Xenharmonic Wiki

Sensi: Difference between revisions

← Older edit
VisualWikitext
Wikispaces>spt3125
**Imported revision 484145556 - Original comment: **
→Music: copypaste one from 46edo
 
(156 intermediate revisions by 16 users not shown)
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{interwiki
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| en = Sensi
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-01-20 21:39:35 UTC</tt>.<br>
| de = Sensi
: The original revision id was <tt>484145556</tt>.<br>
}}
: The revision comment was: <tt></tt><br>
{{Infobox regtemp
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| Title = Sensi
<h4>Original Wikitext content:</h4>
| Subgroups = 2.3.5.7, 2.3.5.7.13
<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">See [[Sensipent family#Sensi]] for more information.
| Comma basis = [[126/125]], [[245/243]] (7-limit); <br>[[91/90]], [[126/125]], [[169/168]] (2.3.5.7.13)
| Edo join 1 = 19 | Edo join 2 = 27
| Mapping = 1; 7 9 13 10
| Generators = 9/7 | Generators tuning = 443.3 | Optimization method = CWE
| MOS scales = [[3L&nbsp;2s]], [[3L&nbsp;5s]], [[8L&nbsp;3s]], [[8L&nbsp;11s]]
| Pergen = (P8, ccP5/7)
| Odd limit 1 = 7 | Mistuning 1 = 7.5 | Complexity 1 = 19
| Odd limit 2 = 2.3.5.7.13 21 | Mistuning 2 = 11.1 | Complexity 2 = 27
}}
'''Sensi''' is a [[rank-2 temperament|rank-2]] [[regular temperament]] that is [[generator|generated]] by an extremely sharp major third of between 442 and 445{{cent}}, which is taken in the [[7-limit]] to represent a sharpened [[9/7]]. The most important equivalence in sensi (i.e. [[tempering out]] the comma [[245/243]]) is known as ''sensamagic'', by which two of these thirds stack to a major sixth which approximates [[5/3]]. Sensi then makes the additional tempering of [[126/125]], through which three of these major sixths approximate [[7/6]], two octaves up. The [[6/1|6th harmonic]] is therefore split into seven, and [[5/4]] is divided into three parts, each identified with [[15/14]]. Furthermore, since the supermajor third is tempered so sharply, it makes sense to have it represent both 9/7 and [[13/10]], which means [[91/90]] is tempered out in the 2.3.5.7.13 [[subgroup]]. There the 15/14 interval also represents [[14/13]] and [[13/12]], which results in [[169/168]] and [[196/195]] being tempered out.


==Interval chain==
The structure whereby 5/3 is split into two supermajor thirds is obviously xenharmonic as this cannot occur in [[12edo]]. But particularly, as the simplest [[EDO]]s with similar structures are [[8edo]] and [[11edo]] (hence the 8-note ([[3L&nbsp;5s]], checkertonic) and 11-note ([[8L&nbsp;3s]], flanatonic) [[MOS scale]]s), sensi has a very xenmelodic character compared to many other ways of organizing the 7-limit (such as [[superpyth]], which is based on the familiar [[chain of fifths]], and even [[porcupine]], which is fundamentally heptatonic).
||~ Generators ||~ Cents* ||~ &lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Approximate ratios†&lt;/span&gt; ||
|| 0 ||&gt; 0.000 ||&lt; 1/1 ||
|| 1 ||&gt; 443.322 || 9/7~13/10 ||
|| 2 ||&gt; 886.644 ||&lt; 5/3~42/25 ||
|| 3 ||&gt; 129.966 ||&lt; 13/12~14/13~15/14 ||
|| 4 ||&gt; 573.288 ||&lt; 7/5~18/13 ||
|| 5 ||&gt; 1016.610 ||&lt; 9/5 ||
|| 6 ||&gt; 259.932 ||&lt; 7/6~15/13 ||
|| 7 ||&gt; 703.253 ||&lt; 3/2 ||
|| 8 ||&gt; 1146.576 ||&lt; 54/28~35/18 ||
|| 9 ||&gt; 389.896 ||&lt; 5/4 ||
|| 10 ||&gt; 833.220 ||&lt; 13/8 ||
|| 11 ||&gt; 76.542 ||&lt; 21/20~25/24 ||
|| 12 ||&gt; 519.864 ||&lt;  ||
|| 13 ||&gt; 963.185 ||&lt; 7/4 ||
|| 14 ||&gt; 206.507 ||&lt; 9/8 ||
|| 15 ||&gt; 649.829 ||&lt; 35/24 (close to 16/11) ||
|| 16 ||&gt; 1093.151 ||&lt; 15/8 ||
|| 17 ||&gt; 336.473 ||&lt; 39/32 ||
|| 18 ||&gt; 779.795 ||&lt; 25/16 ||
|| 19 ||&gt; 23.117 || 49/48~65/64~81/80 ||
|| 20 ||&gt; 466.439 || 21/16 ||
&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;*in 2.3.5.7.13 POTE tuning&lt;/span&gt;
&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;†2.3.5.7.13 ratio interpretations&lt;/span&gt;


