DOCSLIB.ORG

A New Rule-Based Method of Automatic Phonetic Notation On

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
A New Rule-Based Method of Automatic Phonetic Notation On A New Rule-based Method of Automatic Phonetic Notation on Polyphones ZHENG Min， CAI Lianhong (Department of Computer Science and Technology of Tsinghua University, Beijing, 100084) Email: [email protected], [email protected] Abstract: In this paper, a new rule-based method of automatic 2. A rule-based method on polyphones phonetic notation on the 220 polyphones whose appearing frequency exceeds 99% is proposed. Firstly, all the polyphones 2.1 Classify the polyphones beforehand in a sentence are classified beforehand. Secondly, rules are Although the number of polyphones is large, the extracted based on eight features. Lastly, automatic phonetic appearing frequency is widely discrepant. The statistic notation is applied according to the rules. The paper puts forward results in our experiment show: the accumulative a new concept of prosodic functional part of speech in order to frequency of the former 100 polyphones exceeds 93%, improve the numerous and complicated grammatical information. and the accumulative frequency of the former 180 The examples and results of this method are shown at the end of polyphones exceeds 97%. The distributing chart of this paper. Compared with other approaches dealt with polyphones’ accumulative frequency is shown in the polyphones, the results show that this new method improves the chart 3.1. In order to improve the accuracy of the accuracy of phonetic notation on polyphones. grapheme-phoneme conversion more, we classify the Keyword: grapheme-phoneme conversion; polyphone; prosodic 700 polyphones in the GB_2312 Chinese-character word; prosodic functional part of speech; feature extracting; system into three kinds in our text-to-speech system 1. Introduction Grapheme-Phoneme Conversion is a method that transforms text forms into phonetic forms, such as phoneme forms for English and phonetic notation for Chinese. There already many researches are mainly based on reading and spelling rules[1] which are summarized by authorities or based on corresponding relations between alphabetic sequences and phonetic Chart 2.1 Accumulative frequency of polyphones symbol sequences which are obtained by data-driving ¾ More than 200 polyphones are rate, which approaches[2] on alphabetic writing system. Then the scarcely can be seen in usual articles. We select system confirms whether the phonetic notation of a default pronunciations to these rate polyphones. new word exists in the lexicon or not, that is to say, the Such as the “读” is pronounced “dou4” when the system solves an Out-of-vocabulary/OOV problem. But meaning is “停顿” in the ancient. this problem doesn’t exist in Chinese. Generally, every ¾ Some polyphones can not appear alone, the Chinese character has a fixed phonetic notation, but polyphonic situation only occurs when they some special characters have two or more phonetic compose a word with two or three characters. notations. The statistic result from 《词海》, which is Such as “恶” is pronounced “wu4” only in some 2641 polyphones[3] out of 16339 Chinese characters, polyphonic words like “憎恶” or “可恶”. “恶” can shows the considerable proportion hold by polyphones only be pronounced “e4” when it appears alone. in Chinese. So ascertaining the pronunciations of the ¾ More than 160 polyphones often appear alone, two polyphones is a basic and important problem in or more pronunciations and the corresponding part Chinese grapheme-phoneme conversion. of speeches of which must be both kept in the lexicon. Such as the lemma of “好” must be kept as “\hao3x\hao4f”, “发” must be kept as “\fa1d\fa4 a verb. So we can confirm that the pronunciation of “系” is “xi4”. m\fa1l” (x, f, d, m, l represent adjective, adverb, We can also ascertain that the pronunciation of the polyphone verb, noun and measure word respectively) “倒” is “dao4” because it is pronounced “dao3” only in a verb. Excluding the first kind of polyphones, we mainly deal with the second and the third kinds about 220 When we deal with the polyphones in the polyphones which are often used in articles. experiment, the part of speeches are simplified into 18 kinds shown in the following diagram 3.1: Diagram2.1 Abbreviated part-of-speech diagram 2.2 Concept of prosodic functional part of speech Part of speech Part of speech The word-syncopating and word-tagging in a sentence usually have been done before grapheme- pn Decorated word before noun n Noun phoneme conversion in the text-to-speech system. But pv Decorated word before verb v Verb it often adds many complicated tags besides the 26 part pm Decorated word before numeral m Numeral of speeches, (Such as some classified tags for proper bn Decorated word after noun d Adverb noun: nr represents name, ns represents location, nt bv Decorated word after verb q Measure word represents incorporation