{"id":85,"date":"2023-04-24T18:29:25","date_gmt":"2023-04-24T18:29:25","guid":{"rendered":"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/chapter\/intervals\/"},"modified":"2025-08-12T21:47:51","modified_gmt":"2025-08-12T21:47:51","slug":"intervals","status":"publish","type":"chapter","link":"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/chapter\/intervals\/","title":{"raw":"Intervals","rendered":"Intervals"},"content":{"raw":"<div class=\"intervals\">\r\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Learning goals for Chapter 5<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p class=\"import-Normal\">In this chapter, we will learn:<\/p>\r\n\r\n<ul>\r\n \t<li>How to construct and identify intervals<\/li>\r\n \t<li>How to use interval inversion<\/li>\r\n \t<li>How to aurally identify intervals<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<h1><a id=\"Major and minor intervals\"><\/a>Major and minor intervals<\/h1>\r\n<p class=\"import-Normal\">An [pb_glossary id=\"344\"]interval[\/pb_glossary] measures the distance between two pitches and consists of two parts, a [pb_glossary id=\"872\"]quantity[\/pb_glossary] (a number) and a [pb_glossary id=\"871\"]quality[\/pb_glossary] (major, \"MA\" or \"M\"; minor, \"mi\" or \"m\"; perfect, \"P\"; diminished, \"d\" or \"o\"; or augmented, \"A\" or \"+\").<\/p>\r\n<p class=\"import-Normal\"><strong>Quantity. <\/strong>To determine the quantity of an interval, simply count the number of lines and spaces between two notes on the staff, including the notes themselves. Some examples of this process are shown in Example 5\u20111.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example 5\u20111. Determining quantity of intervals<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\"><a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image48.png\" target=\"_blank\" rel=\"noopener\"><img src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image48.png\" alt=\"examples of counting steps to determine interval quantity\" class=\"alignnone\" width=\"1336\" height=\"168\" \/><\/a><\/div>\r\n<\/div>\r\n<p class=\"import-Normal\"><strong>Quality. <\/strong>Determining the quality of an interval is more complicated than determining the quantity. There are two basic types of classification: [pb_glossary id=\"875\"]major\/minor[\/pb_glossary] and [pb_glossary id=\"876\"]perfect[\/pb_glossary]. <span>Each interval quantity fits into only one classification: for<\/span> [pb_glossary id=\"873\"]simple intervals[\/pb_glossary] (those of an octave or smaller)<span>, seconds, thirds, sixths, and sevenths are major\/minor, and unisons, fourths, fifths, and octaves are perfect.<\/span><\/p>\r\n<p class=\"import-Normal\"><strong>Major and <\/strong><strong>m<\/strong><strong>inor <\/strong><strong>i<\/strong><strong>ntervals. <\/strong>We have studied some intervals already\u2014the half step and whole step. Using the major\/minor classification system, we call a half step a minor second (mi2) and a whole step a major second (MA2). Thirds may be understood as combinations of seconds. A minor third (mi3) is equivalent to three half steps or MA2+mi2. A major third (MA3) is equivalent to four half steps or two MA2s.<\/p>\r\n<p class=\"import-Normal\"><span>If you think of the lower note of an interval as tonic of a major scale, you can use that scale to identify any major interval. Example 5-2 shows this technique: A is the lowest note of each interval in this case, so we use the A major scale to determine the higher note.<\/span><\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example 5\u20112. Finding major intervals from the major scale<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\"><a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image49.png\" target=\"_blank\" rel=\"noopener\"><img src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image49.png\" alt=\"examples of deriving major intervals from the A major scale\" class=\"alignnone\" width=\"1336\" height=\"287\" \/><\/a><\/div>\r\n<\/div>\r\n<p class=\"import-Normal\">Minor intervals are always a half step smaller than major ones. Example 5\u20113 shows how to derive minor intervals from the major ones by reducing their size by one half step. This is done by either raising the lower note or lowering the higher note by one half step.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example 5\u20113. Finding minor intervals from major intervals<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\"><img src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.3-1024x106.png\" alt=\"image of intervals in staff notation\" class=\"alignnone wp-image-878 size-large\" width=\"1024\" height=\"106\" \/><\/div>\r\n<\/div>\r\n<p class=\"import-Normal\">Sometimes large intervals can be difficult to identify. If seconds and thirds are easier for you to identify than sixths and sevenths, you may use [pb_glossary id=\"929\"]interval inversion[\/pb_glossary] to make the process easier. Interval inversion\u2014creating the inversion of the original interval\u2014works either by displacing the lower note of an interval up an octave or by displacing the higher note down an octave. Once the interval is inverted, the quality inverts (major intervals become minor and vice versa), and so does the quantity (sevenths become seconds and vice versa, and sixths become thirds and vice versa). Example 5\u20114 shows how interval inversion works for major and minor intervals.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example 5\u20114. Inversion of major and minor intervals<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\"><a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image51.png\" target=\"_blank\" rel=\"noopener\"><img src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image51.png\" alt=\"examples of interval inversion\" class=\"alignnone\" width=\"1378\" height=\"150\" \/><\/a><\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Video: T08 Intro to intervals (3:45)<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[embed]https:\/\/youtu.be\/SUXpKjv_nys[\/embed]\r\n<p class=\"import-Normal\">This video briefly explains what intervals are, the two components involved in labeling (quality and quantity), and how to determine the size (quantity) of the interval between any two notes on the staff.<\/p>\r\n\r\n<div class=\"textbox shaded\">Access slideshow here: <a class=\"rId140\" target=\"_blank\" href=\"https:\/\/docs.google.com\/presentation\/d\/1M1PmwxeD1m0nY07H-8GrTOW4X4RpYp21hJ3RCPJrv7E\/edit?usp=sharing\" rel=\"noopener\"><span class=\"import-Hyperlink\">Intro to intervals slides<\/span><\/a><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Video: T09 Major intervals (4:37)<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[embed]https:\/\/youtu.be\/sq5W3igpeOw[\/embed]\r\n<p class=\"import-Normal\">This video shows how to construct any major interval (MA2, MA3, MA6, MA7) <span>by thinking of the lower note as tonic of a major scale<\/span>.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Video: T10 Minor intervals (5:17)<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[embed]https:\/\/www.youtube.com\/embed\/979sLNfbr3E[\/embed]\r\n<p class=\"import-Normal\">This video shows how to derive minor intervals from their corresponding major intervals by reducing the size of the major interval by one half step. This can be achieved by either lowering the top note or raising the bottom note by a half step.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Video: T11 Interval inversion (6:40)<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[embed]https:\/\/youtu.be\/m3dXjkDKLlo[\/embed]\r\n<p class=\"import-Normal\">This video shows you how to find large major and minor intervals (sixths and sevenths) through a process called \"interval inversion,\" relating them to thirds and seconds respectively. Seconds invert to sevenths, and thirds invert to sixths. Major intervals invert to minor ones, and vice versa.