159edo: Difference between revisions
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{| class="mw-collapsible mw-collapsed wikitable center-1" | {| class="mw-collapsible mw-collapsed wikitable center-1" | ||
|+ style= | |+ style=white-space:nowrap | Table of 159edo intervals | ||
|- | |- | ||
! Step | ! Step | ||
| Line 1,341: | Line 1,341: | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{ | {| class="wikitable center-4 center-5 center-6" | ||
! 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]] (%) | |||
|- | |- | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| Line 1,384: | Line 1,392: | ||
| 0.386 | | 0.386 | ||
| 5.11 | | 5.11 | ||
|} | |||
* 159et has lower absolute errors in the 19- and 23-limit than any previous equal temperaments, past [[152edo|152fg]]. The next equal temperament that does better in the 19-limit is [[161edo|161]], and in the 23-limit, [[183edo|183]]. | * 159et has lower absolute errors in the 19- and 23-limit than any previous equal temperaments, past [[152edo|152fg]]. The next equal temperament that does better in the 19-limit is [[161edo|161]], and in the 23-limit, [[183edo|183]]. | ||
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{| class="commatable wikitable center-all left-3 right-4 left-6" | {| class="commatable wikitable center-all left-3 right-4 left-6" | ||
|- | |- | ||
! [[Harmonic limit|Prime<br>limit]] | ! [[Harmonic limit|Prime <br>limit]] | ||
! [[Ratio]]<ref | ! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref> | ||
! [[Monzo]] | ! [[Monzo]] | ||
! [[Cents]] | ! [[Cents]] | ||
| Line 1,849: | Line 1,857: | ||
Note: 5-limit temperaments supported by 53et are not included. | Note: 5-limit temperaments supported by 53et are not included. | ||
{ | {| class="wikitable center-all right-3 left-5" | ||
|+Table of rank-2 temperaments by generator | |||
! Periods<br>per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br>Ratio* | |||
! Temperament | |||
|- | |- | ||
| 1 | | 1 | ||
| Line 1,964: | Line 1,978: | ||
| 441/260<br>(196/195) | | 441/260<br>(196/195) | ||
| [[Iodine]] | | [[Iodine]] | ||
|} | |||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
== Music == | == Music == | ||
| Line 1,979: | Line 1,993: | ||
; [[Ozan Yarman]] | ; [[Ozan Yarman]] | ||
* [https://www.youtube.com/watch?v=O5Dn6v3UOtM ''ENTIRE ORCHESTRAL 79-tone "Pesendide Fugue" (III. Selim & Ozan Yarman)''] | * [https://www.youtube.com/watch?v=O5Dn6v3UOtM ''ENTIRE ORCHESTRAL 79-tone "Pesendide Fugue" (III. Selim & Ozan Yarman)''] - Ozan Yarman's (5-voice & 2-subject) Choral Fugue of Sultan III. Selim's Pesendide Ağır Semai in Ağır Aksak usul] (re-scored in accordance with Yarman's 79-tone tuning) | ||
* [https://www.youtube.com/watch?v=xoCR1rDXhWI ''Whitecap Visualizer assisted (CHOIR + Digitized Ottoman Singing VocalWriter + STRINGS only)''] | * [https://www.youtube.com/watch?v=xoCR1rDXhWI ''Whitecap Visualizer assisted (CHOIR + Digitized Ottoman Singing VocalWriter + STRINGS only)''] - flow of the ENTIRE "Pesendide Fugue" in the 79-tone Qanun tuning | ||
* [https://www.youtube.com/watch?v=tAcmvGgERC4 ''79'lu sistemde MISIRLI Udi İbrahim Efendi'nin çoksesli Acemaşiran Sazsemaisi -- Ozan Yarman''] | * [https://www.youtube.com/watch?v=tAcmvGgERC4 ''79'lu sistemde MISIRLI Udi İbrahim Efendi'nin çoksesli Acemaşiran Sazsemaisi -- Ozan Yarman''] - Adjemashiran Sazsemai of "Egyptian" Ud-player Ibrahim Efendi in 79 MOS 159-tET as polyphonalized by Ozan Yarman (2005-2022) | ||
* [https://www.youtube.com/watch?v=dT9RssZ1950 ''79-ton RAST KAR-I NATIK (Ozan Yarman -- thicc vokal ver.)''] | * [https://www.youtube.com/watch?v=dT9RssZ1950 ''79-ton RAST KAR-I NATIK (Ozan Yarman -- thicc vokal ver.)''] - RAST KAR-I NATIK by Ozan Yarman in his 79-tone Qanun tuning | ||
== Instruments == | == Instruments == | ||
Currently, there is an instrument under development by [[Erik Natanael]] called the "Neod"<ref>[https://www.youtube.com/watch?v=HwTCF0zeo4o Erik Natanael - neod.1: Explaining my 53edo musical instrument]</ref>, which utilizes this system. Although 53edo is the basis for most of the keys on this instrument, there are additional buttons which modify the pitch by a single step of 159edo. | Currently, there is an instrument under development by [[Erik Natanael]] called the "Neod"<ref>[https://www.youtube.com/watch?v=HwTCF0zeo4o Erik Natanael - neod.1: Explaining my 53edo musical instrument]</ref>, which utilizes this system. Although 53edo is the basis for most of the keys on this instrument, there are additional buttons which modify the pitch by a single step of 159edo. | ||
== Articles == | == Articles == | ||
* [http://www.ozanyarman.com/files/doctorate_thesis.pdf ''79-Tone Tuning & Theory for Turkish Maqam Music''] | * [http://www.ozanyarman.com/files/doctorate_thesis.pdf ''79-Tone Tuning & Theory for Turkish Maqam Music''] – Ozan Yarman's dissertation | ||
* [http://www.ozanyarman.com/files/34ten79a.pdf ''Search For A Theoretical Model Conforming To Turkish Maqam Music Practice: A Selection Of Fixed-Pitch Settings From 34-tone Equal Temperament To The 79-tone Tuning''] | * [http://www.ozanyarman.com/files/34ten79a.pdf ''Search For A Theoretical Model Conforming To Turkish Maqam Music Practice: A Selection Of Fixed-Pitch Settings From 34-tone Equal Temperament To The 79-tone Tuning''] – also by Ozan Yarman, gives a summary | ||
* [http://www.bestii.com/~mschulter/17-MOS-tunings_Letter-to-Ozan.txt Letter to Ozan Yarman] by Margo Schulter [https://www.webcitation.org/5xepptaan (permalink)] | * [http://www.bestii.com/~mschulter/17-MOS-tunings_Letter-to-Ozan.txt Letter to Ozan Yarman] by Margo Schulter [https://www.webcitation.org/5xepptaan (permalink)] | ||
== References == | == References == | ||
<references/> | |||
<references /> | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
| Line 2,002: | Line 2,014: | ||
[[Category:159edo]] | [[Category:159edo]] | ||
[[Category:Guiron]] | [[Category:Guiron]] | ||
[[Category:Maqam]] | [[Category:Maqam]] | ||
[[Category:Nexus]] | [[Category:Nexus]] | ||
[[Category:Tritikleismic]] | |||
[[Category:Quartismic]] | [[Category:Quartismic]] | ||
[[Category:Yarman]] | [[Category:Yarman]] | ||
[[Category:Listen]] | |||