Kisseberth (1970) originally identified a phonological 'conspiracy' as a set of rules that serve the same purpose: to rid the surface forms of the language of certain undesirable (marked) configurations. For example, Pater (1996/1999) discusses the conspiratorial relationship that exists among the following set of rules in the languages Umbundu and Si-Luyana (see Pater 1996/1999 for references).

(1)	The nasal + voiceless consonant conspiracy
	a.	[+nas] -> Ø / __ [–voi, +cont]
	b.	[+nas] -> [x place] / __ [x place]
	c.	[–voi] -> Ø / [+nas] __

Rule (1a) deletes nasals before voiceless fricatives, and rules (1b) and (1c) together guarantee that an underlying nasal + voiceless consonant sequence is realized on the surface 'fused' as a nasal with the same place of articulation as the voiceless consonant. When the rules in (1) are applied in the order given, the latter two rules effectively apply to the consonantal complement of voiceless fricatives; i.e., voiceless stops. This accounts for the data in (2).

(2)	Umbundu (a) and Si-Luyana (b) (from Pater 1996:24/1999:326)

	a.	/N + tuma/ [numa]	'I send'
		/N + seva/ [seva]	'I cook'
	b.	/N + tabi/ [nabi]	'prince'
		/N + supa/ [supa]	'soup'

As Pater explains, the rules in (1) do not capture the conspiratorial generalization underlying them: that surface sequences of nasal + voiceless consonant are avoided. Avoidance of these cross-linguistically marked sequences differs for stops and fricatives in Umbundu and Si-Luyana, but not in Indonesian (where fusion occurs with voiceless fricatives as well as with voiceless stops) nor in Kelantan Malay, Venda, Swahili, and Maore (where nasals delete before voiceless stops as well as before voiceless fricatives). (Again, see Pater 1996/1999 for references.)

Pater analyzes the Umbundu/Si-Luyana nasal + voiceless consonant conspiracy within Optimality Theory (Prince & Smolensky 1993) by first extracting the shared structural description of rules (1a) and (1c)—[+nas][–voi]—as a markedness constraint *NC (where C = voiceless consonant). Deletion of the nasal before voiceless fricatives involves violation of the faithfulness constraint MAX, and fusion of the nasal with other voiceless consonants (i.e., stops) involves violation of the faithfulness constraint LINEARITY (on these and other faithfulness constraints, see McCarthy & Prince 1995, 1997/1999). Both of these constraints must be dominated by *NC (and by any and all other conflicting faithfulness constraints) in Umbundu and Si-Luyana in order to explain the conspiratorial fact that both fusion and deletion are effected in order to avoid surface NC sequences.

The fact that fusion is the default ('elsewhere') case is accounted for by the further ranking of MAX above LINEARITY, as shown in (3) below. This leaves the question of the cases where a violation of LINEARITY is not tolerated; i.e., with fricatives. Pater submits that fusion between a nasal and a fricative fatally violates a faithfulness constraint for the feature [±cont]—since nasals are [–cont] and fricatives are [+cont], fusion between them must sacrifice one or the other value—and so in these cases, and in these cases only, violation of MAX is tolerated instead, as shown in (4) below.

(3)	Fusion with stops (from Pater 1996:25/1999:327)
	Input: /N + tabi/ 'prince' *NC FAITH[±cont] MAX LINEARITY a.     [ntabi] * !       b. F [nabi]       * c.     [tabi]     * !

(4)	Deletion with fricatives (from Pater 1996:26/1999:327)
	Input: /N + supa/ 'soup' *NC FAITH[±cont] MAX LINEARITY a.     [nsupa] * !       b.     [nupa]   * !   * c. F [supa]     *

Based on this example, the logic of the analysis of a conspiracy within OT can be abstracted as follows. A markedness constraint M (here, *NC) conflicts with and dominates two faithfulness constraints F₂ (MAX) and F₁ (LINEARITY), but typically only forces violation of F₁ because F₂ dominates F₁. However, in certain circumstances (here, when the C of the NC is a fricative), violation of F₁ entails violation of another constraint X (FAITH[±cont]) that also conflicts with and dominates F₂. Under these circumstances, F₂ is violated instead of F₁ to satisfy M, since violation of F₂ staves off a violation of X.

