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46edo: Difference between revisions

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→21st century: Add Claudi Meneghin's ''Closing Jingle - Micro Prelude & Fugue - 46EDO Imikrokosmos 22)'' (2026)
→Intervals: split for a CLEAN interval table
Line 28: Line 28:
{| class="wikitable center-all right-2 left-3 left-4 left-7"
{| class="wikitable center-all right-2 left-3 left-4 left-7"
|-
|-
! #
! #
! Cents
! Cents
! Approximate ratios<ref name="interval ratios" group="note">{{sg|limit=2.3.5.7.11.13.17.23&nbsp;subgroup}} However, ratios of 15 are not included here, as except for 15/8 and 16/15 themselves 46edo has intervals involving the 15th harmonic poorly approximated in general. This is because, while the 3rd and 5th harmonics are sharp and their deviations from just intonation add up, 7, 11, and 13 are all tuned flat, making the difference even larger. This prevents it from being [[consistent]] in the [[15-odd-limit]], as there is a discrepancy approximating [[15/13]] and [[26/15]]&mdash;9\46 is closer to 15/13 by a hair, but 10\46 represents the difference between 46edo's 15/8 and 13/8 and is more likely to appear in chords actually functioning as 15/13.</ref>
! Approximate ratios<ref name="interval ratios" group="note">{{safesubst:Subgroup note|limit=2.3.5.7.11.13.17.23-subgroup}} However, ratios of 15 are not included here, as except for 15/8 and 16/15 themselves 46edo has intervals involving the 15th harmonic poorly approximated in general. This is because, while the 3rd and 5th harmonics are sharp and their deviations from just intonation add up, 7, 11, and 13 are all tuned flat, making the difference even larger. This prevents it from being [[consistent]] in the [[15-odd-limit]], as there is a discrepancy approximating [[15/13]] and [[26/15]]&mdash;9\46 is closer to 15/13 by a hair, but 10\46 represents the difference between 46edo's 15/8 and 13/8 and is more likely to appear in chords actually functioning as 15/13.</ref>
! colspan="3" | [[Ups and downs notation]]
! [[Kite's ups and downs notation|Ups and downs notation]]
([[Enharmonic unisons in ups and downs notation|EUs]]: v<sup>5</sup>A1 and ^^d2)
|-
| 0
| 0.0
| [[1/1]]
| {{UDnote|step=0}}
|-
| 1
| 26.1
| [[81/80]], [[64/63]], [[49/48]]
| {{UDnote|step=1}}
|-
| 2
| 52.2
| [[28/27]], [[36/35]], [[33/32]]
| {{UDnote|step=2}}
|-
| 3
| 78.3
| [[25/24]], [[21/20]], [[22/21]], [[24/23]], [[23/22]]
| {{UDnote|step=3}}
