Bohlen-Pierce Chromatic Scale in Steps ID: HG-25 ID: HG-26 ID: HG-27 Medium: Iron Gall Ink on Yupo Medium: Graphite and Red Correction Pencil on Yu

Total Page:16

File Type:pdf, Size:1020Kb

Bohlen-Pierce Chromatic Scale in Steps ID: HG-25 ID: HG-26 ID: HG-27 Medium: Iron Gall Ink on Yupo Medium: Graphite and Red Correction Pencil on Yu Title: Bohlen-Pierce Chromatic Just Scale in Ratios Title: Bohlen-Pierce Chromatic Scale in Steps Title: Bohlen-Pierce Chromatic Scale in Steps ID: HG-25 ID: HG-26 ID: HG-27 Medium: iron gall ink on Yupo Medium: graphite and red correction pencil on Yu... Medium: iron gall ink on Yupo Dimensions: 6" x 6" Dimensions: 6" x 6" Dimensions: 6" x 6" Dated: 05/30/2017 Dated: 06/05/2017 Dated: 05/30/2017 Title: Bohlen-Pierce Just Intonation Intervals Title: Dissonant intervals mapped in degrees around a circle Title: Equal Temperament: 53-tone scale ID: HG-28 octave ID: HG-76 Medium: graphite and colored pencil on Yupo ID: HG-63 Medium: graphite and red pencil on Yupo Dimensions: 21" diameter Medium: graphite and red pencil on Yupo Dimensions: 6" diameter Dated: 08/14/2017 Dimensions: 6" diameter Dated: 08/18/2017 Dated: 08/18/2017 Title: Equal-Temperament: 12-tone Pythagorean interval Title: Frequencies of the Equal Tempered Scale Title: Frequencies of the Equal Tempered Scale cents mapped in degrees around an octave ID: HG-105 ID: HG-107 ID: HG-77 Medium: graphite on Yupo Medium: incised lines of panel Medium: graphite and red pencil on Yupo Dimensions: 5.5" x 5.5" Dimensions: 6" x 6" Dimensions: 6" diameter Dated: 05/21/2017 Dated: 04/30/2017 Dated: 08/18/2017 Title: Frequencies of the Equal-Tempered Scale Title: Frequencies of the Equal-Tempered Scale Title: Harry Partch's 43-tone Genesis Scale ID: HG-108 ID: HG-109 ID: HG-122 Medium: iron gall ink on Yupo Medium: Hero #232 ink on bristol Medium: graphite and red pencil on Yupo Dimensions: 5.5" x 5.5" Dimensions: 17" x 16" Dimensions: 12" diameter Dated: 05/18/2017 Dated: 04/28/2017 Dated: 08/09/2017 Title: Harry Partch's 43-tone Genesis Scale Title: Hindustani 22-Sruti Scale Title: Internal Structure of the 22 Sruti Scale ID: HG-123 ID: HG-130 ID: HG-166 Medium: iron gall ink on Yupo Medium: graphite and red pencil on Yupo Medium: iron gall ink on Yupo Dimensions: 17" x 16-3/4" Dimensions: 12" diameter Dimensions: 6" x 6" Dated: 08/09/2017 Dated: 08/09/2017 Dated: 05/30/2017 Title: Internal Structure of the 22-Sruti Scale Title: Internal Structure of the 22-Sruti Scale Title: Just Chromatic Scale in C transposed visually to 10.5 ID: HG-167 ID: HG-168 ID: HG-172 Medium: iron gall ink on Yupo Medium: oil on canvas Medium: graphite and red correction pencil on Yu... Dimensions: 11" x 11" Dimensions: 32" x 38" Dimensions: 30" x 22" Dated: 06/11/2017 Dated: 06/01/2017 Dated: 05/08/2017 Title: Natural Chromatic Scale Title: Ptolemy's Syntonic Diatonic Scale Title: Ptolemy's Syntonic Diatonic Scale ID: HG-208 ID: HG-270 ID: HG-271 Medium: graphite and red correction pencil on Yu... Medium: graphite and red pencil on Yupo Medium: iron gall ink on Yupo Dimensions: 30" x 22" Dimensions: 6" diameter Dimensions: 6" x 6" Dated: 05/11/2017 