Bohlen-Pierce scale - Factbites

Bohlen-Pierce scale - Factbites
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Topic: Bohlen-Pierce scale

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	Bohlen-Pierce scale - InformationBlast
		While the Bohlen-Pierce scale is currently most often played in equal temperament for practical reasons, that scale is an approximation of a just intonation system based only on ratios of odd whole numbers, similar to the spectra of instruments such as the clarinet which consist of primarily the odd harmonics.
		The tritave is the frequency ratio 3:1 used in the Bohlen-Pierce scale as a pseudo-octave.
		An interesting, or frustrating, aspect of the Bohlen-Pierce scale is that traditional music theory and even one's intuition do not seem to apply.
	www.informationblast.com /Tritave.html (282 words)

	Scale - Wikipedia, the free encyclopedia
		Bohlen-Pierce scale, chromatic scale, Deutsch's scale illusion, diminished scale, mathematics of musical scales, minor scale
		The Richter scale, the Mercalli scale, the Rossi-Forel scale and the Omori are all used to measure the intensity of earthquakes.
		The Fujita scale measures the intensity of tornadoes.
	en.wikipedia.org /wiki/Scale (241 words)

	Relating Tuning and Timbre
		Recently, Mathews and Pierce examined a scale with steps based on the thirteenth root of three, rather than the standard twelfth root of two, which is designed to be played with timbres containing only odd partials.
		Pierce's brief note reported synthesizing a timbre designed specifically to be played in an 8 tone equal tempered scale.
		Pierce, "Attaining Consonance in Arbitrary Scales,"Journal of the Acoustical Society of America.
	eceserv0.ece.wisc.edu /~sethares/consemi.html (4740 words)

	iqexpand.com
		For the equal temperament scale, the frequency of each note in the chromatic scale is related to the...
		Equal Temperament The equal tempered scale is the common musical scale used at present, used for the tuning of pianos and other instruments of relatively fixed scale.
		Australian aboriginal music extensively measured by Ellis (1965) was based on arithmetic scales (the harmonic series is an arithmetic scale, though presumably the Australian scales began an interval smaller than an octave) with an equal separation in hertz.
	equal_temperament.iqexpand.com (1995 words)

	Kees van Prooijen; 13 tones in the 3rd harmonic
		They have done such a wonderful job in studying and documenting this scale that it is only just that it is known by their names: the Bohlen-Pierce scale.
		Apparently in the same timeframe, it was discovered by Heinz Bohlen and John Pierce.
		This scale is constructed from the major triads on the tonic, dominant and sub-dominant and is best depicted in a grid where the dimensions are determined by the 3rd and 5th harmonics.
	www.kees.cc /music/scale13/scale13.html (261 words)

	li'l miss' scale oven: scale gallery
		Pierce split the twelfth (3:1) 13 ways to create a tuning based on a 146.3 cent equally tempered "chromatic scale".
		Pierce subsetted the chromatic scale to feature near-just intervals by specifying a repeat ratio of 3:1 and scale pattern of
		We set the Scale Pattern to 3,1,2,3,2,1,1,1 to create a subset of this interesting tuning which gives a perfect supermajor sixth (12:7) as its Repeat Ratio and a nearly-just subminor third (7:6) that is only about a quarter cent flat.
	www.nonoctave.com /tuning/LilMissScaleOven/gallery.html (3148 words)

	Musical note intervals
		The widest intervals of this Arabic scale are the same size as the smallest ones of the Pythagorean diatonic one, and two wides plus one small are the same size as the wide notes of the Pythagorean diatonic.
		Scales are used to describe how the pitch varies, i.e the way the tune goes up and down in pitch.
		For instance, the Arabic 17-tone scale, if you choose to show the ratio from the previous note, turns out to be made up of intervals of two sizes, 256/243, and 531441/524288, which you can compare with the Pythagorean diatonic with ratios 9/8 and 256/243.
	www.tunesmithy.connectfree.co.uk /musical_note_intervals.htm (4235 words)

	The "Warped Canon" Page
		The Bohlen-Pierce (BP) scale is a 7-limit JI tuning discovered by Heinz Bohlen, which is built from factors of 3, 5, and 7 without any octaves.
		The original BP scale is represented as a sequence of ratios from a base pitch: 1/1 27/25 25/21 9/7 7/5 75/49 5/3 9/5 49/25 15/7 7/3 63/25 25/9 3/1.
		This scale is a subset of the basic Porcupine scale of 15 notes, which is built from a generator of around 160-165 cents.
	www.io.com /~hmiller/music/warped-canon.html (2857 words)

	Act I, 1st Scene
		The scene was written entirely in the Bohlen-Pierce scale, a consonant scale that subdivides the interval of a twelfth in thirteen equal steps.
		This equidistant scale which was described independently by two researchers (Stanford professor John Pierce and German engineer Heinz Bohlen) is characterized by an extraordinary number of unusual, yet consonant intervals in close approximation.
		As this scale, not having any octaves, is an intellectual achievement in itself, it symbolizes the abstract, academic world of a university department.
	www.georghajdu.de /Compositions/DerSprung/1.1.html (409 words)

