UD: Difference between revisions
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== Relationship to other tunings == | == Relationship to other tunings == | ||
=== | === Vs ED === | ||
It is possible to — instead of equally dividing the octave in 12 equal parts by pitch — divide it into 12 equal parts by length. You will have 12-ELDO. | It is possible to — instead of equally dividing the octave in 12 equal parts by pitch — divide it into 12 equal parts by length. You will have 12-ELDO. | ||
=== | === Vs under-n series === | ||
An n-UDO is equivalent to the nth [[Overtone_scale#Next_Steps|undertone mode, or under-n scale]]. | An n-UDO is equivalent to the nth [[Overtone_scale#Next_Steps|undertone mode, or under-n scale]]. | ||
=== | === Vs ELD === | ||
The only difference between n-UDp and [[ELD|n-ELDp (equal length division)]] is that the p for UD | The only difference between n-UDp and [[ELD|n-ELDp (equal length division)]] is that the p for UD must be rational, while the p for an ELD is probably irrational. | ||
=== | === Vs US === | ||
A UD will be equivalent to some [[US|US (utonal sequence)]]. E.g. 8-UD7 = 8-US3/4, because to get from 1 to 7 you cover 6 undertones, and 6 divided by 8 is 3/4. | A UD will be equivalent to some [[US|US (utonal sequence)]]. E.g. 8-UD7 = 8-US3/4, because to get from 1 to 7 you cover 6 undertones, and 6 divided by 8 is 3/4. | ||
=== | === Vs EDL === | ||
An [[EDL|n-EDL]] is equivalent to a 2n-UDO (therefore EDL cannot be used to represent a UDO with an odd value for n). | An [[EDL|n-EDL]] is equivalent to a 2n-UDO (therefore EDL cannot be used to represent a UDO with an odd value for n). | ||
| Line 53: | Line 53: | ||
! 4 | ! 4 | ||
|- | |- | ||
! frequency (f) | ! frequency (''f'', ratio) | ||
|(1/1) | |(1/1) | ||
|8/7 | |8/7 | ||
| Line 60: | Line 60: | ||
|2/1 | |2/1 | ||
|- | |- | ||
! pitch ( | ! pitch (log₂''f'', octaves) | ||
|(0) | |(0) | ||
|0.19 | |0.19 | ||
| Line 67: | Line 67: | ||
|1.00 | |1.00 | ||
|- | |- | ||
! length (1/f) | ! length (1/''f'', ratio) | ||
|(8/8) | |(8/8) | ||
|7/8 | |7/8 | ||
| Line 85: | Line 85: | ||
! 4 | ! 4 | ||
|- | |- | ||
! frequency (f) | ! frequency (''f'', ratio) | ||
|(1/1) | |(1/1) | ||
|4/5 | |4/5 | ||
| Line 92: | Line 92: | ||
|1/2 | |1/2 | ||
|- | |- | ||
! pitch ( | ! pitch (log₂''f'', octaves) | ||
|(0) | |(0) | ||
| -0.32 | | -0.32 | ||
| Line 99: | Line 99: | ||
| -1.00 | | -1.00 | ||
|- | |- | ||
! length (1/f) | ! length (1/''f'', ratio) | ||
|(4/4) | |(4/4) | ||
|5/4 | |5/4 | ||