Dated: 08/18/2017 Dated: 05/24/2017 Title: Ptolemy's Syntonic Diatonic Scale Title: Ptolemy's Syntonic Diatonic Scale Title: Ptolemy's Syntonic Diatonic Scale in Ratios ID: HG-272 ID: HG-273 ID: HG-274 Medium: iron gall ink on Yupo Medium: incised lines on panel Medium: graphite on Yupo Dimensions: 5.5" x 5.5" Dimensions: 6" x 6" Dimensions: 5.5" x 5.5" Dated: 05/17/2017 Dated: 05/22/2017 Dated: 05/16/2017 Title: Pythagorean intonation mapped as a series of 26 Title: Pythagorean Scale in D Title: Pythagorean Scale in D perfect fifths ID: HG-277 ID: HG-278 ID: HG-276 Medium: graphite on Yupo Medium: incised lines on panel Medium: graphite and colored pencil on Yupo Dimensions: 5.5" x 5.5" Dimensions: 6" x 6" Dimensions: 8-1/4" diameter Dated: 05/21/2017 Dated: 05/04/2017 Dated: 08/22/17 Title: Pythagorean Scale in D, one octave Title: Pythagorean Scale in D, one octave Title: Pythagorean Tuning Mapped in Centimeters ID: HG-279 ID: HG-280 ID: HG-281 Medium: iron gall ink on Yupo Medium: iron gall ink on Yupo Medium: graphite and red correction pencil on Yu... Dimensions: 6" x 6" Dimensions: 5.5" x 5.5" Dimensions: 30" x 22" Dated: 05/24/2017 Dated: 05/18/2017 Dated: 05/06/2017 Title: Sisyphean Scale Title: Frequencies of the Equal Tempered Scale Title: ID: HG-297 ID: HG-106 ID: Medium: oil on panel Medium: oil on canvas Medium: Dimensions: 36" x 48" Dimensions: 30" x 30" Dimensions: Dated: 06/15/2017 Dated: 06/01/2017 Dated:.
Recommended publications
  • Development of Musical Scales in Europe
    RABINDRA BHARATI UNIVERSITY VOCAL MUSIC DEPARTMENT COURSE - B.A. ( Compulsory Course ) (CBCS) 2020 Semester - II , Paper - I Teacher - Sri Partha Pratim Bhowmik History of Western Music Development of musical scales in Europe In the 8th century B.C., The musical atmosphere of ancient Greece introduced its development by the influence of then popular aristocratic music. That music was melody- based and the root of that music was rural folk-songs. In each and every country, the development of music was rooted in the folk-songs. The European Aristocratic Music of the Christian Era had been inspired by the developed Greek music. In the 5th century B.C. the renowned Greek Mathematician Pythagoras had first established a relation between science and music. Before him, the scale of Greek music was pentatonic. Pythagoras changed the scale into hexatonic pattern and later into heptatonic pattern. Greek musicians applied the alphabets to indicate the notes of their music. For the natural notes they used the alphabets in normal position and for the deformed notes, the alphabets turned upside down [deformed notes= Vikrita svaras]. The musical instruments, they had invented are – Aulos, Salpinx, pan-pipes, harp, lyre, syrinx etc. In the western music, the term ‘scale’ is derived from Latin word ‘scala’, ie, the ladder; scale means an ascent or descent formation of the musical notes. Each and every scale has a starting note, called ‘tonic note’ [‘tone - tonic’ not the Health-Tonic]. In the Ancient Greece, the musical scale had been formed with the help of lyre , a string instrument, having normally 5 or 6 or 7 strings.
