
	Where results make sense

Topic: Otonalities

In the News (Fri 1 Jan 10)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Otonality and Utonality - Wikipedia, the free encyclopedia
		Otonality and Utonality are terms introduced by Harry Partch to describe chords whose notes are the overtones (multiples) or "undertones" (divisors) of a given fixed tone.
		An Otonality corresponds to an arithmetic series of frequencies or a harmonic series of wavelengths or distances on a string instrument.
		In an Otonality all the difference tones are elements of the same harmonic series, so they reinforce the tonality, but in an Utonality the difference tones are all different and they tend to destabilize the tonality.
	en.wikipedia.org /wiki/Otonality_and_utonality (542 words)

	Anomalous Saturated Suspensions (Site not responding. Last check: 2007-10-23)
		Removing all factors of 2, the otonal 9-limit chord is 1:3:5:7:9.
		Paul Erlich, in a post to the Tuning List showed that there are chords which are neither 9-limit utonalities or otonalities, but all of whose intervals are within the 9-limit.
		Remove the 35, and 3:5:7:15:21 is a subset of the 21-limit otonality, hence it is not saturated.
	www.microtonal.co.uk /ass.htm (1037 words)

	46 Note Subset in 72 ET
		The ratios shown on the 6 (six) keyboards found at 72note.com suggest a 46 note subset.
		These intervals are the 17-limit otonalities and utonalities.
		This means that intervals can be paired as ascending and descending (i.e., m6 ascending is equivalent to a descending P3.) Here, ratios find their closest approximations in 72 tone equal temperament.
	www.72note.com /46notesubset/46notesubset.html (88 words)

	Harry Partch 'A Just Cause' by Paul serotsky- Jan 2004 MusicWeb(UK) (Site not responding. Last check: 2007-10-23)
		The sequences ascending from lower left to upper right between solid lines are the otonalities, and those descending from upper left to lower right between dotted lines are the utonalities.
		Once we have tuned all the intervals of the 5-limit to a unity (1/1), we have not just one true triad based on that unity, but also five other true triads.
		The breathtaking corollary is that the 1, 5, 3 "udentities" of a utonality are a triad of tones in order of descending pitch, which is a mirror image of an otonality.
	www.musicweb-international.com /classrev/2004/Jan04/partch_just_cause2.htm (2667 words)

	Microtonal Music by Prent Rodgers (Site not responding. Last check: 2007-10-23)
		After an opening chord progression of four otonalities on the utonality (overtones on A#, Ab, G--, F or 9:9, 9:10, 9:11, 9:12), the cello plays a melody in A# otonality, with modulations to the utonalities after a few measures.
		This is the basic structure of the song: melody moving from one otonality to another, following the progression of the utonality.
		This is separated by occasional slow chord progressions through the utonality progression.
	prodgers13.home.comcast.net /liner/MirrorWalk.htm (466 words)

	Partch's Diamond
		Otonality, which means that the major tonality progresses in an ascending direction “over” 1/1; and he referred to the latter sequence as a 1/1
		Similarly, the 11-limit Diamond Marimba also consists of 8/5—, 4/3—, 8/7—, 16/9—, 16/11 Otonalities, and 5/4—, 3/2—, 7/4—, 9/8—, 11/8 Utonalities.
		If we lower this central pitch by one “octave” to G4 at 392.0 cps, Figure 60 shows the approximate tones of the 1/1 Otonality and the 1/1 Utonality on the conventional treble staff.
	www.chrysalis-foundation.org /Partch's_Diamond.htm (961 words)

	Tuning-Math Archive Section 7: 6525 - 6549
		since "level 2" results from building complete otonalities and utonalities on all the ratios which lie on the outside of the "level 1" structure...
		i suppose "level 3" would be the structure which results from building complete otonalities and utonalities on the ratios which lie on the outside of the "level 2" structure.
		examples of a diameter-1 structure in the 7- limit lattice would include the otonal tetrad and the utonal tetrad, but not the agglomeration of both stuck together.
	robertinventor.com /tuning-math/s___7/msg_6525-6549.html (3817 words)

	Tuning-Math Archive Section 10: 9750 - 9774
		Well, I don't know about 13-limit, but in 11-limit for example, there appear to be instances where it works, and 19-equal can work with two different mappings (and thus two different "stretch" factors) in the 11-limit.
		There is a consensus that "father" isn't an approximation of 5-limit JI, but I don't think that is because anyone tried it with large otonalities using inharmonic timbres.
		Perhaps we should limit such tests to otonalities having at most one note per prime (or odd) in the limit.
	www.robertinventor.com /tuning-math/s__10/msg_9750-9774.html (6220 words)

	Glass Organ: Layout
		Not surprisingly, I got tired of thinking about the otonalities going diagonally down and right when I played the organ.
		Upper-left to lower-right diagonals are still Otonal (major) and upper-right to lower-left are Utonal (minor).
		Earlier, I mentioned eliminating duplicate notes, yet I kept the duplicate 4/3 and 3/2.
	www.organicdesign.org /peterson/glass_organ/layout.html (715 words)

	KeenanTuning
		There are equal numbers of otonal (major) and utonal (minor) in all cases.
		Many thanks to Graham Breed, who finally got me to see this tuning as a "detempered" 12 of 22-tET.
		They sort of occur in 4 positions in this temperament, however two of these have the transmuted 4:7's in the otonalities while the other two have them in the utonalities.
	users.bigpond.net.au /d.keenan/Music/Strange9.htm (894 words)

	Zoomoozophone Primer
		The above chord is called 1/1 utonality or 1/1 U. Each utonality pitch is the complement of its mirror-image otonality pitch.
		From each pitch in 1/1 U, a new otonality is created:
		He did it by continuing to symmetrically add more otonalities and
	www.deandrummond.com /zoomprimer.htm (1564 words)

	Microtonal Music by Prent Rodgers (Site not responding. Last check: 2007-10-23)
		This is a piece based on the otonalities of the Partch Tonality Diamond.
		The primary tonality is what I call D++, an 8:7 above the center of a tonality diamond based on C as 1:1.
		A sample of the source code for the bridge section:
	home.comcast.net /~prodgers13/liner/Tsantsa.htm (551 words)

Try your search on: Qwika (all wikis)