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<h1><a id=\"EXERCISE 5-1 Drills with major and minor intervals\"><\/a>EXERCISE 5-1 Drills with major and minor intervals<\/h1>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXERCISE 5-1 Drills with major and minor intervals<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p class=\"import-Normal\">PART A. Complete the following intervals, given the lower note.<\/p>\r\n<p class=\"import-Normal\" style=\"padding-left: 40px\">SET 1<\/p>\r\n<p class=\"import-Normal\"><img src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image52.png\" alt=\"notes on staff\" class=\"aligncenter\" width=\"1416\" height=\"171\" \/><\/p>\r\n<p class=\"import-Normal\" style=\"padding-left: 40px\">SET 2<\/p>\r\n<p class=\"import-Normal\"><img src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image53.png\" alt=\"notes on staff\" class=\"aligncenter\" width=\"1419\" height=\"205\" \/><\/p>\r\n<p class=\"import-Normal\">PART B. Provide the label (quality and number) for the following intervals.<\/p>\r\n<p class=\"import-Normal\" style=\"padding-left: 40px\">SET 3<\/p>\r\n<a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/set03.png\" target=\"_blank\" rel=\"noopener\"><img src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/set03-1024x137.png\" alt=\"image of intervals on staff\" class=\"alignnone wp-image-912 size-large\" width=\"1024\" height=\"137\" \/><\/a>\r\n<p class=\"import-Normal\" style=\"padding-left: 40px\">SET 4<\/p>\r\n<a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/set04.png\"><img src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/set04-1024x137.png\" alt=\"image of intervals on staff\" class=\"alignnone wp-image-913 size-large\" width=\"1024\" height=\"137\" \/><\/a>\r\n<div class=\"textbox shaded\">Access a printer-friendly .pdf of the exercise here: <a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/Ex5.1-Drills-with-major-and-minor-intervals.pdf\">Ex5.1 Drills with major and minor intervals<\/a><\/div>\r\n<div class=\"textbox shaded\">\r\n\r\nWant more practice with major and minor intervals? Try these drills:\r\n<p class=\"import-Normal\" style=\"padding-left: 40px\"><a class=\"rId141\" target=\"_blank\" href=\"https:\/\/www.teoria.com\/en\/exercises\/ic.php\" rel=\"noopener\"><span class=\"import-Hyperlink\">Practice constructing major and minor intervals<\/span><\/a>\u00a0(teoria)<\/p>\r\n<p class=\"import-Normal\" style=\"padding-left: 40px\"><a class=\"rId142\" target=\"_blank\" href=\"https:\/\/www.teoria.com\/en\/exercises\/ii.php\" rel=\"noopener\"><span class=\"import-Hyperlink\">Practice identifying major and minor intervals<\/span><\/a>\u00a0(teoria)<\/p>\r\n<p class=\"import-Normal\" style=\"padding-left: 40px\"><a class=\"rId143\" target=\"_blank\" href=\"https:\/\/www.teoria.com\/en\/exercises\/iv.php\" rel=\"noopener\"><span class=\"import-Hyperlink\">Practice identifying major and minor intervals and their inversions<\/span><\/a>\u00a0(teoria)<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"intervals\">\r\n<h1><a id=\"Perfect intervals\"><\/a>Perfect intervals<\/h1>\r\n<p class=\"import-Normal\">Perfect intervals include unisons, fourths, fifths, and octaves. Like with major intervals, you can identify any perfect interval from a major scale <span>by thinking of the lower note as tonic of the scale<\/span>. <span>Example 5-5 shows this technique: A is the lowest note of each interval, so we use the A major scale to determine the higher note in each case.<\/span><\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example 5\u20115. Perfect intervals derived from the major scale<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\"><img src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex5.5-1024x204.png\" alt=\"image of perfect intervals derived from A major scale\" class=\"alignnone wp-image-915 size-large\" width=\"1024\" height=\"204\" \/><\/div>\r\n<\/div>\r\n<p class=\"import-Normal\">Using [pb_glossary id=\"929\"]interval inversion[\/pb_glossary], fourths invert to fifths and vice versa, and unisons invert to octaves and vice versa. Unlike with major and minor intervals, quality does not change when a perfect interval is inverted.<\/p>\r\n\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Video: T12 Perfect intervals (9:05)<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[embed]https:\/\/youtu.be\/MG66S83pnkc[\/embed]\r\n<p class=\"import-Normal\">This video shows how to derive any perfect interval (P1, P8, P4, or P5) from a major scale <span>by thinking of the lower note as tonic of the scale<\/span>.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<h1><a id=\"Diminished and augmented intervals\"><\/a>Diminished and augmented intervals<\/h1>\r\n<p class=\"import-Normal\">Major, minor, and perfect intervals may be modified in additional ways to create [pb_glossary id=\"934\"]diminished[\/pb_glossary] and [pb_glossary id=\"935\"]augmented[\/pb_glossary] intervals, which are less common <span>than the other interval qualities<\/span>.<\/p>\r\n<p class=\"import-Normal\">A [pb_glossary id=\"934\"]diminished[\/pb_glossary] interval results when either a minor or perfect interval is made smaller by one half step. This is done either by raising the lower note or lowering the higher note by one half step, as shown in Example 5\u20116.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example 5\u20116. Diminished intervals derived from minor and perfect intervals<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\"><a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.6.png\" target=\"_blank\" rel=\"noopener\"><img src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.6-1024x106.png\" alt=\"image of intervals on staff\" class=\"alignnone wp-image-937 size-large\" width=\"1024\" height=\"106\" \/><\/a><\/div>\r\n<\/div>\r\n<p class=\"import-Normal\">An [pb_glossary id=\"935\"]augmented[\/pb_glossary] interval results when either a major or perfect interval is made larger by one half step. This is done by either lowering the lower note or raising the higher note by one half step, as shown in Example 5\u20117.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example 5\u20117. Augmented intervals derived from major and perfect intervals<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\"><a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.7.png\" target=\"_blank\" rel=\"noopener\"><img src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.7-1024x103.png\" alt=\"image of intervals on staff\" class=\"alignnone wp-image-940 size-large\" width=\"1024\" height=\"103\" \/><\/a><\/div>\r\n<\/div>\r\n<p class=\"import-Normal\">Using [pb_glossary id=\"929\"]interval inversion[\/pb_glossary], augmented intervals invert to diminished ones and vice versa. Quantities invert in the same way as major, minor, and perfect intervals (seconds become sevenths, thirds become sixths, fourths become fifths, and so forth). No matter what the interval, its own quantity and the quantity of its inversion always add up to nine.<\/p>\r\n\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Video: T13 Augmented and diminished intervals (8:58)<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[embed]https:\/\/youtu.be\/7bRLGvNaByE[\/embed]\r\n<p class=\"import-Normal\">This video shows how to get augmented intervals by making a major or perfect interval one half step larger, and how to get diminished intervals by making a minor or perfect interval one half step smaller.