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353edo: Difference between revisions

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== Table of intervals ==
== Table of intervals ==
{| class="wikitable mw-collapsible mw-collapsed"
{| class="wikitable mw-collapsible mw-collapsed"
|+
!Step
!Note name
<small>(diatonic Hebrew[19] version</small>)
!Associated ratio
<small>(2.5.7.13 subgroup)</small>
|-
|-
|0
! Step
|C
! Note name<br /><span style="font-size: 0.75em;">(diatonic Hebrew[19] version)</span>
|1/1
! Associated ratio<br /><span style="font-size: 0.75em;">(2.5.7.13 subgroup)</span>
|-
|-
|1
| 0
|C-C#
| C
|
| 1/1
|-
|-
|2
| 1
|C-Db
| C-C#
|
|  
|-
|-
|3
| 2
|C-D
| C-Db
|[[196/195]]
|  
|-
|-
|4
| 3
|C-D#
| C-D
|
| [[196/195]]
|-
|-
|19
| 4
|C#
| C-D#
|[[26/25]]
|  
|-
|-
|38
| 19
|Db
| C#
|[[14/13]]
| [[26/25]]
|-
|-
|41
| 38
|Db-D
| Db
|[[13/12]]
| [[14/13]]
|-
|-
|46
| 41
|Db-F
| Db-D
|[[35/32]]
| [[13/12]]
|-
|-
|57
| 46
|D
| Db-F
|
| [[35/32]]
|-
|-
|76
| 57
|D#
| D
|
|  
|-
|-
|95
| 76
|Eb
| D#
|
|  
|-
|-
|114
| 95
|E
| Eb
|[[5/4]]
|  
|-
|-
|133
| 114
|E#
| E
|[[13/10]] I (patent val approximation)
| [[5/4]]
|-
|-
|134
| 133
|E#-C#
| E#
|13/10 II (direct approximation)
| [[13/10]] I (patent val approximation)
|-
|-
|152
| 134
|F
| E#-C#
|
| 13/10 II (direct approximation)
|-
|-
|171
| 152
|F#
| F
|[[7/5]]
|  
|-
|-
|190
| 171
|Gb
| F#
|
| [[7/5]]
|-
|-
|206
| 190
|Gb-Bb
| Gb
|3/2
|  
|-
|-
|209
| 206
|G
| Gb-Bb
|[[98/65]]
| 3/2
|-
|-
|228
| 209
|G#
| G
|
| [[98/65]]
|-
|-
|247
| 228
|Ab
| G#
|[[13/8]]
|  
|-
|-
|266
| 247
|A
| Ab
|
| [[13/8]]
|-
|-
|285
| 266
|A#
| A
|[[7/4]]
|  
|-
|-
|304
| 285
|Bb
| A#
|
| [[7/4]]
|-
|-
|323
| 304
|B
| Bb
|
|  
|-
|-
|342
| 323
|B#/Cb
| B
|
|  
|-
|-
|353
| 342
|C
| B#/Cb
|2/1
|
|-
| 353
| C
| 2/1
|}
|}


== Regular temperament properties ==
== Regular temperament properties ==
Assuming 353edo is treated as the 2.5.7.11.13.17 subgroup temperament.
Assuming 353edo is treated as the 2.5.7.11.13.17 subgroup temperament.
{| class="wikitable center-4 center-5 center-6"
{{comma basis begin}}
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" | Tuning Error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.5
| 2.5
| {{monzo| 820 -353 }}
| {{monzo| 820 -353 }}
| {{mapping| 353 820 }}
| {{mapping| 353 820 }}
| -0.263
| &minus;0.263
| 0.263
| 0.263
| 7.74
| 7.74
Line 166: Line 156:
| 3136/3125, {{monzo| 209 -9 -67 }}
| 3136/3125, {{monzo| 209 -9 -67 }}
| {{mapping| 353 820 991 }}
| {{mapping| 353 820 991 }}
| -0.177
| &minus;0.177
| 0.247
| 0.247
| 7.26
| 7.26
Line 173: Line 163:
| 3136/3125, 5767168/5764801, {{monzo| -20 -6  1 9 }}
| 3136/3125, 5767168/5764801, {{monzo| -20 -6  1 9 }}
| {{mapping| 353 820 991 1221 }}
| {{mapping| 353 820 991 1221 }}
| -0.089
| &minus;0.089
| 0.263
| 0.263
| 7.73
| 7.73
Line 180: Line 170:
| 3136/3125, 4394/4375, 6656/6655, 5767168/5764801
| 3136/3125, 4394/4375, 6656/6655, 5767168/5764801
| {{mapping| 353 820 991 1221 1306 }}
| {{mapping| 353 820 991 1221 1306 }}
| -0.024
| &minus;0.024
| 0.268
| 0.268
| 7.89
| 7.89
Line 187: Line 177:
| 3136/3125, 4394/4375, 7744/7735, 60112/60025, 64141/64000
| 3136/3125, 4394/4375, 7744/7735, 60112/60025, 64141/64000
| {{mapping| 353 820 991 1221 1306 1443 }}
| {{mapping| 353 820 991 1221 1306 1443 }}
| -0.037
| &minus;0.037
| 0.247
| 0.247
| 7.26
| 7.26
|}
{{comma basis end}}


=== Rank-2 temperaments  ===
=== Rank-2 temperaments  ===
{| class="wikitable center-all left-5"
{{rank-2 begin}}
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
|-
| 1
| 1
Line 217: Line 202:
| 27/20
| 27/20
| [[Marvo]] (353c) / [[zarvo]] (353cd)
| [[Marvo]] (353c) / [[zarvo]] (353cd)
|}
{{rank-2 end}}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
{{orf}}


== Scales ==
== Scales ==
* RectifiedHebrew[19] - 18L 1s
* RectifiedHebrew[19] &ndash; 18L 1s
* RectifiedHebrew[130] - 93L 37s
* RectifiedHebrew[130] &ndash; 93L 37s
* Austro-Hungarian Minor[9] - 57 38 38 38 38 38 38 38 30
* Austro-Hungarian Minor[9] &ndash; 57 38 38 38 38 38 38 38 30


== See also ==
== See also ==
Line 231: Line 216:
== Music ==
== Music ==
; [[Eliora]]
; [[Eliora]]
* [https://www.youtube.com/watch?v=JrSEGE6_oys ''Snow On My City''] (2022) - cover of [[wikipedia:Naomi Shemer|Naomi Shemer]] in Rectified Hebrew and apparatus
* [https://www.youtube.com/watch?v=JrSEGE6_oys ''Snow On My City''] (2022) &ndash; cover of [[wikipedia:Naomi Shemer|Naomi Shemer]] in Rectified Hebrew and apparatus
; [[Mercury Amalgam]]
; [[Mercury Amalgam]]
* [https://www.youtube.com/watch?v=z-SxvrnkTzU ''Bottom Text''] (2022) in Rectified Hebrew
* [https://www.youtube.com/watch?v=z-SxvrnkTzU ''Bottom Text''] (2022) in Rectified Hebrew
Retrieved from "https://en.xen.wiki/w/353edo"