(5)	Logic of conspiracy in OT
	a.	Ranking: {M,X} >> F2 >> F1, where
		i.	M = a markedness constraint against the conspiratorily avoided surface configuration,
		ii.	F1 = a faithfulness constraint against an input-output mapping preferred by M,
		iii.	F2 = a faithfulness constraint against another input-output mapping preferred by M,
		iv.	X = a constraint sometimes violated when F1 is violated, but not when F2 is violated.
	b.	M forces violation of F1, unless X is at stake, in which case M forces violation of F2 instead.

It turns out that a very similar logic applies to the analysis of a particular aspect of vowel harmony in Turkish. As is well-known, Turkish has harmony for the features [±back] and [±round]. Padgett 1995ab offers an analysis in terms of the feature class Color, encompassing these two features (see also Odden 1991, Selkirk 1991, and further references in all of these papers); I focus here solely on [±back] harmony. The relevant issue is that while the high vowels of Turkish are well-paired along the front-back dimension (front i with back ï, front ü with back u), the non-high vowels are not so well-paired. Specifically, while front mid ö is well-paired with back mid o, front mid e is ill-paired with back low a: the vowels ë and ä don't exist in Turkish.¹

There is a strong temptation here to claim that this imperfect pairing is due to some phonological 'inertness' of the feature [±low] in Turkish, but this type of analysis does little more than restate the problem. I claim instead (following my own work in Bakovic 2000) that the pairing between these two vowels is the result of an overzealous assimilation constraint, AGREE[±back], demanding that vowels in adjacent syllables share the same value of the feature [±back], even if this must be achieved at the expense of faithfulness to the feature [±low]. In other words, AGREE[±back] dominates not only FAITH[±back] (in order to enforce harmony in the first place) but also FAITH[±low].

But why should AGREE[±back] need to force violation of both of these featural faithfulness constraints, when just FAITH[±back] should do? In fact, as shown in (6) below, violation of FAITH[±low] in addition to FAITH[±back] is fatal when the suffix vowel is high, because violation of just FAITH[±back] is also an option. However, recall that the non-high vowels ë and ä don't exist in Turkish. These are in fact cross-linguistically marked vowels, and to account for their absence in Turkish, a markedness constraint *ä,ë must be ranked above at least one featural faithfulness constraint that can be violated in order to guarantee that the output will be rid of these vowels.² A couple of likely candidates for these featural faithfulness constraints are none other than FAITH[±low] and FAITH[±back]; if *ä,ë dominates at least FAITH[±low], then the result is as shown in (7) below: violation of both FAITH[±low] and FAITH[±back] is forced to achieve ultimate satisfaction of both AGREE[±back] and *ä,ë.³

(6)	Good pairing with high vowels
	Input: /al + di/ 's/he bought' AGREE[±back] *ä,ë FAITH[±low] FAITH[±back] a.     [al + di] * !       b. F [al + dï]       * c.     [al + da]     * ! *

(7)	'Re-pairing' with non-high vowels
	Input: /al + mek/ 'to buy' AGREE[±back] *ä,ë FAITH[±low] FAITH[±back] a.     [al + mek] * !       b.     [al + mëk]   * !   * c. F [al + mak]     * *

Comparing the tableaux in (6) and (7) with those in (3) and (4) reveals the essential similarities between what one might call 'classical' conspiracies and the situation in Turkish vowel harmony. In both cases, a markedness constraint M (in Turkish, AGREE[±back]) dominates two faithfulness constraints F₂ (FAITH[±low]) and F₁ (FAITH[±back]), but typically only forces violation of F₁. In the case of classical conspiracies, this is because F₁ dominates F₂; in Turkish, it is because M conflicts directly with F₁ but not with F₂. In certain circumstances (in Turkish, when the harmonizing suffix vowel is non-high), violation of F₁ entails violation of another constraint X (*ä,ë) that conflicts with and dominates F₂. Under these circumstances, F₂ is violated in addition to F₁ (as opposed to instead of F₁, in the case of classical conspiracies) to satisfy M, since the additional violation of F₂ staves off a violation of X.