|-
| 4
| 104.3
| [[16/15]], [[17/16]], [[18/17]]
| {{UDnote|step=4}}
|-
| 5
| 130.4
| [[13/12]], [[14/13]], [[15/14]]
| {{UDnote|step=5}}
|-
| 6
| 156.5
| [[12/11]], [[11/10]], [[23/21]]
| {{UDnote|step=6}}
|-
| 7
| 182.6
| [[10/9]]
| {{UDnote|step=7}}
|-
| 8
| 208.7
| [[9/8]]
| {{UDnote|step=8}}
|-
| 9
| 234.8
| [[8/7]], [[23/20]]
| {{UDnote|step=9}}
|-
| 10
| 260.9
| [[7/6]]
| {{UDnote|step=10}}
|-
| 11
| 287.0
| [[13/11]], [[20/17]]
| {{UDnote|step=11}}
|-
| 12
| 313.0
| [[6/5]]
| {{UDnote|step=12}}
|-
| 13
| 339.1
| [[11/9]], [[17/14]], [[28/23]]
| {{UDnote|step=13}}
|-
| 14
| 365.2
| [[16/13]], [[26/21]], [[21/17]]
| {{UDnote|step=14}}
|-
| 15
| 391.3
| [[5/4]]
| {{UDnote|step=15}}
|-
| 16
| 417.4
| [[14/11]], [[23/18]]
| {{UDnote|step=16}}
|-
| 17
| 443.5
| [[9/7]], [[13/10]], [[22/17]]
| {{UDnote|step=17}}
|-
| 18
| 469.6
| [[21/16]], [[17/13]]
| {{UDnote|step=18}}
|-
| 19
| 495.7
| [[4/3]]
| {{UDnote|step=19}}
|-
| 20
| 521.7
| [[27/20]], [[23/17]]
| {{UDnote|step=20}}
|-
| 21
| 547.8
| [[11/8]]
| {{UDnote|step=21}}
|-
| 22
| 573.9
| [[7/5]], [[18/13]], [[32/23]]
| {{UDnote|step=22}}
|-
| 23
| 600.0
| [[17/12]], [[24/17]]
| {{UDnote|step=23}}
|-
| 24
| 626.1
| [[10/7]], [[13/9]], [[23/16]]
| {{UDnote|step=24}}
|-
| 25
| 652.2
| [[16/11]]
| {{UDnote|step=25}}
|-
| 26
| 678.3
| [[40/27]], [[34/23]]
| {{UDnote|step=26}}
|-
| 27
| 704.3
| [[3/2]]
| {{UDnote|step=27}}
|-
| 28
| 730.4
| [[32/21]], [[26/17]]
| {{UDnote|step=28}}
|-
| 29
| 756.5
| [[14/9]], [[20/13]], [[17/11]]
| {{UDnote|step=29}}
|-
| 30
| 782.6
| [[11/7]]
| {{UDnote|step=30}}
|-
| 31
| 808.7
| [[8/5]]
| {{UDnote|step=31}}
|-
| 32
| 834.8
| [[13/8]], [[21/13]], [[34/21]]
| {{UDnote|step=32}}
|-
| 33
| 860.9
| [[18/11]], [[28/17]], [[23/14]]
| {{UDnote|step=33}}
|-
| 34
| 887.0
| [[5/3]]
| {{UDnote|step=34}}
|-
| 35
| 913.0
| [[22/13]], [[17/10]]
| {{UDnote|step=35}}
|-
| 36
| 939.1
| [[12/7]]
| {{UDnote|step=36}}
|-
| 37
| 965.2
| [[7/4]], [[40/23]]
| {{UDnote|step=37}}
|-
| 38
| 991.3
| [[16/9]], [[23/13]]
| {{UDnote|step=38}}
|-
| 39
| 1017.4
| [[9/5]]
| {{UDnote|step=39}}
|-
| 40
| 1043.5
| [[11/6]], [[20/11]], [[42/23]]
| {{UDnote|step=40}}
|-
| 41
| 1069.6
| [[24/13]], [[13/7]], [[28/15]]
| {{UDnote|step=41}}
|-
| 42
| 1095.7
| [[15/8]], [[32/17]], [[17/9]]
| {{UDnote|step=42}}
|-
| 43
| 1121.7
| [[48/25]], [[40/21]], [[21/11]], [[23/12]], [[44/23]]
| {{UDnote|step=43}}
|-
| 44
| 1147.8
| [[27/14]], [[35/18]], [[64/33]]
| {{UDnote|step=44}}
|-
| 45
| 1173.9
