Troriluzole in Adult Participants With Spinocerebellar Ataxia

Inclusion Criteria: 1. Participants with a known or suspected diagnosis of the following specific hereditary ataxias: SCA1, SCA2, SCA3, SCA6, SCA7, SCA8 and SCA10. 1. A participant should have a confirmed genotypic diagnosis from a Clinical Laboratory Improvement Amendments (CLIA) certified lab (can produce test results); or, 2. A participant has a family member that has a confirmed genotypic diagnosis from a CLIA certified lab (can produce test results) and must be willing to undergo genetic testing to confirm underlying SCA diagnosis; or, 3. A participant has a confirmed genotypic diagnosis from a lab that is not CLIA certified and must be willing to undergo genetic testing to confirm underlying SCA diagnosis; or, 4. A participant has clinical evidence that supports diagnosis of one of the aforementioned SCA genotypes but does not have producible test results from a CLIA certified lab from either a family member or for his or herself and the participant must be willing to undergo such testing to confirm the SCA diagnosis (in this case, site must wait for results of genotypic testing prior to randomization) 2. Ability to ambulate 8 meters without human assistance (canes and other devices allowed) 3. Screening Modified Functional Scale for the Assessment and Rating of Ataxia (f-SARA) total score ≥3. 4. Score of ≥1 on gait subsection of the f-SARA 5. Determined by the investigator to be medically stable at Baseline/randomization as assessed by medical history, physical examination, laboratory test results, and electrocardiogram testing. Exclusion Criteria: 1. A ≥ 2-point difference on the Modified Functional SARA score between screening and baseline 2. Mini Mental State Exam (MMSE) score \<24 3. Any medical condition other than one of the hereditary ataxias specified in the inclusion criteria that could predominantly explain or contribute significantly to the participants' symptoms of ataxia. 4. A prominent spasticity or dystonia that, in the opinion of the investigator, will compromise the ability of the SARA instrument to assess underlying ataxia severity. 5. A score of 4 on any individual item (Items 1-4) of the f-SARA 6. Participants should be excluded at screening or baseline if medical conditions have arisen or there is a change in disease status that could confound the ability of the SARA to accurately reflect changes in ataxia severity. 7. Active liver disease or a history of hepatic intolerance to medications that in the investigator's judgment, is medically significant.