=&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Sensi Visualizations&lt;/span&gt;=  
Equal temperaments that support sensi include [[19edo]] (generator 7\19; [[soft]] checkertonic), [[27edo]] (generator 10\27; [[supersoft]] checkertonic), as well as [[46edo]] (generator 17\46; {{nowrap| L/s {{=}} 7/5 }}, more optimized for sensi temperament) and [[65edo]] (generator 24\65; {{nowrap| L/s {{=}} 10/7 }}) using the 65f [[val]] with a flat 13.
 
See [[Sensipent family #Sensi]] for more technical data, [[sensi extensions]] for extensions of sensi to include the [[11/1|11th]] and [[17/1|17th]] harmonics, and [[#Related temperaments]] for alternative interpretations of similar structures to sensi.
 
== Theory ==
=== Interval chain ===
In the following table, odd harmonics and subharmonics 1–21 are in '''bold'''.
 
{| class="wikitable right-1 right-2 sortable"
|-
! #
! Cents*
! class="unsortable" | Approximate ratios
|-
| 0
| 0.0
| '''1/1'''
|-
| 1
| 443.4
| 9/7, 13/10
|-
| 2
| 886.7
| 5/3, 42/25
|-
| 3
| 130.1
| 13/12, 14/13, 15/14, 27/25
|-
| 4
| 573.4
| 7/5, 18/13, 25/18
|-
| 5
| 1016.8
| 9/5
|-
| 6
| 260.1
| 7/6, 15/13
|-
| 7
| 703.5
| '''3/2'''
|-
| 8
| 1146.9
| 27/14, 35/18
|-
| 9
| 390.2
| '''5/4'''
|-
| 10
| 833.6
| '''13/8''', 21/13
|-
| 11
| 76.9
| 21/20, 25/24
|-
| 12
| 520.3
| 27/20
|-
| 13
| 963.7
| '''7/4'''
|-
| 14
| 207.0
| '''9/8'''
|-
| 15
| 650.4
| 35/24 (sensor '''16/11''', sensus 22/15)
|-
| 16
| 1093.7
| '''15/8''' (sensor '''32/17''', sensus 17/9)
|-
| 17
| 337.1
| 39/32 (sensus 17/14)
|-
| 18
| 780.4
| 25/16
|-
| 19
| 23.8
| 49/48, 65/64, 81/80
|-
| 20
| 467.2
| '''21/16'''
|}
<nowiki/>* In 2.3.5.7.13 CWE tuning
 
=== Intervals of Sensi[8] ===
Sensi[8] is a [[mos scale]] with a [[3L&nbsp;5s]] pattern. See [[3L&nbsp;5s #Modes]] to see which modes have which qualities for each interval size.
 
Sortable table of Sensi[8]'s major and minor intervals in various sensi tunings:
 
