US: Difference between revisions
Cmloegcmluin (talk | contribs) No edit summary |
Cmloegcmluin (talk | contribs) provide descending pitch version for utonal |
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{| class="wikitable" | {| class="wikitable" | ||
|+example: 8-US(3/4) | |+example: 8-US(3/4) | ||
''(arranged so that the pitches are in ascending order and still begin on 1/1)'' | |||
|- | |- | ||
! quantity | ! quantity | ||
| Line 24: | Line 25: | ||
|(28/28) | |(28/28) | ||
|28/25 | |28/25 | ||
| | |14/11 | ||
|28/19 | |28/19 | ||
| | |7/4 | ||
|28/13 | |28/13 | ||
| | |14/5 | ||
| | |4/1 | ||
| | |7/1 | ||
|- | |- | ||
! pitch (log₂f) | ! pitch (log₂f) | ||
| Line 53: | Line 54: | ||
|7/28 | |7/28 | ||
|4/28 | |4/28 | ||
|} | |||
{| class="wikitable" | |||
|+example: 8-US(3/4) | |||
''(descending pitches)'' | |||
|- | |||
! quantity | |||
! (0) | |||
! 1 | |||
! 2 | |||
! 3 | |||
! 4 | |||
! 5 | |||
! 6 | |||
! 7 | |||
! 8 | |||
|- | |||
! frequency (f) | |||
|(1/1) | |||
|4/7 | |||
|2/5 | |||
|4/13 | |||
|1/4 | |||
|4/19 | |||
|2/11 | |||
|4/25 | |||
|1/7 | |||
|- | |||
! pitch (log₂f) | |||
|(0) | |||
| -0.81 | |||
| -1.32 | |||
| -1.70 | |||
| -2.00 | |||
| -2.25 | |||
| -2.46 | |||
| -2.64 | |||
| -2.81 | |||
|- | |||
! length (1/f) | |||
|(4/4) | |||
|7/4 | |||
|10/4 | |||
|13/4 | |||
|16/4 | |||
|19/4 | |||
|22/4 | |||
|25/4 | |||
|28/4 | |||
|} | |} | ||
Revision as of 22:28, 23 March 2021
A US, or utonal sequence, is a kind of arithmetic and harmonotonic tuning.
The full specification of a US is (n-)USp: (n pitches of a) utonal sequence adding by p.
The n is optional. If not provided, the sequence is open-ended. By specifying n, your sequence will be equivalent to some UD (utonal division). E.g. 8-US3/4 = 8-UD7, because 8(3/4) = 6, so you will have traveled 6 away from the root of 1, and reached 7.
A US is a specific (rational) type of ALS, or arithmetic length sequence. By varying the undertone series step size to some rational number (other than 1) you can produce a US, and varying it to an irrational number you can produce an ALS. In other words, by shifting the undertone series by a constant amount of string length, the step sizes remain equal in terms of length, but their relationship in pitch changes.
| quantity | (0) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|---|
| frequency (f) | (28/28) | 28/25 | 14/11 | 28/19 | 7/4 | 28/13 | 14/5 | 4/1 | 7/1 |
| pitch (log₂f) | (0) | 0.16 | 0.35 | 0.56 | 0.81 | 1.11 | 1.49 | 2.00 | 2.81 |
| length (1/f) | (28/28) | 25/28 | 22/28 | 19/28 | 16/28 | 13/28 | 10/28 | 7/28 | 4/28 |
| quantity | (0) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|---|
| frequency (f) | (1/1) | 4/7 | 2/5 | 4/13 | 1/4 | 4/19 | 2/11 | 4/25 | 1/7 |
| pitch (log₂f) | (0) | -0.81 | -1.32 | -1.70 | -2.00 | -2.25 | -2.46 | -2.64 | -2.81 |
| length (1/f) | (4/4) | 7/4 | 10/4 | 13/4 | 16/4 | 19/4 | 22/4 | 25/4 | 28/4 |