| [[160/81]], [[63/32]], [[96/49]]
| {{UDnote|step=45}}
|-
| 46
| 1200.0
| [[2/1]]
| {{UDnote|step=46}}
|}
<references group="note" />
 
=== Proposed interval names and solfèges ===
{| class="wikitable center-all right-2 left-2 left-3 left-6 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Table of proposed interval names and solfèges
|-
! #
! Cents
! colspan="3" | [[Kite's ups and downs notation|Ups and downs notation]]<br>([[Enharmonic unisons in ups and downs notation|EUs]]: v<sup>5</sup>A1 and ^^d2)
! colspan="3" | [[SKULO interval names|SKULO notation]] (K or S = 1, U = 2)
! colspan="3" | [[SKULO interval names|SKULO notation]] (K or S = 1, U = 2)
! colspan="2" | [[Solfege]]
! colspan="2" | [[Solfège]]s
|-
|-
| 0
| 0
| 0.0
| 0.0
| [[1/1]]
| perfect unison
| perfect unison
| P1
| P1
Line 50: Line 293:
| 1
| 1
| 26.1
| 26.1
| [[81/80]], [[64/63]], [[49/48]]
| up unison
| up unison
| ^1
| ^1
Line 62: Line 304:
| 2
| 2
| 52.2
| 52.2
| [[28/27]], [[36/35]], [[33/32]]
| downminor 2nd
| downminor 2nd
| vm2
| vm2
Line 74: Line 315:
| 3
| 3
| 78.3
| 78.3
| [[25/24]], [[21/20]], [[22/21]], [[24/23]], [[23/22]]
| minor 2nd
| minor 2nd
| m2
| m2
Line 86: Line 326:
| 4
| 4
| 104.3
| 104.3
| [[16/15]], [[17/16]], [[18/17]]
| upminor 2nd
| upminor 2nd
| ^m2
| ^m2
Line 98: Line 337:
| 5
| 5
| 130.4
| 130.4
| [[13/12]], [[14/13]], [[15/14]]
| dupminor 2nd
| dupminor 2nd
| ^^m2
| ^^m2
Line 110: Line 348:
| 6
| 6
| 156.5
| 156.5
| [[12/11]], [[11/10]], [[23/21]]
| dudmajor 2nd
| dudmajor 2nd
| vvM2
| vvM2
Line 122: Line 359:
| 7
| 7
| 182.6
| 182.6
| [[10/9]]
| downmajor 2nd
| downmajor 2nd
| vM2
| vM2
Line 134: Line 370:
| 8
| 8
| 208.7
| 208.7
| [[9/8]]
| major 2nd
| major 2nd
| M2
| M2
Line 146: Line 381:
| 9
| 9
| 234.8
| 234.8
| [[8/7]], [[23/20]]
| upmajor 2nd
| upmajor 2nd
| ^M2
| ^M2
Line 158: Line 392:
| 10
| 10
| 260.9
| 260.9
| [[7/6]]
| downminor 3rd
| downminor 3rd
| vm3
| vm3
Line 170: Line 403:
| 11
| 11
| 287.0
| 287.0
| [[13/11]], [[20/17]]
| minor 3rd
| minor 3rd
| m3
| m3
Line 182: Line 414:
| 12
| 12
| 313.0
| 313.0
| [[6/5]]
| upminor 3rd
| upminor 3rd
| ^m3
| ^m3
Line 194: Line 425:
| 13
| 13
| 339.1
| 339.1
| [[11/9]], [[17/14]], [[28/23]]
| dupminor 3rd
| dupminor 3rd
| ^^m3
| ^^m3
Line 206: Line 436:
| 14
| 14
| 365.2
| 365.2
| [[16/13]], [[26/21]], [[21/17]]
| dudmajor 3rd
| dudmajor 3rd
| vvM3
| vvM3
Line 218: Line 447:
| 15
| 15
| 391.3
| 391.3
| [[5/4]]
| downmajor 3rd
| downmajor 3rd
| vM3
| vM3
