26edo: Difference between revisions
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== Theory == | |||
<b>26edo</b> divides the [[octave]] into 26 equal parts of 46.154 [[cent]]s each. It tempers out 81/80 in the [[5-limit]], making it a meantone tuning with a very flat fifth. In the [[7-limit]], it tempers out 50/49, 525/512 and 875/864, and supports [[injera]], [[flattone]], [[Jubilismic clan#Lemba|lemba]] and [[Jubilismic clan#Doublewide|doublewide]] temperaments. It really comes into its own as a higher-limit temperament, being the smallest equal division which represents the [[13 odd limit]] [[consistent|consistently]]. 26edo has a very good approximation of the harmonic seventh ([[7/4]]). | <b>26edo</b> divides the [[octave]] into 26 equal parts of 46.154 [[cent]]s each. It tempers out 81/80 in the [[5-limit]], making it a meantone tuning with a very flat fifth. In the [[7-limit]], it tempers out 50/49, 525/512 and 875/864, and supports [[injera]], [[flattone]], [[Jubilismic clan#Lemba|lemba]] and [[Jubilismic clan#Doublewide|doublewide]] temperaments. It really comes into its own as a higher-limit temperament, being the smallest equal division which represents the [[13 odd limit]] [[consistent|consistently]]. 26edo has a very good approximation of the harmonic seventh ([[7/4]]). | ||
26edo's "minor sixth" (1.6158) is very close to φ ≈ 1.6180 (i. e., the golden ratio). | 26edo's "minor sixth" (1.6158) is very close to φ ≈ 1.6180 (i. e., the golden ratio). | ||
The structure of 26edo is an interesting beast, with various approaches relating it to various rank two temperaments. | The structure of 26edo is an interesting beast, with various approaches relating it to various rank two temperaments. | ||
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*based on treating 26-EDO as a [[13-limit]] temperament; other approaches are possible. | *based on treating 26-EDO as a [[13-limit]] temperament; other approaches are possible. | ||
Using [[Kite's color notation]], qualities can be loosely associated with colors: | Using [[Kite's color notation|color notation]], qualities can be loosely associated with colors: | ||
{| class="wikitable" style="text-align:center;" | {| class="wikitable" style="text-align:center;" | ||
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== Commas == | == Commas == | ||
26et tempers out the following commas. (Note: This assumes the val < 26 41 60 73 90 96 |.) | 26et tempers out the following [[commas]]. (Note: This assumes the val < 26 41 60 73 90 96 |.) | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! | Ratio | ! | [[Ratio]] | ||
! | Monzo | ! | [[Monzo]] | ||
! | | ! | [[Cents]] | ||
![[Color notation/Temperament Names|Color Name]] | |||
! | Name 1 | ! | Name 1 | ||
! | Name 2 | ! | Name 2 | ||
| Line 550: | Line 551: | ||
| |<nowiki> | -4 4 -1 </nowiki>> | | |<nowiki> | -4 4 -1 </nowiki>> | ||
| style="text-align:right;" | 21.51 | | style="text-align:right;" | 21.51 | ||
| style="text-align:center;" |Gu | |||
| style="text-align:center;" | Syntonic Comma | | style="text-align:center;" | Syntonic Comma | ||
| style="text-align:center;" | Didymos Comma | | style="text-align:center;" | Didymos Comma | ||
| Line 557: | Line 559: | ||
| |<nowiki> | -17 62 -35 </nowiki>> | | |<nowiki> | -17 62 -35 </nowiki>> | ||
| style="text-align:right;" | 0.23 | | style="text-align:right;" | 0.23 | ||
| style="text-align:center;" |Quadla-sepquingu | |||