    [Show full text]
  • 3 Manual Microtonal Organ Ruben Sverre Gjertsen 2013
    3 Manual Microtonal Organ http://www.bek.no/~ruben/Research/Downloads/software.html Ruben Sverre Gjertsen 2013 An interface to existing software A motivation for creating this instrument has been an interest for gaining experience with a large range of intonation systems. This software instrument is built with Max 61, as an interface to the Fluidsynth object2. Fluidsynth offers possibilities for retuning soundfont banks (Sf2 format) to 12-tone or full-register tunings. Max 6 introduced the dictionary format, which has been useful for creating a tuning database in text format, as well as storing presets. This tuning database can naturally be expanded by users, if tunings are written in the syntax read by this instrument. The freely available Jeux organ soundfont3 has been used as a default soundfont, while any instrument in the sf2 format can be loaded. The organ interface The organ window 3 MIDI Keyboards This instrument contains 3 separate fluidsynth modules, named Manual 1-3. 3 keysliders can be played staccato by the mouse for testing, while the most musically sufficient option is performing from connected MIDI keyboards. Available inputs will be automatically recognized and can be selected from the menus. To keep some of the manuals silent, select the bottom alternative "to 2ManualMicroORGANircamSpat 1", which will not receive MIDI signal, unless another program (for instance Sibelius) is sending them. A separate menu can be used to select a foot trigger. The red toggle must be pressed for this to be active. This has been tested with Behringer FCB1010 triggers. Other devices could possibly require adjustments to the patch.
    [Show full text]
  • Unified Music Theories for General Equal-Temperament Systems
    Unified Music Theories for General Equal-Temperament Systems Brandon Tingyeh Wu Research Assistant, Research Center for Information Technology Innovation, Academia Sinica, Taipei, Taiwan ABSTRACT Why are white and black piano keys in an octave arranged as they are today? This article examines the relations between abstract algebra and key signature, scales, degrees, and keyboard configurations in general equal-temperament systems. Without confining the study to the twelve-tone equal-temperament (12-TET) system, we propose a set of basic axioms based on musical observations. The axioms may lead to scales that are reasonable both mathematically and musically in any equal- temperament system. We reexamine the mathematical understandings and interpretations of ideas in classical music theory, such as the circle of fifths, enharmonic equivalent, degrees such as the dominant and the subdominant, and the leading tone, and endow them with meaning outside of the 12-TET system. In the process of deriving scales, we create various kinds of sequences to describe facts in music theory, and we name these sequences systematically and unambiguously with the aim to facilitate future research. - 1 - 1. INTRODUCTION Keyboard configuration and combinatorics The concept of key signatures is based on keyboard-like instruments, such as the piano. If all twelve keys in an octave were white, accidentals and key signatures would be meaningless. Therefore, the arrangement of black and white keys is of crucial importance, and keyboard configuration directly affects scales, degrees, key signatures, and even music theory. To debate the key configuration of the twelve- tone equal-temperament (12-TET) system is of little value because the piano keyboard arrangement is considered the foundation of almost all classical music theories.
    [Show full text]
  • Nora-Louise Müller the Bohlen-Pierce Clarinet An
    Nora-Louise Müller The Bohlen-Pierce Clarinet An Introduction to Acoustics and Playing Technique The Bohlen-Pierce scale was discovered in the 1970s and 1980s by Heinz Bohlen and John R. Pierce respectively. Due to a lack of instruments which were able to play the scale, hardly any compositions in Bohlen-Pierce could be found in the past. Just a few composers who work in electronic music used the scale – until the Canadian woodwind maker Stephen Fox created a Bohlen-Pierce clarinet, instigated by Georg Hajdu, professor of multimedia composition at Hochschule für Musik und Theater Hamburg. Hence the number of Bohlen- Pierce compositions using the new instrument is increasing constantly. This article gives a short introduction to the characteristics of the Bohlen-Pierce scale and an overview about Bohlen-Pierce clarinets and their playing technique. The Bohlen-Pierce scale Unlike the scales of most tone systems, it is not the octave that forms the repeating frame of the Bohlen-Pierce scale, but the perfect twelfth (octave plus fifth), dividing it into 13 steps, according to various mathematical considerations. The result is an alternative harmonic system that opens new possibilities to contemporary and future music. Acoustically speaking, the octave's frequency ratio 1:2 is replaced by the ratio 1:3 in the Bohlen-Pierce scale, making the perfect twelfth an analogy to the octave. This interval is defined as the point of reference to which the scale aligns. The perfect twelfth, or as Pierce named it, the tritave (due to the 1:3 ratio) is achieved with 13 tone steps.