or department, nz represents bm Decorated word after numeral s Location word other proper nouns etc.), which have no use of nr Surname word p Preposition ascertaining pronunciations of polyphones. c Connected word u Auxiliary word t Time word r Pronoun Such as the following sentence: We suppose that Chinese contains three kinds of “我们系倒新来了几名留学生。” prosodic chunks shown in the diagram 3.2. As every Eight grammatical words can be extracted: prosodic chunk is usually composed by a central word ca(1)=“我们”，ca(2)=“系”，ca(3)=“倒”，ca(4)=“新”， and some decorated words before or after it, each kind ca(5)=“来了”，ca(6)=“几”，ca(7)=“名”…… of prosodic chunk adds three kinds of prosodic The sixth grammatical word “几” is pronounced “ji3” functional part of speeches. The difference between because the next grammatical word is a measure word. But the prosodic and grammatical part of speech is that the second and the third grammatical words are monomial former one can be a part of speech both for a single polyphones, whose pronunciations can not be ascertained only grammatical word and for a prosodic word. In fact, the by the neighboring grammatical words or the part of speeches. pronunciation of the polyphone is closely related to the part of speech of the prosodic chunk. In this paper, a new concept called “prosodic Diagram2.2 Prosodic functional part-of-speech diagram functional part of speech” is proposed. When Prosodic Former decorated Central Next decorated pronunciations of polyphones can not be ascertained by chunk word word word usual grammatical words or part of speeches, we can Decorated words noun Prefixal word： turn to their prosodic functional part of speeches. The with “的”: 快乐 （includes 叔叔、工程 concept of prosodic functional part of speech is 的，白的…… foreign 师…… syncopating a sentence into several prosodic chunks Nominal Ajective: 美丽、 symbols Words after and giving a prosodic part of speech to each chunk. prosodic 坏…… etc） institutions: 大 chunk Indicative pronoun, 学,院,局,…… Such as the former sentence can be syncopated into five chunks : pronoun: 这个、 surname Others: 附近、 ca(1)= “我们系”,ca(2)=“倒”，ca(3)=“新来了”， 由、从…… word 左右、得很、的、 ca(4)=“几名”，ca(5)=“留学生” Others: 十分,很, 了、的话、来说、 “系” and “我们” are combined into a nominal prosodic 国内,人均… 等等、之下…… chunk which avoids the ambiguity of pronunciation because “我 pn n,nr,p bn 们系” is apparently a noun and “系” is pronounced “ji4” only in Capable word:愿 Verb Decorated word “愿意” are decorated words before verb, then we 意,可以,能,…… （includes words with can confirm the pronunciation of the “种” is “zhong4”. Time, location 是、有） “ 得 ”: ( 叫 ) 得 In the second sentence, the “ 种 ” is pronounced adverb:在我国… 响,(吃)得快… “zhong3” because “一” is a numeral which helps us Verbal Adverb: 十分… Some auxiliary know that “种” is a decorated word after numeral. prosodic Onomatopoeic words:的,了… 2. Special words before or after polyphones. chunk word: 砰,镗,… Directional These considered grammatical words are usually Decorated words words:( 跑 ) 去 , beside the polyphone or a short distance away. Such as with “地”：积极 走(向),爬(上).. the following polyphone “和”: 地、快速地…… Others:着、不 “曲高和寡”、“和词” pronouced he4 Others:逐字、深 起、（吃）不了、 “豆沙里竟然和了点泥” pronouced huo4 入、让大家,…… 不已、过、以 “我打麻将和了三圈” pronouced hu2 pv v bv “我和他是好朋友” pronouced he2 Indicative Numeral Measure words: The pronunciation of the polyphone “ 和 ” is Numeral pronoun: 这个、 斤、年、吨公里、 greatly related to several special neighboring prosodic 由、从… 块钱、件事…… grammatical words, such as when the sentence contains chunk Others::约、占、 Others:的、正… some grammatical words like “诗”,”词”,”曲”, the 正、负…… pronunciation is “he4” and when the sentence contains pm m bm some grammatical words like “药”,”泥”,”面”, the pronunciation is “huo4” etc. 3. Special characters before or after polyphones； 2.3 Feature extracting This feature provides compensations to the former For convenient, we suppose that the pronunciation one when the grammatical syncopating is wrong. of the polyphone only depends on the related Such as: 他的/确有/事” (false syncopating) information of the words or phrases in the same clause. The pronunciation of “的” will not be falsely This suppose is adapted to many polyphones and we ascertained because of the rules: when “确” is after extract eight features to establish rules based on the “的” the polyphone “的” is mostly pronounced “di2”. grammatical and prosodic functional information. 4. The length of the words(phrases) before or 1. The grammatical and prosodic functional part after the polyphone or the place that is located: of speeches of the words before or after the Such as the polyphone “壳”: polyphone or the place that is located: “鸡蛋壳”、“外壳” pronouced ke2 This feature can handle both the single polyphone “地壳” pronouced qiao4 and the polyphonic word. Such as the polyphone “长”: As the pronunciation “qiao4” of “ 壳 ” only “这棵树长了三厘米”， pronouced zhang3 appears in the word “地壳”, we can ascertain that “壳” “衣服太长了” pronouced chang2 is pronounced “ke2” in a single grammatical word.