| style="text-align:center;" | Senior | | style="text-align:center;" | Senior | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 564: | Line 567: | ||
| |<nowiki> | -9 1 2 1 </nowiki>> | | |<nowiki> | -9 1 2 1 </nowiki>> | ||
| style="text-align:right;" | 43.41 | | style="text-align:right;" | 43.41 | ||
| style="text-align:center;" |Zoyoyo | |||
| style="text-align:center;" | Avicennma | | style="text-align:center;" | Avicennma | ||
| style="text-align:center;" | Avicenna's Enharmonic Diesis | | style="text-align:center;" | Avicenna's Enharmonic Diesis | ||
| Line 571: | Line 575: | ||
| |<nowiki> | 1 0 2 -2 </nowiki>> | | |<nowiki> | 1 0 2 -2 </nowiki>> | ||
| style="text-align:right;" | 34.98 | | style="text-align:right;" | 34.98 | ||
| style="text-align:center;" |Biruyo | |||
| style="text-align:center;" | Tritonic Diesis | | style="text-align:center;" | Tritonic Diesis | ||
| style="text-align:center;" | Jubilisma | | style="text-align:center;" | Jubilisma | ||
| Line 578: | Line 583: | ||
| |<nowiki> | -5 -3 3 1 </nowiki>> | | |<nowiki> | -5 -3 3 1 </nowiki>> | ||
| style="text-align:right;" | 21.90 | | style="text-align:right;" | 21.90 | ||
| style="text-align:center;" |Zotriyo | |||
| style="text-align:center;" | Keema | | style="text-align:center;" | Keema | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 585: | Line 591: | ||
| |<nowiki> | 5 -4 3 -2 </nowiki>> | | |<nowiki> | 5 -4 3 -2 </nowiki>> | ||
| style="text-align:right;" | 13.47 | | style="text-align:right;" | 13.47 | ||
| style="text-align:center;" |Sarurutriyo | |||
| style="text-align:center;" | Octagar | | style="text-align:center;" | Octagar | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 592: | Line 599: | ||
| |<nowiki> | 6 3 -1 -3 </nowiki>> | | |<nowiki> | 6 3 -1 -3 </nowiki>> | ||
| style="text-align:right;" | 13.07 | | style="text-align:right;" | 13.07 | ||
| style="text-align:center;" |Triru-agu | |||
| style="text-align:center;" | Orwellisma | | style="text-align:center;" | Orwellisma | ||
| style="text-align:center;" | Orwell Comma | | style="text-align:center;" | Orwell Comma | ||
| Line 599: | Line 607: | ||
| |<nowiki> | -10 1 0 3 </nowiki>> | | |<nowiki> | -10 1 0 3 </nowiki>> | ||
| style="text-align:right;" | 8.43 | | style="text-align:right;" | 8.43 | ||
| style="text-align:center;" |Latrizo | |||
| style="text-align:center;" | Gamelisma | | style="text-align:center;" | Gamelisma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 606: | Line 615: | ||
| |<nowiki> | -9 8 -4 2 </nowiki>> | | |<nowiki> | -9 8 -4 2 </nowiki>> | ||
| style="text-align:right;" | 8.04 | | style="text-align:right;" | 8.04 | ||
| style="text-align:center;" |Labizogugu | |||
| style="text-align:center;" | Varunisma | | style="text-align:center;" | Varunisma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 613: | Line 623: | ||
| |<nowiki> | -26 -1 1 9 </nowiki>> | | |<nowiki> | -26 -1 1 9 </nowiki>> | ||
| style="text-align:right;" | 3.79 | | style="text-align:right;" | 3.79 | ||
| style="text-align:center;" |Latritrizo-ayo | |||
| style="text-align:center;" | Wadisma | | style="text-align:center;" | Wadisma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 620: | Line 631: | ||
| |<nowiki> | -1 -7 4 1 </nowiki>> | | |<nowiki> | -1 -7 4 1 </nowiki>> | ||
| style="text-align:right;" | 0.40 | | style="text-align:right;" | 0.40 | ||
| style="text-align:center;" |Zoquadyo | |||
| style="text-align:center;" | Ragisma | | style="text-align:center;" | Ragisma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 627: | Line 639: | ||
