Boogie woogie scale - Revision history

VectorGraphics: don't see why we need a heading with the same title as the page

2025-11-07T03:15:10Z

don't see why we need a heading with the same title as the page

← Older revision		Revision as of 03:15, 7 November 2025
Line 1:		Line 1:
	~~=Boogie Woogie Scale=~~

	In [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_65608.html#65608 this posting] of the Yahoo tuning list, Paul G. Hjelmstad wrote:		In [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_65608.html#65608 this posting] of the Yahoo tuning list, Paul G. Hjelmstad wrote:

VectorGraphics: VectorGraphics moved page Boogiewoogiescale to Boogie woogie scale

2025-11-07T03:13:45Z

VectorGraphics moved page Boogiewoogiescale to Boogie woogie scale

← Older revision	Revision as of 03:13, 7 November 2025
(No difference)

Lériendil: Text replacement - "Category:Just intonation scales" to "Category:Just intonation scales Category:Pages with mostly numerical content"

2025-06-24T00:31:16Z

Text replacement - "Category:Just intonation scales" to "Category:Just intonation scales Category:Pages with mostly numerical content"

← Older revision		Revision as of 00:31, 24 June 2025
Line 85:		Line 85:
	[[Category:10-tone scales]]		[[Category:10-tone scales]]
	[[Category:Just intonation scales]]		[[Category:Just intonation scales]]
			[[Category:Pages with mostly numerical content]]
	[[Category:7-limit]]		[[Category:7-limit]]
	[[Category:Pages with Scala files]]		[[Category:Pages with Scala files]]
	[[Category:Archive]]		[[Category:Archive]]

BudjarnLambeth: Categorised this uncategorised page

2023-04-30T05:52:08Z

Categorised this uncategorised page

← Older revision		Revision as of 05:52, 30 April 2023
Line 83:		Line 83:
	JI scales, I think.		JI scales, I think.
	</pre>		</pre>
			[[Category:10-tone scales]]
			[[Category:Just intonation scales]]
			[[Category:7-limit]]
			[[Category:Pages with Scala files]]
			[[Category:Archive]]

CritDeathX: Fixed Yahoo link

2020-06-28T19:37:21Z

Fixed Yahoo link

← Older revision		Revision as of 19:37, 28 June 2020
Line 38:		Line 38:
	-----		-----

	Gene Ward Smith described some additional properties (in [~~http~~://~~launch~~.~~groups~~.~~yahoo.com/group~~/tuning/~~message/~~65610 this posting]):		Gene Ward Smith described some additional properties (in [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_65608.html#65610 this posting]):

	<pre>		<pre>

CritDeathX: Added Yahoo archive link

2020-05-28T22:49:06Z

Added Yahoo archive link

← Older revision		Revision as of 22:49, 28 May 2020
Line 1:		Line 1:
	=Boogie Woogie Scale=		=Boogie Woogie Scale=

	In [~~http~~://~~launch~~.~~groups~~.~~yahoo.com/group~~/tuning/~~message/~~65608 this posting] of the Yahoo tuning list, Paul G. Hjelmstad wrote:		In [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_65608.html#65608 this posting] of the Yahoo tuning list, Paul G. Hjelmstad wrote:

	<pre>		<pre>

Spt3125: reformatted

2018-12-02T18:30:29Z

reformatted

← Older revision		Revision as of 18:30, 2 December 2018
Line 3:		Line 3:
	In [http://launch.groups.yahoo.com/group/tuning/message/65608 this posting] of the Yahoo tuning list, Paul G. Hjelmstad wrote:		In [http://launch.groups.yahoo.com/group/tuning/message/65608 this posting] of the Yahoo tuning list, Paul G. Hjelmstad wrote:

			<pre>
	Take the standard 12-bar boogie-woogie. Let's use F major:		Take the standard 12-bar boogie-woogie. Let's use F major:
			F A C Eb
	F A C Eb		Bb D F Ab
			C E G Bb
	Bb D F Ab

