
| | [[9/8|9/8]]
| style="text-align:center;" | M2
| style="text-align:center;" | E
| | Gray major second
| | re
| | [[Baldy|Baldy]]
| | 11-tone MOS: 6 1 6 6 1 6 1 6 1 6 1
|-
| style="text-align:center;" | 8
| style="text-align:center;" | 234.15
| | [[8/7|8/7]]
| style="text-align:center;" | ^M2
| style="text-align:center;" | E^
| | Red major second
| | ri
| | [[Rodan|Rodan]]/[[guiron|guiron]]
| | 11-tone MOS: 7 1 7 1 7 1 7 1 1 7 1
|-
| style="text-align:center;" | 9
| style="text-align:center;" | 263.41
| | [[7/6|7/6]], [[32/25|32/25]]
| style="text-align:center;" | vm3
| style="text-align:center;" | Fv
| | Blue minor third
| | ma
| | [[Septimin|Septimin]]
| | 9-tone MOS: 5 4 5 5 4 5 4 5 4
|-
| style="text-align:center;" | 10
| style="text-align:center;" | 292.68
| | [[32/27|32/27]]
| style="text-align:center;" | m3
| style="text-align:center;" | F
| | Gray minor third
| | meh
| | [[Quasitemp|Quasitemp]]
| |
|-
| style="text-align:center;" | 11
| style="text-align:center;" | 321.95
| | [[6/5|6/5]]
| style="text-align:center;" | ^m3
| style="text-align:center;" | F^
| | Red minor third
| | me
| | [[Superkleismic|Superkleismic]]
| | 11-tone MOS: 5 3 5 3 3 5 3 3 5 3 3
|-
| style="text-align:center;" | 12
| style="text-align:center;" | 351.22
| | [[11/9|11/9]],[[27/22|27/22]]
| style="text-align:center;" | ~3
| style="text-align:center;" | F^^
| | Neutral third
| | mu
| | [[Hemififths|Hemififths]]/[[karadeniz|karadeniz]]
| | 10-tone MOS: 5 2 5 5 2 5 5 5 2 5
|-
| style="text-align:center;" | 13
| style="text-align:center;" | 380.49
| | [[5/4|5/4]]
| style="text-align:center;" | vM3
| style="text-align:center;" | F#v
| | Blue major third
| | mi
| | [[Magic|Magic]]/[[witchcraft|witchcraft]]
| | 10-tone MOS: 2 9 2 2 9 2 2 9 2 2
|-
| style="text-align:center;" | 14
| style="text-align:center;" | 409.76
| | [[14/11|14/11]], [[81/64|81/64]]
| style="text-align:center;" | M3
| style="text-align:center;" | F#
| | Gray major third
| | maa
| | [[Hocus|Hocus]]
| |
|-
| style="text-align:center;" | 15
| style="text-align:center;" | 439.02
| | [[9/7|9/7]]
| style="text-align:center;" | ^M3
| style="text-align:center;" | F#^
| | Red major third
| | mo
| |
| | 11-tone MOS: 4 3 4 4 4 3 4 4 3 4 4
|-
| style="text-align:center;" | 16
| style="text-align:center;" | 468.29
| | [[21/16|21/16]]
| style="text-align:center;" | v4
| style="text-align:center;" | Gv
| | Blue fourth
| | fe
| | [[Barbad|Barbad]]
| |
|-
| style="text-align:center;" | 17
| style="text-align:center;" | 497.56
| | [[4/3|4/3]]
| style="text-align:center;" | P4
| style="text-align:center;" | G
| | Perfect fourth
| | fa
| | [[Schismatic|Schismatic]] ([[Helmholtz|helmholtz]], [[Garibaldi_temperament|garibaldi]], [[cassandra|cassandra]])
| |
|-
| style="text-align:center;" | 18
| style="text-align:center;" | 526.83
| | [[15/11|15/11]], [[27/20|27/20]]
| style="text-align:center;" | ^4
| style="text-align:center;" | G^
| | Red fourth
| | fih
| | [[Trismegistus|Trismegistus]]
| | 9-tone MOS: 5 5 3 5 5 5 5 3 5
|-
| style="text-align:center;" | 19
| style="text-align:center;" | 556.10
| | [[11/8|11/8]]
| style="text-align:center;" | ^^4
| style="text-align:center;" | G^^
| | Blue minor tritone
| | fu
| |
| |
|-
| style="text-align:center;" | 20
| style="text-align:center;" | 585.37
| | [[7/5|7/5]]
| style="text-align:center;" | vA4, d5
| style="text-align:center;" | G#v,
 
Ab
| | Minor tritone / diminished fifth
| | fi
| | [[Pluto|Pluto]]
| |
|-
| style="text-align:center;" | 21
| style="text-align:center;" | 614.63
| | [[10/7|10/7]]
| style="text-align:center;" | A4, ^d5
| style="text-align:center;" | G#,
 
Ab^
| | Major tritone / augmented fourth
| | se
| |
| |
|-
| style="text-align:center;" | 22
| style="text-align:center;" | 643.90
| | [[16/11|16/11]]
| style="text-align:center;" | vv5
| style="text-align:center;" | Avv
| | Red major tritone
| | su
| |
| |
|-
| style="text-align:center;" | 23
| style="text-align:center;" | 673.17
| | [[22/15|22/15]], [[40/27|40/27]]
| style="text-align:center;" | v5
| style="text-align:center;" | Av
| | Blue fifth
| | sih
| |
| |
|-
| style="text-align:center;" | 24
| style="text-align:center;" | 702.44
| | [[3/2|3/2]]
| style="text-align:center;" | P5
| style="text-align:center;" | A
| | Perfect fifth
| | sol
| |
| |
|-
| style="text-align:center;" | 25
| style="text-align:center;" | 731.71
| | [[32/21|32/21]]
| style="text-align:center;" | ^5
| style="text-align:center;" | A^
| | Red fifth
| | si
| |
| |
|-
| style="text-align:center;" | 26
| style="text-align:center;" | 760.98
| | [[14/9|14/9]], [[25/16|25/16]]
| style="text-align:center;" | vm6
| style="text-align:center;" | Bbv
| | Blue minor sixth
| | lo
| |
| |
|-
| style="text-align:center;" | 27
| style="text-align:center;" | 790.24
| | [[11/7|11/7]], [[128/81|128/81]]
| style="text-align:center;" | m6
| style="text-align:center;" | Bb
| | Gray minor sixth
| | leh
| |
| |
|-
| style="text-align:center;" | 28
| style="text-align:center;" | 819.51
| | [[8/5|8/5]]
| style="text-align:center;" | ^m6
| style="text-align:center;" | Bb^
| | Red minor sixth
| | le
| |
| |
|-
| style="text-align:center;" | 29
| style="text-align:center;" | 848.78
| | [[18/11|18/11]], [[44/27|44/27]]
| style="text-align:center;" | ~6
| style="text-align:center;" | Bvv
| | Neutral sixth
| | lu
| |
| |
|-
| style="text-align:center;" | 30
| style="text-align:center;" | 878.05
| | [[5/3|5/3]]
| style="text-align:center;" | vM6
| style="text-align:center;" | Bv
| | Blue major sixth
| | la
| |
| |
|-
| style="text-align:center;" | 31
| style="text-align:center;" | 907.32
| | [[27/16|27/16]]
| style="text-align:center;" | M6
| style="text-align:center;" | B
| | Gray major sixth
| | laa
| |
| |
|-
| style="text-align:center;" | 32
| style="text-align:center;" | 936.59
| | [[12/7|12/7]]
| style="text-align:center;" | ^M6
| style="text-align:center;" | B^
| | Red major sixth
| | li
| |
| |
|-
| style="text-align:center;" | 33
| style="text-align:center;" | 965.85
| | [[7/4|7/4]]
| style="text-align:center;" | vm7
| style="text-align:center;" | Cv
| | Blue minor seventh
| | ta
| |
| |
|-
| style="text-align:center;" | 34
| style="text-align:center;" | 995.12
| | [[16/9|16/9]]
| style="text-align:center;" | m7
| style="text-align:center;" | C
| | Gray minor seventh
| | teh
| |
| |
|-
| style="text-align:center;" | 35
| style="text-align:center;" | 1024.39
| | [[9/5|9/5]], [[20/11|20/11]]
| style="text-align:center;" | ^m7
| style="text-align:center;" | C^
| | Red minor seventh
| | te
| |
| |
|-
| style="text-align:center;" | 36
| style="text-align:center;" | 1053.66
| | [[11/6|11/6]]
| style="text-align:center;" | ~7
| style="text-align:center;" | C^^
| | Neutral seventh
| | tu
| |
| |
|-
| style="text-align:center;" | 37
| style="text-align:center;" | 1082.93
| | [[15/8|15/8]]
| style="text-align:center;" | vM7
| style="text-align:center;" | C#v
| | Blue major seventh
| | ti
| |
| |
|-
| style="text-align:center;" | 38
| style="text-align:center;" | 1112.20
| | [[40/21|40/21]], [[21/11|21/11]]
| style="text-align:center;" | M7
| style="text-align:center;" | C#
| | Gray major seventh
| | taa
| |
| |
|-
| style="text-align:center;" | 39
| style="text-align:center;" | 1141.46
| | [[48/25|48/25]], [[27/14|27/14]],
 
[[64/33|64/33]]
| style="text-align:center;" | ^M7
| style="text-align:center;" | C#^
| | Red major seventh
| | to
| |
| |
|-
| style="text-align:center;" | 40
| style="text-align:center;" | 1170.73
| | [[160/81|160/81]]
| style="text-align:center;" | v8
| style="text-align:center;" | Dv
| | Blue octave
| | da
| |
| |
|-
| style="text-align:center;" | 41
| style="text-align:center;" | 1200
| | 2/1
| style="text-align:center;" | P8
| style="text-align:center;" | D
| |
| | do
| |
| |
|}
 
Combining ups and downs notation with [[Kite's_color_notation|color notation]], qualities can be loosely associated with colors:
 
{| class="wikitable"
|-
! | quality
! | color
! | monzo format
! | examples
|-
| style="text-align:center;" | downminor
| style="text-align:center;" | blue
| style="text-align:center;" | {a, b, 0, 1}
| style="text-align:center;" | 7/6, 7/4
|-
| style="text-align:center;" | minor
| style="text-align:center;" | fourthward white
| style="text-align:center;" | {a, b}, b &lt; -1
| style="text-align:center;" | 32/27, 16/9
|-
| style="text-align:center;" | upminor
| style="text-align:center;" | green
| style="text-align:center;" | {a, b, -1}
| style="text-align:center;" | 6/5, 9/5
|-
| style="text-align:center;" | mid
| style="text-align:center;" | jade
| style="text-align:center;" | {a, b, 0, 0, 1}
| style="text-align:center;" | 11/9, 11/6
|-
| style="text-align:center;" | "
| style="text-align:center;" | amber
| style="text-align:center;" | {a, b, 0, 0, -1}
| style="text-align:center;" | 12/11, 18/11
|-
| style="text-align:center;" | downmajor
| style="text-align:center;" | yellow
| style="text-align:center;" | {a, b, 1}
| style="text-align:center;" | 5/4, 5/3
|-
| style="text-align:center;" | major
| style="text-align:center;" | fifthward white
| style="text-align:center;" | {a, b}, b &gt; 1
| style="text-align:center;" | 9/8, 27/16
|-
| style="text-align:center;" | upmajor
| style="text-align:center;" | red
| style="text-align:center;" | {a, b, 0, -1}
| style="text-align:center;" | 9/7, 12/7
|}
All 41edo chords can be named using ups and downs. Here are the blue, green, jade, yellow and red triads:
All 41edo chords can be named using ups and downs. Here are the blue, green, jade, yellow and red triads:
||~ color of the 3rd ||~ JI chord ||~ notes as edosteps ||~ notes of C chord ||~ written name ||~ spoken name ||
 