{| class="wikitable right-2 right-3 right-4 sortable"
|-
! class="unsortable" | Degree
! Size in [[19edo]] (soft)
! Size in [[27edo]] (supersoft)
! Size in [[46edo]]
! class="unsortable" | Approximate ratios
! &#35; generators up
|-
| Unison
| 0\19, 0.0
| 0\27, 0.0
| 0\46, 0.0
| 1/1
| 0
|-
| Min. sen2nd
| 2\19, 126.3
| 3\27, 133.3
| 5\46, 130.4
| 14/13
| +3
|-
| Maj. sen2nd
| 3\19, 189.5
| 4\27, 177.8
| 7\46, 182.6
| 10/9
| −5
|-
| Min. sen3rd
| 4\19, 252.6
| 6\27, 266.7
| 10\46, 260.9
| 7/6
| +6
|-
| Maj. sen3rd
| 5\19, 315.8
| 7\27, 311.1
| 12\46, 313.0
| 6/5
| −2
|-
| Perf. sen4th
| 7\19, 442.1
| 10\27, 444.4
| 17\46, 443.5
| 9/7, 13/10
| +1
|-
| Aug. sen4th
| 8\19, 505.3
| 11\27, 488.9
| 19\46, 495.7
| 4/3
| −7
|-
| Min. sen5th
| 9\19, 568.4
| 13\27, 577.8
| 22\46, 573.9
| 7/5, 18/13
| +4
|-
| Maj. sen5th
| 10\19, 631.6
| 14\27, 622.2
| 24\46, 626.1
| 10/7, 13/9
| −4
|-
| Dim. sen6th
| 11\19, 694.7
| 16\27, 711.1
| 27\46, 704.3
| 3/2
| +7
|-
| Perf. sen6th
| 12\19, 757.9
| 17\27, 755.6
| 20\46, 756.5
| 14/9, 20/13
| −1
|-
| Min. sen7th
| 14\19, 884.2
| 20\27, 888.9
| 34\46, 887.0
| 5/3
| +2
|-
| Maj. sen7th
| 15\19, 947.4
| 21\27, 933.3
| 36\46, 939.1
| 12/7
| −6
|-
| Min. sen8th
| 16\19, 1010.5
| 23\27, 1022.2
| 39\46, 1017.4
| 9/5
| +5
|-
| Maj. sen8th
| 17\19, 1073.7
| 24\27, 1066.7
| 41\46, 1069.6
| 13/7
| −3
|}
 
=== Related temperaments ===
It is worth noting that sensi distinguishes itself from other structures, the [[sensamagic clan|sensamagic temperaments]], based around 245/243 (whose basic form in the 2.9/7.5/3 subgroup is known as [[sentry]]) by virtue of its minor third (6/5) being ''flattened'' from just rather than sharpened. This results in the supermajor third being sharpened even more than is typical, so much so that it is tuned [[interseptimal]]ly and may not fulfill all the functions that [[~]]9/7 is intended to have.
 
One way around this is to eschew the generator's interpretation as 9/7 altogether, and focus on the [[5-limit]] part of sensi, which is known as [[sensipent]] (whose comma is [[78732/78125]]). From there, an interpretation of the generator as {{nowrap|[[31/24]]~[[40/31]]}} is apparent. Beyond the 2.3.5.31 subgroup, more accurate interpretations (in comparison to sensi) of sensipent's extended harmony are given by [[sensible]] (adding primes 11, 17, and 23) and [[sendai]] (adding 23 and 29). There are also alternative mappings of 7, including [[sensei]] (+32 generators, with a tuning flat of 65edo) and [[warrior]] (−33 generators, with a tuning between 65edo and 46edo); warrior combines well with the mapping of sensible, and sensei with sendai.
 
==== BPS ====
: ''Main article: [[Relationship between Bohlen–Pierce and octave-ful temperaments#Relationship of rank-2 Bohlen.E2.80.93Pierce.E2.80.93Stearns temperament to octave-ful temperaments|Relationship between Bohlen–Pierce and octave-ful temperaments]].
 
Since the sensamagic comma, 245/243, contains no 2 in its [[monzo|factorization]], only primes 3, 5, and 7, it can be tempered out in a [[3/1|tritave (3/1)]]-repeating, [[3.5.7 subgroup]] context, where the generator (9/7) is now the tritave-reduced 7th subharmonic, two of which give the 5th harmonic. This is known as [[BPS|Bohlen–Pierce–Stearns (BPS)]] temperament, and it generates a [[4L 5s (3/1-equivalent)|4L&nbsp;5s]] scale against the tritave (sometimes known as ''Lambda''). Where this temperament connects to sensi is that, at 7 generators, BPS reaches an interval that it identifies with [[125/63]], which is rather close to the octave; sensi is obtained by treating this interval as the mapping of 2/1, which provides the interesting notion of using sensi in a 3/1-periodic 3.5.7.2 setting.
 
== Chords and harmony ==
{{See also| Chords of sensus }}
 
The fundamental otonal consonance of sensi is 4:5:6:7:9:13. However, the full chord is only available in the 19-note mos.
 