Load more

Recommended publications
  • 500 Natural Sciences and Mathematics
    500 500 Natural sciences and mathematics Natural sciences: sciences that deal with matter and energy, or with objects and processes observable in nature Class here interdisciplinary works on natural and applied sciences Class natural history in 508. Class scientific principles of a subject with the subject, plus notation 01 from Table 1, e.g., scientific principles of photography 770.1 For government policy on science, see 338.9; for applied sciences, see 600 See Manual at 231.7 vs. 213, 500, 576.8; also at 338.9 vs. 352.7, 500; also at 500 vs. 001 SUMMARY 500.2–.8 [Physical sciences, space sciences, groups of people] 501–509 Standard subdivisions and natural history 510 Mathematics 520 Astronomy and allied sciences 530 Physics 540 Chemistry and allied sciences 550 Earth sciences 560 Paleontology 570 Biology 580 Plants 590 Animals .2 Physical sciences For astronomy and allied sciences, see 520; for physics, see 530; for chemistry and allied sciences, see 540; for earth sciences, see 550 .5 Space sciences For astronomy, see 520; for earth sciences in other worlds, see 550. For space sciences aspects of a specific subject, see the subject, plus notation 091 from Table 1, e.g., chemical reactions in space 541.390919 See Manual at 520 vs. 500.5, 523.1, 530.1, 919.9 .8 Groups of people Add to base number 500.8 the numbers following —08 in notation 081–089 from Table 1, e.g., women in science 500.82 501 Philosophy and theory Class scientific method as a general research technique in 001.4; class scientific method applied in the natural sciences in 507.2 502 Miscellany 577 502 Dewey Decimal Classification 502 .8 Auxiliary techniques and procedures; apparatus, equipment, materials Including microscopy; microscopes; interdisciplinary works on microscopy Class stereology with compound microscopes, stereology with electron microscopes in 502; class interdisciplinary works on photomicrography in 778.3 For manufacture of microscopes, see 681.
    [Show full text]
  • The Romantext Format: a Flexible and Standard Method for Representing Roman Numeral Analyses
    THE ROMANTEXT FORMAT: A FLEXIBLE AND STANDARD METHOD FOR REPRESENTING ROMAN NUMERAL ANALYSES Dmitri Tymoczko1 Mark Gotham2 Michael Scott Cuthbert3 Christopher Ariza4 1 Princeton University, NJ 2 Cornell University, NY 3 M.I.T., MA 4 Independent [email protected], [email protected], [email protected] ABSTRACT Absolute chord labels are performer-oriented in the sense that they specify which notes should be played, but Roman numeral analysis has been central to the West- do not provide any information about their function or ern musician’s toolkit since its emergence in the early meaning: thus one and the same symbol can represent nineteenth century: it is an extremely popular method for a tonic, dominant, or subdominant chord. Accordingly, recording subjective analytical decisions about the chords these labels obscure a good deal of musical structure: a and keys implied by a passage of music. Disagreements dominant-functioned G major chord (i.e. G major in the about these judgments have led to extensive theoretical de- local key of C) is considerably more likely to descend by bates and ongoing controversies. Such debates are exac- perfect fifth than a subdominant-functioned G major (i.e. G erbated by the absence of a public corpus of expert Ro- major in the key of D major). This sort of contextual in- man numeral analyses, and by the more fundamental lack formation is readily available to both trained and untrained of an agreed-upon, computer-readable syntax in which listeners, who are typically more sensitive to relative scale those analyses might be expressed. This paper specifies degrees than absolute pitches.