||= blue ||= 6:7:9 ||= 0-9-24 ||= C Ebv G ||= C.vm ||= C downminor ||
{| class="wikitable"
||= green ||= 10:12:15 ||= 0-11-24 ||= C Eb^ G ||= C.^m ||= C upminor ||
|-
||= jade ||= 18:22:27 ||= 0-12-24 ||= C Evv G ||= C~ ||= C mid ||
! | color of the 3rd
||= yellow ||= 4:5:6 ||= 0-13-24 ||= C Ev G ||= C.v ||= C downmajor or C dot down ||
! | JI chord
||= red ||= 14:18:27 ||= 0-15-24 ||= C E^ G ||= C.^ ||= C upmajor or C dot up ||
! | notes as edosteps
! | notes of C chord
! | written name
! | spoken name
|-
| style="text-align:center;" | blue
| style="text-align:center;" | 6:7:9
| style="text-align:center;" | 0-9-24
| style="text-align:center;" | C Ebv G
| style="text-align:center;" | C.vm
| style="text-align:center;" | C downminor
|-
| style="text-align:center;" | green
| style="text-align:center;" | 10:12:15
| style="text-align:center;" | 0-11-24
| style="text-align:center;" | C Eb^ G
| style="text-align:center;" | C.^m
| style="text-align:center;" | C upminor
|-
| style="text-align:center;" | jade
| style="text-align:center;" | 18:22:27
| style="text-align:center;" | 0-12-24
| style="text-align:center;" | C Evv G
| style="text-align:center;" | C~
| style="text-align:center;" | C mid
|-
| style="text-align:center;" | yellow
| style="text-align:center;" | 4:5:6
| style="text-align:center;" | 0-13-24
| style="text-align:center;" | C Ev G
| style="text-align:center;" | C.v
| style="text-align:center;" | C downmajor or C dot down
|-
| style="text-align:center;" | red
| style="text-align:center;" | 14:18:27
| style="text-align:center;" | 0-15-24
| style="text-align:center;" | C E^ G
| style="text-align:center;" | C.^
| style="text-align:center;" | C upmajor or C dot up
|}
0-10-20 = D F Ab = Ddim = "D dim"
0-10-20 = D F Ab = Ddim = "D dim"
0-10-21 = D F Ab^ = Ddim(^5) = "D dim up-five"
0-10-21 = D F Ab^ = Ddim(^5) = "D dim up-five"
0-10-22 = D F Avv = Dm(vv5) = "D minor double-down five", or possibly Ddim(^^5)
0-10-22 = D F Avv = Dm(vv5) = "D minor double-down five", or possibly Ddim(^^5)
0-10-23 = D F Av = Dm(v5) = "D minor down-five"
0-10-23 = D F Av = Dm(v5) = "D minor down-five"
0-10-24 = D F A = Dm = "D minor"
0-10-24 = D F A = Dm = "D minor"
0-14-24 = D F# A = D = "D" or "D major"
0-14-24 = D F# A = D = "D" or "D major"
0-14-25 = D F# A^ = D(^5) = "D up-five"
0-14-25 = D F# A^ = D(^5) = "D up-five"
0-14-26 = D F# A^^ = D(^^5) = "D double-up-five", or possibly Daug(vv5)
0-14-26 = D F# A^^ = D(^^5) = "D double-up-five", or possibly Daug(vv5)
0-14-27 = D F# A#v = Daug(v5) = "D aug down-five"
0-14-27 = D F# A#v = Daug(v5) = "D aug down-five"
0-14-28 = D F# A# is Daug = "D aug"
0-14-28 = D F# A# is Daug = "D aug"
etc.
etc.
For a more complete list, see [[xenharmonic/Ups and Downs Notation#Chord%20names%20in%20other%20EDOs|Ups and Downs Notation - Chord names in other EDOs]].


==Selected just intervals by error==  
For a more complete list, see [[Ups_and_Downs_Notation#Chord names in other EDOs|Ups and Downs Notation - Chord names in other EDOs]].
 
==Selected just intervals by error==
The following table shows how [[Just-24|some prominent just intervals]] are represented in 41edo (ordered by absolute error).
The following table shows how [[Just-24|some prominent just intervals]] are represented in 41edo (ordered by absolute error).
|| **Interval, complement** || **Error (abs., in [[cent|cents]])** ||
||= [[4_3|4/3]], [[3_2|3/2]] ||= 0.484 ||
||= [[9_8|9/8]], [[16_9|16/9]] ||= 0.968 ||
||= [[15_14|15/14]], [[28_15|28/15]] ||= 2.370 ||
||= [[7_5|7/5]], [[10_7|10/7]] ||= 2.854 ||
||= [[8_7|8/7]], [[7_4|7/4]] ||= 2.972 ||
||= [[7_6|7/6]], [[12_7|12/7]] ||= 3.456 ||
||= [[13_11|13/11]], [[22_13|22/13]] ||= 3.473 ||
||= [[11_9|11/9]], [[18_11|18/11]] ||= 3.812 ||
||= [[9_7|9/7]], [[14_9|14/9]] ||= 3.940 ||
||= [[12_11|12/11]], [[11_6|11/6]] ||= 4.296 ||
||= [[11_8|11/8]], [[16_11|16/11]] ||= 4.780 ||
||= [[16_15|16/15]], [[15_8|15/8]] ||= 5.342 ||
||= [[5_4|5/4]], [[8_5|8/5]] ||= 5.826 ||
||= [[6_5|6/5]], [[5_3|5/3]] ||= 6.310 ||
||= [[10_9|10/9]], [[9_5|9/5]] ||= 6.794 ||
||= [[18_13|18/13]], [[13_9|13/9]] ||= 7.285 ||
||= [[14_11|14/11]], [[11_7|11/7]] ||= 7.752 ||
||= [[13_12|13/12]], [[24_13|24/13]] ||= 7.769 ||
||= [[16_13|16/13]], [[13_8|13/8]] ||= 8.253 ||
||= [[15_11|15/11]], [[22_15|22/15]] ||= 10.122 ||
||= [[11_10|11/10]], [[20_11|20/11]] ||= 10.606 ||
||= [[14_13|14/13]], [[13_7|13/7]] ||= 11.225 ||
||= [[15_13|15/13]], [[26_15|26/15]] ||= 13.595 ||
||= [[13_10|13/10]], [[20_13|20/13]] ||= 14.079 ||


=Instruments=  
{| class="wikitable"
[[image:41-EDD elektrische gitaar.jpg width="560" height="745"]]
|-
//41-EDO Electric guitar, by Gregory Sanchez.//
| | '''Interval, complement'''
| | '''Error (abs., in [[cent|cents]])'''
|-
| style="text-align:center;" | [[4/3|4/3]], [[3/2|3/2]]
| style="text-align:center;" | 0.484
|-
| style="text-align:center;" | [[9/8|9/8]], [[16/9|16/9]]
| style="text-align:center;" | 0.968
|-
| style="text-align:center;" | [[15/14|15/14]], [[28/15|28/15]]
| style="text-align:center;" | 2.370
|-
| style="text-align:center;" | [[7/5|7/5]], [[10/7|10/7]]
| style="text-align:center;" | 2.854
|-
| style="text-align:center;" | [[8/7|8/7]], [[7/4|7/4]]
| style="text-align:center;" | 2.972
|-
| style="text-align:center;" | [[7/6|7/6]], [[12/7|12/7]]
| style="text-align:center;" | 3.456
|-
| style="text-align:center;" | [[13/11|13/11]], [[22/13|22/13]]
| style="text-align:center;" | 3.473
|-
| style="text-align:center;" | [[11/9|11/9]], [[18/11|18/11]]
| style="text-align:center;" | 3.812
|-
| style="text-align:center;" | [[9/7|9/7]], [[14/9|14/9]]
| style="text-align:center;" | 3.940
|-
| style="text-align:center;" | [[12/11|12/11]], [[11/6|11/6]]
| style="text-align:center;" | 4.296
|-
| style="text-align:center;" | [[11/8|11/8]], [[16/11|16/11]]
| style="text-align:center;" | 4.780
|-
| style="text-align:center;" | [[16/15|16/15]], [[15/8|15/8]]
| style="text-align:center;" | 5.342
|-
| style="text-align:center;" | [[5/4|5/4]], [[8/5|8/5]]
| style="text-align:center;" | 5.826
|-
| style="text-align:center;" | [[6/5|6/5]], [[5/3|5/3]]
| style="text-align:center;" | 6.310
|-
| style="text-align:center;" | [[10/9|10/9]], [[9/5|9/5]]
| style="text-align:center;" | 6.794
|-
| style="text-align:center;" | [[18/13|18/13]], [[13/9|13/9]]
| style="text-align:center;" | 7.285
|-
| style="text-align:center;" | [[14/11|14/11]], [[11/7|11/7]]
| style="text-align:center;" | 7.752
|-
| style="text-align:center;" | [[13/12|13/12]], [[24/13|24/13]]
| style="text-align:center;" | 7.769
|-
| style="text-align:center;" | [[16/13|16/13]], [[13/8|13/8]]
| style="text-align:center;" | 8.253
|-
| style="text-align:center;" | [[15/11|15/11]], [[22/15|22/15]]
| style="text-align:center;" | 10.122
|-
| style="text-align:center;" | [[11/10|11/10]], [[20/11|20/11]]
| style="text-align:center;" | 10.606
|-
| style="text-align:center;" | [[14/13|14/13]], [[13/7|13/7]]
| style="text-align:center;" | 11.225
|-
| style="text-align:center;" | [[15/13|15/13]], [[26/15|26/15]]
| style="text-align:center;" | 13.595
|-
| style="text-align:center;" | [[13/10|13/10]], [[20/13|20/13]]
| style="text-align:center;" | 14.079
|}
 
=Instruments=
[[File:41-EDD_elektrische_gitaar.jpg|alt=41-EDD elektrische gitaar.jpg|560x745px|41-EDD elektrische gitaar.jpg]]
 
''41-EDO Electric guitar, by Gregory Sanchez.''
 
[[File:Ron_Sword_with_a_41ET_Guitar.jpg|alt=Ron_Sword_with_a_41ET_Guitar.jpg|Ron_Sword_with_a_41ET_Guitar.jpg]]


[[image:Ron_Sword_with_a_41ET_Guitar.jpg]]
''41-EDO Classical guitar, by Ron Sword.''
//41-EDO Classical guitar, by Ron Sword.//


A possible system to tune keyboards in 41EDO is discussed in [[http://launch.groups.yahoo.com/group/tuning/message/74155]].
A possible system to tune keyboards in 41EDO is discussed in [http://launch.groups.yahoo.com/group/tuning/message/74155 http://launch.groups.yahoo.com/group/tuning/message/74155].


=Scales and modes=  
=Scales and modes=


A list of [[41edo modes]] (MOS and others).
A list of [[41edo_modes|41edo modes]] (MOS and others).


===Harmonic Scale===  
===Harmonic Scale===
41edo is the first edo to do some justice to Mode 8 of the [[OverToneSeries|harmonic series]], which Dante Rosati calls the "[[overtone scales|Diatonic Harmonic Series Scale]]," consisting of overtones 8 through 16 (sometimes made to repeat at the octave).
41edo is the first edo to do some justice to Mode 8 of the [[OverToneSeries|harmonic series]], which Dante Rosati calls the "[[overtone_scales|Diatonic Harmonic Series Scale]]," consisting of overtones 8 through 16 (sometimes made to repeat at the octave).


|| Overtones in "Mode 8": || 8 || 9 || 10 || 11 || 12 || 13 || 14 || 15 || 16 ||
{| class="wikitable"
|| ...as JI Ratio from 1/1: || 1/1 || 9/8 || 5/4 || 11/8 || 3/2 || 13/8 || 7/4 || 15/8 || 2/1 ||
|-
|| ...in cents: || 0 || 203.9 || 386.3 || 551.3 || 702.0 || 840.5 || 968.8 || 1088.3 || 1200.0 ||
| | Overtones in "Mode 8":
|| Nearest degree of 41edo: || 0 || 7 || 13 || 19 || 24 || 29 || 33 || 37 || 41 ||
| | 8
|| ...in cents: || 0 || 204.9 || 380.5 || 556.1 || 702.4 || 848.8 || 965.9 || 1082.9 || 1200.0 ||
| | 9
| | 10
| | 11
| | 12
| | 13
| | 14
| | 15
| | 16
|-
| | ...as JI Ratio from 1/1:
| | 1/1
| | 9/8
| | 5/4
| | 11/8
| | 3/2
| | 13/8
| | 7/4
| | 15/8
| | 2/1
|-
| | ...in cents:
| | 0
| | 203.9
| | 386.3
| | 551.3
| | 702.0
| | 840.5
| | 968.8
| | 1088.3
| | 1200.0
|-
| | Nearest degree of 41edo:
| | 0
| | 7
| | 13
| | 19
| | 24
| | 29
| | 33
| | 37
| | 41
|-
| | ...in cents:
| | 0
| | 204.9
| | 380.5
| | 556.1
| | 702.4
| | 848.8
| | 965.9
| | 1082.9
| | 1200.0
|}


While each overtone of Mode 8 is approximated within a reasonable degree of accuracy, the steps between the intervals are not uniquely represented. (41edo is, after all, a temperament.)
While each overtone of Mode 8 is approximated within a reasonable degree of accuracy, the steps between the intervals are not uniquely represented. (41edo is, after all, a temperament.)


7\41 (7 degrees of 41edo) (204.9 cents) stands in for just ratio 9/8 (203.9 cents) -- a close match.
7\41 (7 degrees of 41edo) (204.9 cents) stands in for just ratio 9/8 (203.9 cents) -- a close match.
6\41 (175.6 cents) stands in for both 10/9 (182.4 cents) and 11/10 (165.0 cents).
6\41 (175.6 cents) stands in for both 10/9 (182.4 cents) and 11/10 (165.0 cents).
5\41 (146.3 cents) stands in for both 12/11 (150.6 cents) and 13/12 (138.6 cents).
5\41 (146.3 cents) stands in for both 12/11 (150.6 cents) and 13/12 (138.6 cents).
4\41 (117.1 cents) stands in for 14/13 (128.3 cents), 15/14 (119.4 cents), and 16/15 (111.7 cents).
4\41 (117.1 cents) stands in for 14/13 (128.3 cents), 15/14 (119.4 cents), and 16/15 (111.7 cents).


The scale in 41, as adjacent steps, thus goes: 7 6 6 5 5 4 4 4.
The scale in 41, as adjacent steps, thus goes: 7 6 6 5 5 4 4 4.