One of the most common consonant triads in sensi is the 6:10:13 triad, which spans 3 generators. Sensi[8] has five 6:10:13 triads, four 7:9:13 triads, three 5:6:7:9 tetrads and one 5:6:7:9:13 pentad. Having many diminished triads, it is similar to the 12edo diminished scale in some ways. Sensi is interesting mainly because it gives new 13-limit interpretations to fairly familiar (in the sense of extended meantone-like) intervals. Restricted to the 8-note MOS, it is essentially a [[non-over-1 temperament]].
 
Melodically, Sensi[8] sounds fairly familiar because many intervals are either 5-limit or have familiar categorical interpretations, being represented in the meantone tuning [[19edo]]. For example, the small step of about 130{{c}} categorizes pretty well as a large semitone (except at places in the scale where two of them make a flat subminor third); the large step is a small whole tone representing 10/9.
 
The root-sen5th-sen8th chords in Sensi[8] usually spell 5:7:9 (root-minor sen5th-minor sen8th) and 7:10:13 (root-major sen5th-major sen8th) chords (shown in the Anti-Dylathian mode QJKLMNOPQ = ssLssLsL):
* Q M P = ssLs sLs L ≈ 5:7:9
* J N Q = sLss LsL s is the odd one out
* K O J = LssL sLs s ≈ 7:10:13
* L P K = ssLs Lss L ≈ 5:7:9
* M Q L = sLsL ssL s ≈ 7:10:13
* N J M = LsLs sLs s ≈ 7:10:13
* O K N = sLss Lss L ≈ 5:7:9
* P L O = LssL ssL s ≈ 7:10:13
 
Other otonal chords approximated in the 8-note mos include:
 
* {{dash|Root, maj. sen7th, maj. sen8th ≈ 7:12:13|s=space}}
* {{dash|Root, maj. sen2nd, maj. sen5th ≈ 9:10:13|s=space}}
* {{dash|Root, min. sen3rd, dim. sen6th ≈ 6:7:9|s=space}}
* {{dash|Root, perf. sen4th, dim. sen6th ≈ 10:13:15 (ultramajor triad)|s=space}}
* {{dash|Root, perf. sen4th, maj. sen7th ≈ 7:9:13|s=space}}
* {{dash|Root, perf. sen4th, maj. sen5th, maj. sen7th ≈ 7:9:10:13|s=space}}
* {{dash|Root, perf. sen4th, min. sen7th ≈ 10:13:18|s=space}}
* {{dash|Root, perf. sen4th, min. sen5th, min. sen7th ≈ 10:13:14:18|s=space}}
* {{dash|Root, min. sen7th, min. sen3rd (+ octave) ≈ 3:5:7|s=space}}
* {{dash|Root, min. sen7th, min. sen2nd (+ octave) ≈ 6:10:13|s=space}}
* {{dash|Root, dim. sen6th, min. sen7th ≈ 6:9:10|s=space}}
* {{dash|Root, dim. sen6th, min. sen2nd (+octave) ≈ 6:9:13|s=space}}
 
== Scales ==
* [[Sensi5]]
* [[Sensi8]]
* [[Sensi11]]
* [[Sensi19]]
* [[Sensi27]]
 
== Tunings ==
=== Norm-based tunings ===
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~9/7 = 443.3166{{c}}
| CWE: ~9/7 = 443.3493{{c}}
| POTE: ~9/7 = 443.3827{{c}}
|}
 
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 2.3.5.7.13-subgroup norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~9/7 = 443.4016{{c}}
| CWE: ~9/7 = 443.3581{{c}}
| POTE: ~9/7 = 443.3220{{c}}
|}
 
=== Target tunings ===
{| class="wikitable center-all left-5 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Target tunings
|-
! rowspan="2" | Target
! colspan="2" | Minimax
|-
! Generator
! Eigenmonzo*
|-
| 7-odd-limit
| ~9/7 = 443.756{{c}}
| 7/4
|-
| 9-odd-limit
| ~9/7 = 443.519{{c}}
| 9/5
|-
| no-11 13-odd-limit
| ~9/7 = 443.519{{c}}
| 9/5
|-
| no-11 15-odd-limit
| ~9/7 = 443.136{{c}}
| 3/2
|}
 