	C E G Bb

	Tune to the seven-limit and keep fifths. You get		Tune to the seven-limit and keep fifths. You get

	12 15 18 21		12 15 18 21
			4 5 6 7
	4 5 6 7

	36 45 54 63		36 45 54 63

	Fit into one octave (F, G, Ab,A,Bb,C,D,Eb,E)		Fit into one octave (F,G,Ab,A,Bb,C,D,Eb,E)
			24,27,28,30,32,36,40,42,45 and 63 (extra Bb)

	~~24, 27,28,30,32,36,40,42,45 and 63 (extra Bb)~~		Taking all the ratios, we find that they are all superparticular
			(n/n-1)
	Taking all the ratios, we find that they are all superparticular (n/n-		9/8, 28/27, 15/14, 16/15, 9/8, 10/9, 21/20, 15/14, 16/15
			(and the schisma for Bb/Bb 64/63)
	1)

	9/8, 28/27, 15/14, 16/15, 9/8, 10/9, 21/20, 15/14, 16/15 (and the

	schisma for Bb/Bb 64/63)

	You also get 8/7, 7/6, 6/5, 4/3, 3/2, 1/1, with multiple scale		You also get 8/7, 7/6, 6/5, 4/3, 3/2, 1/1, with multiple scale

	steps..		steps..

	The first seven triangular numbers are used; 1/1, 3/2, 6/5, 10/9,		The first seven triangular numbers are used; 1/1, 3/2, 6/5, 10/9,

	15/14, 21/20, 28/27		15/14, 21/20, 28/27

Line 42:		Line 31:

	8/7 and 7/6 are the only ratios which are not squared or triangular		8/7 and 7/6 are the only ratios which are not squared or triangular

	superparticular ratios but they are still superparticular!		superparticular ratios but they are still superparticular!

	All from the simple boogie woogie!		All from the simple boogie woogie!
			</pre>

	-----		-----

	Gene Ward Smith described some additional properties (in [http://launch.groups.yahoo.com/group/tuning/message/65610 this posting]):		Gene Ward Smith described some additional properties (in [http://launch.groups.yahoo.com/group/tuning/message/65610 this posting]):

			<pre>
	Here it is in Scala format:		Here it is in Scala format:

	! boogie.scl		! boogie.scl

	Paul Hjelmstad's boogie woogie scale		Paul Hjelmstad's boogie woogie scale

	10		10

	!		!

	9/8		9/8

	5/4		5/4

	21/16		21/16

	45/32		45/32

	3/2		3/2

	27/16		27/16

	7/4		7/4

	15/8		15/8

	63/32		63/32

	2/1		2/1

	Three otonal tetrads, no utonal tetrads, not CS or epimorphic,		Three otonal tetrads, no utonal tetrads, not CS or epimorphic,

	superparticular ratios as noted.		superparticular ratios as noted.

	I found a number of ten-note seven limit epimorphic scales with four		I found a number of ten-note seven limit epimorphic scales with four

	tetrads; here's one Paul Erlich found first:		tetrads; here's one Paul Erlich found first:

	! cx1.scl		! cx1.scl
			First 10/4 scale = erlich11 <10 16 23 28\| epimorphic
	First 10/4 scale = erlich11 ~~<~~10 16 23 28\| epimorphic

	10		10

	!		!

	15/14		15/14

	7/6		7/6

	5/4		5/4

	4/3		4/3

	10/7		10/7

	3/2		3/2

	5/3		5/3

	7/4		7/4

	15/8		15/8

	2		2

	! [0, -1, -1], [0, -1, 0], [0, 0, 0], [0, 0, 1]		! [0, -1, -1], [0, -1, 0], [0, 0, 0], [0, 0, 1]

	Quite a lot of musical possibilities in these relatively small 7-limit		Quite a lot of musical possibilities in these relatively small 7-limit

	JI scales, I think.		JI scales, I think.
			</pre>

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

Show changes

Wikispaces>guest: Imported revision 151471511 - Original comment:

2010-07-03T21:33:45Z

**Imported revision 151471511 - Original comment: **

← Older revision		Revision as of 21:33, 3 July 2010
Line 1:		Line 1:
	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:~~hstraub~~\|~~hstraub~~]] and made on <tt>~~2006~~-09-~~07 09~~:03:18 UTC</tt>.<br>		: This revision was by author [[User:guest\|guest]] and made on <tt>2010-07-03 21:33:45 UTC</tt>.<br>
	: The original revision id was <tt>~~1150522~~</tt>.<br>		: The original revision id was <tt>151471511</tt>.<br>
	: The revision comment was: <tt>~~Paul G. Hjelmstad's boogie woogie scale~~</tt><br>		: The revision comment was: <tt></tt><br>
	The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
	<h4>Original Wikitext content:</h4>		<h4>Original Wikitext content:</h4>
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=Boogie Woogie Scale=		<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=Boogie Woogie Scale=

	In [[http://launch.groups.yahoo.com/group/tuning/message/65608\|this posting]] of the Yahoo tuning list, Paul G. Hjelmstad wrote:		In [[http://launch.groups.yahoo.com/group/tuning/message/65608\|this posting]] of the Yahoo tuning list, Paul G. Hjelmstad wrote:
Line 59:		Line 59:
	15/8		15/8
	63/32		63/32
	2		2/1

	Three otonal tetrads, no utonal tetrads, not CS or epimorphic,		Three otonal tetrads, no utonal tetrads, not CS or epimorphic,
Line 87:		Line 87:
	<h4>Original HTML content:</h4>		<h4>Original HTML content:</h4>
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>boogiewoogiescale</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Boogie Woogie Scale"></a><!-- ws:end:WikiTextHeadingRule:0 -->Boogie Woogie Scale</h1>		<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>boogiewoogiescale</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Boogie Woogie Scale"></a><!-- ws:end:WikiTextHeadingRule:0 -->Boogie Woogie Scale</h1>
	<br />		<br />
	In <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/65608" rel="nofollow">this posting</a> of the Yahoo tuning list, Paul G. Hjelmstad wrote:<br />		In <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/65608" rel="nofollow">this posting</a> of the Yahoo tuning list, Paul G. Hjelmstad wrote:<br />
	<br />		<br />
Line 139:		Line 139:
	15/8<br />		15/8<br />
	63/32<br />		63/32<br />
	2<br />		2/1<br />
	<br />		<br />
	Three otonal tetrads, no utonal tetrads, not CS or epimorphic,<br />		Three otonal tetrads, no utonal tetrads, not CS or epimorphic,<br />

Wikispaces>hstraub: Imported revision 1150522 - Original comment: Paul G. Hjelmstad's boogie woogie scale

2006-09-07T09:03:18Z

**Imported revision 1150522 - Original comment: Paul G. Hjelmstad's boogie woogie scale**

New page

<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference: 
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2006-09-07 09:03:18 UTC</tt>. 
: The original revision id was <tt>1150522</tt>. 
: The revision comment was: <tt>Paul G. Hjelmstad's boogie woogie scale</tt> 
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it. 
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=Boogie Woogie Scale=

In [[http://launch.groups.yahoo.com/group/tuning/message/65608|this posting]] of the Yahoo tuning list, Paul G. Hjelmstad wrote:

Take the standard 12-bar boogie-woogie. Let's use F major:

F A C Eb
Bb D F Ab
C E G Bb

Tune to the seven-limit and keep fifths. You get

12 15 18 21
4 5 6 7
36 45 54 63

Fit into one octave (F, G, Ab,A,Bb,C,D,Eb,E)
24, 27,28,30,32,36,40,42,45 and 63 (extra Bb)

Taking all the ratios, we find that they are all superparticular (n/n-
1)
9/8, 28/27, 15/14, 16/15, 9/8, 10/9, 21/20, 15/14, 16/15 (and the
schisma for Bb/Bb 64/63)

You also get 8/7, 7/6, 6/5, 4/3, 3/2, 1/1, with multiple scale
steps..