Line 230: Line 458:
| 16
| 16
| 417.4
| 417.4
| [[14/11]], [[23/18]]
| major 3rd
| major 3rd
| M3
| M3
Line 242: Line 469:
| 17
| 17
| 443.5
| 443.5
| [[9/7]], [[13/10]], [[22/17]]
| upmajor 3rd
| upmajor 3rd
| ^M3
| ^M3
Line 254: Line 480:
| 18
| 18
| 469.6
| 469.6
| [[21/16]], [[17/13]]
| down 4th
| down 4th
| v4
| v4
Line 266: Line 491:
| 19
| 19
| 495.7
| 495.7
| [[4/3]]
| perfect 4th
| perfect 4th
| P4
| P4
Line 278: Line 502:
| 20
| 20
| 521.7
| 521.7
| [[27/20]], [[23/17]]
| up 4th
| up 4th
| ^4
| ^4
Line 290: Line 513:
| 21
| 21
| 547.8
| 547.8
| [[11/8]]
| dup 4th
| dup 4th
| ^^4
| ^^4
Line 302: Line 524:
| 22
| 22
| 573.9
| 573.9
| [[7/5]], [[18/13]], [[32/23]]
| dudaug 4th, <br>dim 5th
| dudaug 4th, <br>dim 5th
| vvA4, d5
| vvA4, d5
Line 314: Line 535:
| 23
| 23
| 600.0
| 600.0
| [[17/12]], [[24/17]]
| downaug 4th, updim 5th
| downaug 4th, updim 5th
| vA4, ^d5
| vA4, ^d5
Line 326: Line 546:
| 24
| 24
| 626.1
| 626.1
| [[10/7]], [[13/9]], [[23/16]]
| aug 4th, dupdim 5th
| aug 4th, dupdim 5th
| A4, ^^d5
| A4, ^^d5
Line 338: Line 557:
| 25
| 25
| 652.2
| 652.2
| [[16/11]]
| dud 5th
| dud 5th
| vv5
| vv5
Line 350: Line 568:
| 26
| 26
| 678.3
| 678.3
| [[40/27]], [[34/23]]
| down 5th
| down 5th
| v5
| v5
Line 362: Line 579:
| 27
| 27
| 704.3
| 704.3
| [[3/2]]
| perfect 5th
| perfect 5th
| P5
| P5
Line 374: Line 590:
| 28
| 28
| 730.4
| 730.4
| [[32/21]], [[26/17]]
| up 5th
| up 5th
| ^5
| ^5
Line 386: Line 601:
| 29
| 29
| 756.5
| 756.5
| [[14/9]], [[20/13]], [[17/11]]
| downminor 6th
| downminor 6th
| vm6
| vm6
Line 398: Line 612:
| 30
| 30
| 782.6
| 782.6
| [[11/7]]
| minor 6th
| minor 6th
| m6
| m6
Line 410: Line 623:
| 31
| 31
| 808.7
| 808.7
| [[8/5]]
| upminor 6th
| upminor 6th
| ^m6
| ^m6
Line 422: Line 634:
| 32
| 32
| 834.8
| 834.8
| [[13/8]], [[21/13]], [[34/21]]
| dupminor 6th
| dupminor 6th
| ^^m6
| ^^m6
Line 434: Line 645:
| 33
| 33
| 860.9
| 860.9
| [[18/11]], [[28/17]], [[23/14]]
| dudmajor 6th
| dudmajor 6th
| vvM6
| vvM6
Line 446: Line 656:
| 34
| 34
| 887.0
| 887.0
| [[5/3]]
| downmajor 6th
| downmajor 6th
| vM6
| vM6
Line 458: Line 667:
| 35
| 35
| 913.0
| 913.0
| [[22/13]], [[17/10]]
| major 6th
| major 6th
| M6
| M6
Line 470: Line 678:
| 36
| 36
| 939.1
| 939.1
| [[12/7]]
| upmajor 6th
| upmajor 6th
| ^M6
| ^M6
Line 482: Line 689:
| 37
| 37
| 965.2
| 965.2
| [[7/4]], [[40/23]]
| downminor 7th
| downminor 7th
| vm7
| vm7
Line 494: Line 700:
| 38
| 38
| 991.3
| 991.3
| [[16/9]], [[23/13]]
| minor 7th
| minor 7th
