<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">I use these kinds of interval cycles all the time when I'm composing; they're a useful way to make scales (or arpeggios if you use larger intervals) that don't repeat at the octave. If anyone is interested I'd be happy to send a Sibelius plug-in I wrote which can generate lots of these; a screenshot is below. It works on Sibelius 5 and later. (In Sib 7 the plug-in will appear under the "Note Input" tab after you install it.)<div><br></div><div>Just for fun, on the screenshot I have circled Jay Rahn's 4-semitone interval cycle (see his message below), to show where it occurs as the 'mode' repeats.<br><div><br></div><div><img id="cc5dbfb0-7ee8-4c84-8e38-e11a7974cbc6" height="925" width="758" apple-width="yes" apple-height="yes" src="cid:994F9C4D-B990-47F8-BC9A-26DF3A7B93B4"></div><div><br><div apple-content-edited="true">
<span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; font-size: medium; "><span class="Apple-style-span" style="border-collapse: separate; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; -webkit-text-decorations-in-effect: none; text-indent: 0px; -webkit-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div>_________________________________</div><div>Stephen Taylor</div><div>Associate Professor of Composition-Theory</div><div>School of Music</div><div>University of Illinois at Urbana-Champaign</div><div><a href="http://www.stephenandrewtaylor.net">http://www.stephenandrewtaylor.net</a></div></div><br class="Apple-interchange-newline"></span></span><br class="Apple-interchange-newline">
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<br><div><div>On Jan 19, 2013, at 21:09, JAY RAHN wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><meta http-equiv="Content-Type" content="text/html; charset=utf-8"><table cellspacing="0" cellpadding="0" border="0"><tbody><tr><td valign="top" style="font: inherit;">One could think of this 'mode' as a non-degenerate well-formed scale having a 7-semitone interval as its modulus, within which a 4-semitone interval cycles as follows: 0 4 1 5 2. <br><br>A counterpart having the usual octave as it modulus would be the pentatonic scale employed in the 'equiheptatonic' tuning of Thai classical music: 0 1 2 4 5 (7). A rhythmic counterpart would be the e e q e q timeline employed in Haitian traditional music.<br><br>Jay Rahn, York University (Toronto) <br><br>--- On <b>Sat, 1/19/13, Zachary Bernstein <i><<a href="mailto:zachbernst@aol.com">zachbernst@aol.com</a>></i></b> wrote:<br><blockquote style="border-left: 2px solid rgb(16, 16, 255); margin-left: 5px; padding-left: 5px;"><br>From: Zachary Bernstein <<a href="mailto:zachbernst@aol.com">zachbernst@aol.com</a>><br>Subject: Re: [Smt-talk] fw: Lindberg mode<br>To: <a href="mailto:daphne.leong@Colorado.EDU">daphne.leong@Colorado.EDU</a>, <a href="mailto:smt-talk@lists.societymusictheory.org">smt-talk@lists.societymusictheory.org</a><br>Cc:
<a href="mailto:Jonathan.Leathwood@du.edu">Jonathan.Leathwood@du.edu</a><br>Date: Saturday, January 19, 2013, 12:26 PM<br><br><div id="yiv2095637952"><font color="black" face="arial" size="2"><font face="Arial, Helvetica, sans-serif" size="2"><span style="line-height:21px;">Prof. Leong,</span><br style="line-height:21px;"></font>
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<div style="line-height:21px;"><font face="Arial, Helvetica, sans-serif" size="2">I'm going out on a limb here, given that I don't know <i>Mano a Mano </i>and don't know too much else of Lindberg all that intimately. But since he has been known to refer to certain old historical ideas - think of his frequent use of chaconne - is it possible that this scale is built from the Daseian scale of the <i>Enchiriadis </i>treatises? That scale links Tone-Semitone-Tone tetrachords together, separated by a tone. In modern notation, the result is G, A, Bb, C--D. E, F, G--A, B, C, D--E, F#, G, A--B, C#. As you can see, it's also periodic at the fifth. Indeed, the pattern is completely congruent with Lindberg's scale, except that he adds a single interpolated semitone in each fifth. Thus, aligning the two scales (having the Lindberg scale begin with the bottom of the <11212> pattern):</font></div>