The first seven triangular numbers are used; 1/1, 3/2, 6/5, 10/9,
15/14, 21/20, 28/27
Five of the squares are used: 1/1, 4/3, 9/8, 16/15 and 64/63

8/7 and 7/6 are the only ratios which are not squared or triangular
superparticular ratios but they are still superparticular!

All from the simple boogie woogie!
----
Gene Ward Smith described some additional properties (in [[http://launch.groups.yahoo.com/group/tuning/message/65610|this posting]]):

Here it is in Scala format:

! boogie.scl
Paul Hjelmstad's boogie woogie scale
10
!
9/8
5/4
21/16
45/32
3/2
27/16
7/4
15/8
63/32
2

Three otonal tetrads, no utonal tetrads, not CS or epimorphic,
superparticular ratios as noted.

I found a number of ten-note seven limit epimorphic scales with four
tetrads; here's one Paul Erlich found first:

! cx1.scl
First 10/4 scale = erlich11 <10 16 23 28| epimorphic
10
!
15/14
7/6
5/4
4/3
10/7
3/2
5/3
7/4
15/8
2
! [0, -1, -1], [0, -1, 0], [0, 0, 0], [0, 0, 1]

Quite a lot of musical possibilities in these relatively small 7-limit
JI scales, I think.</pre></div>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>boogiewoogiescale</title></head><body><h1 id="toc0"><a name="Boogie Woogie Scale"></a>Boogie Woogie Scale</h1>
 
In <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/65608" rel="nofollow">this posting</a> of the Yahoo tuning list, Paul G. Hjelmstad wrote: 
 
Take the standard 12-bar boogie-woogie. Let's use F major: 
 
F A C Eb 
Bb D F Ab 
C E G Bb 
 
Tune to the seven-limit and keep fifths. You get 
 
12 15 18 21 
4 5 6 7 
36 45 54 63 
 
Fit into one octave (F, G, Ab,A,Bb,C,D,Eb,E) 
24, 27,28,30,32,36,40,42,45 and 63 (extra Bb) 
 
Taking all the ratios, we find that they are all superparticular (n/n- 
1) 
9/8, 28/27, 15/14, 16/15, 9/8, 10/9, 21/20, 15/14, 16/15 (and the 
schisma for Bb/Bb 64/63) 
 
You also get 8/7, 7/6, 6/5, 4/3, 3/2, 1/1, with multiple scale 
steps.. 
 
The first seven triangular numbers are used; 1/1, 3/2, 6/5, 10/9, 
15/14, 21/20, 28/27 
Five of the squares are used: 1/1, 4/3, 9/8, 16/15 and 64/63 
 
8/7 and 7/6 are the only ratios which are not squared or triangular 
superparticular ratios but they are still superparticular! 
 
All from the simple boogie woogie! 
<hr />
Gene Ward Smith described some additional properties (in <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/65610" rel="nofollow">this posting</a>): 
 
Here it is in Scala format: 
 
! boogie.scl 
Paul Hjelmstad's boogie woogie scale 
10 
! 
9/8 
5/4 
21/16 
45/32 
3/2 
27/16 
7/4 
15/8 
63/32 
2 
 
Three otonal tetrads, no utonal tetrads, not CS or epimorphic, 
superparticular ratios as noted. 
 
I found a number of ten-note seven limit epimorphic scales with four 
tetrads; here's one Paul Erlich found first: 
 
! cx1.scl 
First 10/4 scale = erlich11 &lt;10 16 23 28| epimorphic 
10 
! 
15/14 
7/6 
5/4 
4/3 
10/7 
3/2 
5/3 
7/4 
15/8 
2 
! [0, -1, -1], [0, -1, 0], [0, 0, 0], [0, 0, 1] 
 
Quite a lot of musical possibilities in these relatively small 7-limit 
JI scales, I think.</body></html></pre></div>