=Nonoctave Temperaments=  
=Nonoctave Temperaments=
Taking every third degree of 41edo produces a scale extremely close to [[88cET]] or 88-cent equal temperament (or the 8th root of 3:2). Likewise, taking every fifth degree produces a scale very close to the equal-tempered &lt;span class="wiki_link_new"&gt;[[BP|Bohlen-Pierce]]&lt;/span&gt;[[BP| Scale]] (or the 13th root of 3). See chart:
Taking every third degree of 41edo produces a scale extremely close to [[88cET|88cET]] or 88-cent equal temperament (or the 8th root of 3:2). Likewise, taking every fifth degree produces a scale very close to the equal-tempered <span style="">[[BP|Bohlen-Pierce]]</span>[[BP| Scale]] (or the 13th root of 3). See chart:


||||||= 3 degrees of 41edo (near 88cET) ||= overlap ||||||= 5 degrees of 41edo (near BP) ||
{| class="wikitable"
||~ deg of 41edo ||~ deg of 88cET ||~ cents ||~ cents ||~ cents ||~ deg of BP ||~ deg of 41edo ||
|-
||= 0 ||= 0 ||=   ||= 0 ||=   ||= 0 ||= 0 ||
| colspan="3" style="text-align:center;" | 3 degrees of 41edo (near 88cET)
||= 3 ||= 1 ||= 87.8 ||=   ||=   ||=   ||=   ||
| style="text-align:center;" | overlap
||=   ||=   ||=   ||=   ||= 146.3 ||= 1 ||= 5 ||
| colspan="3" style="text-align:center;" | 5 degrees of 41edo (near BP)
||= 6 ||= 2 ||= 175.6 ||=   ||=   ||=   ||=   ||
|-
||= 9 ||= 3 ||= 263.4 ||=   ||=   ||=   ||=   ||
! | deg of 41edo
||=   ||=   ||=   ||=   ||= 292.7 ||= 2 ||= 10 ||
! | deg of 88cET
||= 12 ||= 4 ||= 351.2 ||=   ||=   ||=   ||=   ||
! | cents
||= 15 ||= 5 ||=   ||= 439.0 ||=   ||= 3 ||= 15 ||
! | cents
||= 18 ||= 6 ||= 526.8 ||=   ||=   ||=   ||=   ||
! | cents
||=   ||=   ||=   ||=   ||= 585.4 ||= 4 ||= 20 ||
! | deg of BP
||= 21 ||= 7 ||= 614.6 ||=   ||=   ||=   ||=   ||
! | deg of 41edo
||= 24 ||= 8 ||= 702.4 ||=   ||=   ||=   ||=   ||
|-
||=   ||=   ||=   ||=   ||= 731.7 ||= 5 ||= 25 ||
| style="text-align:center;" | 0
||= 27 ||= 9 ||= 790.2 ||=   ||=   ||=   ||=   ||
| style="text-align:center;" | 0
||= 30 ||= 10 ||=   ||= 878.0 ||=   ||= 6 ||= 30 ||
| style="text-align:center;" |  
||= 33 ||= 11 ||= 965.9 ||=   ||=   ||=   ||=   ||
| style="text-align:center;" | 0
||=   ||=   ||=   ||=   ||= 1024.4 ||= 7 ||= 35 ||
| style="text-align:center;" |  
||= 36 ||= 12 ||= 1053.7 ||=   ||=   ||=   ||=   ||
| style="text-align:center;" | 0
||= 39 ||= 13 ||= 1141.5 ||=   ||=   ||=   ||=   ||
| style="text-align:center;" | 0
||=   ||=   ||=   ||=   ||= 1170.7 ||= 8 ||= 40 ||
|-
||||||||||||||~ [ second octave ] ||
| style="text-align:center;" | 3
||= 1 ||= 14 ||= 29.2 ||=   ||=   ||=   ||=   ||
| style="text-align:center;" | 1
||= 4 ||= 15 ||=   ||= 117.1 ||=   ||= 9 ||= 4 ||
| style="text-align:center;" | 87.8
||= 7 ||= 16 ||= 204.9 ||=   ||=   ||=   ||=   ||
| style="text-align:center;" |  
||=   ||=   ||=   ||=   ||= 263.4 ||= 10 ||= 9 ||
| style="text-align:center;" |  
||= 10 ||= 17 ||= 292.7 ||=   ||=   ||=   ||=   ||
| style="text-align:center;" |  
||= 13 ||= 18 ||= 380.5 ||=   ||=   ||=   ||=   ||
| style="text-align:center;" |  
||=   ||=   ||=   ||=   ||= 409.8 ||= 11 ||= 14 ||
|-
||= 16 ||= 19 ||= 468.3 ||=   ||=   ||=   ||=   ||
| style="text-align:center;" |  
||= 19 ||= 20 ||=   ||= 556.1 ||=   ||= 12 ||= 19 ||
| style="text-align:center;" |  
||= 22 ||= 21 ||= 643.9 ||=   ||=   ||=   ||=   ||
| style="text-align:center;" |  
||=   ||=   ||=   ||=   ||= 702.4 ||= 13 ||= 24 ||
| style="text-align:center;" |  
||= 25 ||= 22 ||= 731.7 ||=   ||=   ||=   ||=   ||
| style="text-align:center;" | 146.3
||= 28 ||= 23 ||= 819.5 ||=   ||=   ||=   ||=   ||
| style="text-align:center;" | 1
||=   ||=   ||=   ||=   ||= 848.8 ||= 14 ||= 29 ||
| style="text-align:center;" | 5
||= 31 ||= 24 ||= 907.3 ||=   ||=   ||=   ||=   ||
|-
||= 34 ||= 25 ||=   ||= 995.1 ||=   ||= 15 ||= 34 ||
| style="text-align:center;" | 6
||= 37 ||= 26 ||= 1082.9 ||=   ||=   ||=   ||=   ||
| style="text-align:center;" | 2
||=   ||=   ||=   ||=   ||= 1141.5 ||= 16 ||= 39 ||
| style="text-align:center;" | 175.6
||= 40 ||= 27 ||= 1170.7 ||=   ||=   ||=   ||=   ||
| style="text-align:center;" |  
||||||||||||||~ [ third octave ] ||
| style="text-align:center;" |  
||= 2 ||= 28 ||= 58.5 ||=   ||=   ||=   ||=   ||
| style="text-align:center;" |  
||=   ||=   ||=   ||=   ||= 87.8 ||= 17 ||= 3 ||
| style="text-align:center;" |  
||= 5 ||= 29 ||= 146.3 ||=   ||=   ||=   ||=   ||
|-
||= 8 ||= 30 ||=   ||= 234.1 ||=   ||= 18 ||= 8 ||
| style="text-align:center;" | 9
||= 11 ||= 31 ||= 322.0 ||=   ||=   ||=   ||=   ||
| style="text-align:center;" | 3
||=   ||=   ||=   ||=   ||= 380.5 ||= 19 ||= 13 ||
| style="text-align:center;" | 263.4
||= 14 ||= 32 ||= 409.8 ||=   ||=   ||=   ||=   ||
| style="text-align:center;" |  
||= 17 ||= 33 ||= 497.6 ||=   ||=   ||=   ||=   ||
| style="text-align:center;" |  
||=   ||=   ||=   ||=   ||= 526.8 ||= 20 ||= 18 ||
| style="text-align:center;" |  
||= 20 ||= 34 ||= 585.3 ||=   ||=   ||=   ||=   ||
| style="text-align:center;" |  
||= 23 ||= 35 ||=   ||= 673.2 ||=   ||= 21 ||= 23 ||
|-
||= 26 ||= 36 ||= 761.0 ||=   ||=   ||=   ||=   ||
| style="text-align:center;" |  
||=   ||=   ||=   ||=   ||= 819.5 ||= 22 ||= 28 ||
| style="text-align:center;" |  
||= 29 ||= 37 ||= 848.8 ||=   ||=   ||=   ||=   ||
| style="text-align:center;" |  
||= 32 ||= 38 ||= 936.6 ||=   ||=   ||=   ||=   ||
| style="text-align:center;" |  
||=   ||=   ||=   ||=   ||= 965.9 ||= 23 ||= 33 ||
| style="text-align:center;" | 292.7
||= 35 ||= 39 ||= 1024.4 ||=   ||=   ||=   ||=   ||
| style="text-align:center;" | 2
||= 38 ||= 40 ||=   ||= 1112.2 ||=   ||= 24 ||= 38 ||
| style="text-align:center;" | 10
|-
| style="text-align:center;" | 12
| style="text-align:center;" | 4
| style="text-align:center;" | 351.2
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
| style="text-align:center;" | 15
| style="text-align:center;" | 5
| style="text-align:center;" |  
| style="text-align:center;" | 439.0
| style="text-align:center;" |  
| style="text-align:center;" | 3
| style="text-align:center;" | 15
|-
| style="text-align:center;" | 18
| style="text-align:center;" | 6
| style="text-align:center;" | 526.8
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 585.4
| style="text-align:center;" | 4
| style="text-align:center;" | 20
|-
| style="text-align:center;" | 21
| style="text-align:center;" | 7
| style="text-align:center;" | 614.6
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
| style="text-align:center;" | 24
| style="text-align:center;" | 8
| style="text-align:center;" | 702.4
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 731.7
| style="text-align:center;" | 5
| style="text-align:center;" | 25
|-
| style="text-align:center;" | 27
| style="text-align:center;" | 9
| style="text-align:center;" | 790.2
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
| style="text-align:center;" | 30
| style="text-align:center;" | 10
| style="text-align:center;" |  
| style="text-align:center;" | 878.0
| style="text-align:center;" |  
| style="text-align:center;" | 6
| style="text-align:center;" | 30
|-
| style="text-align:center;" | 33
| style="text-align:center;" | 11
| style="text-align:center;" | 965.9
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 1024.4
| style="text-align:center;" | 7
| style="text-align:center;" | 35
|-
| style="text-align:center;" | 36
| style="text-align:center;" | 12
| style="text-align:center;" | 1053.7
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
| style="text-align:center;" | 39
| style="text-align:center;" | 13
| style="text-align:center;" | 1141.5
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 1170.7
| style="text-align:center;" | 8
| style="text-align:center;" | 40
|-
! colspan="7" | [ second octave ]
|-
| style="text-align:center;" | 1
| style="text-align:center;" | 14
| style="text-align:center;" | 29.2
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
| style="text-align:center;" | 4
| style="text-align:center;" | 15
| style="text-align:center;" |  
| style="text-align:center;" | 117.1
| style="text-align:center;" |  
| style="text-align:center;" | 9
| style="text-align:center;" | 4
|-
| style="text-align:center;" | 7
| style="text-align:center;" | 16
| style="text-align:center;" | 204.9
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 263.4
| style="text-align:center;" | 10
| style="text-align:center;" | 9
|-
| style="text-align:center;" | 10
| style="text-align:center;" | 17
| style="text-align:center;" | 292.7
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
| style="text-align:center;" | 13
| style="text-align:center;" | 18
| style="text-align:center;" | 380.5
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 409.8
| style="text-align:center;" | 11
| style="text-align:center;" | 14
|-
| style="text-align:center;" | 16
| style="text-align:center;" | 19
| style="text-align:center;" | 468.3
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
| style="text-align:center;" | 19
| style="text-align:center;" | 20
| style="text-align:center;" |  
| style="text-align:center;" | 556.1
| style="text-align:center;" |  
| style="text-align:center;" | 12
| style="text-align:center;" | 19
|-
| style="text-align:center;" | 22
| style="text-align:center;" | 21
| style="text-align:center;" | 643.9
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 702.4
| style="text-align:center;" | 13
| style="text-align:center;" | 24
|-
| style="text-align:center;" | 25
| style="text-align:center;" | 22
| style="text-align:center;" | 731.7
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
| style="text-align:center;" | 28
| style="text-align:center;" | 23
| style="text-align:center;" | 819.5
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 848.8
| style="text-align:center;" | 14
| style="text-align:center;" | 29
|-
| style="text-align:center;" | 31
| style="text-align:center;" | 24
| style="text-align:center;" | 907.3
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
| style="text-align:center;" | 34
| style="text-align:center;" | 25
| style="text-align:center;" |  
| style="text-align:center;" | 995.1
| style="text-align:center;" |  
| style="text-align:center;" | 15
| style="text-align:center;" | 34
|-
| style="text-align:center;" | 37
| style="text-align:center;" | 26
| style="text-align:center;" | 1082.9
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 1141.5
| style="text-align:center;" | 16
| style="text-align:center;" | 39
|-
| style="text-align:center;" | 40
| style="text-align:center;" | 27
| style="text-align:center;" | 1170.7
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
! colspan="7" | [ third octave ]
|-
| style="text-align:center;" | 2
| style="text-align:center;" | 28
| style="text-align:center;" | 58.5
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 87.8
| style="text-align:center;" | 17
| style="text-align:center;" | 3
|-
| style="text-align:center;" | 5
| style="text-align:center;" | 29
| style="text-align:center;" | 146.3
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
| style="text-align:center;" | 8
| style="text-align:center;" | 30
| style="text-align:center;" |  
| style="text-align:center;" | 234.1
| style="text-align:center;" |  
| style="text-align:center;" | 18
| style="text-align:center;" | 8
|-
| style="text-align:center;" | 11
| style="text-align:center;" | 31
| style="text-align:center;" | 322.0
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 380.5
| style="text-align:center;" | 19
| style="text-align:center;" | 13
|-
| style="text-align:center;" | 14
| style="text-align:center;" | 32
| style="text-align:center;" | 409.8
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
| style="text-align:center;" | 17
| style="text-align:center;" | 33
| style="text-align:center;" | 497.6
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 526.8
| style="text-align:center;" | 20
| style="text-align:center;" | 18
|-
| style="text-align:center;" | 20
| style="text-align:center;" | 34
| style="text-align:center;" | 585.3
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
| style="text-align:center;" | 23
| style="text-align:center;" | 35
| style="text-align:center;" |  
| style="text-align:center;" | 673.2
| style="text-align:center;" |  
| style="text-align:center;" | 21
| style="text-align:center;" | 23
|-
| style="text-align:center;" | 26
| style="text-align:center;" | 36
| style="text-align:center;" | 761.0
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 819.5
| style="text-align:center;" | 22
| style="text-align:center;" | 28
|-
| style="text-align:center;" | 29
| style="text-align:center;" | 37
| style="text-align:center;" | 848.8
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
| style="text-align:center;" | 32
| style="text-align:center;" | 38
| style="text-align:center;" | 936.6
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 965.9
| style="text-align:center;" | 23
| style="text-align:center;" | 33
|-
| style="text-align:center;" | 35
| style="text-align:center;" | 39
| style="text-align:center;" | 1024.4
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
| style="text-align:center;" | 38
| style="text-align:center;" | 40
| style="text-align:center;" |  
| style="text-align:center;" | 1112.2
| style="text-align:center;" |  
| style="text-align:center;" | 24
| style="text-align:center;" | 38
|}