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<div style="line-height:21px;"><font face="Arial, Helvetica, sans-serif" size="2">Lindberg<span class="yiv2095637952Apple-tab-span" style="white-space:pre;"> </span>F, F#, G, A, Bb, C, C#, D, E, F, G, G#, A, B, C, D, Eb, E, F#, G, A, A#, B, C#</font></div>
<div style="line-height:21px;"><font face="Arial, Helvetica, sans-serif" size="2">Enchiriadis<span class="yiv2095637952Apple-tab-span" style="white-space:pre;"> </span> G, A, Bb, C, D, E, F, G, A, B, C, D, E, F#, G, A, B, C#</font></div>
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<div style="line-height:21px;"><font size="2">Could it be?</font></div>
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<div style="line-height:21px;"><font face="Arial, Helvetica, sans-serif" size="2">Best,</font></div>
<div style="line-height:21px;"><font face="Arial, Helvetica, sans-serif" size="2">Zack</font></div>
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<div style="line-height:21px;"><font face="Arial, Helvetica, sans-serif" size="2">Zachary Bernstein</font></div>
<div style="line-height:21px;"><font face="Arial, Helvetica, sans-serif" size="2">PhD Candidate</font></div>
<div style="line-height:21px;"><font face="Arial, Helvetica, sans-serif" size="2">CUNY Graduate Center</font></div>
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<div style="font-size:10pt;font-family:helvetica, arial;color:black;">-----Original Message-----<br>
From: Daphne Leong <<a href="mailto:daphne.leong@Colorado.EDU">daphne.leong@Colorado.EDU</a>><br>
To: smt-talk <<a href="mailto:smt-talk@lists.societymusictheory.org">smt-talk@lists.societymusictheory.org</a>><br>
Cc: Jonathan Leathwood <<a href="mailto:Jonathan.Leathwood@du.edu">Jonathan.Leathwood@du.edu</a>><br>
Sent: Fri, Jan 18, 2013 9:27 pm<br>
Subject: [Smt-talk] fw: Lindberg mode<br>
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<div>I'm forwarding the following query at the request of my colleague Jonathan Leathwood:</div>
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<div>I'm currently working on a long guitar piece by Magnus Lindberg from 2004 called <i>Mano a Mano</i>. I have a little familiarity with some of his earlier music and the influence of the spectralists is very obvious to the ear, and there is some literature about that. So far, however, I don't see much in the guitar piece in common with those works: in fact, I would never have guessed they were by the same composer. Instead, I see that the guitar piece it is mostly based on a curious mode that runs (in semitones) <11212…>, repeating the pattern every perfect fifth. For example: <C, C#, D, E, F, G, G#, A, B, c, d, eb, e, f#, g, a…>. </div>
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<div>Lindberg often uses common segments with other more common modes to switch back and forth. It turns out that the repeating pattern yields all pcs of the aggregate within a span of 22 semitones, and so he sometimes suggests other modes by selecting only the relevant pcs while allowing the governing mode to constrain the spacing. Finally, the mode is rich enough that you can write interesting music by choosing only the common tones between two of its transpositions, something I've noted in one passage so far.</div>
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<div>My question is simply whether you have encountered this mode -- perhaps it's quite well known and I just haven't seen it before. One thing I wished I had was a good labeling convention for it.</div>
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<div>__________________________________________________________________________</div>
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<div>Daphne Leong <span class="yiv2095637952Apple-tab-span" style="white-space:pre;"> </span><a rel="nofollow" ymailto="mailto:Daphne.Leong@colorado.edu" target="_blank" href="x-msg://461/mc/compose?to=Daphne.Leong@colorado.edu">Daphne.Leong@colorado.edu</a></div>
<div>Associate Professor, Music Theory<span class="yiv2095637952Apple-tab-span" style="white-space:pre;"> </span>tel: (303) 492-4337</div>
<div>Chair, Theory and Composition<span class="yiv2095637952Apple-tab-span" style="white-space:pre;"> </span>fax: (303) 492-5619</div>
<div>University of Colorado at Boulder</div>
<div>College of Music, 301 UCB</div>
<div>Boulder, CO 80309-0301</div>
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