    [Show full text]
  • Figured-Bass Notation
    MU 182: Theory II R. Vigil FIGURED-BASS NOTATION General In common-practice tonal music, chords are generally understood in two different ways. On the one hand, they can be seen as triadic structures emanating from a generative root . In this system, a root-position triad is understood as the "ideal" or "original" form, and other forms are understood as inversions , where the root has been placed above one of the other chord tones. This approach emphasizes the structural similarity of chords that share a common root (a first- inversion C major triad and a root-position C major triad are both C major triads). This type of thinking is represented analytically in the practice of applying Roman numerals to various chords within a given key - all chords with allegiance to the same Roman numeral are understood to be related, regardless of inversion and voicing, texture, etc. On the other hand, chords can be understood as vertical arrangements of tones above a given bass . This system is not based on a judgment as to the primacy of any particular chordal arrangement over another. Rather, it is simply a descriptive mechanism, for identifying what notes are present in addition to the bass. In this regime, chords are described in terms of the simplest possible arrangement of those notes as intervals above the bass. The intervals are represented as Arabic numerals (figures), and the resulting nomenclatural system is known as figured bass . Terminological Distinctions Between Roman Numeral Versus Figured Bass Approaches When dealing with Roman numerals, everything is understood in relation to the root; therefore, the components of a triad are the root, the third, and the fifth.
    [Show full text]
  • Notation Guide for Precalculus and Calculus Students
    Notation Guide for Precalculus and Calculus Students Sean Raleigh Last modified: August 27, 2007 Contents 1 Introduction 5 2 Expression versus equation 7 3 Handwritten math versus typed math 9 3.1 Numerals . 9 3.2 Letters . 10 4 Use of calculators 11 5 General organizational principles 15 5.1 Legibility of work . 15 5.2 Flow of work . 16 5.3 Using English . 18 6 Precalculus 21 6.1 Multiplication and division . 21 6.2 Fractions . 23 6.3 Functions and variables . 27 6.4 Roots . 29 6.5 Exponents . 30 6.6 Inequalities . 32 6.7 Trigonometry . 35 6.8 Logarithms . 38 6.9 Inverse functions . 40 6.10 Order of functions . 42 7 Simplification of answers 43 7.1 Redundant notation . 44 7.2 Factoring and expanding . 45 7.3 Basic algebra . 46 7.4 Domain matching . 47 7.5 Using identities . 50 7.6 Log functions and exponential functions . 51 7.7 Trig functions and inverse trig functions . 53 1 8 Limits 55 8.1 Limit notation . 55 8.2 Infinite limits . 57 9 Derivatives 59 9.1 Derivative notation . 59 9.1.1 Lagrange’s notation . 59 9.1.2 Leibniz’s notation . 60 9.1.3 Euler’s notation . 62 9.1.4 Newton’s notation . 63 9.1.5 Other notation issues . 63 9.2 Chain rule . 65 10 Integrals 67 10.1 Integral notation . 67 10.2 Definite integrals . 69 10.3 Indefinite integrals . 71 10.4 Integration by substitution . 72 10.5 Improper integrals . 77 11 Sequences and series 79 11.1 Sequences .
