Meantone intervals: Difference between revisions

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See also [[Wikipedia: List of meantone intervals]]
See also [[Wikipedia: List of meantone intervals]]


{| class="wikitable"
{| class="wikitable right-2"
|-
|-
! | Name
! Name
! | Size
! Size
! | Ratios
! Ratios
|-
|-
! colspan="3" | Unisons
! colspan="3" | Unisons
|-
|-
| | Perfect unison (P1)
| Perfect unison (P1)
| | 0
| 0.0
| | 1/1
| 1/1
|-
|-
| | Augmented unison (A1)
| Augmented unison (A1)
| | 75.5
| 75.5
| | 28/27~25/24~21/20
| 28/27~25/24~21/20
|-
|-
! colspan="3" | Seconds
! colspan="3" | Seconds
|-
|-
| | Diminished second (d2)
| Diminished second (d2)
| | 42.0
| 42.0
| | 128/125~64/63~50/49~36/35
| 128/125~64/63~50/49~36/35
|-
|-
| | Minor second (m2)
| Minor second (m2)
| | 117.5
| 117.5
| | 16/15~15/14
| 16/15~15/14
|-
|-
| | Major second (M2)
| Major second (M2)
| | 193.0
| 193.0
| | 10/9~9/8~28/25
| 10/9~9/8~28/25
|-
|-
| | Augmented second (A2)
| Augmented second (A2)
| | 268.5
| 268.5
| | 7/6
| 7/6
|-
|-
! colspan="3" | Thirds
! colspan="3" | Thirds
|-
|-
| | Diminished third (d3)
| Diminished third (d3)
| | 235.0
| 235.0
| | 8/7
| 8/7
|-
|-
| | Minor third (m3)
| Minor third (m3)
| | 310.5
| 310.5
| | 6/5
| 6/5
|-
|-
| | Major third (M3)
| Major third (M3)
| | 386.0
| 386.0
| | 5/4
| 5/4
|-
|-
| | Augmented third (A3)
| Augmented third (A3)
| | 461.5
| 461.5
| | 21/16
| 21/16
|-
|-
! colspan="3" | Fourths
! colspan="3" | Fourths
|-
|-
|Double diminished fourth (dd4)
| Double diminished fourth (dd4)
|343.5
| 343.5
|49/40~60/49
| 49/40~60/49
|-
|-
| | Diminished fourth (d4)
| Diminished fourth (d4)
| | 428.0
| 428.0
| | 9/7 (a bit 14/11-ish)
| 9/7 (a bit 14/11-ish)
|-
|-
| | Perfect fourth (P4)
| Perfect fourth (P4)
| | 503.5
| 503.5
| | 4/3
| 4/3
|-
|-
| | Augmented fourth (A4)
| Augmented fourth (A4)
| | 579.0
| 579.0
| | 7/5
| 7/5
|-
|-
| | Double augmented fourth (AA4)
| Double augmented fourth (AA4)
| | 654.5
| 654.5
| | Close to 16/11
| Close to 16/11
|-
|-
! colspan="3" | Fifths
! colspan="3" | Fifths
|-
|-
| | Double diminished fifth (dd5)
| Double diminished fifth (dd5)
| | 545.5
| 545.5
| | Close to 11/8
| Close to 11/8
|-
|-
| | Diminished fifth (d5)
| Diminished fifth (d5)
| | 621.0
| 621.0
| | 10/7
| 10/7
|-
|-
| | Perfect fifth (P5)
| Perfect fifth (P5)
| | 696.5
| 696.5
| | 3/2
| 3/2
|-
|-
| | Augmented fifth (A5)
| Augmented fifth (A5)
| | 772.0
| 772.0
| | 14/9 (a bit 11/7-ish)
| 14/9 (a bit 11/7-ish)
|-
|-
|Double augmented fifth (AA5)
| Double augmented fifth (AA5)
|842.5
| 842.5
|49/30~80/49
| 49/30~80/49
|-
|-
! colspan="3" | Sixths
! colspan="3" | Sixths
|-
|-
| | Diminished sixth (d6)
| Diminished sixth (d6)
| | 738.5
| 738.5
| | 32/21
| 32/21
|-
|-
| | Minor sixth (m6)
| Minor sixth (m6)
| | 814.0
| 814.0
| | 8/5
| 8/5
|-
|-
| | Major sixth (M6)
| Major sixth (M6)
| | 889.5
| 889.5
| | 5/3
| 5/3
|-
|-
| | Augmented sixth (A6)
| Augmented sixth (A6)
| | 965.0
| 965.0
| | 7/4
| 7/4
|-
|-
! colspan="3" | Sevenths
! colspan="3" | Sevenths
|-
|-
| | Diminished seventh (d7)
| Diminished seventh (d7)
| | 931.5
| 931.5
| | 12/7
| 12/7
|-
|-
| | Minor seventh (m7)
| Minor seventh (m7)
| | 1007.0
| 1007.0
| | 16/9~9/5~25/14
| 16/9~9/5~25/14
|-
|-
| | Major seventh (M7)
| Major seventh (M7)
| | 1082.5
| 1082.5
| | 15/8~28/15
| 15/8~28/15
|-
|-
| | Augmented seventh (A7)
| Augmented seventh (A7)
| | 1158.0
| 1158.0
| | 35/18~49/25~63/32
| 35/18~49/25~63/32
|-
|-
! colspan="3" | Octaves
! colspan="3" | Octaves
|-
|-
| | Diminished octave (d8)
| Diminished octave (d8)
| | 1124.5
| 1124.5
| | 27/14~48/25~40/21
| 27/14~48/25~40/21
|-
|-
| | Perfect octave (P8)
| Perfect octave (P8)
| | 1200
| 1200.0
| | 2/1
| 2/1
|-
|-
| | Augmented octave (A8)
| Augmented octave (A8)
| | 1275.5
| 1275.5
| | 25/12~21/10
| 25/12~21/10
|}
|}