| m7
| m7
Line 506: Line 711:
| 39
| 39
| 1017.4
| 1017.4
| [[9/5]]
| upminor 7th
| upminor 7th
| ^m7
| ^m7
Line 518: Line 722:
| 40
| 40
| 1043.5
| 1043.5
| [[11/6]], [[20/11]], [[42/23]]
| dupminor 7th
| dupminor 7th
| ^^m7
| ^^m7
Line 530: Line 733:
| 41
| 41
| 1069.6
| 1069.6
| [[24/13]], [[13/7]], [[28/15]]
| dudmajor 7th
| dudmajor 7th
| vvM7
| vvM7
Line 543: Line 745:
| 42
| 42
| 1095.7
| 1095.7
| [[15/8]], [[32/17]], [[17/9]]
| downmajor 7th
| downmajor 7th
| vM7
| vM7
Line 556: Line 757:
| 43
| 43
| 1121.7
| 1121.7
| [[48/25]], [[40/21]], [[21/11]], [[23/12]], [[44/23]]
| major 7th
| major 7th
| M7
| M7
Line 568: Line 768:
| 44
| 44
| 1147.8
| 1147.8
| [[27/14]], [[35/18]], [[64/33]]
| upmajor 7th
| upmajor 7th
| ^M7
| ^M7
Line 580: Line 779:
| 45
| 45
| 1173.9
| 1173.9
| [[160/81]], [[63/32]], [[96/49]]
| down 8ve
| down 8ve
| v8
| v8
Line 592: Line 790:
| 46
| 46
| 1200.0
| 1200.0
| [[2/1]]
| perfect 8ve
| perfect 8ve
| P8
| P8
Line 602: Line 799:
| do
| do
|}
|}
<references group="note" />


=== Interval quality and chord names in color notation ===
=== Interval quality and chord names in color notation ===
Line 611: Line 807:
! Quality
! Quality
! Color
! Color
! Monzo Format
! Monzo format
! Examples
! Examples
|-
|-
| downminor
| downminor
| zo
| zo
| [a, b, 0, 1>
| {{Monzo| ''a'' ''b'' 0 1 }}
| 7/6, 7/4
| 7/6, 7/4
|-
|-
| minor
| minor
| fourthward wa
| fourthward wa
| [a, b>, b &lt; −1
| {{Monzo| ''a'' ''b'' }}, ''b'' < −1
| 32/27, 16/9
| 32/27, 16/9
|-
|-
| upminor
| upminor
| gu
| gu
| [a, b, −1>
| {{Monzo| ''a'' ''b'' −1 }}
| 6/5, 9/5
| 6/5, 9/5
|-
|-
| dupminor
| dupminor
| ilo
| ilo
| [a, b, 0, 0, 1>
| {{Monzo| ''a'' ''b'' 0 0 1 }}
| 11/9, 11/6
| 11/9, 11/6
|-
|-
| dudmajor
| dudmajor
| lu
| lu
| [a, b, 0, 0, −1>
| {{Monzo| ''a'' ''b'' 0 0 −1 }}
| 12/11, 18/11
| 12/11, 18/11
|-
|-
| downmajor
| downmajor
| yo
| yo
| [a, b, 1>
| {{Monzo| ''a'' ''b'' 1 }}
| 5/4, 5/3
| 5/4, 5/3
|-
|-
| major
| major
| fifthward wa
| fifthward wa
| [a, b>, b &gt; 1
| {{Monzo| ''a'' ''b'' }}, ''b'' > 1
| 9/8, 27/16
| 9/8, 27/16
|-
|-
| upmajor
| upmajor
| ru
| ru
| [a, b, 0, −1>
| {{Monzo| ''a'' ''b'' 0 −1 }}
| 9/7, 12/7
| 9/7, 12/7
|}
|}
Line 659: Line 855:
|-
|-
! Color of the 3rd
! Color of the 3rd
! JI Chord
! JI chord
! Notes as Edosteps
! Notes as edosteps
! Notes of C Chord
! Notes of C chord
! Written Name
! Written name
! Spoken Name
! Spoken name
|-
|-
| zo
| zo
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