{"id":"https://openalex.org/W2018883323","doi":"https://doi.org/10.2307/843532","title":"The Consonant Eleventh and the Expansion of the Musical Tetractys: A Study of Ancient Pythagoreanism","display_name":"The Consonant Eleventh and the Expansion of the Musical Tetractys: A Study of Ancient Pythagoreanism","publication_year":1984,"publication_date":"1984-01-01","ids":{"openalex":"https://openalex.org/W2018883323","doi":"https://doi.org/10.2307/843532","mag":"2018883323"},"language":"en","primary_location":{"id":"doi:10.2307/843532","doi":"https://doi.org/10.2307/843532","is_oa":false,"landing_page_url":"https://doi.org/10.2307/843532","pdf_url":null,"source":{"id":"https://openalex.org/S19201476","display_name":"Journal of Music Theory","issn_l":"0022-2909","issn":["0022-2909","1941-7497"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","erih-plus","jufo-2","norway-1","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315572","host_organization_name":"Duke University","host_organization_lineage":["https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Music Theory","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083540002","display_name":"Andr\u00e9 Barbera","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Andre Barbera","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5083540002"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.16242166,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"28","issue":"2","first_page":"191","last_page":"191"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10941","display_name":"Musicology and Musical Analysis","score":0.7788000106811523,"subfield":{"id":"https://openalex.org/subfields/1210","display_name":"Music"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10941","display_name":"Musicology and Musical Analysis","score":0.7788000106811523,"subfield":{"id":"https://openalex.org/subfields/1210","display_name":"Music"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11463","display_name":"Classical Philosophy and Thought","score":0.17990000545978546,"subfield":{"id":"https://openalex.org/subfields/1211","display_name":"Philosophy"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.02199999988079071,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/pythagoreanism","display_name":"Pythagoreanism","score":0.7770000100135803},{"id":"https://openalex.org/keywords/consonance-and-dissonance","display_name":"consonance and dissonance","score":0.8960000276565552},{"id":"https://openalex.org/keywords/diapason","display_name":"diapason","score":0.6320000290870667},{"id":"https://openalex.org/keywords/diatessaron","display_name":"Diatessaron","score":0.8669999837875366},{"id":"https://openalex.org/keywords/rationalism-and-empiricism","display_name":"rationalism and empiricism","score":0.7110000252723694},{"id":"https://openalex.org/keywords/history-of-music-theory","display_name":"history of music theory","score":0.6330000162124634},{"id":"https://openalex.org/keywords/medieval-music-theory","display_name":"medieval music theory","score":0.5929999947547913}],"concepts":[{"id":"https://openalex.org/C2779796141","wikidata":"https://www.wikidata.org/wiki/Q1930430","display_name":"Eleventh","level":2,"score":0.9608439207077026},{"id":"https://openalex.org/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.5989856123924255},{"id":"https://openalex.org/C2778203577","wikidata":"https://www.wikidata.org/wiki/Q38035","display_name":"Consonant","level":3,"score":0.5880345702171326},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.5328009128570557},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.3763755261898041},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.34738120436668396},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3406601846218109},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.2831820845603943},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.1639971137046814},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.1179015040397644},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06383198499679565},{"id":"https://openalex.org/C2779581591","wikidata":"https://www.wikidata.org/wiki/Q36244","display_name":"Vowel","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/843532","doi":"https://doi.org/10.2307/843532","is_oa":false,"landing_page_url":"https://doi.org/10.2307/843532","pdf_url":null,"source":{"id":"https://openalex.org/S19201476","display_name":"Journal of Music Theory","issn_l":"0022-2909","issn":["0022-2909","1941-7497"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","erih-plus","jufo-2","norway-1","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315572","host_organization_name":"Duke University","host_organization_lineage":["https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Music Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4389318379","https://openalex.org/W3021615163","https://openalex.org/W4231000072","https://openalex.org/W2494850521","https://openalex.org/W4404293149","https://openalex.org/W4387118412","https://openalex.org/W4255725902","https://openalex.org/W606444850","https://openalex.org/W7067194156","https://openalex.org/W625285601"],"abstract_inverted_index":{"The":[0,122,211],"interval":[1,29,184,203],"of":[2,103,110,125,182,213],"the":[3,7,13,28,31,38,52,62,76,95,100,104,108,137,178,202],"eleventh,":[4,32,63,105],"that":[5,194],"is,":[6,195],"octave":[8],"plus":[9,54,58],"fourth,":[10],"stands":[11],"at":[12],"crease":[14],"between":[15],"rationalism":[16],"and":[17,33,43,56,71,120,133],"empiricism":[18],"in":[19,112,143],"ancient":[20,42,69,89],"musical":[21,114,147],"treatises.":[22],"For":[23],"convenience,":[24],"I":[25,64,106],"refer":[26,46],"to":[27,34,47,74,83,94,116,129,150,168,185,205],"as":[30,37,51,80,82,153],"its":[35,206],"neighbor":[36],"twelfth,":[39],"although":[40],"most":[41],"medieval":[44],"treatises":[45],"these":[48],"intervals,":[49],"respectively,":[50],"diapason":[53,57],"diatessaron":[55],"diapente.":[59],"By":[60,98],"extracting":[61],"perform":[65],"a":[66,154,170,173,186,197],"biopsy":[67],"on":[68],"Pythagoreanism":[70,90],"thus":[72],"hope":[73],"elucidate":[75],"Pythagorean":[77,101,144],"world":[78],"view":[79],"well":[81],"indicate":[84],"some":[85],"avenues":[86],"along":[87],"which":[88],"may":[91],"have":[92],"traveled":[93],"Middle":[96],"Ages.'":[97],"tracing":[99],"treatment":[102],"show":[107],"role":[109,139],"number":[111,126,142],"early":[113],"theory":[115,148],"be":[117,130],"both":[118],"causal":[119,123],"descriptive.":[121],"nature":[124],"would":[127],"seem":[128],"more":[131],"primitive":[132],"therefore":[134],"older":[135],"than":[136],"descriptive":[138],"played":[140],"by":[141],"harmonics.":[145],"Modern":[146],"tends":[149],"use":[151],"numbers":[152,176,189],"general,":[155],"abstract":[156],"system":[157],"or":[158,180,208],"metaphor":[159,199],"for":[160],"sound.":[161],"Thus,":[162],"our":[163],"modern":[164],"disposition":[165],"invites":[166],"us":[167],"see":[169],"development":[171,217],"from":[172],"time":[174,187],"when":[175,188],"determined":[177],"consonance":[179],"dissonance":[181],"an":[183,192],"simply":[190],"described":[191],"interval,":[193],"provided":[196],"quantitative":[198],"without":[200],"evaluating":[201],"according":[204],"consonant":[207],"dissonant":[209],"character.":[210],"history":[212],"mathematics":[214],"reflects":[215],"this":[216]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":20},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2016-06-24T00:00:00"}