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<h1><a id=\"Compound intervals\"><\/a>Compound intervals<\/h1>\r\n<p class=\"import-Normal\">The previous examples deal with [pb_glossary id=\"873\"]simple intervals[\/pb_glossary], which are intervals that are an octave or smaller. [pb_glossary id=\"947\"]Compound intervals[\/pb_glossary] are intervals that are larger than an octave. Convert any simple interval to a compound one by adding seven to its quantity and displacing the higher note by one octave, as shown in Example 5\u20118.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example 5\u20118. Simple intervals and their compound counterparts<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\"><img src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.8-1024x125.png\" alt=\"simple and compound intervals (MA3, MA10, MA6, MA13, P5, P12)\" class=\"alignnone wp-image-945 size-large\" width=\"1024\" height=\"125\" \/><\/div>\r\n<\/div>\r\n<h1><a id=\"EXERCISE 5-2: Analysis of Judith Cloud, Six Forays for Flute and Clarinet, mvt. 2\"><\/a>EXERCISE 5-2: Analysis of Judith Cloud, Six Forays for Flute and Clarinet, mvt. 2<\/h1>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXERCISE 5-2: Analysis of Judith Cloud, <em>Six Forays for Flute and Clarinet<\/em>, mvt. 2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p class=\"import-Normal\">Listen to Judith Cloud\u2019s <em>Six Forays for Flute and Clarinet<\/em> and provide labels for each harmonic interval formed between the flute and clarinet in the score below. The first measure is done for you.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Worksheet example 5\u20111. Judith Cloud, <em>Six Forays for Flute and Clarinet<\/em>, mvt. 2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\"><img src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image60.png\" alt=\"score of Judith Cloud's Six Forays, movement 2\" class=\"alignnone\" width=\"1333\" height=\"578\" \/><\/div>\r\n<div style=\"text-align: center\">Used with permission of the composer \u00a9 Judith Cloud, all rights reserved<\/div>\r\n<div><\/div>\r\n<div>\r\n\r\n[audio mp3=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/Audio-for-Cloud-Six-Forays-mvt.-2.mp3\"][\/audio]\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox shaded\">Learn about living American composer <strong>Judith Cloud<\/strong> by reading her bio <a class=\"rId139\" target=\"_blank\" href=\"https:\/\/www.summitrecords.com\/artist\/judith-cloud\/\" rel=\"noopener\"><span class=\"import-Hyperlink\">here<\/span><\/a>.<\/div>\r\n<div>\r\n<div class=\"textbox shaded\">Access a printer-friendly .pdf of the exercise here: <a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/Ex5.2-Analysis-with-Judith-Cloud-Six-Forays-mvt-2.pdf\" target=\"_blank\" rel=\"noopener\">Ex5.2 Analysis with Judith Cloud Six Forays mvt 2<\/a><\/div>\r\n<\/div>\r\n<div class=\"textbox shaded\">\r\n\r\nWant more practice identifying intervals? Try these drills:\r\n<p class=\"import-Normal\"><a class=\"rId144\" target=\"_blank\" href=\"https:\/\/www.teoria.com\/en\/exercises\/ii.php\" rel=\"noopener\"><span class=\"import-Hyperlink\">Practice identifying all intervals in various clefs<\/span><\/a> (teoria)<\/p>\r\n<p class=\"import-Normal\"><a class=\"rId145\" target=\"_blank\" href=\"https:\/\/www.musictheory.net\/exercises\/interval-construction\" rel=\"noopener\"><span class=\"import-Hyperlink\">Practice identifying all intervals in various clefs<\/span><\/a> (musictheory.net)<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<h1><a id=\"Identifying intervals aurally\"><\/a>Identifying intervals aurally<\/h1>\r\n<p class=\"import-Normal\">Learning how to identify intervals aurally can be a daunting task. If this is a goal you wish to achieve, I offer here some techniques for mastering aural interval identification. A combination of three different techniques\u2014song association, tonal implication, and degree of dissonance\u2014may be used for optimum success.<\/p>\r\n\r\n<h2>Song association<\/h2>\r\n<p class=\"import-Normal\">Are there particular intervals that you have difficulty identifying? Try associating the interval with a catchy tune that you already know. Figure 5\u20111 summarizes some common musical themes with ascending, descending, and harmonic intervals. You can add your own favorite tunes to this chart, as needed.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Figure 5\u20111. Song association interval chart<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n<a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image61.png\" target=\"_blank\" rel=\"noopener\"><img src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image61-1024x909.png\" alt=\"image of chart\" width=\"1024\" height=\"909\" class=\"alignnone wp-image-81 size-large\" \/><\/a>\r\n<div class=\"textbox shaded\">Access a screen-reader friendly .pdf of this figure here: <a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/fig-5.1.pdf\" target=\"_blank\" rel=\"noopener\">Figure 5-1. Song association interval chart<\/a><\/div>\r\n<div class=\"textbox shaded\">Listen to the audio examples featured in this figure here: <a href=\"https:\/\/open.spotify.com\/playlist\/4dh9lfbYujBykrZqnCbd3S?si=8b38077ed13042b2\" target=\"_blank\" rel=\"noopener\">Interval ID playlist on Spotify<\/a><\/div>\r\n<\/div>\r\n<\/div>\r\n<h2>Tonal implication<\/h2>\r\n<p class=\"import-Normal\">Depending on an interval's context ([pb_glossary id=\"978\"]timbre[\/pb_glossary], register placement, and so forth), using song associations may not always render successful results. However, with a solid knowledge of relative pitch relationships through solfege, you can learn to identify intervals. Figure 5\u20112 relates intervals to their most common usages in tonal music.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Figure 5\u20112. Tonal implication interval chart<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\"><a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image62.png\" target=\"_blank\" rel=\"noopener\"><img src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image62.png\" alt=\"intervals associated with solfege patterns\" class=\"alignnone\" width=\"836\" height=\"1273\" \/><\/a><\/div>\r\n<div class=\"textbox__content\">\r\n<div class=\"textbox shaded\">Access a screen-reader friendly .pdf of this figure here: <a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/fig-5.2.pdf\" target=\"_blank\" rel=\"noopener\">Figure 5-2. Tonal implication interval chart<\/a><\/div>\r\n<\/div>\r\n<\/div>\r\n<h2>Degree of dissonance<\/h2>\r\n<p class=\"import-Normal\">For millennia, scholars have examined the properties of intervals, often classifying them as dissonant or consonant. Some intervals have been considered dissonant during one era and later considered consonant, and vice versa. Active in the 20th century, composer, theorist, and pedagogue Paul Hindemith created a table (called \u201cSeries 2\u201d) that places intervals along a continuum ranging from most consonant to most dissonant. This table is reproduced in Figure 5\u20113.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Figure 5\u20113. Hindemith's \"Series 2\"[footnote]Paul Hindemith, <em>The Craft of Musical Composition<\/em>, vol. 1 (1937), trans. Arthur Mendel (New York and London: Schott &amp; Co., 1942), 81.[\/footnote]<small><span class=\"import-FootnoteReference\"><\/span><\/small><\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\"><a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image63.png\" target=\"_blank\" rel=\"noopener\"><img src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image63.png\" alt=\"Hindemith's series 2 chart: P8 on leftmost side, tritone on rightmost side\" class=\"alignnone\" width=\"1331\" height=\"180\" \/><\/a><\/div>\r\n<\/div>\r\n<p class=\"import-Normal\"><span>You can listen for an interval\u2019s degree of consonance or dissonance to help you aurally identify it.<\/span> Pedagogue and scholar Rudy Marcozzi has developed a strategy for interval identification based on binary logic. His flowchart summarizing binary decision-making appears in Figure 5\u20114.