	The Bohlen-Pierce Site: BP Scale Structures
		Four values of the assumed scale are present from the very beginning: 1/1 as the base tone, then 5/3 and 7/3 to form the 7/5/3 triad with the base tone, and finally 3/1 as the top tone (first phase).
		Now let's assume that the traditional major scale of the Western musical system developed from the desire to accommodate the major triad (be it as an entity or in parts), in as many varieties as possible, within the framework of the octave.
		The chromatic scale has 13 steps, and again 13 steps are sufficient to create an equally tempered scale that deviates less from the BP scales in just tuning than the equally tempered western scale from its just relatives.
	members.aol.com /bpsite/scales.html (1781 words)

	Stephen Fox Clarinets
		While the mathematics of the Bohlen-Pierce scale have been analyzed in some depth over the last thirty years or so, so far the body of music created on this basis is still small, and the field is wide open to exploration by composers.
		The goal is to design and build a family of clarinet-type instruments - soprano, tenor and bass - tuned to the Bohlen-Pierce scale, for the purpose of exploring and demonstrating the musical potential of the concept.
		The history, construction and previous musical application of the scale are described in detail on a website maintained by its co-inventor, Heinz Bohlen.
	www.sfoxclarinets.com /bpclar.html (504 words)

	post178.html
		Paul Erlich mentioned that an interval of 33 scale-steps of the Bohlen-Pierce scale sounds like an interval of 4 octaves.
		However, Paul E. did not mention whether he was talking about "an interval of 33 Pierce steps" melodically or harmonically. That is, sounding the interval as a vertical dyad or as two sequential notes one after the other.
		On the one hand, listeners will tend to hear intervals in these scales very differently melodically than harmonically if the interval is slightly off from a familiar interval.
	www.microtonal.freeservers.com /mclaren/post178.html (1094 words)

	Sites about Microtonal Scales for Your Perusal
		The Bohlen-Pierce Site is exactly what it says it is. A whole website devoted to the Bohlen-Pierce scale, which is a non-octave equal temperament.
		Paul Erlich has a paper on some scales within 22-tone equal temperament which does a really good job of applying tonal principles to a new kind of scale.
		Which are consistent with 24-equal, the much heard of quartertone scale that Real Theorists tend to look down on.
	www.microtonal.co.uk /scales.html (175 words)

	Odd Piano
		It is in the so called Bohlen-Pierce scale.
		I wrote this piece on July 8, 2000 on the occasion of the 100th anniversary of the birth of the American composer George Antheil.
		It was written in MPEG4 Structured Audio and executed with Sfront.
	www.kees.cc /music/oddpiano/oddpiano.html (57 words)

	K2000/K2500 Equal Tempered Scales
		To achieve the fractional cents tuning of the other scales, the KEYMAP KeyTrack parameter is used as a coarse step tuning control and the PITCH Modulator 1 or 2 is used as a fine tuning control.
		With some simple VAST programming, equal tempered scales of any degree can be accomplished to an accuracy of 1 cent over the entire MIDI note range of 128 keys.
		Next is an example of the 31 tone equal tempered scale, which uses a FUN.
	home.austin.rr.com /ginasbaskets/microtonal-synthesis/k2x00eq.html (504 words)

	User guide 2
		The scale will be shown with the 1/1 in the centre, so the 7/4 for instance is shown as a 7/8 to the left rather than to the right (transposed down an octave).
		For instance, if you have the just temperament twelve tone scale, and the preset colours, any lines that fall in the interval 1 to 16/15 are shown in blue, ones in the interval 16/15 to 9/8 in red, 9/8 to 6/5 in yellow, and so on.
		When you use it to play the main window scale or arpeggio then normally it is set to the left key in the third row of your keyboard - the 'a' on a qwerty keyboard.
	tunesmithy.netfirms.com /fts_help/User_guide2.htm (11267 words)

	Elaine Walker's Bohlen-Pierce Scale Research 2000
		Elaine's Proposed Keyboard Layout for Bohlen-Pierce Scale, Referencing the C-Lambda Mode
		The story of the Bohlen-Pierce Scale is a bittersweet one.
		When John R. Pierce recently passed away, Heinz's dream of meeting him and discussing their co-invented scale in person, died with him.
	www.ziaspace.com /elaine/BP (309 words)

	steven yi :: music » Blog Archive » Sounds and Scales
		I have been exploring the Bohlen-Pierce scale for the past month, sketching out ideas for a new piece, getting my ear attuned to its character, trying out different chords and colors, exploring that sound world.
		It’s strange how I initially found the scale quite warm, but later found that the ideas I was working on feel muted in color.
		Last night, after working up a sketch to a size where I felt I was getting a taste for that palette of sound I found that I couldn’t quite get the colors I wanted, and so I think I will move on from exploring this scale for now.
	www.kunstmusik.com /?p=51 (240 words)