    [Show full text]
  • Microtonality As an Expressive Device: an Approach for the Contemporary Saxophonist
    Technological University Dublin ARROW@TU Dublin Dissertations Conservatory of Music and Drama 2009 Microtonality as an Expressive Device: an Approach for the Contemporary Saxophonist Seán Mac Erlaine Technological University Dublin, [email protected] Follow this and additional works at: https://arrow.tudublin.ie/aaconmusdiss Part of the Composition Commons, Musicology Commons, Music Pedagogy Commons, Music Performance Commons, and the Music Theory Commons Recommended Citation Mac Erlaine, S.: Microtonality as an Expressive Device: an Approach for the Contemporary Saxophonist. Masters Dissertation. Technological University Dublin, 2009. This Dissertation is brought to you for free and open access by the Conservatory of Music and Drama at ARROW@TU Dublin. It has been accepted for inclusion in Dissertations by an authorized administrator of ARROW@TU Dublin. For more information, please contact [email protected], [email protected]. This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License Microtonality as an expressive device: An approach for the contemporary saxophonist September 2009 Seán Mac Erlaine www.sean-og.com Table of Contents Abstract i Introduction ii CHAPTER ONE 1 1.1 Tuning Theory 1 1.1.1 Tuning Discrepancies 1 1.2 Temperament for Keyboard Instruments 2 1.3 Non‐fixed Intonation Instruments 5 1.4 Dominance of Equal Temperament 7 1.5 The Evolution of Equal Temperament: Microtonality 9 CHAPTER TWO 11 2.1 Twentieth Century Tradition of Microtonality 11 2.2 Use of Microtonality
    [Show full text]
  • A Study of Microtones in Pop Music
    University of Huddersfield Repository Chadwin, Daniel James Applying microtonality to pop songwriting: A study of microtones in pop music Original Citation Chadwin, Daniel James (2019) Applying microtonality to pop songwriting: A study of microtones in pop music. Masters thesis, University of Huddersfield. This version is available at http://eprints.hud.ac.uk/id/eprint/34977/ The University Repository is a digital collection of the research output of the University, available on Open Access. Copyright and Moral Rights for the items on this site are retained by the individual author and/or other copyright owners. Users may access full items free of charge; copies of full text items generally can be reproduced, displayed or performed and given to third parties in any format or medium for personal research or study, educational or not-for-profit purposes without prior permission or charge, provided: • The authors, title and full bibliographic details is credited in any copy; • A hyperlink and/or URL is included for the original metadata page; and • The content is not changed in any way. For more information, including our policy and submission procedure, please contact the Repository Team at: [email protected]. http://eprints.hud.ac.uk/ Applying microtonality to pop songwriting A study of microtones in pop music Daniel James Chadwin Student number: 1568815 A thesis submitted to the University of Huddersfield in partial fulfilment of the requirements for the degree of Master of Arts University of Huddersfield May 2019 1 Abstract While temperament and expanded tunings have not been widely adopted by pop and rock musicians historically speaking, there has recently been an increased interest in microtones from modern artists and in online discussion.
    [Show full text]
  • The Chromatic Scale
    Getting to Know Your Guitar: The Chromatic Scale Your Guitar is designed as a chromatic instrument – that is, guitar frets represent chromatic “semi- tones” or “half-steps” up and down the guitar fretboard. This enables you to play scales and chords in any key, and handle pretty much any music that comes from the musical traditions of the Western world. In this sense, the chromatic scale is more foundational than it is useful as a soloing tool. Put another way, almost all of the music you will ever play will be made interesting not by the use of the chromatic scale, but by the absence of many of the notes of the chromatic scale! All keys, chords, scales, melodies and harmonies, could be seen simply the chromatic scale minus some notes. For all the examples that follow, play up and down (both ascending and descending) the fretboard. Here is what you need to know in order to understand The Chromatic Scale: 1) The musical alphabet contains 7 letters: A, B, C, D, E, F, G. The notes that are represented by those 7 letters we will call the “Natural” notes 2) There are other notes in-between the 7 natural notes that we’ll call “Accidental” notes. They are formed by taking one of the natural notes and either raising its pitch up, or lowering its pitch down. When we raise a note up, we call it “Sharp” and use the symbol “#” after the note name. So, if you see D#, say “D sharp”. When we lower the note, we call it “Flat” and use the symbol “b” after the note.
