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Thursday, May 14, 2020 | History

6 edition of Essay On Musical Intervals, Harmonics And The Temperament Of The Musical Scale found in the catalog.

Essay On Musical Intervals, Harmonics And The Temperament Of The Musical Scale

by Wesley Stoker B. Woolhouse

  • 60 Want to read
  • 11 Currently reading

Published by Kessinger Publishing, LLC .
Written in English


The Physical Object
FormatHardcover
Number of Pages108
ID Numbers
Open LibraryOL10520431M
ISBN 100548180423
ISBN 109780548180426
OCLC/WorldCa179777254

The Harmonic Series Edit. An illustration of the harmonic series in musical notation. The numbers above the harmonic indicate the number of cents difference from equal temperament (rounded to the nearest cent). Blue notes are flat and red notes are sharp. Harmonic series as musical notation with intervals between harmonics labeled. In music, 19 equal temperament, called 19 TET, 19 EDO ("Equal Division of the Octave"), or 19 ET, is the tempered scale derived by dividing the octave into 19 equal steps (equal frequency ratios). Each step represents a frequency ratio of 19 √2, or cents (Play).

A History of Widely Used Medieval and Renaissance Tunings and Temperaments and Their Role in Modern Performance and Recording For much of the twentieth century, one specific system of tuning the pitches of our twelve-tone scale has enjoyed almost exclusive and unchallenged usage, a trait shared by no other tuning system. 1 Known as equal temperament, it is the straightforward concept of. An interesting musical scale may be defined by letting successive tones have the ratios to one another of the natural logarithms of successive whole numbers. While melodies in the scale sound somewhat exotic, novel musical possibilities arise from mathematical properties of logarithms, particularly with respect to the construction of chords.

Now in paper for the first time, Bitter Music is a generous volume of writings by one of the twentieth century's great musical iconoclasts. Rejecting the equal temperament and concert traditions that have dominated western music, Harry Partch adopted the pure intervals of just intonation and devised a tone-to-the-octave scale, which in turn forced him into inventing numerous musical 4/5(1). The equal tempered scale usually refers to the musical scale with 12 equal divisions of the octave, but here I take an equal-tempered scale to be any scale where the frequency of each note is related to the next by a constant multiplier. For example, in the standard note equal-tempered scale (which I will call E12 from now on) we go up by.


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Essay On Musical Intervals, Harmonics And The Temperament Of The Musical Scale by Wesley Stoker B. Woolhouse Download PDF EPUB FB2

Essay on musical intervals, harmonics, and the temperament of the musical scale, &c 3d key-note latter length limma logarithms major Major-sixth Major-third major-tone mean semitones melody minor-tone monochord motion MUSICAL INTERVALS musical scale musical sounds musical string musicians number of beats number of equal number of vibrations.

Essay on Musical Intervals, Harmonics, and the Temperament of the Musical Scale, &c. Souter, London. xii + 84 p. This small book is divided into 48 'articles', which are grouped into 6 chapters: Sound Musical Intervals Harmonics Temperament Beats of Imperfect Concords Miscellaneous Additions.

Add tags for "Essay on musical intervals, harmonics, and the temperament of the musical scale, &c.,". Be the first. cents of pure intervals 38 analysis of deviations using the cent 39 evaluation of equal temperament 41 evaluation method for unequal temperaments 43 evaluation of pythagorean intonation 44 harmonic waste of the fifths 46 harmonic waste of the major thirds The Harmonic Series: A path to understanding musical intervals, scales, tuning and timbre.

by Reginald Bain Page - 3 - String Length and Musical Interval Fig. 3 shows an illustration of a monochord that appeared in Hindemith's book. Fig. A monochord.

A monochord is a simple instrument used by theorists since the Middle Ages to investigate theFile Size: 59KB. An old construction of the musical scale going back to Pythagoras (at least) is based on a series of six intervals of a 5 th, the ratio in frequency, which generates the seven notes of the octave in this order: F C G D A E B.

(to put the notes back in order of ascending pitch. Scales: Just vs Equal Temperament (and related topics) The "Just Scale" (sometimes referred to as "harmonic tuning" or "Helmholtz's scale") occurs naturally as a result of the overtone series for simple systems such as vibrating strings or air columns.

All the notes in the scale. Simple and Compound Intervals The 3rd Harmonic and the Interval of a Fifth Inversion of an Interval and the Interval of a Fourth The 5th Harmonic and the Intervals of a Third Consonance, Dissonance and Harmonic Intervals.

