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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|353}}  
{{ED intro}}  


== Theory ==
== Theory ==
353edo is in[[consistent]] in the [[5-odd-limit]] and [[harmonic]] [[3/1|3]] is about halfway between its steps. It is suitable for use with the 2.9.15.7.11.13.17.23.29.31.37 [[subgroup]]. This makes 353edo an "upside-down" edo – poor approximation of the low harmonics, but an improvement over the high ones. Nonetheless, it provides the [[optimal patent val]] for [[didacus]], the 2.5.7 subgroup temperament tempering out [[3136/3125]].  
353edo is in[[consistent]] in the [[5-odd-limit]] and [[harmonic]] [[3/1|3]] is about halfway between its steps. It is suitable for use with the 2.9.15.7.11.13.17.23.29.31.37 [[subgroup]]. This makes 353edo an "upside-down" edo—poor approximation of the low harmonics, but an improvement over the high ones. Nonetheless, it provides the [[optimal patent val]] for [[didacus]], the 2.5.7 subgroup temperament tempering out [[3136/3125]], and serves as a very close approximation of its just-[[7/4]] tuning.


Using the [[patent val]] nonetheless, 353edo supports [[apparatus]], [[marvo]] and [[zarvo]].
Using the [[patent val]] nonetheless, 353edo supports [[apparatus]], [[marvo]] and [[zarvo]].
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The number 353 in this version of the Hebrew calendar must not be confused with the number of days in ''shanah chaserah'' (שנה חסרה), the deficient year.  
The number 353 in this version of the Hebrew calendar must not be confused with the number of days in ''shanah chaserah'' (שנה חסרה), the deficient year.  


It is possible to use a superpyth-ish fifth of Rectified Hebrew fifth, 209\353, as a generator. In this case, 76 & 353 temperament is obtained. In the 2.5.7.13 subgroup, this results in the fifth being equal to 98/65 and the comma basis of 10985/10976, {{Monzo|-103 0 -38 51 0 13}}.
It is possible to use a superpyth-ish fifth of Rectified Hebrew fifth, 209\353, as a generator. In this case, {{nowrap|76 & 353}} temperament is obtained. In the 2.5.7.13 subgroup, this results in the fifth being equal to 98/65 and the comma basis of 10985/10976, {{Monzo|-103 0 -38 51 0 13}}.


== 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*
|1/1
! Associated ratio**
|-
|-
|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
|}
|}
<nowiki />* Diatonic Hebrew[19] version
<nowiki />** 2.5.7.13 subgroup


== 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"
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning Error
! colspan="2" | Tuning error
|-
|-
! [[TE error|Absolute]] (¢)
! [[TE error|Absolute]] (¢)
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| {{monzo| 820 -353 }}
| {{monzo| 820 -353 }}
| {{mapping| 353 820 }}
| {{mapping| 353 820 }}
| -0.263
| −0.263
| 0.263
| 0.263
| 7.74
| 7.74
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| 3136/3125, {{monzo| 209 -9 -67 }}
| 3136/3125, {{monzo| 209 -9 -67 }}
| {{mapping| 353 820 991 }}
| {{mapping| 353 820 991 }}
| -0.177
| −0.177
| 0.247
| 0.247
| 7.26
| 7.26
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| 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
| −0.089
| 0.263
| 0.263
| 7.73
| 7.73
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| 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
| −0.024
| 0.268
| 0.268
| 7.89
| 7.89
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| 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
| −0.037
| 0.247
| 0.247
| 7.26
| 7.26
|}
|}


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
! Periods<br>per 8ve
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
! Periods<br />per 8ve
! Generator*
! Generator*
! Cents*
! Cents*
! Associated<br>Ratio*
! Associated<br />ratio*
! Temperaments
! Temperament
|-
|-
| 1
| 1
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| [[Marvo]] (353c) / [[zarvo]] (353cd)
| [[Marvo]] (353c) / [[zarvo]] (353cd)
|}
|}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct


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


== See also ==
== See also ==
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== 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) – 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"