| |<nowiki> | -1 2 0 -2 1 </nowiki>> | | |<nowiki> | -1 2 0 -2 1 </nowiki>> | ||
| style="text-align:right;" | 17.58 | | style="text-align:right;" | 17.58 | ||
| style="text-align:center;" |Loruru | |||
| style="text-align:center;" | Mothwellsma | | style="text-align:center;" | Mothwellsma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 634: | Line 647: | ||
| |<nowiki> | 2 -2 2 0 -1 </nowiki>> | | |<nowiki> | 2 -2 2 0 -1 </nowiki>> | ||
| style="text-align:right;" | 17.40 | | style="text-align:right;" | 17.40 | ||
| style="text-align:center;" |Luyoyo | |||
| style="text-align:center;" | Ptolemisma | | style="text-align:center;" | Ptolemisma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 641: | Line 655: | ||
| |<nowiki> | -3 1 1 1 0 -1 </nowiki>> | | |<nowiki> | -3 1 1 1 0 -1 </nowiki>> | ||
| style="text-align:right;" | 16.57 | | style="text-align:right;" | 16.57 | ||
| style="text-align:center;" |Thuzoyo | |||
| style="text-align:center;" | Animist | | style="text-align:center;" | Animist | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 648: | Line 663: | ||
| |<nowiki> | 16 0 0 -2 -3 </nowiki>> | | |<nowiki> | 16 0 0 -2 -3 </nowiki>> | ||
| style="text-align:right;" | 8.39 | | style="text-align:right;" | 8.39 | ||
| style="text-align:center;" |Satrilu-aruru | |||
| style="text-align:center;" | Orgonisma | | style="text-align:center;" | Orgonisma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 655: | Line 671: | ||
| |<nowiki> | -7 -1 1 1 1 </nowiki>> | | |<nowiki> | -7 -1 1 1 1 </nowiki>> | ||
| style="text-align:right;" | 4.50 | | style="text-align:right;" | 4.50 | ||
| style="text-align:center;" |Lozoyo | |||
| style="text-align:center;" | Keenanisma | | style="text-align:center;" | Keenanisma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 662: | Line 679: | ||
| |<nowiki> | -3 2 -1 2 -1 </nowiki>> | | |<nowiki> | -3 2 -1 2 -1 </nowiki>> | ||
| style="text-align:right;" | 3.93 | | style="text-align:right;" | 3.93 | ||
| style="text-align:center;" |Luzozogu | |||
| style="text-align:center;" | Werckisma | | style="text-align:center;" | Werckisma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 669: | Line 687: | ||
| |<nowiki> | -4 -3 2 -1 2 </nowiki>> | | |<nowiki> | -4 -3 2 -1 2 </nowiki>> | ||
| style="text-align:right;" | 0.57 | | style="text-align:right;" | 0.57 | ||
| style="text-align:center;" |Loloruyoyo | |||
| style="text-align:center;" | Lehmerisma | | style="text-align:center;" | Lehmerisma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 676: | Line 695: | ||
| |<nowiki> | -3 4 -2 -2 2 </nowiki>> | | |<nowiki> | -3 4 -2 -2 2 </nowiki>> | ||
| style="text-align:right;" | 0.18 | | style="text-align:right;" | 0.18 | ||
| style="text-align:center;" |Bilorugu | |||
| style="text-align:center;" | Kalisma | | style="text-align:center;" | Kalisma | ||
| style="text-align:center;" | Gauss' Comma | | style="text-align:center;" | Gauss' Comma | ||
| Line 815: | Line 835: | ||
[http://www.ronsword.com Sword, Ron. **Icosihexaphonic Scales for Guitar**. IAAA Press. 2010 - A Guitar-scale thesaurus for 26-EDO.] | [http://www.ronsword.com Sword, Ron. **Icosihexaphonic Scales for Guitar**. IAAA Press. 2010 - A Guitar-scale thesaurus for 26-EDO.] | ||
== | == Music == | ||
[http://soonlabel.com/xenharmonic/archives/3335 Canon 3-in-1 on a ground ‘The tempest’, by Claudi Meneghin] | [http://soonlabel.com/xenharmonic/archives/3335 Canon 3-in-1 on a ground ‘The tempest’, by Claudi Meneghin] | ||