	What's new up to 5th Sept 2003
		The mean tone scale one now responds instantly whenever you change any of the numbers including the sizes of the tempered and wolf fifths, thirds or minor thirds, and now you also see entries for seconds and the chromatic and diatonic semitones.
		You can't retune the 1/1 or any of the scale repeats using this method - if you try you find you pitch bend the note, but it doesn't change the scale at all and when you release and try again the 1/1 is tuned the way it always was.
		This is useful for work with the product scales, lattice and other 2D scales, so as a result, you will find the Lambdoma keyboard icon on those pages now.
	www.robertinventor.com /whats_new2.htm (12775 words)

	Bohlen-Pierce Tuning - a tuning where the 3:1 ratio is the identity interval
		The equivalence-interval of the Bohlen-Pierce scale is called the tritave.
		A just-intonation tuning discovered in 1972 and published in 1978 by Heinz Bohlen, and discovered independently and published in 1984 by John Robinson Pierce, in which the 3/1 ratio (the pythagorean "perfect-12th", i.e., perfect-5th plus octave) is divided into 13 unequal steps.
	tonalsoft.com /enc/b/bohlen-pierce.aspx (292 words)

	micro
		A unique and popular non-octave scale, the Bohlen-Pierce scale, is studied at http://members.aol.com/bpsite/index.html Erv Wilson was one of the geniuses of microtonal theory and many of his papers, featuring beautiful but mathematically rigorous diagrams, are collected at http://www.anaphoria.com/wilson.html.
	www.math.niu.edu /~rusin/papers/uses-math/music/micro (345 words)

	steven yi :: music » Blog Archive » Recent Musical Experiences
		Of the scales I’ve gotten to experiment with so far, I’ve found that the Bohlen-Pierce Scale to be very appealing to me right now, and the one I’ve been working with most.
		The study of these scales has been enjoyable, and though compositionally I haven’t created anything in that time, I feel like these scale studies will become very much a part of where I am going musically.
		I’ve gotten quite into tuning systems lately, something that I have been wanting to study for quite some time but was always put on the side as other interests were made priorities.
	www.kunstmusik.com /?p=47 (1162 words)

	pseudo octave
		Another example is the tritave of the Bohlen-Pierce scale.
	www.fact-library.com /pseudo_octave.html (132 words)

	Tuning-Math Archive Section 8: 7325 - 7349
		Considering d note scales in c-equal, they define the genus as the step sizes of the gaps between the notes of the chord, modulo transposition, in terms of d, and the species as the same in terms of c.
		The fine print here is "reduced scale"; they reduce a scale with Myhill's Property by lowering the size of the et c so that the sizes of the scale steps are 1 and 2.
		>Considering d note scales in c-equal, they define the genus as the >step sizes of the gaps between the notes of the chord, modulo >transposition, in terms of d, and the species as the same in terms of >c.
	www.robertinventor.com /tuning-math/s___8/msg_7325-7349.html (2505 words)

	SCALE
		Find graves of people named SCALE at Find-a-Grave.com (or add one that you know).
		Search the SCALE Family Message Boards at Ancestry.com (if available).
		Search the SCALE Family Resource Center at RootsWeb.com (if available).
	www.worldhistory.com /surname/US/S/SCALE.htm (73 words)

	The Bohlen-Pierce Site
		This site contains a collection of practical and theoretical material related to the Bohlen-Pierce scale (BP scale).
		BP is a harmonic, non-octave scale; its 13 tone steps fill the framework of the twelfth (3:1).
		It is meant to permit creation and performance of harmonic music in tonal relations that are different from those of traditional scales.
	members.aol.com /bpsite (193 words)

	The Absolute Sound: Music Reviews from Issue 104
		After all, the scale is based on mathematical relationships, and the notes do relate to one another in specific ways—it's not just random noise.
		Quoting Carpenter, "rather than building the scale around the major triad, the scale is built around the ratios of 3:5:7 and 5:7:9...the scale is non-repetitive, each step-wise interval moving 146 cents away from a given center frequency." Take that, La Monte Young!
		At first, it's extremely disconcerting—the music doesn't sound "in tune," but doesn't sound "out of tune" either, as there exist complex overtones and harmonies, consonances and dissonances as in any music, whether Western, microtonal Indian, or microtonal Muddy Waters.
	www.frankdoris.com /writing/tas/carpenterhall.htm (894 words)

	Amazon.com: Books: Current Directions in Computer Music Research (System Development Foundation Benchmark Series)
		A chapter authored jointly by Mathews and Pierce describes a new musical scale they have been working on for the past few years.
		Among the specific topics covered are speech songs, synthesis of the singing voice, spatial reverberation, the simulation of bowed instruments, and a conductor program utilizing a mechanical baton.
		These twenty-one original contributions by composers, behavioral scientists, engineers, and other specialists from many of the international centers of research in computer music provide an inside report on the most sophisticated aspects of digital synthesis, control and understanding of musical sound, and related work on perception.
	www.amazon.com /exec/obidos/tg/detail/-/0262631393?v=glance (512 words)

	Composition Directives
		Nine pitch classes of the Bohlen-Pierce scale are spread over the range of five octaves going from roughly F2 in the traditional well tempered scale up to D7.
		Each pitch class is assigned five or seven rhythmic pattern permutations.
	ccrma-www.stanford.edu /~juanig/descrips/vientoshtml/Composition_Directives.html (197 words)

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