2 ANCIENT GREEK ORIGINS OF THE WESTERN MUSICAL SCALE Proportion and Harmony Tetrachord. On equal temperament this is uniformly dull, and music of this type fails dismally to engage the listener.

However, in meantone tuning a quite different picture emerges. The half-steps of the scale are all of differing sizes, and the chromatic scale, far from being smooth and oily, becomes a bumpy, eccentric and challenging affair.

In musical tuning, a temperament is a tuning system that slightly compromises the pure intervals of just intonation to meet other requirements. Most modern Western musical instruments are tuned in the equal temperament system. Tempering is the process of altering the size of an interval by making it narrower or wider than pure.

A temperament is any plan that describes the adjustments to the sizes of some or all of the twelve fifth intervals. Chapter 3: Modes, overtones, and harmonics 27 ACTIVITY: Interpreting Musical Instrument Power Spectra 34 Beginning to Think About Musical Scales 37 Beats 38 Chapter 4: Musical Scales 40 ACTIVITY: Consonance 44 The Pythagorean Scale 45 The Just Intonation Scale 47 The Equal Temperament Scale 50 A Critical Comparison of Scales His book, Essays on Musical Intervals, Harmonics, and the Temperament of the Musical Scale, advocated tone equal temperament and used a division of the octave into parts, now designated as Woolhouse units, for measuring musical intervals.

He is credited with a formula for numerical integration. First, a normal example in standard tone equal temperament; Now, the same tune played with all the overtones "stretched" so they no longer correspond to the harmonic series: standard music intervals now sound dissonant; But what if we stretch the scale underlying the tune too.

A great book, but understand what it is before you buy it. It addresses the HISTORY of temperament and tuning, not temperament itself. Specifically, it focuses on how an understanding of tuning and temperament followed the growth of intellectual development in western civilization.4/4(74).

An Elementary Treatise on Musical Intervals and Temperament (Bosanquet, Robert Holford Macdowall) An Essay on Musical Expression (Avison, Charles) An Essay on Practical Music Composition (Kollmann, Augustus Frederic Christopher) An Essay Theoretical and Practical (Gunn, John) An Essay Towards a Rational System of Music (Holden, John).

The Development of the Equal Temperament Scale 6 By substitution these equations arise: '' 0 '' '' + = − = =− m ky y m ky y my ky Since this is a study of pitch, this representation of a musical sound does not include harmonics, which will be discussed in the next chapter.

The functions that satisfy the. The scale of harmonics is a musical scale based on the noded positions of the natural harmonics existing on a string. This musical scale is present on the guqin, regarded as one of the first string instruments with a musical scale.

Most fret positions appearing on Non-Western string instruments are equal to positions of this scale. Unexpectedly, these fret positions are actually the corresponding undertones of the overtones from the harmonic series.

How Equal Temperament Ruined Harmony book. Read 38 reviews from the world's largest community for readers. Ross W. Duffin presents an engaging and elegantly reasoned exposé of musical temperament and its impact on the way in which we experience music.

This was an eye opening work for me regarding how the standard scale of music came to /5. The Mathematics of Musical Instruments Rachel W. Hall and Kre simir Josi c Sethares’ fascinating book [25] proposes that Western music uses scales based on small integer ratios of frequencies precisely because the sound of winds and strings consists of harmonics.

When two such instruments play notes from the same scale, many of the. A musical scale consists of several tones (usually 12) at well-defined intervals between a tonic and the octave (twice the frequency of the tonic). If all the tones are raised by one octave by multiplying their frequencies by 2, the new, higher tones have exactly the same musical and mathematical relationships with one another as before.

Thus the musical effect of the harmonic major scale is a sound intermediate between harmonic minor and diatonic major, and partaking of both. The harmonic major scale may be used in any system of meantone tuning, such as 19 equal temperament or 31 equal temperament, as well as 12 equal temperament.Lab 10 The Harmonic Series, Scales, Tuning, and Cents Musical Intervals An interval in music is defined as the distance between two notes.

In western European music intervals are named both by the number of inclusive half steps between the two notes and also by the inclusive number of lines and spaces separating the notes on the music Size: 1MB.A musical scale is a discrete set of pitches used in making or describing music.

The most important scale in the Western tradition is the diatonic scale but many others have been used and proposed in various historical eras and parts of the world.

Each pitch corresponds to a particular frequency, expressed in hertz (Hz), sometimes referred to as cycles per second (c.p.s.).