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Figure 5\u20114. Marcozzi's interval flowchart[footnote]Rudy Marcozzi, <em>Strategies and Patterns for Ear Training<\/em> (Upper Saddle River, NJ: Prentice Hall, 2009), 153. Used with the permission of the author.[\/footnote]<small><span class=\"import-FootnoteReference\"><\/span><\/small><\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\"><a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image64.png\" target=\"_blank\" rel=\"noopener\"><img src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image64.png\" alt=\"Marcozzi's binary decision making chart\" class=\"alignnone\" width=\"1269\" height=\"781\" \/><\/a><\/div>\r\n<\/div>\r\n<div class=\"textbox shaded\">\r\n\r\nWant practice identifying intervals by ear? Try one of these online drills:\r\n<p class=\"import-Normal\" style=\"padding-left: 40px\"><a class=\"rId146\" href=\"https:\/\/tonesavvy.com\/music-practice-exercise\/215\/interval-identification-ear-training\/\" target=\"_blank\" rel=\"noopener\"><span class=\"import-Hyperlink\">I<\/span><span class=\"import-Hyperlink\">nterval ear trainer<\/span><\/a>\u00a0(tonesavvy)<\/p>\r\n<p class=\"import-Normal\" style=\"padding-left: 40px\"><a class=\"rId147\" href=\"https:\/\/www.teoria.com\/en\/exercises\/ie.php\" target=\"_blank\" rel=\"noopener\"><span class=\"import-Hyperlink\">Interval ear trainer<\/span><\/a>\u00a0(teoria)<\/p>\r\n<p class=\"import-Normal\" style=\"padding-left: 40px\"><a class=\"rId148\" href=\"https:\/\/www.musictheory.net\/exercises\/ear-interval\" target=\"_blank\" rel=\"noopener\"><span class=\"import-Hyperlink\">Interval ear trainer<\/span><\/a> (musictheory.net)<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<h1><a id=\"Supplemental resources\"><\/a>Supplemental resources<\/h1>\r\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Supplemental resources for Chapter 5<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p class=\"import-Normal\"><a class=\"rId149\" href=\"https:\/\/trainer.thetamusic.com\/en\/course\/intervals-i\" target=\"_blank\" rel=\"noopener\"><span class=\"import-Hyperlink\">Theta Music Trainer chapter on intervals<\/span><\/a><\/p>\r\n<p class=\"import-Normal\"><a class=\"rId150\" href=\"https:\/\/milnepublishing.geneseo.edu\/fundamentals-function-form\/chapter\/11-intervals\/\" target=\"_blank\" rel=\"noopener\"><span class=\"import-Hyperlink\">Andre Mount's chapter on intervals<\/span><\/a><\/p>\r\n<p class=\"import-Normal\"><a class=\"rId151\" href=\"https:\/\/musictheorymaterials.utk.edu\/wp-content\/uploads\/2018\/09\/Intervals.pdf\" target=\"_blank\" rel=\"noopener\"><span class=\"import-Hyperlink\">Barbara Murphy's primer on intervals<\/span><\/a><\/p>\r\n<p class=\"import-Normal\"><a class=\"rId152\" href=\"https:\/\/gmajormusictheory.org\/Fundamentals\/Ch08.pdf\" target=\"_blank\" rel=\"noopener\"><span class=\"import-Hyperlink\">Gilbert <\/span><span class=\"import-Hyperlink\">DeBenedetti's<\/span><span class=\"import-Hyperlink\"> chapter on intervals<\/span><\/a><\/p>\r\n<p class=\"import-Normal\"><a class=\"rId153\" href=\"http:\/\/musictheory.pugetsound.edu\/mt21c\/Intervals.html\" target=\"_blank\" rel=\"noopener\"><span class=\"import-Hyperlink\">Robert Hutchinson's chapter on intervals<\/span><\/a><\/p>\r\n<a href=\"https:\/\/viva.pressbooks.pub\/openmusictheory\/chapter\/intervals\/\" target=\"_blank\" rel=\"noopener\">Chelsey Hamm and Bryn Hughes's chapter on intervals<\/a> (Open Music Theory)\r\n\r\n<\/div>\r\n<\/div>","rendered":"<div class=\"intervals\">\n<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning goals for Chapter 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p class=\"import-Normal\">In this chapter, we will learn:<\/p>\n<ul>\n<li>How to construct and identify intervals<\/li>\n<li>How to use interval inversion<\/li>\n<li>How to aurally identify intervals<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1><a><\/a>Major and minor intervals<\/h1>\n<p class=\"import-Normal\">An <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_85_344\">interval<\/a> measures the distance between two pitches and consists of two parts, a <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_85_872\">quantity<\/a> (a number) and a <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_85_871\">quality<\/a> (major, &#8220;MA&#8221; or &#8220;M&#8221;; minor, &#8220;mi&#8221; or &#8220;m&#8221;; perfect, &#8220;P&#8221;; diminished, &#8220;d&#8221; or &#8220;o&#8221;; or augmented, &#8220;A&#8221; or &#8220;+&#8221;).<\/p>\n<p class=\"import-Normal\"><strong>Quantity. <\/strong>To determine the quantity of an interval, simply count the number of lines and spaces between two notes on the staff, including the notes themselves. Some examples of this process are shown in Example 5\u20111.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example 5\u20111. Determining quantity of intervals<\/p>\n<\/header>\n<div class=\"textbox__content\"><a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image48.png\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image48.png\" alt=\"examples of counting steps to determine interval quantity\" class=\"alignnone\" width=\"1336\" height=\"168\" \/><\/a><\/div>\n<\/div>\n<p class=\"import-Normal\"><strong>Quality. <\/strong>Determining the quality of an interval is more complicated than determining the quantity. There are two basic types of classification: <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_85_875\">major\/minor<\/a> and <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_85_876\">perfect<\/a>. <span>Each interval quantity fits into only one classification: for<\/span> <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_85_873\">simple intervals<\/a> (those of an octave or smaller)<span>, seconds, thirds, sixths, and sevenths are major\/minor, and unisons, fourths, fifths, and octaves are perfect.<\/span><\/p>\n<p class=\"import-Normal\"><strong>Major and <\/strong><strong>m<\/strong><strong>inor <\/strong><strong>i<\/strong><strong>ntervals. <\/strong>We have studied some intervals already\u2014the half step and whole step. Using the major\/minor classification system, we call a half step a minor second (mi2) and a whole step a major second (MA2). Thirds may be understood as combinations of seconds. A minor third (mi3) is equivalent to three half steps or MA2+mi2. A major third (MA3) is equivalent to four half steps or two MA2s.<\/p>\n<p class=\"import-Normal\"><span>If you think of the lower note of an interval as tonic of a major scale, you can use that scale to identify any major interval. Example 5-2 shows this technique: A is the lowest note of each interval in this case, so we use the A major scale to determine the higher note.<\/span><\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example 5\u20112. Finding major intervals from the major scale<\/p>\n<\/header>\n<div class=\"textbox__content\"><a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image49.png\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image49.png\" alt=\"examples of deriving major intervals from the A major scale\" class=\"alignnone\" width=\"1336\" height=\"287\" \/><\/a><\/div>\n<\/div>\n<p class=\"import-Normal\">Minor intervals are always a half step smaller than major ones. Example 5\u20113 shows how to derive minor intervals from the major ones by reducing their size by one half step. This is done by either raising the lower note or lowering the higher note by one half step.