==Notation==  
==Notation==


A red-note/blue-note system, similar to the one proposed for [[36edo]], is one option for notating 41edo. (This is separate from and not compatible with Kite's [[xenharmonic/Kite's color notation|color notation]].) We have the "white key" albitonic notes A-G (7 in total), the "black key" sharps and flats (10 in total), a "red" and "blue" version of each albitonic note (14 in total), a "red" (dark red?) version of each sharp and a "blue" (dark blue?) version of each flat (10 in total), adding up to 41. This would result in quite a colorful keyboard! Note that there are no red flats or blue sharps. Using this nomenclature the notes are:
A red-note/blue-note system, similar to the one proposed for [[36edo|36edo]], is one option for notating 41edo. (This is separate from and not compatible with Kite's [[Kite's_color_notation|color notation]].) We have the "white key" albitonic notes A-G (7 in total), the "black key" sharps and flats (10 in total), a "red" and "blue" version of each albitonic note (14 in total), a "red" (dark red?) version of each sharp and a "blue" (dark blue?) version of each flat (10 in total), adding up to 41. This would result in quite a colorful keyboard! Note that there are no red flats or blue sharps. Using this nomenclature the notes are:


A, red A, blue Bb, Bb, A#, red A#, blue B, B, red B, blue C, C, red C, blue Db, Db, C#, red C#, blue D, D, red D, blue Eb, Eb, D#, red D#, blue E, E, red E, blue F, F, red F, blue Gb, Gb, F#, red F#, blue G, G, red G, blue Ab, Ab, G#, red G#, blue A, A.
A, red A, blue Bb, Bb, A#, red A#, blue B, B, red B, blue C, C, red C, blue Db, Db, C#, red C#, blue D, D, red D, blue Eb, Eb, D#, red D#, blue E, E, red E, blue F, F, red F, blue Gb, Gb, F#, red F#, blue G, G, red G, blue Ab, Ab, G#, red G#, blue A, A.
Line 304: Line 1,548:
The step size of 41edo is small enough that the smallest interval (the "red/blue unison", seventh-tone, comma, diesis or whatever you want to call it) is actually fairly consonant with most timbres; it resembles a "noticeably out of tune unison" rather than a minor second, and has its own distinct character and appeal.
The step size of 41edo is small enough that the smallest interval (the "red/blue unison", seventh-tone, comma, diesis or whatever you want to call it) is actually fairly consonant with most timbres; it resembles a "noticeably out of tune unison" rather than a minor second, and has its own distinct character and appeal.


If "red" is replaced by "up", "blue" by "down", and "neutral" by "mid", and if "gray" is omitted, this notation becomes essentially the same as [[Ups and Downs Notation|ups and downs notation]]. The only difference is the use of minor tritone and major tritone.
If "red" is replaced by "up", "blue" by "down", and "neutral" by "mid", and if "gray" is omitted, this notation becomes essentially the same as [[Ups_and_Downs_Notation|ups and downs notation]]. The only difference is the use of minor tritone and major tritone.
 
 
=Music=
[[http://soundcloud.com/cameron-bobro/eveninghorizon-cbobro|EveningHorizon]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3|play]] by Cameron Bobro
 