The logic of the Turkish vowel harmony analysis is summarized in (8), which is to be compared with (5) above.

(8)	Logic of the Turkish vowel harmony analysis
	a.	Ranking: {M,X} >> {F2,F1}, where
		i.	M = a markedness constraint against the conspiratorily avoided surface configuration,
		ii.	F1 = a faithfulness constraint against an input-output mapping preferred by M,
		iii.	F2 = a faithfulness constraint against an input-output mapping preferred by X,
		iv.	X = a constraint sometimes violated when F1 is violated.
	b.	M forces violation of F1, unless X is at stake, in which case M forces violation of F2 as well.

As can now be appreciated, the situation in Turkish vowel harmony is quite parallel to a classical conspiracy, the primary difference being that in Turkish, M only conflicts directly with F₁ and only indirectly with F₂ via the interaction with X. Despite this difference, re-ranking F₂ above X in either case leads to another parallel pair of situations. In the case of *NC, fusion ends up applying equally to stops and fricatives, as in Indonesian, shown in (9) and (10) below...⁴

(9)	Fusion with stops
	Input: /meN + tulis/ 'to write' *NC MAX FAITH[±cont] LINEARITY a.     [mentulis] * !       b. F [menulis]       * c.     [metulis]   * !

(10)	Fusion with fricatives
	Input: /meN + sapu/ 'to sweep' *NC MAX FAITH[±cont] LINEARITY a.     [meñsapu] * !       b. F [meñapu]     * * c.     [mesapu]   * !

...and in the case of AGREE[±back], harmony ends up applying equally to high and non-high vowels, as in Finnish (see e.g. Kiparsky 1981, Ringen 1975/1988), shown in (11) and (12) below.⁵

(11)	Good pairing with high vowels
	Input: /tuhma + üüs/ 'naughtiness' AGREE[±back] FAITH[±low] *ä,ë FAITH[±back] a.     [tuhm + üüs] * !       b. F [tuhm + uus]       * c.     [tuhm + aas]   * !   *

(12)	Good pairing with non-high vowels
	Input: /tühmä + sta/ 'stupid (ellative)' AGREE[±back] FAITH[±low] *ä,ë FAITH[±back] a.     [tühmä + sta] * !       b. F [tühmä + stä]     * * c.     [tühmä + ste]   * !   *

In sum, I hope to have shown that there are some interesting formal similarities between classical conspiracies on the one hand and Turkish vowel harmony on the other, at least as both of these have been analyzed within Optimality Theory. Further investigation of these similarities may lead to a deeper understanding of both of these phenomena, which were previously believed to be quite unrelated.

References

Bakovic, Eric. 2000. Harmony, Dominance and Control. Doctoral dissertation, Rutgers University. [Back]

Kiparsky, Paul. 1981. 'Vowel harmony.' Ms., MIT. [Back]

Kisseberth, Charles. 1970. 'On the functional unity of phonological rules.' Linguistic Inquiry 1:291–306. [Back]

McCarthy, John and Alan Prince. 1995. 'Faithfulness and Reduplicative Identity.' In J. Beckman et al. (eds.), UMOP 18: Papers in Optimality Theory, 249–384. Graduate Linguistic Student Association, University of Massachusetts, Amherst. [ROA-60.] [Back]

