Page 10 - Summer 2010

Fig. 2. The helical model of pitch. Musical pitch is depicted as varying along both a linear dimension of height and also a circular dimension of pitch class. The helix completes one full turn per octave, so that tones that stand in octave relation are in close spatial proximity, as shown by D#, D#’, and D#.”
DOWNLOAD THE SOUND DEMO AUDIO CLIPS
Shortly after the print copy of this issue is mailed, it will also be published in the Acoustical Society of America's Digital Library. The Table of Contents may be reached directly by going to your internet browser and typing the following Uniform Resource Locator (URL) in the address block: http://scitation.aip.org/dbt/dbt.jsp?KEY=ATCODK&Volu me=6&Issue=3. At some point in the download process you will probably be asked for your ID and Password if you are using a computer that is not networked to an institution with a subscription to the ASA Digital Library. These are the same username and password that you use as an ASA member to access the Journal of the Acoustical Society of America. Open the abstract for this article by clicking on Abstract. At the bottom of the abstract will be a link. Click on the link and a zipped folder (DeutschData.zip) will be downloaded to your computer (wherever you usually receive downlinks). Unzip the entire folder (as a whole), save the unzipped folder to your desktop, and open the folder DeutschData. (Note: Before the zip files are extract- ed, Winzip asks whether you want all files/folders in the current folder unzipped. Check the box that you do. There are 10 demos. Do not remove any file—simply open the file called 00_DeutschOpenMe.pdf. It is an interactive pdf file. By clicking on any of the hyperlink clips in this file, you should hear the audio clip associated with that link. (If your computer says that it cannot find the file when you click on a demo, then the files are still zipped. Unzip the files indi- vidually). The best way to enjoy reading the article is to open the magazine. Open the 00_DeutschOpenMe.pdf file on your computer. With mouse in hand, read the article from the magazine and when a demo clip is mentioned, click on the computer link associated with the clip. The author suggests that good computer speakers or earphones will greatly enhance your perception of the subtleties pres- ent in the demos. The audio clips were recorded in .WAV format. If you have difficulty in playing it, you might down- load the PC or MAC version of VLC Media Player from www.videolan.org. This is a non-profit organization that has created a very powerful, cross-platform, free and open source player that works with almost all video and audio formats. Questions? Email the Scitation Help Desk at help@scitation.org or call 1-800-874-6383.
To demonstrate that such tones have circular properties when the position of the spectral envelope remains fixed, Shepard presented listeners with ordered pairs of such tones, and they judged for each pair whether it formed an ascend- ing or a descending pattern. When the tones within a pair were separated by a small distance along the pitch class circle, judgments of relative height were determined entirely by proximity. As the distance between the tones increased, the tendency to follow by proximity lessened, and when the tones were separated by a half-octave, averaging across pitch class- es and across a large group of subjects, ascending and
2
an intriguing demonstration: When the pitch class circle is repeatedly traversed in clockwise steps, one obtains the impression of a scale that ascends endlessly in pitch: C# sounds higher than C; D as higher than C#, D# as higher than D; A# as higher than A; B as higher than A#; C as higher than B; and so on endlessly. One such scale is presented in Sound
descending judgments occurred equally often.
Shepard then employed such a bank of tones to produce
Fig. 3. Spectral representation of Shepard’s algorithm for generating pitch circular- ity. Circularity is obtained by rigidly shifting the partials up or down in log fre- quency, while the spectral envelope is held fixed. As examples, the red lines represent
partials at note C, and the blue lines represent partials at note C#. Adapted from
Shepard.
2
Demonstration 1 (See Sidebar). When the circle is traversed in counterclockwise steps, the scale appears to descend end- lessly instead. This pitch paradox has been used to accompa- ny numerous videos of bouncing balls, stick men, and other objects traversing the Penrose staircase, with each step accompanied by a step along the Shepard scale.
Jean-Claude Risset has produced remarkable variants of
5, 6
One set of vari- ants consists of endlessly ascending and descending glissan- di. Sound Demonstration 2 presents an example. In other variants, the dimensions of pitch height and pitch class are decoupled by moving the position of the spectral envelope in
this illusion, using the same basic principle.
Pitch Circularity 9