=Links=
* [[http://en.wikipedia.org/wiki/41_equal_temperament|Wikipedia article on 41edo]]
* [[Magic22 as srutis#magic22assrutis]] describes a possible use of 41edo for [[indian]] music.
* see also [[Magic family]]
* Sword, Ron. [[@http://www.ronsword.com|"Tetracontamonophonic Scales for Guitar"]]
* Taylor, Cam. [[https://drive.google.com/open?id=0B3wIGTmjY_VZYllwcHI0d3hEc3M|Intervals, Scales and Chords in 41EDO]], a work in progress using just intonation concepts and simplified Sagittal notation.</pre></div>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;41edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="color: #004d25; font-family: 'Times New Roman',Times,serif; font-size: 20px;"&gt;&lt;strong&gt;41 Tone Equal Temperament&lt;/strong&gt;&lt;/span&gt;&lt;br /&gt;
&lt;span style="display: block; text-align: right;"&gt;&lt;a class="wiki_link" href="http://xenharmonie.wikispaces.com/41edo"&gt;Deutsch&lt;/a&gt;&lt;br /&gt;
&lt;/span&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextTocRule:33:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextTocRule:34: --&gt;&lt;a href="#Introduction"&gt;Introduction&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:34 --&gt;&lt;!-- ws:start:WikiTextTocRule:35: --&gt; | &lt;a href="#Commas"&gt;Commas&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:35 --&gt;&lt;!-- ws:start:WikiTextTocRule:36: --&gt; | &lt;a href="#Temperaments"&gt;Temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:36 --&gt;&lt;!-- ws:start:WikiTextTocRule:37: --&gt; | &lt;a href="#Intervals"&gt;Intervals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:37 --&gt;&lt;!-- ws:start:WikiTextTocRule:38: --&gt;&lt;!-- ws:end:WikiTextTocRule:38 --&gt;&lt;!-- ws:start:WikiTextTocRule:39: --&gt; | &lt;a href="#Instruments"&gt;Instruments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:39 --&gt;&lt;!-- ws:start:WikiTextTocRule:40: --&gt; | &lt;a href="#Scales and modes"&gt;Scales and modes&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:40 --&gt;&lt;!-- ws:start:WikiTextTocRule:41: --&gt;&lt;!-- ws:end:WikiTextTocRule:41 --&gt;&lt;!-- ws:start:WikiTextTocRule:42: --&gt; | &lt;a href="#Nonoctave Temperaments"&gt;Nonoctave Temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:42 --&gt;&lt;!-- ws:start:WikiTextTocRule:43: --&gt;&lt;!-- ws:end:WikiTextTocRule:43 --&gt;&lt;!-- ws:start:WikiTextTocRule:44: --&gt; | &lt;a href="#Music"&gt;Music&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:44 --&gt;&lt;!-- ws:start:WikiTextTocRule:45: --&gt; | &lt;a href="#Links"&gt;Links&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:45 --&gt;&lt;!-- ws:start:WikiTextTocRule:46: --&gt;
&lt;!-- ws:end:WikiTextTocRule:46 --&gt;&lt;hr /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:9:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Introduction"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:9 --&gt;Introduction&lt;/h1&gt;
The 41-tET, 41-EDO, or 41-ET, is the scale derived by dividing the octave into 41 equally-sized steps. Each step represents a frequency ratio of 29.268 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s, an &lt;a class="wiki_link" href="/interval"&gt;interval&lt;/a&gt; close in size to &lt;a class="wiki_link" href="/64_63"&gt;64/63&lt;/a&gt;, the &lt;a class="wiki_link" href="/Septimal%20comma"&gt;septimal comma&lt;/a&gt;. 41-ET can be seen as a tuning of the &lt;em&gt;&lt;a class="wiki_link" href="/Schismatic%20family#Garibaldi"&gt;Garibaldi temperament&lt;/a&gt;&lt;/em&gt; &lt;!-- ws:start:WikiTextRefRule:2:&amp;amp;lt;ref&amp;amp;gt;&amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;http://x31eq.com/schismic.htm&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;&amp;amp;quot;Schismic Temperaments&amp;amp;quot;&amp;lt;/a&amp;gt; at x31eq.com the website of &amp;lt;a class=&amp;quot;wiki_link&amp;quot; href=&amp;quot;/Graham%20Breed&amp;quot;&amp;gt;Graham Breed&amp;lt;/a&amp;gt;&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-1" class="reference"&gt;&lt;a href="#cite_note-1"&gt;[1]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:2 --&gt; , &lt;!-- ws:start:WikiTextRefRule:4:&amp;amp;lt;ref&amp;amp;gt;&amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;http://x31eq.com/decimal_lattice.htm&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;&amp;amp;quot;Lattices with Decimal Notation&amp;amp;quot;&amp;lt;/a&amp;gt; at x31eq.com&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-2" class="reference"&gt;&lt;a href="#cite_note-2"&gt;[2]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:4 --&gt; , &lt;!-- ws:start:WikiTextRefRule:6:&amp;amp;lt;ref&amp;amp;gt;&amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;http://en.wikipedia.org/wiki/Schismatic_temperament&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;Schismatic temperament&amp;lt;/a&amp;gt;&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-3" class="reference"&gt;&lt;a href="#cite_note-3"&gt;[3]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:6 --&gt; the &lt;em&gt;&lt;a class="wiki_link" href="/Magic%20family"&gt;Magic temperament&lt;/a&gt;&lt;/em&gt; &lt;!-- ws:start:WikiTextRefRule:8:&amp;amp;lt;ref&amp;amp;gt;&amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;http://en.wikipedia.org/wiki/Magic_temperament&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;Magic temperament&amp;lt;/a&amp;gt;&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-4" class="reference"&gt;&lt;a href="#cite_note-4"&gt;[4]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:8 --&gt; and the superkleismic (41&amp;amp;26) temperament. It is the second smallest equal temperament (after &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt;) whose perfect fifth is closer to just intonation than that of &lt;a class="wiki_link" href="/12edo"&gt;12-ET&lt;/a&gt;, and is the seventh &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists"&gt;zeta integral edo&lt;/a&gt; after 31; it is not, however, a &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists"&gt;zeta gap edo&lt;/a&gt;. This has to do with the fact that it can deal with the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; fairly well, and the &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; perhaps close enough for government work, though its &lt;a class="wiki_link" href="/13_10"&gt;13/10&lt;/a&gt; is 14 cents sharp. Various 13-limit &lt;a class="wiki_link" href="/magic%20extensions"&gt;magic extensions&lt;/a&gt; are supported by 41: 13-limit magic, and less successfully necromancy and witchcraft, all merge into one in 41edo tuning. The 41f val provides a superb tuning for sorcery, giving a less-complex version of the 13-limit, and the 41ef val likewise works well for telepathy; telepathy and sorcery merging into one however not in 41edo but in 22edo.&lt;br /&gt;
&lt;br /&gt;
41edo is consistent in the 15 odd limit. In fact, &lt;em&gt;all&lt;/em&gt; of its intervals between 100 and 1100 cents in size are 15-odd-limit consonances. (In comparison, &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; is only consistent up to the 11-limit, and the intervals 12/31 and 19/31 have no 11-limit approximations).&lt;br /&gt;
&lt;br /&gt;
41-ET forms the foundation of the &lt;a class="wiki_link_ext" href="http://www.h-pi.com/theory/huntsystem1.html" rel="nofollow"&gt;H-System&lt;/a&gt;, which uses the scale degrees of 41-ET as the basic &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; intervals requiring fine tuning +/- 1 &lt;a class="wiki_link_ext" href="http://www.h-pi.com/theory/huntsystem2.html" rel="nofollow"&gt;average JND&lt;/a&gt; from the 41-ET circle in &lt;a class="wiki_link" href="/205edo"&gt;205edo&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
41edo is the 13th &lt;a class="wiki_link" href="/prime%20numbers"&gt;prime&lt;/a&gt; edo, following &lt;a class="wiki_link" href="/37edo"&gt;37edo&lt;/a&gt; and coming before &lt;a class="wiki_link" href="/43edo"&gt;43edo&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:11:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:11 --&gt;Commas&lt;/h1&gt;
41 EDO tempers out the following commas using its patent val, &amp;lt; 41 65 95 115 142 152 168 174 185 199 203 |.&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;th&gt;Name&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Monzo&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Ratio&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Cents&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;odiheim&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -1 2 -4 5 -2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0.15&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;harmonisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 3 -2 0 -1 3 -2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;10648/10647&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0.16&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;tridecimal schisma, Sagittal schismina&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 12 -2 -1 -1 0 -1/1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4096/4095&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0.42&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Lehmerisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -4 -3 2 -1 2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3025/3024&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0.57&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Breedsma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -5 -1 -2 4 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2401/2400&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0.72&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Eratosthenes' comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 6 -5 -1 0 0 0 0 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1216/1215&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1.42&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;schisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -15 8 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;32805/32768&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1.95&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;squbema&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -3 6 0 -1 0 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;729/728&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2.38&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;septendecimal bridge comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -1 -1 1 -1 1 1 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;715/714&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2.42&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Swets' comma, swetisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 2 3 1 -2 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;540/539&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3.21&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;undevicesimal comma, Boethius' comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -9 3 0 0 0 0 0 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;513/512&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3.38&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;moctdel&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -2 0 3 -3 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1375/1372&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3.78&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Beta 2, septimal schisma, garischisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 25 -14 0 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3.80&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Werckmeister's undecimal septenarian schisma, werckisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -3 2 -1 2 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;441/440&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3.93&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;cuthbert&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 0 0 -1 1 2 -2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;847/845&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4.09&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;undecimal kleisma, keenanisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -7 -1 1 1 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;385/384&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4.50&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;gentle comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 2 -1 0 1 -2 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;364/363&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4.76&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;minthma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 5 -3 0 0 1 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;352/351&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4.93&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;marveltwin&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -2 -4 2 0 0 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;325/324&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5.34&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Beta 5, Garibaldi comma, hemifamity&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 10 -6 1 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5120/5103&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5.76&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;hemimage&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 5 -7 -1 3 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;10976/10935&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6.48&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;septendecimal kleisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 8 -1 -1 0 0 0 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;256/255&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6.78&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;small BP diesis, mirkwai&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 0 3 4 -5 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;16875/16807&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6.99&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;neutral third comma, rastma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -1 5 0 0 -2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;243/242&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7.14&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;kestrel comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 2 3 0 -1 1 -2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1188/1183&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7.30&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;septimal kleisma, marvel comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -5 2 2 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;225/224&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7.71&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;huntma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 7 0 1 -2 0 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;640/637&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8.13&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;spleen comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 1 1 1 1 -1 0 0 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;210/209&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8.26&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;orgonisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 16 0 0 -2 -3 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;65536/65219&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8.39&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;gamelan residue, gamelisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -10 1 0 3 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1029/1024&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8.43&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;septendecimal comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -7 7 0 0 0 0 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2187/2176&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8.73&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;mynucuma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 2 -1 -1 2 0 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;196/195&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8.86&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;quince&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -15 0 -2 7 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9.15&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;undecimal semicomma, pentacircle (minthma * gentle)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 7 -4 0 1 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;896/891&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9.69&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;29th-partial chroma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -4 -2 1 0 0 0 0 0 0 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;145/144&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11.98&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;grossma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 4 2 0 0 -1 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;144/143&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12.06&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;gassorma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 0 -1 2 -1 1 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;275/273&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12.64&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;septimal semicomma, octagar&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 5 -4 3 -2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4000/3969&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13.47&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;minor BP diesis, sensamagic&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 0 -5 1 2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;245/243&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14.19&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;secorian&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 12 -7 0 1 0 -1/1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;28672/28431&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14.61&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;mirwomo comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -15 3 2 2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;33075/32768&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16.14&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;vicesimotertial comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 5 -6 0 0 0 0 0 0 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;736/729&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16.54&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;small tridecimal comma, animist&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -3 1 1 1 0 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;105/104&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16.57&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;hemimin&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 6 1 0 1 -3 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1344/1331&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16.83&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Ptolemy's comma, ptolemisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 2 -2 2 0 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;100/99&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;17.40&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;'41-tone' comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 65 -41 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19.84&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;tolerma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 10 -11 2 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19.95&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;major BP diesis, gariboh&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 0 -2 5 -3 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3125/3087&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;21.18&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;cassacot&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -1 0 1 2 -2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;245/242&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;21.33&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;keema&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -5 -3 3 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;875/864&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;21.90&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;blackjackisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -10 7 8 -7 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;22.41&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;roda&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 20 -17 3 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;25.71&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;minimal diesis, tetracot comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 5 -9 4 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;20000/19683&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;27.66&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;small diesis, magic comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -10 -1 5 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3125/3072&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;29.61&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;thuja comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 15 0 1 0 -5 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;29.72&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Ampersand's comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -25 7 6 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;31.57&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;great BP diesis&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 0 -7 6 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;15625/15309&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;35.37&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;shibboleth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -5 -10 9 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;57.27&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:13:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:13 --&gt;Temperaments&lt;/h1&gt;
&lt;a class="wiki_link" href="/List%20of%20edo-distinct%2041et%20rank%20two%20temperaments"&gt;List of edo-distinct 41et rank two temperaments&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:15:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:15 --&gt;Intervals&lt;/h1&gt;
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;cents value&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Approximate&lt;br /&gt;
Ratios in the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;th colspan="2"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"&gt;ups and&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"&gt;downs&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"&gt;notation&lt;/a&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Proposed names&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Andrew's&lt;br /&gt;
solfege&lt;br /&gt;
syllable&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;generator for&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;some MOS and MODMOS Scales available&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0.00&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/1_1"&gt;1/1&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;P1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Unison&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;29.27&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/81_80"&gt;81/80&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;D^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Red unison&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;di&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;58.54&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/25_24"&gt;25/24&lt;/a&gt;, &lt;a class="wiki_link" href="/28_27"&gt;28/27&lt;/a&gt;,&lt;br /&gt;
&lt;a class="wiki_link" href="/33_32"&gt;33/32&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;vm2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Ebv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Blue minor second&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;ro&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Hemimiracle"&gt;Hemimiracle&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;87.80&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/21_20"&gt;21/20&lt;/a&gt;, &lt;a class="wiki_link" href="/22_21"&gt;22/21&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;m2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Eb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Gray minor second&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;rih&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;88cET (approx),&lt;br /&gt;
&lt;a class="wiki_link" href="/octacot"&gt;octacot&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;117.07&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/16_15"&gt;16/15&lt;/a&gt;, &lt;a class="wiki_link" href="/15_14"&gt;15/14&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^m2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Eb^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Red minor second&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;ra&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Miracle"&gt;Miracle&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;146.34&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/12_11"&gt;12/11&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;~2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Evv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Neutral second&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;ru&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Bohlen-Pierce"&gt;Bohlen-Pierce&lt;/a&gt;/&lt;a class="wiki_link" href="/bohpier"&gt;bohpier&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;175.61&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/10_9"&gt;10/9&lt;/a&gt;, &lt;a class="wiki_link" href="/11_10"&gt;11/10&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;vM2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Ev&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Blue major second&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;reh&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Tetracot"&gt;Tetracot&lt;/a&gt;/&lt;a class="wiki_link" href="/bunya"&gt;bunya&lt;/a&gt;/&lt;a class="wiki_link" href="/monkey"&gt;monkey&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13-tone MOS: 1 5 1 5 1 5 1 5 5 1 5 1 5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;204.88&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/9_8"&gt;9/8&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;M2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;E&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Gray major second&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;re&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Baldy"&gt;Baldy&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11-tone MOS: 6 1 6 6 1 6 1 6 1 6 1&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;234.15&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/8_7"&gt;8/7&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^M2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;E^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Red major second&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;ri&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Rodan"&gt;Rodan&lt;/a&gt;/&lt;a class="wiki_link" href="/guiron"&gt;guiron&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11-tone MOS: 7 1 7 1 7 1 7 1 1 7 1&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;263.41&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt;, &lt;a class="wiki_link" href="/32_25"&gt;32/25&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;vm3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Fv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Blue minor third&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;ma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Septimin"&gt;Septimin&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9-tone MOS: 5 4 5 5 4 5 4 5 4&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;292.68&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/32_27"&gt;32/27&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;m3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Gray minor third&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;meh&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Quasitemp"&gt;Quasitemp&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;321.95&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/6_5"&gt;6/5&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^m3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Red minor third&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;me&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Superkleismic"&gt;Superkleismic&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11-tone MOS: 5 3 5 3 3 5 3 3 5 3 3&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;351.22&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/11_9"&gt;11/9&lt;/a&gt;,&lt;a class="wiki_link" href="/27_22"&gt;27/22&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;~3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F^^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Neutral third&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;mu&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Hemififths"&gt;Hemififths&lt;/a&gt;/&lt;a class="wiki_link" href="/karadeniz"&gt;karadeniz&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10-tone MOS: 5 2 5 5 2 5 5 5 2 5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;380.49&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;vM3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F#v&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Blue major third&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;mi&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Magic"&gt;Magic&lt;/a&gt;/&lt;a class="wiki_link" href="/witchcraft"&gt;witchcraft&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10-tone MOS: 2 9 2 2 9 2 2 9 2 2&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;409.76&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/14_11"&gt;14/11&lt;/a&gt;, &lt;a class="wiki_link" href="/81_64"&gt;81/64&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;M3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F#&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Gray major third&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;maa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Hocus"&gt;Hocus&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;439.02&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/9_7"&gt;9/7&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^M3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F#^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Red major third&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;mo&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11-tone MOS: 4 3 4 4 4 3 4 4 3 4 4&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;468.29&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/21_16"&gt;21/16&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;v4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Gv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Blue fourth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;fe&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Barbad"&gt;Barbad&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;497.56&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/4_3"&gt;4/3&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;G&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Perfect fourth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Schismatic"&gt;Schismatic&lt;/a&gt; (&lt;a class="wiki_link" href="/helmholtz"&gt;helmholtz&lt;/a&gt;, &lt;a class="wiki_link" href="/Garibaldi%20temperament"&gt;garibaldi&lt;/a&gt;, &lt;a class="wiki_link" href="/cassandra"&gt;cassandra&lt;/a&gt;)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;18&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;526.83&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/15_11"&gt;15/11&lt;/a&gt;, &lt;a class="wiki_link" href="/27_20"&gt;27/20&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;G^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Red fourth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;fih&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Trismegistus"&gt;Trismegistus&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9-tone MOS: 5 5 3 5 5 5 5 3 5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;556.10&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/11_8"&gt;11/8&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^^4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;G^^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Blue minor tritone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;fu&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;20&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;585.37&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/7_5"&gt;7/5&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;vA4, d5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;G#v,&lt;br /&gt;
Ab&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Minor tritone / diminished fifth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;fi&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Pluto"&gt;Pluto&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;614.63&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/10_7"&gt;10/7&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A4, ^d5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;G#,&lt;br /&gt;
Ab^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Major tritone / augmented fourth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;se&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;22&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;643.90&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/16_11"&gt;16/11&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;vv5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Avv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Red major tritone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;su&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;23&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;673.17&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/22_15"&gt;22/15&lt;/a&gt;, &lt;a class="wiki_link" href="/40_27"&gt;40/27&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;v5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Av&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Blue fifth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;sih&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;24&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;702.44&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;P5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Perfect fifth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;sol&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;25&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;731.71&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/32_21"&gt;32/21&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Red fifth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;si&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;26&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;760.98&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/14_9"&gt;14/9&lt;/a&gt;, &lt;a class="wiki_link" href="/25_16"&gt;25/16&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;vm6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Bbv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Blue minor sixth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;lo&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;27&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;790.24&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/11_7"&gt;11/7&lt;/a&gt;, &lt;a class="wiki_link" href="/128_81"&gt;128/81&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;m6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Bb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Gray minor sixth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;leh&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;28&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;819.51&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/8_5"&gt;8/5&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^m6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Bb^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Red minor sixth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;le&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;29&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;848.78&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/18_11"&gt;18/11&lt;/a&gt;, &lt;a class="wiki_link" href="/44_27"&gt;44/27&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;~6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Bvv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Neutral sixth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;lu&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;30&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;878.05&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/5_3"&gt;5/3&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;vM6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Bv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Blue major sixth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;la&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;31&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;907.32&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/27_16"&gt;27/16&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;M6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;B&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Gray major sixth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;laa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;32&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;936.59&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/12_7"&gt;12/7&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^M6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;B^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Red major sixth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;li&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;965.85&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;vm7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Cv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Blue minor seventh&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;ta&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;34&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;995.12&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/16_9"&gt;16/9&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;m7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Gray minor seventh&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;teh&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;35&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1024.39&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/9_5"&gt;9/5&lt;/a&gt;, &lt;a class="wiki_link" href="/20_11"&gt;20/11&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^m7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Red minor seventh&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;te&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;36&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1053.66&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/11_6"&gt;11/6&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;~7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C^^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Neutral seventh&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;tu&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;37&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1082.93&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/15_8"&gt;15/8&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;vM7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C#v&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Blue major seventh&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;ti&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;38&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1112.20&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/40_21"&gt;40/21&lt;/a&gt;, &lt;a class="wiki_link" href="/21_11"&gt;21/11&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;M7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C#&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Gray major seventh&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;taa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;39&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1141.46&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/48_25"&gt;48/25&lt;/a&gt;, &lt;a class="wiki_link" href="/27_14"&gt;27/14&lt;/a&gt;,&lt;br /&gt;
&lt;a class="wiki_link" href="/64_33"&gt;64/33&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^M7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C#^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Red major seventh&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;to&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;40&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1170.73&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;a class="wiki_link" href="/160_81"&gt;160/81&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;v8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Dv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Blue octave&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;da&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;41&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1200&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;2/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;P8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
Combining ups and downs notation with &lt;a class="wiki_link" href="/Kite%27s%20color%20notation"&gt;color notation&lt;/a&gt;, qualities can be loosely associated with colors:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;th&gt;quality&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;color&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;monzo format&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;examples&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;downminor&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;blue&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;{a, b, 0, 1}&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7/6, 7/4&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;minor&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;fourthward white&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;{a, b}, b &amp;lt; -1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;32/27, 16/9&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;upminor&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;green&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;{a, b, -1}&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6/5, 9/5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;mid&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;jade&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;{a, b, 0, 0, 1}&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;11/9, 11/6&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&amp;quot;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;amber&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;{a, b, 0, 0, -1}&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;12/11, 18/11&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;downmajor&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;yellow&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;{a, b, 1}&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5/4, 5/3&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;major&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;fifthward white&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;{a, b}, b &amp;gt; 1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;9/8, 27/16&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;upmajor&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;red&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;{a, b, 0, -1}&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;9/7, 12/7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
All 41edo chords can be named using ups and downs. Here are the blue, green, jade, yellow and red triads:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;th&gt;color of the 3rd&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;JI chord&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;notes as edosteps&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;notes of C chord&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;written name&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;spoken name&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;blue&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6:7:9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0-9-24&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C Ebv G&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C.vm&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C downminor&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;green&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;10:12:15&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0-11-24&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C Eb^ G&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C.^m&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C upminor&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;jade&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;18:22:27&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0-12-24&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C Evv G&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C~&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C mid&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;yellow&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4:5:6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0-13-24&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C Ev G&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C.v&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C downmajor or C dot down&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;red&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;14:18:27&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0-15-24&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C E^ G&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C.^&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C upmajor or C dot up&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
0-10-20 = D F Ab = Ddim = &amp;quot;D dim&amp;quot;&lt;br /&gt;
0-10-21 = D F Ab^ = Ddim(^5) = &amp;quot;D dim up-five&amp;quot;&lt;br /&gt;
0-10-22 = D F Avv = Dm(vv5) = &amp;quot;D minor double-down five&amp;quot;, or possibly Ddim(^^5)&lt;br /&gt;
0-10-23 = D F Av = Dm(v5) = &amp;quot;D minor down-five&amp;quot;&lt;br /&gt;
0-10-24 = D F A = Dm = &amp;quot;D minor&amp;quot;&lt;br /&gt;
0-14-24 = D F# A = D = &amp;quot;D&amp;quot; or &amp;quot;D major&amp;quot;&lt;br /&gt;
0-14-25 = D F# A^ = D(^5) = &amp;quot;D up-five&amp;quot;&lt;br /&gt;
0-14-26 = D F# A^^ = D(^^5) = &amp;quot;D double-up-five&amp;quot;, or possibly Daug(vv5)&lt;br /&gt;
0-14-27 = D F# A#v = Daug(v5) = &amp;quot;D aug down-five&amp;quot;&lt;br /&gt;
0-14-28 = D F# A# is Daug = &amp;quot;D aug&amp;quot;&lt;br /&gt;
etc.&lt;br /&gt;
For a more complete list, see &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Chord%20names%20in%20other%20EDOs"&gt;Ups and Downs Notation - Chord names in other EDOs&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:17:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Intervals-Selected just intervals by error"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:17 --&gt;Selected just intervals by error&lt;/h2&gt;
The following table shows how &lt;a class="wiki_link" href="/Just-24"&gt;some prominent just intervals&lt;/a&gt; are represented in 41edo (ordered by absolute error).&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;Interval, complement&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;Error (abs., in &lt;a class="wiki_link" href="/cent"&gt;cents&lt;/a&gt;)&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/4_3"&gt;4/3&lt;/a&gt;, &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0.484&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/9_8"&gt;9/8&lt;/a&gt;, &lt;a class="wiki_link" href="/16_9"&gt;16/9&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0.968&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/15_14"&gt;15/14&lt;/a&gt;, &lt;a class="wiki_link" href="/28_15"&gt;28/15&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2.370&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/7_5"&gt;7/5&lt;/a&gt;, &lt;a class="wiki_link" href="/10_7"&gt;10/7&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2.854&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/8_7"&gt;8/7&lt;/a&gt;, &lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2.972&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt;, &lt;a class="wiki_link" href="/12_7"&gt;12/7&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3.456&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/13_11"&gt;13/11&lt;/a&gt;, &lt;a class="wiki_link" href="/22_13"&gt;22/13&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3.473&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/11_9"&gt;11/9&lt;/a&gt;, &lt;a class="wiki_link" href="/18_11"&gt;18/11&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3.812&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/9_7"&gt;9/7&lt;/a&gt;, &lt;a class="wiki_link" href="/14_9"&gt;14/9&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3.940&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/12_11"&gt;12/11&lt;/a&gt;, &lt;a class="wiki_link" href="/11_6"&gt;11/6&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4.296&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/11_8"&gt;11/8&lt;/a&gt;, &lt;a class="wiki_link" href="/16_11"&gt;16/11&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4.780&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/16_15"&gt;16/15&lt;/a&gt;, &lt;a class="wiki_link" href="/15_8"&gt;15/8&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5.342&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt;, &lt;a class="wiki_link" href="/8_5"&gt;8/5&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5.826&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/6_5"&gt;6/5&lt;/a&gt;, &lt;a class="wiki_link" href="/5_3"&gt;5/3&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6.310&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/10_9"&gt;10/9&lt;/a&gt;, &lt;a class="wiki_link" href="/9_5"&gt;9/5&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6.794&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/18_13"&gt;18/13&lt;/a&gt;, &lt;a class="wiki_link" href="/13_9"&gt;13/9&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7.285&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/14_11"&gt;14/11&lt;/a&gt;, &lt;a class="wiki_link" href="/11_7"&gt;11/7&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7.752&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/13_12"&gt;13/12&lt;/a&gt;, &lt;a class="wiki_link" href="/24_13"&gt;24/13&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7.769&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/16_13"&gt;16/13&lt;/a&gt;, &lt;a class="wiki_link" href="/13_8"&gt;13/8&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;8.253&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/15_11"&gt;15/11&lt;/a&gt;, &lt;a class="wiki_link" href="/22_15"&gt;22/15&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;10.122&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/11_10"&gt;11/10&lt;/a&gt;, &lt;a class="wiki_link" href="/20_11"&gt;20/11&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;10.606&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/14_13"&gt;14/13&lt;/a&gt;, &lt;a class="wiki_link" href="/13_7"&gt;13/7&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;11.225&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/15_13"&gt;15/13&lt;/a&gt;, &lt;a class="wiki_link" href="/26_15"&gt;26/15&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;13.595&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/13_10"&gt;13/10&lt;/a&gt;, &lt;a class="wiki_link" href="/20_13"&gt;20/13&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;14.079&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:19:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Instruments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:19 --&gt;Instruments&lt;/h1&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:2900:&amp;lt;img src=&amp;quot;/file/view/41-EDD%20elektrische%20gitaar.jpg/610818537/560x745/41-EDD%20elektrische%20gitaar.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 745px; width: 560px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/41-EDD%20elektrische%20gitaar.jpg/610818537/560x745/41-EDD%20elektrische%20gitaar.jpg" alt="41-EDD elektrische gitaar.jpg" title="41-EDD elektrische gitaar.jpg" style="height: 745px; width: 560px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:2900 --&gt;&lt;br /&gt;
&lt;em&gt;41-EDO Electric guitar, by Gregory Sanchez.&lt;/em&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:2901:&amp;lt;img src=&amp;quot;/file/view/Ron_Sword_with_a_41ET_Guitar.jpg/221056094/Ron_Sword_with_a_41ET_Guitar.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Ron_Sword_with_a_41ET_Guitar.jpg/221056094/Ron_Sword_with_a_41ET_Guitar.jpg" alt="Ron_Sword_with_a_41ET_Guitar.jpg" title="Ron_Sword_with_a_41ET_Guitar.jpg" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:2901 --&gt;&lt;br /&gt;
&lt;em&gt;41-EDO Classical guitar, by Ron Sword.&lt;/em&gt;&lt;br /&gt;
&lt;br /&gt;
A possible system to tune keyboards in 41EDO is discussed in &lt;a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/74155" rel="nofollow"&gt;http://launch.groups.yahoo.com/group/tuning/message/74155&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:21:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Scales and modes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:21 --&gt;Scales and modes&lt;/h1&gt;
&lt;br /&gt;
A list of &lt;a class="wiki_link" href="/41edo%20modes"&gt;41edo modes&lt;/a&gt; (MOS and others).&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:23:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="Scales and modes--Harmonic Scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:23 --&gt;Harmonic Scale&lt;/h3&gt;
41edo is the first edo to do some justice to Mode 8 of the &lt;a class="wiki_link" href="/OverToneSeries"&gt;harmonic series&lt;/a&gt;, which Dante Rosati calls the &amp;quot;&lt;a class="wiki_link" href="/overtone%20scales"&gt;Diatonic Harmonic Series Scale&lt;/a&gt;,&amp;quot; consisting of overtones 8 through 16 (sometimes made to repeat at the octave).&lt;br /&gt;
&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;Overtones in &amp;quot;Mode 8&amp;quot;:&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;...as JI Ratio from 1/1:&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2/1&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;...in cents:&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;203.9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;386.3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;551.3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;702.0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;840.5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;968.8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1088.3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1200.0&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Nearest degree of 41edo:&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;24&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;41&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;...in cents:&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;204.9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;380.5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;556.1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;702.4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;848.8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;965.9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1082.9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1200.0&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
While each overtone of Mode 8 is approximated within a reasonable degree of accuracy, the steps between the intervals are not uniquely represented. (41edo is, after all, a temperament.)&lt;br /&gt;
&lt;br /&gt;
7\41 (7 degrees of 41edo) (204.9 cents) stands in for just ratio 9/8 (203.9 cents) -- a close match.&lt;br /&gt;
6\41 (175.6 cents) stands in for both 10/9 (182.4 cents) and 11/10 (165.0 cents).&lt;br /&gt;
5\41 (146.3 cents) stands in for both 12/11 (150.6 cents) and 13/12 (138.6 cents).&lt;br /&gt;
4\41 (117.1 cents) stands in for 14/13 (128.3 cents), 15/14 (119.4 cents), and 16/15 (111.7 cents).&lt;br /&gt;
&lt;br /&gt;
The scale in 41, as adjacent steps, thus goes: 7 6 6 5 5 4 4 4.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:25:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Nonoctave Temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:25 --&gt;Nonoctave Temperaments&lt;/h1&gt;
Taking every third degree of 41edo produces a scale extremely close to &lt;a class="wiki_link" href="/88cET"&gt;88cET&lt;/a&gt; or 88-cent equal temperament (or the 8th root of 3:2). Likewise, taking every fifth degree produces a scale very close to the equal-tempered &lt;span class="wiki_link_new"&gt;&lt;a class="wiki_link" href="/BP"&gt;Bohlen-Pierce&lt;/a&gt;&lt;/span&gt;&lt;a class="wiki_link" href="/BP"&gt; Scale&lt;/a&gt; (or the 13th root of 3). See chart:&lt;br /&gt;
&lt;br /&gt;
 