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example 5\u20113. Finding minor intervals from major intervals<\/p>\n<\/header>\n<div class=\"textbox__content\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.3-1024x106.png\" alt=\"image of intervals in staff notation\" class=\"alignnone wp-image-878 size-large\" width=\"1024\" height=\"106\" srcset=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.3-1024x106.png 1024w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.3-300x31.png 300w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.3-768x79.png 768w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.3-1536x159.png 1536w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.3-2048x212.png 2048w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.3-65x7.png 65w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.3-225x23.png 225w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.3-350x36.png 350w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div>\n<\/div>\n<p class=\"import-Normal\">Sometimes large intervals can be difficult to identify. If seconds and thirds are easier for you to identify than sixths and sevenths, you may use <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_85_929\">interval inversion<\/a> to make the process easier. Interval inversion\u2014creating the inversion of the original interval\u2014works either by displacing the lower note of an interval up an octave or by displacing the higher note down an octave. Once the interval is inverted, the quality inverts (major intervals become minor and vice versa), and so does the quantity (sevenths become seconds and vice versa, and sixths become thirds and vice versa). Example 5\u20114 shows how interval inversion works for major and minor intervals.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example 5\u20114. Inversion of major and minor intervals<\/p>\n<\/header>\n<div class=\"textbox__content\"><a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image51.png\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image51.png\" alt=\"examples of interval inversion\" class=\"alignnone\" width=\"1378\" height=\"150\" \/><\/a><\/div>\n<\/div>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Video: T08 Intro to intervals (3:45)<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"T08 Intro to Intervals\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/SUXpKjv_nys?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p class=\"import-Normal\">This video briefly explains what intervals are, the two components involved in labeling (quality and quantity), and how to determine the size (quantity) of the interval between any two notes on the staff.<\/p>\n<div class=\"textbox shaded\">Access slideshow here: <a class=\"rId140\" target=\"_blank\" href=\"https:\/\/docs.google.com\/presentation\/d\/1M1PmwxeD1m0nY07H-8GrTOW4X4RpYp21hJ3RCPJrv7E\/edit?usp=sharing\" rel=\"noopener\"><span class=\"import-Hyperlink\">Intro to intervals slides<\/span><\/a><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Video: T09 Major intervals (4:37)<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"T09 Major Intervals\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/sq5W3igpeOw?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p class=\"import-Normal\">This video shows how to construct any major interval (MA2, MA3, MA6, MA7) <span>by thinking of the lower note as tonic of a major scale<\/span>.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Video: T10 Minor intervals (5:17)<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"T10 Minor Intervals\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/979sLNfbr3E?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p class=\"import-Normal\">This video shows how to derive minor intervals from their corresponding major intervals by reducing the size of the major interval by one half step. This can be achieved by either lowering the top note or raising the bottom note by a half step.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Video: T11 Interval inversion (6:40)<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><iframe loading=\"lazy\" id=\"oembed-4\" title=\"T11 Interval Inversion\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/m3dXjkDKLlo?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p class=\"import-Normal\">This video shows you how to find large major and minor intervals (sixths and sevenths) through a process called &#8220;interval inversion,&#8221; relating them to thirds and seconds respectively. Seconds invert to sevenths, and thirds invert to sixths. Major intervals invert to minor ones, and vice versa.<\/p>\n<\/div>\n<\/div>\n<h1><a><\/a>EXERCISE 5-1 Drills with major and minor intervals<\/h1>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXERCISE 5-1 Drills with major and minor intervals<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p class=\"import-Normal\">PART A. Complete the following intervals, given the lower note.<\/p>\n<p class=\"import-Normal\" style=\"padding-left: 40px\">SET 1<\/p>\n<p class=\"import-Normal\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image52.png\" alt=\"notes on staff\" class=\"aligncenter\" width=\"1416\" height=\"171\" \/><\/p>\n<p class=\"import-Normal\" style=\"padding-left: 40px\">SET 2<\/p>\n<p class=\"import-Normal\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image53.png\" alt=\"notes on staff\" class=\"aligncenter\" width=\"1419\" height=\"205\" \/><\/p>\n<p class=\"import-Normal\">PART B. Provide the label (quality and number) for the following intervals.<\/p>\n<p class=\"import-Normal\" style=\"padding-left: 40px\">SET 3<\/p>\n<p><a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/set03.png\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/set03-1024x137.png\" alt=\"image of intervals on staff\" class=\"alignnone wp-image-912 size-large\" width=\"1024\" height=\"137\" srcset=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/set03-1024x137.png 1024w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/set03-300x40.png 300w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/set03-768x102.png 768w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/set03-1536x205.png 1536w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/set03-65x9.png 65w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/set03-225x30.png 225w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/set03-350x47.png 350w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/set03.png 1935w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><\/p>\n<p class=\"import-Normal\" style=\"padding-left: 40px\">SET 4<\/p>\n<p><a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/set04.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/set04-1024x137.png\" alt=\"image of intervals on staff\" class=\"alignnone wp-image-913 size-large\" width=\"1024\" height=\"137\" srcset=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/set04-1024x137.png 1024w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/set04-300x40.png 300w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/set04-768x102.png 768w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/set04-1536x205.png 1536w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/set04-65x9.png 65w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/set04-225x30.png 225w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/set04-350x47.png 350w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/set04.png 1934w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><\/p>\n<div class=\"textbox shaded\">Access a printer-friendly .pdf of the exercise here: <a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/Ex5.1-Drills-with-major-and-minor-intervals.pdf\">Ex5.1 Drills with major and minor intervals<\/a><\/div>\n<div class=\"textbox shaded\">\n<p>Want more practice with major and minor intervals? Try these drills:<\/p>\n<p class=\"import-Normal\" style=\"padding-left: 40px\"><a class=\"rId141\" target=\"_blank\" href=\"https:\/\/www.teoria.com\/en\/exercises\/ic.php\" rel=\"noopener\"><span class=\"import-Hyperlink\">Practice constructing major and minor intervals<\/span><\/a>\u00a0(teoria)<\/p>\n<p class=\"import-Normal\" style=\"padding-left: 40px\"><a class=\"rId142\" target=\"_blank\" href=\"https:\/\/www.teoria.com\/en\/exercises\/ii.php\" rel=\"noopener\"><span class=\"import-Hyperlink\">Practice identifying major and minor intervals<\/span><\/a>\u00a0(teoria)<\/p>\n<p class=\"import-Normal\" style=\"padding-left: 40px\"><a class=\"rId143\" target=\"_blank\" href=\"https:\/\/www.teoria.com\/en\/exercises\/iv.php\" rel=\"noopener\"><span class=\"import-Hyperlink\">Practice identifying major and minor intervals and their inversions<\/span><\/a>\u00a0(teoria)<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"intervals\">\n<h1><a><\/a>Perfect intervals<\/h1>\n<p class=\"import-Normal\">Perfect intervals include unisons, fourths, fifths, and octaves. Like with major intervals, you can identify any perfect interval from a major scale <span>by thinking of the lower note as tonic of the scale<\/span>. <span>Example 5-5 shows this technique: A is the lowest note of each interval, so we use the A major scale to determine the higher note in each case.