=== Tuning spectrum ===
{| class="wikitable center-all left-4"
|-
! Edo<br>generators
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]*
! Generator (¢)
! Comments
|-
|
| 9/7
| 435.084
|
|-
| [[11edo|4\11]]
|
| 436.364
| 11cdf val
|-
|
| 15/14
| 439.814
|
|-
|
| 13/9
| 440.846
|
|-
|
| 15/13
| 441.290
|
|-
| [[19edo|7\19]]
|
| 442.105
| Lower bound of 7- and 9-odd-limit, <br>2.3.5.7.13-subgroup 13-, 15-, and 21-odd-limit diamond monotone
|-
|
| 5/3
| 442.179
|
|-
|
| 13/7
| 442.766
|
|-
|
| 5/4
| 442.924
| 5-odd-limit minimax
|-
|
| 15/8
| 443.017
|
|-
|
| 21/13
| 443.025
|
|-
| [[65edo|24\65]]
|
| 443.077
| 65f val
|-
|
| 3/2
| 443.136
| 2.3.5.7.13-subgroup 15- and 21-odd-limit minimax
|-
| [[46edo|17\46]]
|
| 443.478
|
|-
|
| 9/5
| 443.519
| 9-odd-limit and 2.3.5.7.13-subgroup 13-odd-limit minimax
|-
|
| 21/16
| 443.539
|
|-
|
| 7/4
| 443.756
| 7-odd-limit minimax
|-
| [[73edo|27\73]]
|
| 443.836
|
|-
|
| 21/20
| 444.042
|
|-
|
| 13/8
| 444.053
|
|-
| [[27edo|10\27]]
|
| 444.444
| Upper bound of 9-odd-limit, <br>2.3.5.7.13-subgroup 13-, 15-, and 21-odd-limit diamond monotone
|-
|
| 7/6
| 444.478
|
|-
|
| 117/70
| 444.649
| Exact geometric mean of 9/7 and 13/10
|-
|
| 7/5
| 445.628
|
|-
|
| 13/12
| 446.191
|
|-
| [[8edo|3\8]]
|
| 450.000
| 8d val, upper bound of 7-odd-limit diamond monotone
|-
|
| 13/10
| 454.214
|
|}
<nowiki/>* Besides the octave
 
== Visualizations ==
=== Steps of sensi ===
This diagram shows Sensi[5], [8], [11], and [19] with intervals named in relation to the L and s of Sensi[8].
 
[[File:steps_of_sensi.png|Steps of sensi|alt=steps_of_sensi.png]]


===&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;A Diagram of Sensi[5], [8], [11], and [19] with intervals named in relation to the L and s of Sensi[8]:&lt;/span&gt;===
[[image:steps_of_sensi.png]]
Note that X, M and Z are not standard, but d and A are; they are short for "diminished" and "augmented".
Note that X, M and Z are not standard, but d and A are; they are short for "diminished" and "augmented".


===A Diagram relating the Sensi generator chain (horizontal axis) to the steps within the octave (vertical axis) for Sensi[8] and [11]:===
=== Map of sensi ===
[[image:map_of_sensi[8].png]][[image:map_of_sensi[11]_correction2.png]]
These diagrams relate the sensi generator chain (horizontal axis) to the steps within the octave (vertical axis) for Sensi[8] and [11].
 
[[File:map_of_sensi-8-.png|Map of Sensi[8]|alt=map_of_sensi[8].png]]
[[File:map_of_sensi-11-_correction2.png|Map of Sensi[11]|alt=map_of_sensi[11]_correction2.png]]
 
=== Isomorphic layout ===
{{See also| Lumatone mapping for sensi }}
 
This diagram shows a layout for playing sensi temperament on an [[isomorphic keyboard]].
 
[[File:sensi_isomorphic_layout.png|sensi_isomorphic_layout.png|alt=sensi_isomorphic_layout.png]]


