Xenharmonic Wiki

Blackwood: Difference between revisions

← Older edit
VisualWikitext
Inthar (talk | contribs)
autopatrolled, emailconfirmed
15,668 edits
No edit summary
No edit summary
 
(30 intermediate revisions by 9 users not shown)
Line 1: Line 1:
'''Blackwood''' may refer to:
{{interwiki
| de = Blackwood-Limmisch
| en = Blackwood
}}
: ''This article is about the regular temperament. For the musician, see [[Easley Blackwood Jr.]] For the scale structure sometimes associated with it, see [[5L 5s]].''
{{Infobox regtemp
| Title = Blackwood
| Subgroups = 2.3.5, 2.3.5.7
| Comma basis = [[256/243]] (2.3.5); <br>[[28/27]], [[49/48]] (2.3.5.7)
| Edo join 1 = 5 | Edo join 2 = 10
| Mapping = 5; 0 1 0
| Generators = 5/4
| Generators tuning = 391.1
| Optimization method = CWE
| Pergen = (P8/5, ^1)
| Color name = Sawati
| MOS scales = [[5L&nbsp;5s]], [[10L&nbsp;5s]]
| Odd limit 1 = 5 | Mistuning 1 = 18.0 | Complexity 1 = 10
| Odd limit 2 = 9 | Mistuning 2 = 44.9 | Complexity 2 = 10
}}
'''Blackwood''' is a [[regular temperament|temperament]] that takes [[5edo]]'s [[circle of fifths]] for the [[3-limit]], but adds multiple copies to improve the tuning of the [[5-limit]]. In the fundamental sense, it is the 5-limit temperament that [[tempering out|tempers out]] the [[Pythagorean limma]], and it extends to the [[7-limit]] (sometimes known as ''blacksmith'') by recognizing that 4\5 is a good [[7/4|harmonic seventh]], thus tempering out [[28/27]], [[49/48]], and [[64/63]], making it a member of [[trienstonic clan]], [[semaphoresmic clan]], and [[archytas clan]].


* [[5L 5s]], a MOS pattern
The main interest in this temperament is in its [[mos scale]]s, featuring [[5L 5s|pentawood (5L 5s)]]. 15edo provides an excellent tuning for this temperament as well as for pentawood.
* [[Archytas clan#Blacksmith|Blackwood]], a 5-limit temperament tempering out [[256/243]]


[[Category:todo:expand]]
Blackwood was named in honor of [[Easley Blackwood Jr.]]
[[Category:15edo]]
 
[[Category:blacksmith]]
See [[Limmic temperaments #Blackwood]] for technical data.
[[Category:blackwood]]
__TOC__
[[Category:harmony]]
{{Clear}}
[[Category:interval]]
 
[[Category:triad]]
== Interval chain ==
In the following table, odd harmonics 1–9 are in '''bold'''.
 
{| class="wikitable center-1 right-2 right-4"
! rowspan="2" | Period
! colspan="2" | Generator 0
! colspan="2" | Generator 1
|-
! Cents*
! Approx. ratios
! Cents*
! Approx. ratios
|-
| 0
| 0.0
| '''1/1'''
|
|
|-
| 1
| 240.0
| 7/6, 8/7, '''9/8'''
| 151.1
| 10/9, 15/14
|-
| 2
| 480.0
| 4/3
| 391.1
| '''5/4'''
|-
| 3
| 720.0
| '''3/2'''
| 631.1
| 10/7
|-
| 4
| 960.0
| '''7/4''', 12/7, 16/9
| 871.1
| 5/3
|-
| 5
| 1200.0
| '''2/1'''
| 1111.1
| 15/8, 40/21
|}
<nowiki/>* In 7-limit CWE tuning, octave reduced
 
== Scales ==
[[File:blacksmith10.jpg|alt=blacksmith10.jpg|thumb|Lattice of Blackwood[10]]]
[[File:BlackwoodMajor 15edo.mp3]] [[:File:BlackwoodMajor 15edo.mp3|Blackwood major scale in 15edo]]
 
== Tunings ==
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 5-limit norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Equilateral
| CEE: ~5/4 = 386.3137{{c}}
| CSEE: ~5/4 = 392.3287{{c}}
| POEE: ~5/4 = 405.2729{{c}}
|-
! Tenney
| CTE: ~5/4 = 386.3137{{c}}
| CWE: ~5/4 = 395.1256{{c}}
| POTE: ~5/4 = 399.5938{{c}}
|-
! Benedetti, <br>Wilson
| CBE: ~5/4 = 386.3137{{c}}
| CSBE: ~5/4 = 396.3386{{c}}
| POBE: ~5/4 = 400.3211{{c}}
|}
 
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Equilateral
| CEE: ~5/4 = 386.3137{{c}}
| CSEE: ~5/4 = 388.6185{{c}}
| POEE: ~5/4 = 387.1612{{c}}
|-
! Tenney
| CTE: ~5/4 = 386.3137{{c}}
| CWE: ~5/4 = 391.0976{{c}}
| POTE: ~5/4 = 392.7675{{c}}
|-
! Benedetti, <br>Wilson
| CBE: ~5/4 = 386.3137{{c}}
| CSBE: ~5/4 = 392.2565{{c}}
| POBE: ~5/4 = 395.3830{{c}}
|}
 
=== Tuning spectrum ===
{| class="wikitable center-all left-4"
|-
! Edo<br>generator
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]*
! Generator (¢)
! Comments
|-
|
| 15/14
| 359.443
|
|-
| 3\10
|
| 360.000
| Lower bound of 7- and 9-odd-limit diamond monotone
|-
|
| 15/8
| 368.269
| -1/5-limma
|-
|11\35
|
| 377.143
|35b val
|-
|
| 7/5
| 377.488
|
|-
| 8\25
|
| 384.000
|
|-
|
| 5/4
| 386.314
| Untempered, 5- and 7-limit CTE, etc.
|-
|
| 25/24
| 395.336
| 1/10-limma
|-
|
| 21/20
| 395.533
|
|-
|
|
|397.163
|DR-optimized 4:5:6 tuning
|-
| 5\15
|
| 400.000
|
|-
|
| 5/3
| 404.359
| 1/5-limma
|-
| 7\20
|
| 420.000
| 20c val
|-
|
| 9/5
| 422.404
| 2/5-limma
|-
| 2\5
|
| 480.000
| Upper bound of 7- and 9-odd-limit diamond monotone
|}
<nowiki/>* Besides the octave
 
== Music ==
; [[E8 Heterotic]]
* [https://www.youtube.com/watch?v=67hj_bs_9e4 ''Cyberfunk''] (2020) – in Blackwood[10], 15edo tuning
 
; [[Sevish]]
* From ''[[Harmony Hacker]]'' (2017)
** "[[Freathy]]" – in Blackwood[10], TOP tuning
** "[[So Thankful]]" – in Blackwood[10], 15edo tuning
 
== See also ==
* [[Blackwood temperament modal harmony (in 15edo)]]
 
[[Category:Blackwood| ]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Exotemperaments]]
[[Category:Trienstonic clan]]
[[Category:Semaphoresmic clan]]
[[Category:Archytas clan]]
Retrieved from "https://en.xen.wiki/w/Blackwood"