&lt;table class="wiki_table"&gt;
=Music=
    &lt;tr&gt;
[http://soundcloud.com/cameron-bobro/eveninghorizon-cbobro EveningHorizon] [http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3 play] by Cameron Bobro
        &lt;td colspan="3" style="text-align: center;"&gt;3 degrees of 41edo (near 88cET)&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;overlap&lt;br /&gt;
&lt;/td&gt;
        &lt;td colspan="3" style="text-align: center;"&gt;5 degrees of 41edo (near BP)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th&gt;deg of 41edo&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;deg of 88cET&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;cents&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;cents&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;cents&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;deg of BP&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;deg of 41edo&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;87.8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;146.3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;175.6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;263.4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;292.7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;10&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;351.2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;439.0&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;15&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;18&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;526.8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;585.4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;20&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;614.6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;24&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;702.4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;731.7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;25&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;27&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;790.2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;30&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;878.0&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;30&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;965.9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1024.4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;35&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;36&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1053.7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;39&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1141.5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1170.7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;40&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th colspan="7"&gt;[ second octave ]&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;29.2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;117.1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;204.9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;263.4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;9&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;292.7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;18&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;380.5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;409.8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;14&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;468.3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;20&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;556.1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;19&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;22&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;643.9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;702.4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;24&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;25&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;22&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;731.7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;28&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;23&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;819.5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;848.8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;29&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;31&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;24&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;907.3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;34&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;25&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;995.1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;34&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;37&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;26&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1082.9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1141.5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;39&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;40&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;27&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1170.7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th colspan="7"&gt;[ third octave ]&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;28&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;58.5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;87.8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;29&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;146.3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;30&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;234.1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;18&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;8&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;31&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;322.0&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;380.5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;13&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;32&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;409.8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;33&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;497.6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;526.8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;20&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;18&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;20&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;34&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;585.3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;23&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;35&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;673.2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;23&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;26&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;36&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;761.0&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;819.5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;22&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;28&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;29&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;37&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;848.8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;32&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;38&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;936.6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;965.9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;23&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;33&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;35&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;39&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1024.4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;38&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;40&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1112.2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;24&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;38&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
=Links=
&lt;!-- ws:start:WikiTextHeadingRule:27:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Nonoctave Temperaments-Notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:27 --&gt;Notation&lt;/h2&gt;
<ul><li>[http://en.wikipedia.org/wiki/41_equal_temperament Wikipedia article on 41edo]</li><li>[[Magic22_as_srutis#magic22assrutis|Magic22 as srutis]] describes a possible use of 41edo for [[Indian|indian]] music.</li><li>see also [[Magic_family|Magic family]]</li><li>Sword, Ron. [http://www.ronsword.com "Tetracontamonophonic Scales for Guitar"]</li><li>Taylor, Cam. [https://drive.google.com/open?id=0B3wIGTmjY_VZYllwcHI0d3hEc3M Intervals, Scales and Chords in 41EDO], a work in progress using just intonation concepts and simplified Sagittal notation.</li></ul>
&lt;br /&gt;
-----
A red-note/blue-note system, similar to the one proposed for &lt;a class="wiki_link" href="/36edo"&gt;36edo&lt;/a&gt;, is one option for notating 41edo. (This is separate from and not compatible with Kite's &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Kite%27s%20color%20notation"&gt;color notation&lt;/a&gt;.) We have the &amp;quot;white key&amp;quot; albitonic notes A-G (7 in total), the &amp;quot;black key&amp;quot; sharps and flats (10 in total), a &amp;quot;red&amp;quot; and &amp;quot;blue&amp;quot; version of each albitonic note (14 in total), a &amp;quot;red&amp;quot; (dark red?) version of each sharp and a &amp;quot;blue&amp;quot; (dark blue?) version of each flat (10 in total), adding up to 41. This would result in quite a colorful keyboard! Note that there are no red flats or blue sharps. Using this nomenclature the notes are:&lt;br /&gt;
<ol><li>[[#cite_ref-1|^]] [http://x31eq.com/schismic.htm "Schismic Temperaments"] at x31eq.com the website of [[Graham_Breed|Graham Breed]]</li><li>[[#cite_ref-2|^]] [http://x31eq.com/decimal_lattice.htm "Lattices with Decimal Notation"] at x31eq.com</li><li>[[#cite_ref-3|^]] [http://en.wikipedia.org/wiki/Schismatic_temperament Schismatic temperament]</li><li>[[#cite_ref-4|^]] [http://en.wikipedia.org/wiki/Magic_temperament Magic temperament]</li></ol>      [[Category:41edo]]
&lt;br /&gt;
[[Category:edo]]
A, red A, blue Bb, Bb, A#, red A#, blue B, B, red B, blue C, C, red C, blue Db, Db, C#, red C#, blue D, D, red D, blue Eb, Eb, D#, red D#, blue E, E, red E, blue F, F, red F, blue Gb, Gb, F#, red F#, blue G, G, red G, blue Ab, Ab, G#, red G#, blue A, A.&lt;br /&gt;
[[Category:magic]]
&lt;br /&gt;
[[Category:prime_edo]]
Interval classes could also be named by analogy. The natural, colorless, or gray interval classes are the Pythagorean ones (which show up in the standard diatonic scale), while &amp;quot;red&amp;quot; and &amp;quot;blue&amp;quot; versions are one step higher or lower. Gray thirds, sixths, and sevenths are usually more dissonant than their colorful counterparts, but the reverse is true of fourths and fifths.&lt;br /&gt;
[[Category:pythagorean]]
&lt;br /&gt;
[[Category:zeta]]
The step size of 41edo is small enough that the smallest interval (the &amp;quot;red/blue unison&amp;quot;, seventh-tone, comma, diesis or whatever you want to call it) is actually fairly consonant with most timbres; it resembles a &amp;quot;noticeably out of tune unison&amp;quot; rather than a minor second, and has its own distinct character and appeal.&lt;br /&gt;
&lt;br /&gt;
If &amp;quot;red&amp;quot; is replaced by &amp;quot;up&amp;quot;, &amp;quot;blue&amp;quot; by &amp;quot;down&amp;quot;, and &amp;quot;neutral&amp;quot; by &amp;quot;mid&amp;quot;, and if &amp;quot;gray&amp;quot; is omitted, this notation becomes essentially the same as &lt;a class="wiki_link" href="/Ups%20and%20Downs%20Notation"&gt;ups and downs notation&lt;/a&gt;. The only difference is the use of minor tritone and major tritone.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:29:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:29 --&gt;Music&lt;/h1&gt;
&lt;a class="wiki_link_ext" href="http://soundcloud.com/cameron-bobro/eveninghorizon-cbobro" rel="nofollow"&gt;EveningHorizon&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3" rel="nofollow"&gt;play&lt;/a&gt; by Cameron Bobro&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:31:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:31 --&gt;Links&lt;/h1&gt;
&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/41_equal_temperament" rel="nofollow"&gt;Wikipedia article on 41edo&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Magic22%20as%20srutis#magic22assrutis"&gt;Magic22 as srutis&lt;/a&gt; describes a possible use of 41edo for &lt;a class="wiki_link" href="/indian"&gt;indian&lt;/a&gt; music.&lt;/li&gt;&lt;li&gt;see also &lt;a class="wiki_link" href="/Magic%20family"&gt;Magic family&lt;/a&gt;&lt;/li&gt;&lt;li&gt;Sword, Ron. &lt;a class="wiki_link_ext" href="http://www.ronsword.com" rel="nofollow" target="_blank"&gt;&amp;quot;Tetracontamonophonic Scales for Guitar&amp;quot;&lt;/a&gt;&lt;/li&gt;&lt;li&gt;Taylor, Cam. &lt;a class="wiki_link_ext" href="https://drive.google.com/open?id=0B3wIGTmjY_VZYllwcHI0d3hEc3M" rel="nofollow"&gt;Intervals, Scales and Chords in 41EDO&lt;/a&gt;, a work in progress using just intonation concepts and simplified Sagittal notation.&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextReferencesRule:4394: --&gt;&lt;hr class="references" /&gt;&lt;ol class="references"&gt;
&lt;li id="cite_note-1"&gt;&lt;a href="#cite_ref-1"&gt;^&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://x31eq.com/schismic.htm" rel="nofollow"&gt;&amp;quot;Schismic Temperaments&amp;quot;&lt;/a&gt; at x31eq.com the website of &lt;a class="wiki_link" href="/Graham%20Breed"&gt;Graham Breed&lt;/a&gt;&lt;/li&gt;
&lt;li id="cite_note-2"&gt;&lt;a href="#cite_ref-2"&gt;^&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://x31eq.com/decimal_lattice.htm" rel="nofollow"&gt;&amp;quot;Lattices with Decimal Notation&amp;quot;&lt;/a&gt; at x31eq.com&lt;/li&gt;
&lt;li id="cite_note-3"&gt;&lt;a href="#cite_ref-3"&gt;^&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Schismatic_temperament" rel="nofollow"&gt;Schismatic temperament&lt;/a&gt;&lt;/li&gt;
&lt;li id="cite_note-4"&gt;&lt;a href="#cite_ref-4"&gt;^&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Magic_temperament" rel="nofollow"&gt;Magic temperament&lt;/a&gt;&lt;/li&gt;
&lt;/ol&gt;&lt;!-- ws:end:WikiTextReferencesRule:4394 --&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