[[Category:Meantone]]
[[Category:Meantone]]
[[Category:List]]
[[Category:List]]

Revision as of 14:39, 28 January 2021

This table shows all the simple intervals of POTE septimal meantone, which includes the entire 7-limit tonality diamond. Other relevant tables of meantone intervals are the table of quarter-comma meantone intervals and the table of 31 edo intervals.

In 12edo the diminished second vanishes, so this cornucopia of intervals collapses to a mere 12. None of the intervals is inherently septimal in 12edo, because they all have simpler 5-limit descriptions.

In 19edo, in contrast, the double diminished second vanishes, so the equivalences are A1~d2, A2~d3, A3~d4, A4~dd5, AA4~d5, A5~d6, A6~d7, and A7~d8. Thus some intervals are undeniably septimal, but ambiguously so because 49/48 vanishes.

More complex meantone tunings such as 31edo distinguish all intervals listed on this table.

See also Wikipedia: List of meantone intervals

Name Size Ratios
Unisons
Perfect unison (P1) 0.0 1/1
Augmented unison (A1) 75.5 28/27~25/24~21/20
Seconds
Diminished second (d2) 42.0 128/125~64/63~50/49~36/35
Minor second (m2) 117.5 16/15~15/14
Major second (M2) 193.0 10/9~9/8~28/25
Augmented second (A2) 268.5 7/6
Thirds
Diminished third (d3) 235.0 8/7
Minor third (m3) 310.5 6/5
Major third (M3) 386.0 5/4
Augmented third (A3) 461.5 21/16
Fourths
Double diminished fourth (dd4) 343.5 49/40~60/49
Diminished fourth (d4) 428.0 9/7 (a bit 14/11-ish)
Perfect fourth (P4) 503.5 4/3
Augmented fourth (A4) 579.0 7/5
Double augmented fourth (AA4) 654.5 Close to 16/11
Fifths
Double diminished fifth (dd5) 545.5 Close to 11/8
Diminished fifth (d5) 621.0 10/7
Perfect fifth (P5) 696.5 3/2
Augmented fifth (A5) 772.0 14/9 (a bit 11/7-ish)
Double augmented fifth (AA5) 842.5 49/30~80/49
Sixths
Diminished sixth (d6) 738.5 32/21
Minor sixth (m6) 814.0 8/5
Major sixth (M6) 889.5 5/3
Augmented sixth (A6) 965.0 7/4
Sevenths
Diminished seventh (d7) 931.5 12/7
Minor seventh (m7) 1007.0 16/9~9/5~25/14
Major seventh (M7) 1082.5 15/8~28/15
Augmented seventh (A7) 1158.0 35/18~49/25~63/32
Octaves
Diminished octave (d8) 1124.5 27/14~48/25~40/21
Perfect octave (P8) 1200.0 2/1
Augmented octave (A8) 1275.5 25/12~21/10
Retrieved from "https://en.xen.wiki/index.php?title=Meantone_intervals&oldid=60300"