    [Show full text]
  • Universal Tuning Editor
    Universal Tuning Editor Ηπ INSTRUMENTS Aaron Andrew Hunt Ηπ INSTRUMENTS hpi.zentral.zone · Universal Tuning Editor · documentation v11 1.May.2021 Changes from Previous Documentation 5 Current Version, v11 — 1. May 2021 ....................................................................5 Previous Versions ............................................................................................5 Introduction 9 Features List .................................................................................................9 User Interface Basics ......................................................................................11 Maximising the Detail View ..............................................................................12 Maximising the Tuning List ..............................................................................13 Toolbar .......................................................................................................13 Bug Reporting & Feedback ...............................................................................14 Feature Requests ..........................................................................................14 File Handling 15 Preferences ..................................................................................................15 Auto store unsaved projects internally ...............................................................15 Restore external projects at next session ...........................................................15 Prompt to handle each open project
    [Show full text]
  • In Search of the Perfect Musical Scale
    In Search of the Perfect Musical Scale J. N. Hooker Carnegie Mellon University, Pittsburgh, USA [email protected] May 2017 Abstract We analyze results of a search for alternative musical scales that share the main advantages of classical scales: pitch frequencies that bear simple ratios to each other, and multiple keys based on an un- derlying chromatic scale with tempered tuning. The search is based on combinatorics and a constraint programming model that assigns frequency ratios to intervals. We find that certain 11-note scales on a 19-note chromatic stand out as superior to all others. These scales enjoy harmonic and structural possibilities that go significantly beyond what is available in classical scales and therefore provide a possible medium for innovative musical composition. 1 Introduction The classical major and minor scales of Western music have two attractive characteristics: pitch frequencies that bear simple ratios to each other, and multiple keys based on an underlying chromatic scale with tempered tuning. Simple ratios allow for rich and intelligible harmonies, while multiple keys greatly expand possibilities for complex musical structure. While these tra- ditional scales have provided the basis for a fabulous outpouring of musical creativity over several centuries, one might ask whether they provide the natural or inevitable framework for music. Perhaps there are alternative scales with the same favorable characteristics|simple ratios and multiple keys|that could unleash even greater creativity. This paper summarizes the results of a recent study [8] that undertook a systematic search for musically appealing alternative scales. The search 1 restricts itself to diatonic scales, whose adjacent notes are separated by a whole tone or semitone.
    [Show full text]
  • Mto.95.1.4.Cuciurean
    Volume 1, Number 4, July 1995 Copyright © 1995 Society for Music Theory John D. Cuciurean KEYWORDS: scale, interval, equal temperament, mean-tone temperament, Pythagorean tuning, group theory, diatonic scale, music cognition ABSTRACT: In Mathematical Models of Musical Scales, Mark Lindley and Ronald Turner-Smith attempt to model scales by rejecting traditional Pythagorean ideas and applying modern algebraic techniques of group theory. In a recent MTO collaboration, the same authors summarize their work with less emphasis on the mathematical apparatus. This review complements that article, discussing sections of the book the article ignores and examining unique aspects of their models. [1] From the earliest known music-theoretical writings of the ancient Greeks, mathematics has played a crucial role in the development of our understanding of the mechanics of music. Mathematics not only proves useful as a tool for defining the physical characteristics of sound, but abstractly underlies many of the current methods of analysis. Following Pythagorean models, theorists from the middle ages to the present day who are concerned with intonation and tuning use proportions and ratios as the primary language in their music-theoretic discourse. However, few theorists in dealing with scales have incorporated abstract algebraic concepts in as systematic a manner as the recent collaboration between music scholar Mark Lindley and mathematician Ronald Turner-Smith.(1) In their new treatise, Mathematical Models of Musical Scales: A New Approach, the authors “reject the ancient Pythagorean idea that music somehow &lsquois’ number, and . show how to design mathematical models for musical scales and systems according to some more modern principles” (7).
