Nicolic chords: Difference between revisions
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'''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. | |||
The nicolic triads include the following palindromic form, | The nicolic triads include the following palindromic form, | ||
* 1-[[15/11]]-[[13/7]] with steps 15/11-15/11-[[14/13]], | * 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 15/11-[[15/13]]-[[14/11]], and | * 1-15/11-[[11/7]] with steps of 15/11-[[15/13]]-[[14/11]], and | ||
* 1-15/11-[[26/15]] with steps 15/11-14/11-15/13. | * 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: | |||
* 1-15/13-15/11-11/7 | * 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 {{ | [[Equal temperament]]s with nicolic chords include {{Optimal ET sequence| 58, 72, 87, 103, 121, 130, 190, 217, 224, 311, 414, 441, 665 and 855 }}. | ||
Here is a listening sample, tempered to TE tuning of nicolic. | Here is a listening sample, tempered to TE tuning of nicolic. | ||
| Line 30: | Line 43: | ||
[[Category:Triads]] | [[Category:Triads]] | ||
[[Category:Tetrads]] | [[Category:Tetrads]] | ||
[[Category:Pentads]] | |||
[[Category:Nicolic]] | [[Category:Nicolic]] | ||
[[Category:Listen]] | [[Category:Listen]] | ||
Revision as of 00:04, 5 November 2023
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,
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 58, 72, 87, 103, 121, 130, 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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