41 Tone Equal Temperament

de:41edo Deutsch

Introduction

The 41-tET, 41-EDO, or 41-ET, is the scale derived by dividing the octave into 41 equally-sized steps. Each step represents a frequency ratio of 29.268 cents, an interval close in size to 64/63, the septimal comma. 41-ET can be seen as a tuning of the Garibaldi temperament [1] , [2] , [3] the Magic temperament [4] and the superkleismic (41&26) temperament. It is the second smallest equal temperament (after 29edo) whose perfect fifth is closer to just intonation than that of 12-ET, and is the seventh zeta integral edo after 31; it is not, however, a zeta gap edo. This has to do with the fact that it can deal with the 11-limit fairly well, and the 13-limit perhaps close enough for government work, though its 13/10 is 14 cents sharp. Various 13-limit magic extensions are supported by 41: 13-limit magic, and less successfully necromancy and witchcraft, all merge into one in 41edo tuning. The 41f val provides a superb tuning for sorcery, giving a less-complex version of the 13-limit, and the 41ef val likewise works well for telepathy; telepathy and sorcery merging into one however not in 41edo but in 22edo.

41edo is consistent in the 15 odd limit. In fact, all of its intervals between 100 and 1100 cents in size are 15-odd-limit consonances. (In comparison, 31edo is only consistent up to the 11-limit, and the intervals 12/31 and 19/31 have no 11-limit approximations).

41-ET forms the foundation of the H-System, which uses the scale degrees of 41-ET as the basic 13-limit intervals requiring fine tuning +/- 1 average JND from the 41-ET circle in 205edo.

41edo is the 13th prime edo, following 37edo and coming before 43edo.

Commas

41 EDO tempers out the following commas using its patent val, < 41 65 95 115 142 152 168 174 185 199 203 |.

Name Monzo Ratio Cents
odiheim | -1 2 -4 5 -2 > 0.15
harmonisma | 3 -2 0 -1 3 -2 > 10648/10647 0.16
tridecimal schisma, Sagittal schismina | 12 -2 -1 -1 0 -1/1 > 4096/4095 0.42
Lehmerisma | -4 -3 2 -1 2 > 3025/3024 0.57
Breedsma | -5 -1 -2 4 > 2401/2400 0.72
Eratosthenes' comma | 6 -5 -1 0 0 0 0 1 > 1216/1215 1.42
schisma | -15 8 1 > 32805/32768 1.95
squbema | -3 6 0 -1 0 -1 > 729/728 2.38
septendecimal bridge comma | -1 -1 1 -1 1 1 -1 > 715/714 2.42
Swets' comma, swetisma | 2 3 1 -2 -1 > 540/539 3.21
undevicesimal comma, Boethius' comma | -9 3 0 0 0 0 0 1 > 513/512 3.38
moctdel | -2 0 3 -3 1 > 1375/1372 3.78
Beta 2, septimal schisma, garischisma | 25 -14 0 -1 > 3.80
Werckmeister's undecimal septenarian schisma, werckisma | -3 2 -1 2 -1 > 441/440 3.93
cuthbert | 0 0 -1 1 2 -2 > 847/845 4.09
undecimal kleisma, keenanisma | -7 -1 1 1 1 > 385/384 4.50
gentle comma | 2 -1 0 1 -2 1 > 364/363 4.76
minthma | 5 -3 0 0 1 -1 > 352/351 4.93
marveltwin | -2 -4 2 0 0 1 > 325/324 5.34
Beta 5, Garibaldi comma, hemifamity | 10 -6 1 -1 > 5120/5103 5.76
hemimage | 5 -7 -1 3 > 10976/10935 6.48
septendecimal kleisma | 8 -1 -1 0 0 0 -1 > 256/255 6.78
small BP diesis, mirkwai | 0 3 4 -5 > 16875/16807 6.99
neutral third comma, rastma | -1 5 0 0 -2 > 243/242 7.14
kestrel comma | 2 3 0 -1 1 -2 > 1188/1183 7.30
septimal kleisma, marvel comma | -5 2 2 -1 > 225/224 7.71
huntma | 7 0 1 -2 0 -1 > 640/637 8.13
spleen comma | 1 1 1 1 -1 0 0 -1 > 210/209 8.26
orgonisma | 16 0 0 -2 -3 > 65536/65219 8.39
gamelan residue, gamelisma | -10 1 0 3 > 1029/1024 8.43
septendecimal comma | -7 7 0 0 0 0 -1 > 2187/2176 8.73
mynucuma | 2 -1 -1 2 0 -1 > 196/195 8.86
quince | -15 0 -2 7 > 9.15
undecimal semicomma, pentacircle (minthma * gentle) | 7 -4 0 1 -1 > 896/891 9.69
29th-partial chroma | -4 -2 1 0 0 0 0 0 0 1 > 145/144 11.98
grossma | 4 2 0 0 -1 -1 > 144/143 12.06
gassorma | 0 -1 2 -1 1 -1 > 275/273 12.64
septimal semicomma, octagar | 5 -4 3 -2 > 4000/3969 13.47
minor BP diesis, sensamagic | 0 -5 1 2 > 245/243 14.19
secorian | 12 -7 0 1 0 -1/1 > 28672/28431 14.61
mirwomo comma | -15 3 2 2 > 33075/32768 16.14
vicesimotertial comma | 5 -6 0 0 0 0 0 0 1 > 736/729 16.54
small tridecimal comma, animist | -3 1 1 1 0 -1 > 105/104 16.57
hemimin | 6 1 0 1 -3 > 1344/1331 16.83
Ptolemy's comma, ptolemisma | 2 -2 2 0 -1 > 100/99 17.40
'41-tone' comma | 65 -41 > 19.84
tolerma | 10 -11 2 1 > 19.95
major BP diesis, gariboh | 0 -2 5 -3 > 3125/3087 21.18
cassacot | -1 0 1 2 -2 > 245/242 21.33
keema | -5 -3 3 1 > 875/864 21.90
blackjackisma | -10 7 8 -7 > 22.41
roda | 20 -17 3 > 25.71
minimal diesis, tetracot comma | 5 -9 4 > 20000/19683 27.66
small diesis, magic comma | -10 -1 5 > 3125/3072 29.61
thuja comma | 15 0 1 0 -5 > 29.72
Ampersand's comma | -25 7 6 > 31.57
great BP diesis | 0 -7 6 -1 > 15625/15309 35.37
shibboleth | -5 -10 9 > 57.27