    [Show full text]
  • Grapheme-To-Phoneme Models for (Almost) Any Language
    Grapheme-to-Phoneme Models for (Almost) Any Language Aliya Deri and Kevin Knight Information Sciences Institute Department of Computer Science University of Southern California {aderi, knight}@isi.edu Abstract lang word pronunciation eng anybody e̞ n iː b ɒ d iː Grapheme-to-phoneme (g2p) models are pol żołądka z̻owon̪t̪ka rarely available in low-resource languages, ben শ嗍 s̪ ɔ k t̪ ɔ as the creation of training and evaluation ʁ a l o m o t חלומות heb data is expensive and time-consuming. We use Wiktionary to obtain more than 650k Table 1: Examples of English, Polish, Bengali, word-pronunciation pairs in more than 500 and Hebrew pronunciation dictionary entries, with languages. We then develop phoneme and pronunciations represented with the International language distance metrics based on phono- Phonetic Alphabet (IPA). logical and linguistic knowledge; apply- ing those, we adapt g2p models for high- word eng deu nld resource languages to create models for gift ɡ ɪ f tʰ ɡ ɪ f t ɣ ɪ f t related low-resource languages. We pro- class kʰ l æ s k l aː s k l ɑ s vide results for models for 229 adapted lan- send s e̞ n d z ɛ n t s ɛ n t guages. Table 2: Example pronunciations of English words 1 Introduction using English, German, and Dutch g2p models. Grapheme-to-phoneme (g2p) models convert words into pronunciations, and are ubiquitous in For most of the world’s more than 7,100 lan- speech- and text-processing systems. Due to the guages (Lewis et al., 2009), no data exists and the diversity of scripts, phoneme inventories, phono- many technologies enabled by g2p models are in- tactic constraints, and spelling conventions among accessible.
    [Show full text]
  • Style and Notation Guide
    Physical Review Style and Notation Guide Instructions for correct notation and style in preparation of REVTEX compuscripts and conventional manuscripts Published by The American Physical Society First Edition July 1983 Revised February 1993 Compiled and edited by Minor Revision June 2005 Anne Waldron, Peggy Judd, and Valerie Miller Minor Revision June 2011 Copyright 1993, by The American Physical Society Permission is granted to quote from this journal with the customary acknowledgment of the source. To reprint a figure, table or other excerpt requires, in addition, the consent of one of the original authors and notification of APS. No copying fee is required when copies of articles are made for educational or research purposes by individuals or libraries (including those at government and industrial institutions). Republication or reproduction for sale of articles or abstracts in this journal is permitted only under license from APS; in addition, APS may require that permission also be obtained from one of the authors. Address inquiries to the APS Administrative Editor (Editorial Office, 1 Research Rd., Box 1000, Ridge, NY 11961). Physical Review Style and Notation Guide Anne Waldron, Peggy Judd, and Valerie Miller (Received: ) Contents I. INTRODUCTION 2 II. STYLE INSTRUCTIONS FOR PARTS OF A MANUSCRIPT 2 A. Title ..................................................... 2 B. Author(s) name(s) . 2 C. Author(s) affiliation(s) . 2 D. Receipt date . 2 E. Abstract . 2 F. Physics and Astronomy Classification Scheme (PACS) indexing codes . 2 G. Main body of the paper|sequential organization . 2 1. Types of headings and section-head numbers . 3 2. Reference, figure, and table numbering . 3 3.
    [Show full text]
  • Scientific Notations for the Digital
    Scientific notations for the digital era Konrad Hinsen Centre de Biophysique Moléculaire (UPR4301 CNRS) Rue Charles Sadron, 45071 Orléans Cédex 2, France [email protected] Synchrotron SOLEIL, Division Expériences B.P. 48, 91192 Gif sur Yvette, France Abstract Computers have profoundly changed the way scientific research is done. Whereas the importance of computers as research tools is evident to every- one, the impact of the digital revolution on the representation of scientific knowledge is not yet widely recognized. An ever increasing part of today’s scientific knowledge is expressed, published, and archived exclusively in the form of software and electronic datasets. In this essay, I compare these digital scientific notations to the the traditional scientific notations that have been used for centuries, showing how the digital notations optimized for computerized processing are often an obstacle to scientific communi- cation and to creative work by human scientists. I analyze the causes and propose guidelines for the design of more human-friendly digital scientific notations. Note: This article is also available in the Self-Journal of Science, where it is open for public discussion and review. 1 Introduction arXiv:1605.02960v1 [physics.soc-ph] 10 May 2016 Today’s computing culture is focused on results. Computers and software are seen primarily as tools that get a job done. They are judged by the utility of the results they produce, by the resources (mainly time and energy) they consume, and by the effort required for their construction and maintenance. In fact, we have the same utilitarian attitude towards computers and software as towards other technical artifacts such as refrigerators or airplanes.