===A Diagram showing a layout for playing Sensi Temperament on an Isomorphic Keyboard:===
[[image:sensi_isomorphic_layout.png]]
The darkest hexagons represent the same note (eg. C), but offset by octaves. The next-darkest hexagons show the notes of Sensi[5]. Imagine stepping from hex to hex as you move across the keyboard from left to right, landing only on the darkest and next-darkest hexes. The light red hexagons show additional notes needed to play Sensi[8]. The Large step of Sensi[8] is represented by a move straight down, so this pattern is a little more zig-zaggy than the pattern for Sensi[5]. Add the white hexes and you have Sensi[11]. The small step of Sensi[11] (indicated in the diagram as "c" for chroma), is represented by a move straight down and down-left. This pattern actually involves moving backward in the horizontal direction, and is therefore more zig-zaggy.
The darkest hexagons represent the same note (eg. C), but offset by octaves. The next-darkest hexagons show the notes of Sensi[5]. Imagine stepping from hex to hex as you move across the keyboard from left to right, landing only on the darkest and next-darkest hexes. The light red hexagons show additional notes needed to play Sensi[8]. The Large step of Sensi[8] is represented by a move straight down, so this pattern is a little more zig-zaggy than the pattern for Sensi[5]. Add the white hexes and you have Sensi[11]. The small step of Sensi[11] (indicated in the diagram as "c" for chroma), is represented by a move straight down and down-left. This pattern actually involves moving backward in the horizontal direction, and is therefore more zig-zaggy.


===A Sensi[19] Guitar (one octave):===  
=== Sensi[19] guitar ===
[[image:sensi[19]in46.jpg]]
[[File:sensi-19-in46.jpg|sensi[19]in46.jpg|alt=sensi[19]in46.jpg]]
SOMEONE PLEASE MAKE ONE OF THESE AND SEND IT TO DUSTIN SCHALLERT!
 
== Music ==
; [[Andrew Heathwaite]]
* [[Technical Notes for Newbeams #Tumbledown Stew|"Tumbledown Stew" from ''Newbeams'']]
* [[Technical Notes for Newbeams #Hypnocloudsmack 3|"Hypnocloudsmack 3" from ''Newbeams'']]


=Music=
; [[Budjarn Lambeth]]
[[Technical Notes for Newbeams#Track%20notes:-Tumbledown%20Stew|Tumbledown Stew]] and [[Technical Notes for Newbeams#Track%20notes:-Hypnocloudsmack%203|Hypnocloudsmack 3]] by [[Andrew Heathwaite]]</pre></div>
* [https://www.youtube.com/watch?v=qc0CkUKj7t4 ''Music in Sensi Temperament (+ Tempered Octaves)''] (2024)
<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;Sensi&lt;/title&gt;&lt;/head&gt;&lt;body&gt;See &lt;a class="wiki_link" href="/Sensipent%20family#Sensi"&gt;Sensipent family&lt;/a&gt; for more information.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Interval chain"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Interval chain&lt;/h2&gt;