<\/span><\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example 5\u20115. Perfect intervals derived from the major scale<\/p>\n<\/header>\n<div class=\"textbox__content\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex5.5-1024x204.png\" alt=\"image of perfect intervals derived from A major scale\" class=\"alignnone wp-image-915 size-large\" width=\"1024\" height=\"204\" srcset=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex5.5-1024x204.png 1024w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex5.5-300x60.png 300w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex5.5-768x153.png 768w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex5.5-1536x306.png 1536w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex5.5-2048x408.png 2048w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex5.5-65x13.png 65w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex5.5-225x45.png 225w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex5.5-350x70.png 350w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div>\n<\/div>\n<p class=\"import-Normal\">Using <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_85_929\">interval inversion<\/a>, fourths invert to fifths and vice versa, and unisons invert to octaves and vice versa. Unlike with major and minor intervals, quality does not change when a perfect interval is inverted.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Video: T12 Perfect intervals (9:05)<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><iframe loading=\"lazy\" id=\"oembed-5\" title=\"T12 Perfect Intervals\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/MG66S83pnkc?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p class=\"import-Normal\">This video shows how to derive any perfect interval (P1, P8, P4, or P5) from a major scale <span>by thinking of the lower note as tonic of the scale<\/span>.<\/p>\n<\/div>\n<\/div>\n<h1><a><\/a>Diminished and augmented intervals<\/h1>\n<p class=\"import-Normal\">Major, minor, and perfect intervals may be modified in additional ways to create <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_85_934\">diminished<\/a> and <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_85_935\">augmented<\/a> intervals, which are less common <span>than the other interval qualities<\/span>.<\/p>\n<p class=\"import-Normal\">A <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_85_934\">diminished<\/a> interval results when either a minor or perfect interval is made smaller by one half step. This is done either by raising the lower note or lowering the higher note by one half step, as shown in Example 5\u20116.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example 5\u20116. Diminished intervals derived from minor and perfect intervals<\/p>\n<\/header>\n<div class=\"textbox__content\"><a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.6.png\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.6-1024x106.png\" alt=\"image of intervals on staff\" class=\"alignnone wp-image-937 size-large\" width=\"1024\" height=\"106\" srcset=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.6-1024x106.png 1024w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.6-300x31.png 300w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.6-768x79.png 768w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.6-1536x159.png 1536w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.6-2048x212.png 2048w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.6-65x7.png 65w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.6-225x23.png 225w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.6-350x36.png 350w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><\/div>\n<\/div>\n<p class=\"import-Normal\">An <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_85_935\">augmented<\/a> interval results when either a major or perfect interval is made larger by one half step. This is done by either lowering the lower note or raising the higher note by one half step, as shown in Example 5\u20117.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example 5\u20117. Augmented intervals derived from major and perfect intervals<\/p>\n<\/header>\n<div class=\"textbox__content\"><a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.7.png\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.7-1024x103.png\" alt=\"image of intervals on staff\" class=\"alignnone wp-image-940 size-large\" width=\"1024\" height=\"103\" srcset=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.7-1024x103.png 1024w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.7-300x30.png 300w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.7-768x77.png 768w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.7-1536x154.png 1536w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.7-2048x205.png 2048w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.7-65x7.png 65w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.7-225x23.png 225w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.7-350x35.png 350w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><\/div>\n<\/div>\n<p class=\"import-Normal\">Using <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_85_929\">interval inversion<\/a>, augmented intervals invert to diminished ones and vice versa. Quantities invert in the same way as major, minor, and perfect intervals (seconds become sevenths, thirds become sixths, fourths become fifths, and so forth). No matter what the interval, its own quantity and the quantity of its inversion always add up to nine.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Video: T13 Augmented and diminished intervals (8:58)<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><iframe loading=\"lazy\" id=\"oembed-6\" title=\"T13 Augmented &amp; Diminished Intervals\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/7bRLGvNaByE?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p class=\"import-Normal\">This video shows how to get augmented intervals by making a major or perfect interval one half step larger, and how to get diminished intervals by making a minor or perfect interval one half step smaller.<\/p>\n<\/div>\n<\/div>\n<h1><a><\/a>Compound intervals<\/h1>\n<p class=\"import-Normal\">The previous examples deal with <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_85_873\">simple intervals<\/a>, which are intervals that are an octave or smaller. <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_85_947\">Compound intervals<\/a> are intervals that are larger than an octave. Convert any simple interval to a compound one by adding seven to its quantity and displacing the higher note by one octave, as shown in Example 5\u20118.