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Topic: Tritave

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	Tritave. Who is Tritave? What is Tritave? Where is Tritave? Definition of Tritave. Meaning of Tritave.
		Despite being a harmonic scale, instead of an octave, a ratio of 2:1, the scale uses the "tritave", 3:1.
		One then usually divides this tritave into 13 equal tempered intervals, instead of the usual twelve.
		The tritave is the frequency ratio 3:1 used in the Bohlen-Pierce scale as a pseudo-octave.
	www.knowledgerush.com /kr/encyclopedia/Tritave (294 words)

	Bohlen-Pierce scale - Wikipedia, the free encyclopedia
		Pierce, who, with Max V. Mathews and others, published his discovery in 1984, renamed the scale the Bohlen-Pierce scale after learning of Bohlen's earlier publication.
		This means that its pitch classes are based on the interval 3:1 (tritave or "perfect 12th" in diatonic nomenclature) rather than the 2:1 (octave).
		Though Bohlen originally expressed the BP scale in just intonation, a tempered form of the scale, which divides the tritave into 13 equal steps, has become the most popular form.
	en.wikipedia.org /wiki/Bohlen-Pierce_scale (248 words)

	Keyboard Based On New Musical Scale (Site not responding. Last check: 2007-11-05)
		A tritave is the interval in this new scale from a note to the next note with the same letter.
		The tuning of the entire scale is based on the thirteenth root of three, rather than the traditional twelfth root of two, which seems to be very mathematically promising.
		In this clip, the chromatic tritave scale (that is, all 13 notes from C to C) is played first, followed by the same chromatic scale with a root petal tone playing throughout to show all 13 possible harmonies.
	www.hwscience.com /hwjs/archives/keyboard/keyboard.html (295 words)

	Musical tuning
		It must be realized however, that just as many people who play music today in equal temperament without having heard of it, many musicians throughout the world and the past used just intonation without "knowing" it.
		The octave (or even other intervals, such as the so-called tritave, or twelfth) can advantageously be divided into a number of equal steps different than twelve.
		Popular choices for such an equal temperament include 19, 22, 31, 53 and 72 parts to an octave, each of these and the many other choices possible have their own distinct characteristics.
	encyclopedia.codeboy.net /wikipedia/m/mu/musical_tuning.html (818 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		Alpha does the same to a minor third to create a scale of 78 cent steps.
		The equal tempered version of the Bohlen-Pierce scale consists of the ratio 3:1, 1902 cents, conventionally an octave and a just fifth, used as a tritave, and split into a thirteen tone equal temperament where each step is
		This provides a very close match to justly tuned intervals consisting only of odd numbers.
	www.informationgenius.com /encyclopedia/e/eq/equal_temperament.html (575 words)

	Rob's Holistic Detective Agency
		A tritave refers to a framework interval of the ratio 3/1.
		The Bohlen-Pierce scale was the first to use the tritave in the 1970's, it was born out of plain curiosity rather than because of its musical properties.
		It turns out that there is a just intonation scale of 13 almost equal steps within the framework of the tritave.
	rob.scotdesign.net /software/xenharmonics/scales.html (386 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		The tritave scale might have interesting possibilities as a musical medium.
		We want to listen to music composed in tritave, so we wrote to Max Mathews and John Pierce.
		If you know of any tritave recordings, or of recordings in any alternative scales, we would be grateful to hear from you.
	www.math.niu.edu /~rusin/uses-math/music/recordings (222 words)

	untitled (Site not responding. Last check: 2007-11-05)
		The results of a search along these lines, growing the blue and green lines outward as it were, can be found here.
		The same for 7-limit in the ‘1:3 tritave’ is here.
		To extend this in the third dimension for 7-limit in the octave is slightly more complicated.
	www.kees.cc /tuning/perbl.html (370 words)

	Tuning-Math Archive Section 2: 1200 - 1224
		It's all in the timbre to me. Tritaves with odd-number partials have a stronger tritave equivalence than octaves with sawtooth timbres.
		And there will be times when folks will not want to always write "and their tritave equivalents" because they feel it is given by the context.
		It should have been: So for a tritave repeating scale I think "7 limit" should mean ratios of all non-multiples of 3 up to 7, i.e.
	www.robertinventor.com /tuning-math/s___2/msg_1200-1224.html (4249 words)

	The Bohlen-Pierce Site: BP Interval Properties
		Nevertheless, he also had a hard time getting used to "tritave", an artificial word that John Pierce invented when he came across BP.
		But despite Bohlen's aversion against verbal contraptions, he had to admit that it served well the claim that 3:1 has the same pivotal importance for BP, which the octave has for the traditional Western scale.
		Thus "tritave" has become the generally accepted expression for 3:1.
	members.aol.com /bpsite/intervals.html (793 words)

	[No title]
		For example, an interval of 33 Pierce steps exhibits equivalence, even though it is a very harmonic partials.
		For example, an interval of 33 Pierce steps exhibits equivalence, even though it is a very different pitch class in the tritave scheme.
		Even when the even partials are removed, I believe the virtual pitch sensation is not very octave-specific." My ears agree with Paul Erlich's here.
	www.microtonal.freeservers.com /post178.html (1094 words)

	PianoRoll (Site not responding. Last check: 2007-11-05)
		This PianoRoll is unique in that it is Microtonal: it supports loading any Scala scale file and editing of notes adapts to that scale.
		For example, in the picture above, the scale loaded is a Bohlen-Pierce scale with 13 tones to the tritave.
		The PianoRoll above has adapted to that scale to show 13 scale degrees per octave of its editor.
	www.csounds.com /stevenyi/blue/blueDocs/pianoRoll.html (923 words)

	The Bohlen-Pierce Site: 271 Tone BP Scale
		But, as Paul Erlich points out, referring to an interesting web page of
		: "...a scale of 271 notes per tritave - in just intonation - is the smallest such set that can be considered a more closed system than 13 notes - in just intonation -.
		The following considerations give at least a flavor of their shape.
	members.aol.com /bpsite/271tones.html (722 words)

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