&lt;table class="wiki_table"&gt;
; [[Claudi Meneghin]]
    &lt;tr&gt;
* [https://www.youtube.com/watch?v=rmgWC_jruSg ''Sensi Fugue''] (2024) – fugue for two organs, in sensi, 46edo tuning
        &lt;th&gt;Generators&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Cents*&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Approximate ratios†&lt;/span&gt;&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;0.000&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;1/1&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;443.322&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/7~13/10&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;886.644&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;5/3~42/25&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;129.966&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;13/12~14/13~15/14&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;573.288&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;7/5~18/13&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;1016.610&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;9/5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;259.932&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;7/6~15/13&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;703.253&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;3/2&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;1146.576&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;54/28~35/18&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;389.896&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;5/4&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;833.220&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;13/8&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;76.542&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;21/20~25/24&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;519.864&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;963.185&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;7/4&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;206.507&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;9/8&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;649.829&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;35/24 (close to 16/11)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;1093.151&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;15/8&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;336.473&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;39/32&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;18&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;779.795&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;25/16&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;23.117&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;49/48~65/64~81/80&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;20&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;466.439&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;21/16&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;*in 2.3.5.7.13 POTE tuning&lt;/span&gt;&lt;br /&gt;
[[Category:Sensi| ]] <!-- Main article -->
&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;†2.3.5.7.13 ratio interpretations&lt;/span&gt;&lt;br /&gt;
[[Category:Rank-2 temperaments]]
&lt;br /&gt;
[[Category:Sensipent family]]
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Sensi Visualizations"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;Sensi Visualizations&lt;/span&gt;&lt;/h1&gt;
[[Category:Sensamagic clan]]
&lt;br /&gt;
[[Category:Starling temperaments]]
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="Sensi Visualizations--A Diagram of Sensi[5], [8], [11], and [19] with intervals named in relation to the L and s of Sensi[8]:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;A Diagram of Sensi[5], [8], [11], and [19] with intervals named in relation to the L and s of Sensi[8]:&lt;/span&gt;&lt;/h3&gt;
[[Category:Sengic temperaments]]
&lt;!-- ws:start:WikiTextLocalImageRule:192:&amp;lt;img src=&amp;quot;/file/view/steps_of_sensi.png/288547928/steps_of_sensi.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/steps_of_sensi.png/288547928/steps_of_sensi.png" alt="steps_of_sensi.png" title="steps_of_sensi.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:192 --&gt;&lt;br /&gt;
[[Category:Naiadic]]
Note that X, M and Z are not standard, but d and A are; they are short for &amp;quot;diminished&amp;quot; and &amp;quot;augmented&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="Sensi Visualizations--A Diagram relating the Sensi generator chain (horizontal axis) to the steps within the octave (vertical axis) for Sensi[8] and [11]:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;A Diagram relating the Sensi generator chain (horizontal axis) to the steps within the octave (vertical axis) for Sensi[8] and [11]:&lt;/h3&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:193:&amp;lt;img src=&amp;quot;/file/view/map_of_sensi%5B8%5D.png/287845258/map_of_sensi%5B8%5D.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/map_of_sensi%5B8%5D.png/287845258/map_of_sensi%5B8%5D.png" alt="map_of_sensi[8].png" title="map_of_sensi[8].png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:193 --&gt;&lt;!-- ws:start:WikiTextLocalImageRule:194:&amp;lt;img src=&amp;quot;/file/view/map_of_sensi%5B11%5D_correction2.png/287859614/map_of_sensi%5B11%5D_correction2.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/map_of_sensi%5B11%5D_correction2.png/287859614/map_of_sensi%5B11%5D_correction2.png" alt="map_of_sensi[11]_correction2.png" title="map_of_sensi[11]_correction2.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:194 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="Sensi Visualizations--A Diagram showing a layout for playing Sensi Temperament on an Isomorphic Keyboard:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;A Diagram showing a layout for playing Sensi Temperament on an Isomorphic Keyboard:&lt;/h3&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:195:&amp;lt;img src=&amp;quot;/file/view/sensi_isomorphic_layout.png/288547914/sensi_isomorphic_layout.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/sensi_isomorphic_layout.png/288547914/sensi_isomorphic_layout.png" alt="sensi_isomorphic_layout.png" title="sensi_isomorphic_layout.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:195 --&gt;&lt;br /&gt;
The darkest hexagons represent the same note (eg. C), but offset by octaves. The next-darkest hexagons show the notes of Sensi[5]. Imagine stepping from hex to hex as you move across the keyboard from left to right, landing only on the darkest and next-darkest hexes. The light red hexagons show additional notes needed to play Sensi[8]. The Large step of Sensi[8] is represented by a move straight down, so this pattern is a little more zig-zaggy than the pattern for Sensi[5]. Add the white hexes and you have Sensi[11]. The small step of Sensi[11] (indicated in the diagram as &amp;quot;c&amp;quot; for chroma), is represented by a move straight down and down-left. This pattern actually involves moving backward in the horizontal direction, and is therefore more zig-zaggy.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="Sensi Visualizations--A Sensi[19] Guitar (one octave):"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;A Sensi[19] Guitar (one octave):&lt;/h3&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:196:&amp;lt;img src=&amp;quot;/file/view/sensi%5B19%5Din46.jpg/312605652/sensi%5B19%5Din46.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/sensi%5B19%5Din46.jpg/312605652/sensi%5B19%5Din46.jpg" alt="sensi[19]in46.jpg" title="sensi[19]in46.jpg" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:196 --&gt;&lt;br /&gt;
SOMEONE PLEASE MAKE ONE OF THESE AND SEND IT TO DUSTIN SCHALLERT!&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Music&lt;/h1&gt;
&lt;a class="wiki_link" href="/Technical%20Notes%20for%20Newbeams#Track%20notes:-Tumbledown%20Stew"&gt;Tumbledown Stew&lt;/a&gt; and &lt;a class="wiki_link" href="/Technical%20Notes%20for%20Newbeams#Track%20notes:-Hypnocloudsmack%203"&gt;Hypnocloudsmack 3&lt;/a&gt; by &lt;a class="wiki_link" href="/Andrew%20Heathwaite"&gt;Andrew Heathwaite&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
Retrieved from "https://en.xen.wiki/w/Sensi"