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example 5\u20118. Simple intervals and their compound counterparts<\/p>\n<\/header>\n<div class=\"textbox__content\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.8-1024x125.png\" alt=\"simple and compound intervals (MA3, MA10, MA6, MA13, P5, P12)\" class=\"alignnone wp-image-945 size-large\" width=\"1024\" height=\"125\" srcset=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.8-1024x125.png 1024w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.8-300x37.png 300w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.8-768x94.png 768w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.8-1536x188.png 1536w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.8-2048x250.png 2048w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.8-65x8.png 65w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.8-225x27.png 225w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/ex-5.8-350x43.png 350w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div>\n<\/div>\n<h1><a><\/a>EXERCISE 5-2: Analysis of Judith Cloud, Six Forays for Flute and Clarinet, mvt. 2<\/h1>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXERCISE 5-2: Analysis of Judith Cloud, <em>Six Forays for Flute and Clarinet<\/em>, mvt. 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p class=\"import-Normal\">Listen to Judith Cloud\u2019s <em>Six Forays for Flute and Clarinet<\/em> and provide labels for each harmonic interval formed between the flute and clarinet in the score below. The first measure is done for you.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Worksheet example 5\u20111. Judith Cloud, <em>Six Forays for Flute and Clarinet<\/em>, mvt. 2<\/p>\n<\/header>\n<div class=\"textbox__content\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image60.png\" alt=\"score of Judith Cloud's Six Forays, movement 2\" class=\"alignnone\" width=\"1333\" height=\"578\" \/><\/div>\n<div style=\"text-align: center\">Used with permission of the composer \u00a9 Judith Cloud, all rights reserved<\/div>\n<div><\/div>\n<div>\n<p><audio class=\"wp-audio-shortcode\" id=\"audio-85-1\" preload=\"none\" style=\"width: 100%;\" controls=\"controls\"><source type=\"audio\/mpeg\" src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/Audio-for-Cloud-Six-Forays-mvt.-2.mp3?_=1\" \/><a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/Audio-for-Cloud-Six-Forays-mvt.-2.mp3\">https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/Audio-for-Cloud-Six-Forays-mvt.-2.mp3<\/a><\/audio><\/p>\n<\/div>\n<\/div>\n<div class=\"textbox shaded\">Learn about living American composer <strong>Judith Cloud<\/strong> by reading her bio <a class=\"rId139\" target=\"_blank\" href=\"https:\/\/www.summitrecords.com\/artist\/judith-cloud\/\" rel=\"noopener\"><span class=\"import-Hyperlink\">here<\/span><\/a>.<\/div>\n<div>\n<div class=\"textbox shaded\">Access a printer-friendly .pdf of the exercise here: <a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/Ex5.2-Analysis-with-Judith-Cloud-Six-Forays-mvt-2.pdf\" target=\"_blank\" rel=\"noopener\">Ex5.2 Analysis with Judith Cloud Six Forays mvt 2<\/a><\/div>\n<\/div>\n<div class=\"textbox shaded\">\n<p>Want more practice identifying intervals? Try these drills:<\/p>\n<p class=\"import-Normal\"><a class=\"rId144\" target=\"_blank\" href=\"https:\/\/www.teoria.com\/en\/exercises\/ii.php\" rel=\"noopener\"><span class=\"import-Hyperlink\">Practice identifying all intervals in various clefs<\/span><\/a> (teoria)<\/p>\n<p class=\"import-Normal\"><a class=\"rId145\" target=\"_blank\" href=\"https:\/\/www.musictheory.net\/exercises\/interval-construction\" rel=\"noopener\"><span class=\"import-Hyperlink\">Practice identifying all intervals in various clefs<\/span><\/a> (musictheory.net)<\/p>\n<\/div>\n<\/div>\n<\/div>\n<h1><a><\/a>Identifying intervals aurally<\/h1>\n<p class=\"import-Normal\">Learning how to identify intervals aurally can be a daunting task. If this is a goal you wish to achieve, I offer here some techniques for mastering aural interval identification. A combination of three different techniques\u2014song association, tonal implication, and degree of dissonance\u2014may be used for optimum success.<\/p>\n<h2>Song association<\/h2>\n<p class=\"import-Normal\">Are there particular intervals that you have difficulty identifying? Try associating the interval with a catchy tune that you already know. Figure 5\u20111 summarizes some common musical themes with ascending, descending, and harmonic intervals. You can add your own favorite tunes to this chart, as needed.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Figure 5\u20111. Song association interval chart<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image61.png\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image61-1024x909.png\" alt=\"image of chart\" width=\"1024\" height=\"909\" class=\"alignnone wp-image-81 size-large\" srcset=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image61-1024x909.png 1024w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image61-300x266.png 300w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image61-768x682.png 768w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image61-65x58.png 65w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image61-225x200.png 225w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image61-350x311.png 350w, https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image61.png 1409w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><\/p>\n<div class=\"textbox shaded\">Access a screen-reader friendly .pdf of this figure here: <a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/fig-5.1.pdf\" target=\"_blank\" rel=\"noopener\">Figure 5-1. Song association interval chart<\/a><\/div>\n<div class=\"textbox shaded\">Listen to the audio examples featured in this figure here: <a href=\"https:\/\/open.spotify.com\/playlist\/4dh9lfbYujBykrZqnCbd3S?si=8b38077ed13042b2\" target=\"_blank\" rel=\"noopener\">Interval ID playlist on Spotify<\/a><\/div>\n<\/div>\n<\/div>\n<h2>Tonal implication<\/h2>\n<p class=\"import-Normal\">Depending on an interval&#8217;s context (<a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_85_978\">timbre<\/a>, register placement, and so forth), using song associations may not always render successful results. However, with a solid knowledge of relative pitch relationships through solfege, you can learn to identify intervals. Figure 5\u20112 relates intervals to their most common usages in tonal music.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Figure 5\u20112. Tonal implication interval chart<\/p>\n<\/header>\n<div class=\"textbox__content\"><a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image62.png\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image62.png\" alt=\"intervals associated with solfege patterns\" class=\"alignnone\" width=\"836\" height=\"1273\" \/><\/a><\/div>\n<div class=\"textbox__content\">\n<div class=\"textbox shaded\">Access a screen-reader friendly .pdf of this figure here: <a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/fig-5.2.pdf\" target=\"_blank\" rel=\"noopener\">Figure 5-2. Tonal implication interval chart<\/a><\/div>\n<\/div>\n<\/div>\n<h2>Degree of dissonance<\/h2>\n<p class=\"import-Normal\">For millennia, scholars have examined the properties of intervals, often classifying them as dissonant or consonant. Some intervals have been considered dissonant during one era and later considered consonant, and vice versa. Active in the 20th century, composer, theorist, and pedagogue Paul Hindemith created a table (called \u201cSeries 2\u201d) that places intervals along a continuum ranging from most consonant to most dissonant. This table is reproduced in Figure 5\u20113.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Figure 5\u20113. Hindemith&#8217;s &#8220;Series 2&#8221;<a class=\"footnote\" title=\"Paul Hindemith, The Craft of Musical Composition, vol. 1 (1937), trans. Arthur Mendel (New York and London: Schott &amp; Co., 1942), 81.