Xenharmonic Wiki

18edo: Difference between revisions

← Older editNewer edit →
VisualWikitext
Inthar (talk | contribs)
autopatrolled, emailconfirmed
15,677 edits
Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
precision unified, table syntax simplified, all monzos in comma table via template now
Line 25: Line 25:
The second way preserves the <u>harmonic</u> meaning of sharp/flat, major/minor and aug/dim, in that the former is always further fifthwards on the chain of fifths than the latter. Sharp is lower in pitch than flat, and major/aug is narrower than minor/dim. While this approach may seem bizarre at first, interval arithmetic and chord names work as usual. Furthermore, conventional 12edo music can be directly translated to 18edo "on the fly".
The second way preserves the <u>harmonic</u> meaning of sharp/flat, major/minor and aug/dim, in that the former is always further fifthwards on the chain of fifths than the latter. Sharp is lower in pitch than flat, and major/aug is narrower than minor/dim. While this approach may seem bizarre at first, interval arithmetic and chord names work as usual. Furthermore, conventional 12edo music can be directly translated to 18edo "on the fly".


{| class="wikitable" style="text-align:center"  
{| class="wikitable center-all right-2"
! Degree
! Degree
! Cents
! Cents
Line 251: Line 251:
== Representations of Just Intervals ==
== Representations of Just Intervals ==


{| class="wikitable"
{| class="wikitable center-all right-2"
! Degree
! Degree
! Cents
! Cents
Line 259: Line 259:
|-
|-
| 0
| 0
| 0.00
| 0.000
| 1/1
| 1/1
| 0
| 0
Line 265: Line 265:
|-
|-
| 1
| 1
| 66.67
| 66.667
| 27/26
| 27/26
| +1.329
| +1.329
Line 271: Line 271:
|-
|-
| 2
| 2
| 133.33
| 133.333
| 27/25
| 27/25
| +0.096
| +0.096
Line 277: Line 277:
|-
|-
| 3
| 3
| 200
| 200.000
| 9/8
| 9/8
| -3.910
| -3.910
Line 283: Line 283:
|-
|-
| 4
| 4
| 266.67
| 266.667
| 7/6
| 7/6
| -0.204
| -0.204
Line 289: Line 289:
|-
|-
| 5
| 5
| 333.33
| 333.333
| 17/14 or 40/33
| 17/14 or 40/33
| -2.796 +0.293
| -2.796 +0.293
Line 295: Line 295:
|-
|-
| 6
| 6
| 400
| 400.000
| 5/4 or 44/35
| 5/4 or 44/35
| +13.686 +3.822
| +13.686 +3.822
Line 301: Line 301:
|-
|-
| 7
| 7
| 466.67
| 466.667
| 21/16
| 21/16
| -4.114
| -4.114
Line 307: Line 307:
|-
|-
| 8
| 8
| 533.33
| 533.333
| 15/11
| 15/11
| -3.617
| -3.617
Line 313: Line 313:
|-
|-
| 9
| 9
| 600
| 600.000
| 17/12 or 24/17
| 17/12 or 24/17
| -3.000 +3.000
| -3.000 +3.000
Line 319: Line 319:
|-
|-
| 10
| 10
| 666.67
| 666.667
| 22/15
| 22/15
| +3.617
| +3.617
Line 325: Line 325:
|-
|-
| 11
| 11
| 733.33
| 733.333
| 32/21
| 32/21
| +4.114
| +4.114
Line 331: Line 331:
|-
|-
| 12
| 12
| 800
| 800.000
| 8/5 or 35/22
| 8/5 or 35/22
| -13.686 -3.822
| -13.686 -3.822
Line 337: Line 337:
|-
|-
| 13
| 13
| 866.67
| 866.667
| 28/17 or 33/20
| 28/17 or 33/20
| +2.796 -0.293
| +2.796 -0.293
Line 343: Line 343:
|-
|-
| 14
| 14
| 933.33
| 933.333
| 12/7
| 12/7
| +0.204
| +0.204
Line 349: Line 349:
|-
|-
| 15
| 15
| 1000
| 1000.000
| 16/9
| 16/9
| +3.910
| +3.910
Line 355: Line 355:
|-
|-
| 16
| 16
| 1066.67
| 1066.667
| 50/27
| 50/27
| -0.096
| -0.096
Line 361: Line 361:
|-
|-
| 17
| 17
| 1133.33
| 1133.333
| 52/27
| 52/27
| -1.329
| -1.329
Line 367: Line 367:
|-
|-
| 18
| 18
| 1200
| 1200.000
| 2/1
| 2/1
| 0
| 0
Line 380: Line 380:
18 EDO [[tempering out|tempers out]] the following [[Comma|commas]]. (Note: This assumes the [[val]] &lt; 18 29 42 51 62 67 |.)
18 EDO [[tempering out|tempers out]] the following [[Comma|commas]]. (Note: This assumes the [[val]] &lt; 18 29 42 51 62 67 |.)