    [Show full text]
  • List of Mathematical Symbols by Subject from Wikipedia, the Free Encyclopedia
    List of mathematical symbols by subject From Wikipedia, the free encyclopedia This list of mathematical symbols by subject shows a selection of the most common symbols that are used in modern mathematical notation within formulas, grouped by mathematical topic. As it is virtually impossible to list all the symbols ever used in mathematics, only those symbols which occur often in mathematics or mathematics education are included. Many of the characters are standardized, for example in DIN 1302 General mathematical symbols or DIN EN ISO 80000-2 Quantities and units – Part 2: Mathematical signs for science and technology. The following list is largely limited to non-alphanumeric characters. It is divided by areas of mathematics and grouped within sub-regions. Some symbols have a different meaning depending on the context and appear accordingly several times in the list. Further information on the symbols and their meaning can be found in the respective linked articles. Contents 1 Guide 2 Set theory 2.1 Definition symbols 2.2 Set construction 2.3 Set operations 2.4 Set relations 2.5 Number sets 2.6 Cardinality 3 Arithmetic 3.1 Arithmetic operators 3.2 Equality signs 3.3 Comparison 3.4 Divisibility 3.5 Intervals 3.6 Elementary functions 3.7 Complex numbers 3.8 Mathematical constants 4 Calculus 4.1 Sequences and series 4.2 Functions 4.3 Limits 4.4 Asymptotic behaviour 4.5 Differential calculus 4.6 Integral calculus 4.7 Vector calculus 4.8 Topology 4.9 Functional analysis 5 Linear algebra and geometry 5.1 Elementary geometry 5.2 Vectors and matrices 5.3 Vector calculus 5.4 Matrix calculus 5.5 Vector spaces 6 Algebra 6.1 Relations 6.2 Group theory 6.3 Field theory 6.4 Ring theory 7 Combinatorics 8 Stochastics 8.1 Probability theory 8.2 Statistics 9 Logic 9.1 Operators 9.2 Quantifiers 9.3 Deduction symbols 10 See also 11 References 12 External links Guide The following information is provided for each mathematical symbol: Symbol: The symbol as it is represented by LaTeX.
    [Show full text]
  • Phonological Notations As Models*
    JOHN J.OHALA Phonological Notations as Models* Phonological notations need major overhaul. I would like to suggest how this can be succesfully done. My argument has four parts. First, I would like to make a simple distinction — well known in semiotics — between what I will call notations as symbols and notations as models. Notations which merely symbolize the thing they stand for are in all respects arbitrary in their form except insofar as they must be differentiated from other symbols used in the same context. Notations which model the thing they stand for are, in at least one respect, non- arbitrary in their form, that is. in some way they are or purport to be isomorphic with the thing they represent. A few simple examples of these two types of notations are given in Figure 1. In the case of the notation under the heading ‘symbols’, there is no recognizable part of the symbols that is isomorphic with any part of the entities they stand for. Only in Playboy cartoons and for humorous purposes is any' isomorphism suggested to exist between the scientific symbols for 'male' and 'female' and actual males and females. Likewise the graphic symbol '7' does not have seven distinct parts, although the tally mark for '7', on the other side, does. Words, of course, are well known as arbitrary symbols for the things or concepts they stand for. Thus, we do not find it inappropriate that the word 'big' is so small nor that the word 'microscopic' is relatively large. Most mathematical notations are symbols in this sense.
    [Show full text]
  • Roman Numerals Roman Numerals Are the Ancient Roman Counting System That Used Letters to Denote Quantities
    Roman Numerals Roman numerals are the ancient Roman counting system that used letters to denote quantities. In Western music, it can be common to use Roman numerals as a form of notation, indicating the position of the root note in each chord on the scale of that composition. If a piece is written in C major, then C major is the tonic chord, D is the second, E the third, etc. Roman numerals, therefore, indicate which chord the notes in the music belong to. If the Roman numerals are: I II III IV V VI VII VIII 1 2 3 4 5 6 7 8 I II III IV V VI VII VIII 1 2 3 4 5 6 7 8 Different Symbols If the Roman numerals are there to help you understand which chord those notes belong to, then why are some Roman numerals in upper case, while others are in lower case? That's because not all chords are the same. Different kinds of chords have different notations. There are four major ones. • When the Roman numerals are in upper case (I, IV, V, etc.), then the chord is major • If the Roman numerals are in lower case (i, iv, v, etc.), then the chord is minor • If the Roman numerals are in upper case with a plus sign next to them, then the chord is augmented • If the Roman numerals are in the lower case with a small circle next to them, then the chord is diminished Major Chord AIM Reference Roman Numerals - Page 1 2019 Copyright UMTA AIM Syllabus – May be copied by UMTA Members for their personal use only These notations matter because every scale has a natural progression of major and minor chords.
