Fluid just intonation: Difference between revisions
→Description: Manually corrected cent values in table |
→Description: I'm still in the Zoom meeting right now but quickly updated the page during a lull in the meeting to include both versions of the table, original and corrected |
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Each chord contains a ''common note'' shared with the previous chord. The tuning of the common note stays exactly the same, and all other notes of the new chord are tuned in pure [[JI]] ratios relative to the common note. | Each chord contains a ''common note'' shared with the previous chord. The tuning of the common note stays exactly the same, and all other notes of the new chord are tuned in pure [[JI]] ratios relative to the common note. | ||
The allowed ratios, and how much they differ from their [[12edo]] tempered version, are listed in the following table: | The allowed ratios, and how much they differ from their [[12edo]] tempered version, are listed in the following table. | ||
(''Note: Some of the cents values given by the original table - the one included in the sheet music - do not match the actual cents values of the JI values given. So, the "original" column documents the values given by the original table, and the "corrected" column documents the accurate values for each JI interval. It is unclear which of these was used in the piece itself.'') | |||
{| class="wikitable" | {| class="wikitable" | ||
! Scale degree!! Ratio!!Tuning adjustment in [[cents]] | ! rowspan="2" | Scale degree!! rowspan="2" | Ratio!! colspan="2" |Tuning adjustment in [[cents]] | ||
|- | |||
!Original | |||
!Corrected | |||
|- | |- | ||
|1||1/1||0 | |1||1/1||0 | ||
|0 | |||
|- | |- | ||
|b2||16/15||+12 | |b2||16/15||+5 | ||
| +12 | |||
|- | |- | ||
|2||9/8||+4 | |2||9/8||+4 | ||
| +4 | |||
|- | |- | ||
|b3||6/5||+16 | |b3||6/5||+16 | ||
| +16 | |||
|- | |- | ||
|3||5/4||-14 | |3||5/4||-14 | ||
| -14 | |||
|- | |- | ||
|4||4/3||-2 | |4||4/3||-2 | ||
| -2 | |||
|- | |- | ||
|#4/b5||11/8||-49 | |#4/b5||11/8||-49 | ||
| -49 | |||
|- | |- | ||
|5||3/2||+2 | |5||3/2||+2 | ||
| +2 | |||
|- | |- | ||
|b6||8/5||+14 | |b6||8/5||+41 | ||
| +14 | |||
|- | |- | ||
|6||5/3||-16 | |6||5/3||+6 | ||
| -16 | |||
|- | |- | ||
| rowspan="2" |b7||7/4 (dom7)||-31 (dom7) | | rowspan="2" |b7||7/4 (dom7)||-31 (dom7) | ||
| -31 (dom7) | |||
|- | |- | ||
|9/5 (m7)||+18 (m7) | |9/5 (m7)||+18 (m7) | ||
| +18 (m7) | |||
|- | |- | ||
|7||15/8||-12 | |7||15/8||-12 | ||
| -12 | |||
|- | |- | ||
|8ve||2/1||0 | |8ve||2/1||0 | ||
|0 | |||
|} | |} | ||