{| class="wikitable" style="text-align:center;"
{| class="wikitable center-all left-2 right-3"
! [[Ratio]]
! [[Ratio]]
! [[Monzo]]
! [[Monzo]]
Line 389: Line 389:
|-
|-
| 128/125
| 128/125
| style="text-align:left;" | <nowiki> | 7 0 -3 </nowiki>&gt;
| {{Monzo| 7 0 -3 }}
| style="text-align:right;" | 41.06
| 41.06
| Trigu
| Trigu
| Diesis
| Diesis
| Augmented Comma
| Augmented Comma
|-
|-
| style="text-align:center;" | ???
| ???
| style="text-align:left;" | <nowiki> | 23 6 -14 </nowiki>&gt;
| {{Monzo| 23 6 -14 }}
| style="text-align:right;" | 3.34
| 3.34
| Sasa-sepbigu
| Sasa-sepbigu
| Vishnuzma
| Vishnuzma
Line 403: Line 403:
|-
|-
| 50/49
| 50/49
| style="text-align:left;" | <nowiki> | 1 0 2 -2 </nowiki>&gt;
| {{Monzo| 1 0 2 -2 }}
| style="text-align:right;" | 34.98
| 34.98
| Biruyo
| Biruyo
| Tritonic Diesis
| Tritonic Diesis
Line 410: Line 410:
|-
|-
| 686/675
| 686/675
| style="text-align:left;" | <nowiki> | 1 -3 -2 3 </nowiki>&gt;
| {{Monzo| 1 -3 -2 3 }}
| style="text-align:right;" | 27.99
| 27.99
| Trizo-agugu
| Trizo-agugu
| Senga
| Senga
Line 417: Line 417:
|-
|-
| 875/864
| 875/864
| style="text-align:left;" | {{Monzo| -5 -3 3 1 }}
| {{Monzo| -5 -3 3 1 }}
| style="text-align:right;" | 21.90
| 21.90
| Zotriyo
| Zotriyo
| Keema
| Keema
Line 424: Line 424:
|-
|-
| 1728/1715
| 1728/1715
| style="text-align:left;" | {{Monzo| 6 3 -1 -3 }}
| {{Monzo| 6 3 -1 -3 }}
| style="text-align:right;" | 13.07
| 13.07
| Triru-agu
| Triru-agu
| Orwellisma
| Orwellisma
Line 431: Line 431:
|-
|-
| 16875/16807
| 16875/16807
| style="text-align:left;" | {{Monzo| 0 3 4 -5 }}
| {{Monzo| 0 3 4 -5 }}
| style="text-align:right;" | 6.99
| 6.99
| Quinru-aquadyo
| Quinru-aquadyo
| Mirkwai
| Mirkwai
Line 438: Line 438:
|-
|-
| 3136/3125
| 3136/3125
| style="text-align:left;" | {{Monzo| 6 0 -5 2 }}
| {{Monzo| 6 0 -5 2 }}
| style="text-align:right;" | 6.08
| 6.08
| Zozoquingu
| Zozoquingu
| Hemimean
| Hemimean
Line 445: Line 445:
|-
|-
| 99/98
| 99/98
| style="text-align:left;" | {{Monzo| -1 2 0 -2 1 }}
| {{Monzo| -1 2 0 -2 1 }}
| style="text-align:right;" | 17.58
| 17.58
| Loruru
| Loruru
| Mothwellsma
| Mothwellsma
Line 452: Line 452:
|-
|-
| 100/99
| 100/99
| style="text-align:left;" | {{Monzo| 2 -2 2 0 -1 }}
| {{Monzo| 2 -2 2 0 -1 }}
| style="text-align:right;" | 17.40
| 17.40
| Luyoyo
| Luyoyo
| Ptolemisma
| Ptolemisma
Line 459: Line 459:
|-
|-
| 65536/65219
| 65536/65219
| style="text-align:left;" | {{Monzo| 16 0 0 -2 -3 }}
| {{Monzo| 16 0 0 -2 -3 }}
| style="text-align:right;" | 8.39
| 8.39
| Satrilu-aruru
| Satrilu-aruru
| Orgonisma
| Orgonisma
Line 466: Line 466:
|-
|-
| 385/384
| 385/384
| style="text-align:left;" | {{Monzo| -7 -1 1 1 1 }}
| {{Monzo| -7 -1 1 1 1 }}
| style="text-align:right;" | 4.50
| 4.50
| Lozoyo
| Lozoyo
| Keenanisma
| Keenanisma
Line 473: Line 473:
|-
|-
| 9801/9800
| 9801/9800
| style="text-align:left;" | {{Monzo| -3 4 -2 -2 2 }}
| {{Monzo| -3 4 -2 -2 2 }}
| style="text-align:right;" | 0.18
| 0.18
| Bilorugu
| Bilorugu
| Kalisma
| Kalisma
Line 480: Line 480:
|-
|-
| 91/90
| 91/90
| style="text-align:left;" | {{Monzo| -1 -2 -1 1 0 1 }}
| {{Monzo| -1 -2 -1 1 0 1 }}
| style="text-align:right;" | 19.13
| 19.13
| Thozogu
| Thozogu
| Superleap
| Superleap
Line 536: Line 536:
[[Category:18-tone]]
[[Category:18-tone]]
[[Category:18edo]]
[[Category:18edo]]
[[Category:edo]]
[[Category:Edo]]
[[Category:listen]]
[[Category:Listen]]
[[Category:scale]]
[[Category:Scale]]
[[Category:subgroup]]
[[Category:Subgroup]]
[[Category:teentuning]]
[[Category:Teentuning]]
[[Category:theory]]
[[Category:Theory]]
[[Category:todo:unify_precision]]
Retrieved from "https://en.xen.wiki/w/18edo"