    [Show full text]
  • Introduction to General Chemistry Calculations and Concepts
    Preparatory Chemistry: Introduction to General Chemistry Calculations and Concepts ABOZENADAH BISHOP BITTNER FLATT LOPEZ WILEY Published by Western Oregon University under Creative Commons Licensing as Attribution-NonCommercial-ShareAlike CC BY-NC-SA 3.0 on Dec 15th, 2017 To Share or Adapt this Content please Reference: Abozenadah, H., Bishop, A., Bittner, S.. Flatt, P.M., Lopez, O., and Wiley, C. (2017) Con- sumer Chemistry: How Organic Chemistry Impacts Our Lives. CC BY-NC-SA. Available at: Cover photo adapted from: https://upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Chemicals_in_flasks. jpg/675px-Chemicals_in_flasks.jpg Chapter 1 materials have been adapted from the following creative commons resources unless otherwise noted: 1. Anonymous. (2012) Introduction to Chemistry: General, Organic, and Biological (V1.0). Published under Creative Commons by-nc-sa 3.0. Available at: http://2012books.lard- bucket.org/books/introduction-to-chemistry-general-organic-and-biological/index.html 2. Poulsen, T. (2010) Introduction to Chemistry. Published under Creative Commons by- nc-sa 3.0. Available at: http://openedgroup.org/books/Chemistry.pdf 3. OpenStax (2015) Atoms, Isotopes, Ions, and Molecules: The Building Blocks. OpenStax CNX.Available at: http://cnx.org/contents/be8818d0-2dba-4bf3-859a-737c25fb2c99@12. Table of Contents Section 1: Chemistry and Matter 4 What is Chemistry? 4 Physical vs. Chemical Properties 4 Elements and Compounds 5 Mixtures 7 States of Matter 8 Section 2: How Scientists Study Chemistry 10 The Scientific Method 10 Section 3: Scientific Notation 11 Section 4: Units of Measurement 14 International System of Units and the Metric System 14 Mass 16 Length 16 Temperature 17 Time 18 Amount 18 Derived SI Units 19 Volume 19 Energy 20 Density 20 Section 5: Making Measurements in the Lab 21 Precision vs.
    [Show full text]
  • 12 Notation and List of Symbols
    12 Notation and List of Symbols Alphabetic ℵ0, ℵ1, ℵ2,... cardinality of infinite sets ,r,s,... lines are usually denoted by lowercase italics Latin letters A,B,C,... points are usually denoted by uppercase Latin letters π,ρ,σ,... planes and surfaces are usually denoted by lowercase Greek letters N positive integers; natural numbers R real numbers C complex numbers 5 real part of a complex number 6 imaginary part of a complex number R2 Euclidean 2-dimensional plane (or space) P2 projective 2-dimensional plane (or space) RN Euclidean N-dimensional space PN projective N-dimensional space Symbols General ∈ belongs to such that ∃ there exists ∀ for all ⊂ subset of ∪ set union ∩ set intersection A. Inselberg, Parallel Coordinates, DOI 10.1007/978-0-387-68628-8, © Springer Science+Business Media, LLC 2009 532 Notation and List of Symbols ∅ empty st (null set) 2A power set of A, the set of all subsets of A ip inflection point of a curve n principal normal vector to a space curve nˆ unit normal vector to a surface t vector tangent to a space curve b binormal vector τ torsion (measures “non-planarity” of a space curve) × cross product → mapping symbol A → B correspondence (also used for duality) ⇒ implies ⇔ if and only if <, > less than, greater than |a| absolute value of a |b| length of vector b norm, length L1 L1 norm L L norm, Euclidean distance 2 2 summation Jp set of integers modulo p with the operations + and × ≈ approximately equal = not equal parallel ⊥ perpendicular, orthogonal (,,) homogeneous coordinates — ordered triple representing
    [Show full text]