Temperaments

List of edo-distinct 41et rank two temperaments

Intervals

cents value Approximate

Ratios in the 11-limit

ups and

downs

notation

Proposed names Andrew's

solfege

syllable

generator for some MOS and MODMOS Scales available
0 0.00 1/1 P1 D Unison do
1 29.27 81/80 ^1 D^ Red unison di
2 58.54 25/24, 28/27,

33/32

vm2 Ebv Blue minor second ro Hemimiracle
3 87.80 21/20, 22/21 m2 Eb Gray minor second rih 88cET (approx),

octacot

4 117.07 16/15, 15/14 ^m2 Eb^ Red minor second ra Miracle
5 146.34 12/11 ~2 Evv Neutral second ru Bohlen-Pierce/bohpier
6 175.61 10/9, 11/10 vM2 Ev Blue major second reh Tetracot/bunya/monkey 13-tone MOS: 1 5 1 5 1 5 1 5 5 1 5 1 5
7 204.88 9/8 M2 E Gray major second re Baldy 11-tone MOS: 6 1 6 6 1 6 1 6 1 6 1
8 234.15 8/7 ^M2 E^ Red major second ri Rodan/guiron 11-tone MOS: 7 1 7 1 7 1 7 1 1 7 1
9 263.41 7/6, 32/25 vm3 Fv Blue minor third ma Septimin 9-tone MOS: 5 4 5 5 4 5 4 5 4
10 292.68 32/27 m3 F Gray minor third meh Quasitemp
11 321.95 6/5 ^m3 F^ Red minor third me Superkleismic 11-tone MOS: 5 3 5 3 3 5 3 3 5 3 3
12 351.22 11/9,27/22 ~3 F^^ Neutral third mu Hemififths/karadeniz 10-tone MOS: 5 2 5 5 2 5 5 5 2 5
13 380.49 5/4 vM3 F#v Blue major third mi Magic/witchcraft 10-tone MOS: 2 9 2 2 9 2 2 9 2 2
14 409.76 14/11, 81/64 M3 F# Gray major third maa Hocus
15 439.02 9/7 ^M3 F#^ Red major third mo 11-tone MOS: 4 3 4 4 4 3 4 4 3 4 4
16 468.29 21/16 v4 Gv Blue fourth fe Barbad
17 497.56 4/3 P4 G Perfect fourth fa Schismatic (helmholtz, garibaldi, cassandra)
18 526.83 15/11, 27/20 ^4 G^ Red fourth fih Trismegistus 9-tone MOS: 5 5 3 5 5 5 5 3 5
19 556.10 11/8 ^^4 G^^ Blue minor tritone fu
20 585.37 7/5 vA4, d5 G#v,

Ab

Minor tritone / diminished fifth fi Pluto
21 614.63 10/7 A4, ^d5 G#,

Ab^

Major tritone / augmented fourth se
22 643.90 16/11 vv5 Avv Red major tritone su
23 673.17 22/15, 40/27 v5 Av Blue fifth sih
24 702.44 3/2 P5 A Perfect fifth sol
25 731.71 32/21 ^5 A^ Red fifth si
26 760.98 14/9, 25/16 vm6 Bbv Blue minor sixth lo
27 790.24 11/7, 128/81 m6 Bb Gray minor sixth leh
28 819.51 8/5 ^m6 Bb^ Red minor sixth le
29 848.78 18/11, 44/27 ~6 Bvv Neutral sixth lu
30 878.05 5/3 vM6 Bv Blue major sixth la
31 907.32 27/16 M6 B Gray major sixth laa
32 936.59 12/7 ^M6 B^ Red major sixth li
33 965.85 7/4 vm7 Cv Blue minor seventh ta
34 995.12 16/9 m7 C Gray minor seventh teh
35 1024.39 9/5, 20/11 ^m7 C^ Red minor seventh te
36 1053.66 11/6 ~7 C^^ Neutral seventh tu
37 1082.93 15/8 vM7 C#v Blue major seventh ti
38 1112.20 40/21, 21/11 M7 C# Gray major seventh taa
39 1141.46 48/25, 27/14,

64/33

^M7 C#^ Red major seventh to
40 1170.73 160/81 v8 Dv Blue octave da
41 1200 2/1 P8 D do

Combining ups and downs notation with color notation, qualities can be loosely associated with colors:

quality color monzo format examples
downminor blue {a, b, 0, 1} 7/6, 7/4
minor fourthward white {a, b}, b < -1 32/27, 16/9
upminor green {a, b, -1} 6/5, 9/5
mid jade {a, b, 0, 0, 1} 11/9, 11/6
" amber {a, b, 0, 0, -1} 12/11, 18/11
downmajor yellow {a, b, 1} 5/4, 5/3
major fifthward white {a, b}, b > 1 9/8, 27/16
upmajor red {a, b, 0, -1} 9/7, 12/7

All 41edo chords can be named using ups and downs. Here are the blue, green, jade, yellow and red triads:

color of the 3rd JI chord notes as edosteps notes of C chord written name spoken name
blue 6:7:9 0-9-24 C Ebv G C.vm C downminor
green 10:12:15 0-11-24 C Eb^ G C.^m C upminor
jade 18:22:27 0-12-24 C Evv G C~ C mid
yellow 4:5:6 0-13-24 C Ev G C.v C downmajor or C dot down
red 14:18:27 0-15-24 C E^ G C.^ C upmajor or C dot up

0-10-20 = D F Ab = Ddim = "D dim"

0-10-21 = D F Ab^ = Ddim(^5) = "D dim up-five"

0-10-22 = D F Avv = Dm(vv5) = "D minor double-down five", or possibly Ddim(^^5)

0-10-23 = D F Av = Dm(v5) = "D minor down-five"

0-10-24 = D F A = Dm = "D minor"

0-14-24 = D F# A = D = "D" or "D major"

0-14-25 = D F# A^ = D(^5) = "D up-five"

0-14-26 = D F# A^^ = D(^^5) = "D double-up-five", or possibly Daug(vv5)

0-14-27 = D F# A#v = Daug(v5) = "D aug down-five"

0-14-28 = D F# A# is Daug = "D aug"

etc.

For a more complete list, see Ups and Downs Notation - Chord names in other EDOs.

Selected just intervals by error

The following table shows how some prominent just intervals are represented in 41edo (ordered by absolute error).

Interval, complement Error (abs., in cents)
4/3, 3/2 0.484
9/8, 16/9 0.968
15/14, 28/15 2.370
7/5, 10/7 2.854
8/7, 7/4 2.972
7/6, 12/7 3.456
13/11, 22/13 3.473
11/9, 18/11 3.812
9/7, 14/9 3.940
12/11, 11/6 4.296
11/8, 16/11 4.780
16/15, 15/8 5.342
5/4, 8/5 5.826
6/5, 5/3 6.310
10/9, 9/5 6.794
18/13, 13/9 7.285
14/11, 11/7 7.752
13/12, 24/13 7.769
16/13, 13/8 8.253
15/11, 22/15 10.122
11/10, 20/11 10.606
14/13, 13/7 11.225
15/13, 26/15 13.595
13/10, 20/13 14.079

Instruments

41-EDD elektrische gitaar.jpg

41-EDO Electric guitar, by Gregory Sanchez.

Ron_Sword_with_a_41ET_Guitar.jpg

41-EDO Classical guitar, by Ron Sword.

A possible system to tune keyboards in 41EDO is discussed in http://launch.groups.yahoo.com/group/tuning/message/74155.

Scales and modes

A list of 41edo modes (MOS and others).

Harmonic Scale

41edo is the first edo to do some justice to Mode 8 of the harmonic series, which Dante Rosati calls the "Diatonic Harmonic Series Scale," consisting of overtones 8 through 16 (sometimes made to repeat at the octave).

Overtones in "Mode 8": 8 9 10 11 12 13 14 15 16
...as JI Ratio from 1/1: 1/1 9/8 5/4 11/8 3/2 13/8 7/4 15/8 2/1
...in cents: 0 203.9 386.3 551.3 702.0 840.5 968.8 1088.3 1200.0
Nearest degree of 41edo: 0 7 13 19 24 29 33 37 41
...in cents: 0 204.9 380.5 556.1 702.4 848.8 965.9 1082.9 1200.0

While each overtone of Mode 8 is approximated within a reasonable degree of accuracy, the steps between the intervals are not uniquely represented. (41edo is, after all, a temperament.)

7\41 (7 degrees of 41edo) (204.9 cents) stands in for just ratio 9/8 (203.9 cents) -- a close match.

6\41 (175.6 cents) stands in for both 10/9 (182.4 cents) and 11/10 (165.0 cents).

5\41 (146.3 cents) stands in for both 12/11 (150.6 cents) and 13/12 (138.6 cents).

4\41 (117.1 cents) stands in for 14/13 (128.3 cents), 15/14 (119.4 cents), and 16/15 (111.7 cents).

The scale in 41, as adjacent steps, thus goes: 7 6 6 5 5 4 4 4.

Nonoctave Temperaments

Taking every third degree of 41edo produces a scale extremely close to 88cET or 88-cent equal temperament (or the 8th root of 3:2). Likewise, taking every fifth degree produces a scale very close to the equal-tempered Bohlen-Pierce Scale (or the 13th root of 3). See chart:

3 degrees of 41edo (near 88cET) overlap 5 degrees of 41edo (near BP)
deg of 41edo deg of 88cET cents cents cents deg of BP deg of 41edo
0 0 0 0 0
3 1 87.8
146.3 1 5
6 2 175.6
9 3 263.4
292.7 2 10
12 4 351.2
15 5 439.0 3 15
18 6 526.8
585.4 4 20
21 7 614.6
24 8 702.4
731.7 5 25
27 9 790.2
30 10 878.0 6 30
33 11 965.9
1024.4 7 35
36 12 1053.7
39 13 1141.5
1170.7 8 40
[ second octave ]
1 14 29.2
4 15 117.1 9 4
7 16 204.9
263.4 10 9
10 17 292.7
13 18 380.5
409.8 11 14
16 19 468.3
19 20 556.1 12 19
22 21 643.9
702.4 13 24
25 22 731.7
28 23 819.5
848.8 14 29
31 24 907.3
34 25 995.1 15 34
37 26 1082.9
1141.5 16 39
40 27 1170.7
[ third octave ]
2 28 58.5
87.8 17 3
5 29 146.3
8 30 234.1 18 8
11 31 322.0
380.5 19 13
14 32 409.8
17 33 497.6
526.8 20 18
20 34 585.3
23 35 673.2 21 23
26 36 761.0
819.5 22 28
29 37 848.8
32 38 936.6
965.9 23 33
35 39 1024.4
38 40 1112.2 24 38

Notation

A red-note/blue-note system, similar to the one proposed for 36edo, is one option for notating 41edo. (This is separate from and not compatible with Kite's color notation.) We have the "white key" albitonic notes A-G (7 in total), the "black key" sharps and flats (10 in total), a "red" and "blue" version of each albitonic note (14 in total), a "red" (dark red?) version of each sharp and a "blue" (dark blue?) version of each flat (10 in total), adding up to 41. This would result in quite a colorful keyboard! Note that there are no red flats or blue sharps. Using this nomenclature the notes are:

A, red A, blue Bb, Bb, A#, red A#, blue B, B, red B, blue C, C, red C, blue Db, Db, C#, red C#, blue D, D, red D, blue Eb, Eb, D#, red D#, blue E, E, red E, blue F, F, red F, blue Gb, Gb, F#, red F#, blue G, G, red G, blue Ab, Ab, G#, red G#, blue A, A.

Interval classes could also be named by analogy. The natural, colorless, or gray interval classes are the Pythagorean ones (which show up in the standard diatonic scale), while "red" and "blue" versions are one step higher or lower. Gray thirds, sixths, and sevenths are usually more dissonant than their colorful counterparts, but the reverse is true of fourths and fifths.

The step size of 41edo is small enough that the smallest interval (the "red/blue unison", seventh-tone, comma, diesis or whatever you want to call it) is actually fairly consonant with most timbres; it resembles a "noticeably out of tune unison" rather than a minor second, and has its own distinct character and appeal.

If "red" is replaced by "up", "blue" by "down", and "neutral" by "mid", and if "gray" is omitted, this notation becomes essentially the same as ups and downs notation. The only difference is the use of minor tritone and major tritone.

Music

EveningHorizon play by Cameron Bobro

Links

  1. ^ "Schismic Temperaments" at x31eq.com the website of Graham Breed
  2. ^ "Lattices with Decimal Notation" at x31eq.com
  3. ^ Schismatic temperament
  4. ^ Magic temperament
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