McCarthy, John and Alan Prince. 1997/1999. 'Faithfulness and Identity in Prosodic Morphology.' ROA-216. / In R. Kager et al. (eds.), The Prosody-Morphology Interface, 218–309. Cambridge University Press, Cambridge. [Back]

Moreton, Elliott. 1996/1999. 'Non-computable functions in Optimalty Theory.' ROA-364. [Back]

Odden, David. 1991. 'Vowel Geometry.' Phonology 8:261–290. [Back]

Padgett, Jaye. 1995a. 'Feature classes.' In J. Beckman et al. (eds.), UMOP 18: Papers in Optimality Theory, 385–420. Graduate Linguistic Student Association, University of Massachusetts, Amherst. [ROA-112.] [Back]

Padgett, Jaye. 1995b. 'Partial class behavior and nasal place assimilation.' ROA-113. [Back]

Pater, Joe. 1996/1999. 'Austronesian nasal substitution and other NC effects.' ROA-160. / In R. Kager et al. (eds.), The Prosody-Morphology Interface, 310–343. Cambridge University Press, Cambridge. [Back]

Prince, Alan and Paul Smolensky. 1993. Optimality Theory: Constraint Interaction in Generative Grammar. RuCCS Technical Report TR-2, Rutgers Center for Cognitive Science, Piscataway, NJ. [To appear, MIT Press.] [Back]

Ringen, Catherine. 1975/1988. Vowel Harmony: Theoretical Implications. Doctoral dissertation, Indiana University / Garland, New York. [Back]

Selkirk, Elizabeth. 1991. 'Major Place in the Vowel Space: Vowel Height.' Ms., University of Massachusetts, Amherst. [Back]

Endnotes

^* The formal analysis of Turkish vowel harmony commented on in this squib is from my dissertation. As an undergraduate at UCSC, I thought that Jorge Hankamer had taught me everything I ever needed to know about Turkish vowel harmony. Though this is probably true to a significant extent, the interest in Turkish vowel harmony that Jorge first sparked in me has led me to discover new and theoretically interesting things about the phenomenon, as I hope this squib will show. [Back]

¹ Though it should be clear from context, I use the symbol ï to represent the [+high, +back, –round] vowel of Turkish, and the symbols ë and ä to represent the hypothetical [–high, –low, +back, –round] and [+low, –back, –round] vowels, respectively. [Back]

² The markedness constraint is clearly ad hoc as stated; I merely use it as an expositorily-motivated shorthand for the markedness of the feature combinations in each of these vowels. [Back]

³ I assume a kind of 'worst-case scenario' in these two tableaux, underlyingly specifying the suffix vowel as the other member of the front-back pair than appears in the actual surface form. Since it is partly the appropriate ranking of faithfulness constraints that is at issue here, this worst-case scenario is expositorily necessary and indeed sufficient: any 'better-specified' underlying form is guaranteed to lead to the same output, though with fewer faithfulness violations (Moreton 1996/1999). Incidentally, this accounts for the fact that the harmonic feature value of suffix vowels in Turkish is perfectly predictable (modulo bona fide exceptions, or course). [Back]

⁴ The prefixal e in these examples represents schwa. According to Pater (1996:24, note 17 / 1999:338, note 18), the resulting palatal nasal ñ when fused with s, as in the example in (10), is a 'well-known complication' in Austronesian languages—a complication I put aside here. [Back]

⁵ Vowel-initial suffixes such as the abstract noun suffix -uus/-üüs in (11) trigger regular deletion of stem-final vowels, as reflected in the candidate outputs of that tableau. I treat the long vowel in this suffix as a single vowel for the purposes of calculating constraint violations; nothing crucial rests on this expositorily-motivated decision. Another irrelevant complication in Finnish is that neither i nor e have [+back] counterparts, resulting in the transparency of these vowels to [±back] harmony—hence the choice of a high round suffix vowel in (11) and a low suffix vowel in (12) to illustrate the relevant result. [Back]