    [Show full text]
  • European Philosophy and the Triumph of Equal Temperament/ Noel David Hudson University of Massachusetts Amherst
    University of Massachusetts Amherst ScholarWorks@UMass Amherst Masters Theses 1911 - February 2014 2007 Abandoning nature :: European philosophy and the triumph of equal temperament/ Noel David Hudson University of Massachusetts Amherst Follow this and additional works at: https://scholarworks.umass.edu/theses Hudson, Noel David, "Abandoning nature :: European philosophy and the triumph of equal temperament/" (2007). Masters Theses 1911 - February 2014. 1628. Retrieved from https://scholarworks.umass.edu/theses/1628 This thesis is brought to you for free and open access by ScholarWorks@UMass Amherst. It has been accepted for inclusion in Masters Theses 1911 - February 2014 by an authorized administrator of ScholarWorks@UMass Amherst. For more information, please contact [email protected]. ABANDONING NATURE: EUROPEAN PHILOSOPHY AND THE TRIUMPH OF EQUAL TEMPERAMENT A Thesis Presented by NOEL DAVID HUDSON Submitted to the Graduate School of the University of Massachusetts Amherst in partial fulfillment of the requirements for the degree of MASTER OF ARTS February 2007 UMASS/Five College Graduate Program in History © Copyright by Noel David Hudson 2006 All Rights Reserved ABANDONING NATURE: EUROPEAN PHILOSOPHY AND THE TRIUMPH OF EQUAL TEMPERAMENT A Thesis Presented by NOEL DAVID HUDSON Approved as to style and content by: Daniel Gordon, th^ir Bruce Laurie, Member Brian Ogilvie, Member Audrey Altstadt, Department Head Department of History CONTKNTS ( HAPTER Page 1. [NTR0D1 f< i ion 2. what is TEMPERAMENT? 3. THE CLASSICAL LEGACY 4. THE ENGLISH, MUSICAL INSTRUMENTS, AND OTHER PROBLEMS 5. A TROUBLING SOLUTION (>. ANCIEN1 HABITS OF MUSICAL THOUGHT IN THE "NEW PHILOSOPHY" 7. FROM THEORY TO PRACTICE X. A THEORETICAL INTERLUDE 9.
    [Show full text]
  • Theory IV – Study Guide Dr. Amy Dunker Clarke College Dubuque, IA 52001 Classical Serialism Arnold Schoenb
    Theory IV – Study Guide Dr. Amy Dunker Clarke College Dubuque, IA 52001 www.amydunker.com Classical Serialism Arnold Schoenberg composed the first twelve-tone piece in the summer of 1921 (Suite, Op. 25 (completed in 1923). Schoenberg had developed a method of composing with twelve tones that are related only with one another. He saw twelve-tone or serial composition as the natural extension of chromaticism on the tonal system. Anton Webern and Alban Berg: Schoenberg’s two pupils who composed in the twelve- tone method. Tone Row (also called , Row, Set, Basic Set, Series): an arrangement of the twelve pitches of the chromatic scale so that no notes repeat (except immediately after it is heard and trills/tremolos) until all pitches of the row have sounded in order. Dodecaphonic Scale: Twelve tone scale Four Forms of the Tone Row: Prime: The original set (do not confuse this with the terms use in Non-Serial Atonality) Retrograde: The original set in reverse order (i.e. backwards) Inversion: The mirror inversion of the original set Retrograde Inversion: The inversion in reverse order Abbreviations: P=Prime R=Retrograde I=Inversion RI=Retrograde Inversion *In addition, each of the four basic forms has twelve transpositions Order Numbers: numbers assigned to the row which indicate each notes intervallic distance from the first note of the row. The first note of the row is assigned the number zero (0). Twelve-Tone Matrix (“Magic Square”): a method of determining all 48 possible versions of the tone row. To construct a Twelve-Tone Matrix do the following: 1.) Fill in the Prime or Original row across the top ( from left to right) using the row’s order numbers.
    [Show full text]