Nicolic chords: Difference between revisions
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'''Nicolic chords''' are [[ | '''Nicolic chords''' are [[dyadic chord|essentially tempered chords]] tempered by the nicola, [[1575/1573]]. | ||
There are three triads, six tetrads and two pentads as [[15-odd-limit]] essentially tempered chords. | There are three triads, six tetrads and two pentads as [[15-odd-limit]] essentially tempered chords. | ||
The nicolic triads include the following palindromic form, | The nicolic triads include the following palindromic form, | ||
* | * 1–[[15/11]]–[[13/7]] with steps of 15/11, 15/11, [[14/13]], | ||
and a pair in inverse relationship, | and a pair in inverse relationship, | ||
* | * 1–15/11–[[11/7]] with steps of 15/11, [[15/13]], [[14/11]], and | ||
* | * 1–15/11–[[26/15]] with steps of 15/11, 14/11, 15/13. | ||
For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are | For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are | ||
* | * 1–15/13–15/11–11/7 with steps of 15/13, [[13/11]], 15/13, 14/11; | ||
* | * 1–15/13–[[22/15]]–11/7 with steps of 15/13, 14/11, [[15/14]], 14/11. | ||
The inversely related pairs of chords are | The inversely related pairs of chords are | ||
* | * 1–15/11–11/7–13/7 with steps of 15/11, 15/13, 13/11, 14/13, and its inverse | ||
* | * 1–15/11–22/15–26/15 with steps of 15/11, 14/13, 13/11, 15/13; | ||
* | * 1–15/11–26/15–13/7 with steps of 15/11, 14/11, 15/14, 14/13, and its inverse | ||
* | * 1–15/11–22/15–11/7 with steps of 15/11, 14/13, 15/14, 14/11. | ||
They can be extended to pentads: | They can be extended to pentads: | ||
* | * 1–15/14–15/13–15/11–11/7 with steps of 15/14, 14/13, 13/11, 15/13, 14/11, and its inverse | ||
* | * 1–15/13–15/11–22/15–11/7 with steps of 15/13, 13/11, 14/13, 15/14, 14/11. | ||
[[Equal temperament]]s with nicolic chords include {{Optimal ET sequence| 29, 31, 43, 58, 72, 87, 94, 103, 121, 130, 159, 190, 217, 224, 311, 414, 441, 665 and 855 }}. | [[Equal temperament]]s with nicolic chords include {{Optimal ET sequence| 29, 31, 43, 58, 72, 87, 94, 103, 121, 130, 159, 190, 217, 224, 311, 414, 441, 665 and 855 }}. | ||
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[[Category:15-odd-limit]] | [[Category:15-odd-limit chords]] | ||
[[Category:Essentially tempered chords]] | [[Category:Essentially tempered chords]] | ||
[[Category:Triads]] | [[Category:Triads]] | ||
Revision as of 14:21, 20 March 2025
Nicolic chords are essentially tempered chords tempered by the nicola, 1575/1573.
There are three triads, six tetrads and two pentads as 15-odd-limit essentially tempered chords.
The nicolic triads include the following palindromic form,
and a pair in inverse relationship,
- 1–15/11–11/7 with steps of 15/11, 15/13, 14/11, and
- 1–15/11–26/15 with steps of 15/11, 14/11, 15/13.
For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are
- 1–15/13–15/11–11/7 with steps of 15/13, 13/11, 15/13, 14/11;
- 1–15/13–22/15–11/7 with steps of 15/13, 14/11, 15/14, 14/11.
The inversely related pairs of chords are
- 1–15/11–11/7–13/7 with steps of 15/11, 15/13, 13/11, 14/13, and its inverse
- 1–15/11–22/15–26/15 with steps of 15/11, 14/13, 13/11, 15/13;
- 1–15/11–26/15–13/7 with steps of 15/11, 14/11, 15/14, 14/13, and its inverse
- 1–15/11–22/15–11/7 with steps of 15/11, 14/13, 15/14, 14/11.
They can be extended to pentads:
- 1–15/14–15/13–15/11–11/7 with steps of 15/14, 14/13, 13/11, 15/13, 14/11, and its inverse
- 1–15/13–15/11–22/15–11/7 with steps of 15/13, 13/11, 14/13, 15/14, 14/11.
Equal temperaments with nicolic chords include 29, 31, 43, 58, 72, 87, 94, 103, 121, 130, 159, 190, 217, 224, 311, 414, 441, 665 and 855.
Here is a listening sample, tempered to TE tuning of nicolic.
| Ratio | 1/1 | 15/13 | 15/11 | 11/7 |
|---|---|---|---|---|
| Cents | 0.000 | 247.099 | 536.086 | 783.185 |
| Sound [info] |
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