\" id=\"return-footnote-85-1\" href=\"#footnote-85-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a><small><span class=\"import-FootnoteReference\"><\/span><\/small><\/p>\n<\/header>\n<div class=\"textbox__content\"><a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image63.png\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image63.png\" alt=\"Hindemith's series 2 chart: P8 on leftmost side, tritone on rightmost side\" class=\"alignnone\" width=\"1331\" height=\"180\" \/><\/a><\/div>\n<\/div>\n<p class=\"import-Normal\"><span>You can listen for an interval\u2019s degree of consonance or dissonance to help you aurally identify it.<\/span> Pedagogue and scholar Rudy Marcozzi has developed a strategy for interval identification based on binary logic. His flowchart summarizing binary decision-making appears in Figure 5\u20114.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Figure 5\u20114. Marcozzi&#8217;s interval flowchart<a class=\"footnote\" title=\"Rudy Marcozzi, Strategies and Patterns for Ear Training (Upper Saddle River, NJ: Prentice Hall, 2009), 153. Used with the permission of the author.\" id=\"return-footnote-85-2\" href=\"#footnote-85-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a><small><span class=\"import-FootnoteReference\"><\/span><\/small><\/p>\n<\/header>\n<div class=\"textbox__content\"><a href=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image64.png\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/files\/2023\/04\/image64.png\" alt=\"Marcozzi's binary decision making chart\" class=\"alignnone\" width=\"1269\" height=\"781\" \/><\/a><\/div>\n<\/div>\n<div class=\"textbox shaded\">\n<p>Want practice identifying intervals by ear? Try one of these online drills:<\/p>\n<p class=\"import-Normal\" style=\"padding-left: 40px\"><a class=\"rId146\" href=\"https:\/\/tonesavvy.com\/music-practice-exercise\/215\/interval-identification-ear-training\/\" target=\"_blank\" rel=\"noopener\"><span class=\"import-Hyperlink\">I<\/span><span class=\"import-Hyperlink\">nterval ear trainer<\/span><\/a>\u00a0(tonesavvy)<\/p>\n<p class=\"import-Normal\" style=\"padding-left: 40px\"><a class=\"rId147\" href=\"https:\/\/www.teoria.com\/en\/exercises\/ie.php\" target=\"_blank\" rel=\"noopener\"><span class=\"import-Hyperlink\">Interval ear trainer<\/span><\/a>\u00a0(teoria)<\/p>\n<p class=\"import-Normal\" style=\"padding-left: 40px\"><a class=\"rId148\" href=\"https:\/\/www.musictheory.net\/exercises\/ear-interval\" target=\"_blank\" rel=\"noopener\"><span class=\"import-Hyperlink\">Interval ear trainer<\/span><\/a> (musictheory.net)<\/p>\n<\/div>\n<\/div>\n<h1><a><\/a>Supplemental resources<\/h1>\n<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Supplemental resources for Chapter 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p class=\"import-Normal\"><a class=\"rId149\" href=\"https:\/\/trainer.thetamusic.com\/en\/course\/intervals-i\" target=\"_blank\" rel=\"noopener\"><span class=\"import-Hyperlink\">Theta Music Trainer chapter on intervals<\/span><\/a><\/p>\n<p class=\"import-Normal\"><a class=\"rId150\" href=\"https:\/\/milnepublishing.geneseo.edu\/fundamentals-function-form\/chapter\/11-intervals\/\" target=\"_blank\" rel=\"noopener\"><span class=\"import-Hyperlink\">Andre Mount&#8217;s chapter on intervals<\/span><\/a><\/p>\n<p class=\"import-Normal\"><a class=\"rId151\" href=\"https:\/\/musictheorymaterials.utk.edu\/wp-content\/uploads\/2018\/09\/Intervals.pdf\" target=\"_blank\" rel=\"noopener\"><span class=\"import-Hyperlink\">Barbara Murphy&#8217;s primer on intervals<\/span><\/a><\/p>\n<p class=\"import-Normal\"><a class=\"rId152\" href=\"https:\/\/gmajormusictheory.org\/Fundamentals\/Ch08.pdf\" target=\"_blank\" rel=\"noopener\"><span class=\"import-Hyperlink\">Gilbert <\/span><span class=\"import-Hyperlink\">DeBenedetti&#8217;s<\/span><span class=\"import-Hyperlink\"> chapter on intervals<\/span><\/a><\/p>\n<p class=\"import-Normal\"><a class=\"rId153\" href=\"http:\/\/musictheory.pugetsound.edu\/mt21c\/Intervals.html\" target=\"_blank\" rel=\"noopener\"><span class=\"import-Hyperlink\">Robert Hutchinson&#8217;s chapter on intervals<\/span><\/a><\/p>\n<p><a href=\"https:\/\/viva.pressbooks.pub\/openmusictheory\/chapter\/intervals\/\" target=\"_blank\" rel=\"noopener\">Chelsey Hamm and Bryn Hughes&#8217;s chapter on intervals<\/a> (Open Music Theory)<\/p>\n<\/div>\n<\/div>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-85-1\">Paul Hindemith, <em>The Craft of Musical Composition<\/em>, vol. 1 (1937), trans. Arthur Mendel (New York and London: Schott &amp; Co., 1942), 81. <a href=\"#return-footnote-85-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-85-2\">Rudy Marcozzi, <em>Strategies and Patterns for Ear Training<\/em> (Upper Saddle River, NJ: Prentice Hall, 2009), 153. Used with the permission of the author. <a href=\"#return-footnote-85-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><\/ol><\/div><div class=\"glossary\"><span class=\"screen-reader-text\" id=\"definition\">definition<\/span><template id=\"term_85_344\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_85_344\"><div tabindex=\"-1\"><p>the measure of distance between two pitches<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_85_872\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_85_872\"><div tabindex=\"-1\"><p>for intervals, the number of steps between two notes, including the starting and ending note<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_85_871\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_85_871\"><div tabindex=\"-1\"><p>for intervals and chords, the specific configuration of interval content resulting in a unique and identifiable sound; for intervals, quality may be major, minor, perfect, diminished, or augmented; for triads, quality may be major, minor, diminished, or augmented; and for seventh chords, quality may be major, major-minor (dominant), minor, half-diminished, or fully diminished<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_85_875\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_85_875\"><div tabindex=\"-1\"><p>qualities that can describe intervals, scales, or chords; with regard to intervals, this pairing refers to simple intervals of seconds, thirds, sixths, and sevenths and their compound interval equivalents<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_85_876\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_85_876\"><div tabindex=\"-1\"><p>with regard to intervals, the quality of simple intervals of unisons, fourths, fifths, and octaves, as well as their compound interval equivalents<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_85_873\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_85_873\"><div tabindex=\"-1\"><p>intervals smaller than a ninth: unisons (1), seconds (2), thirds (3), fourths (4), fifths (5), sixths (6), sevenths (7), and octaves (8)<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_85_929\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_85_929\"><div tabindex=\"-1\"><p>property of interval relations that occurs when the lower note of an interval is placed an octave higher, or the higher note is placed an octave lower; this relation makes major intervals minor, minor intervals major, diminished intervals augmented, and augmented intervals diminished; perfect intervals invert to perfect intervals, unisons invert to octaves, seconds invert to sevenths, thirds invert to sixths, and fourths invert to fifths<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_85_934\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_85_934\"><div tabindex=\"-1\"><p>term denoting quality of an interval (one half step smaller in size than its minor or perfect counterpart), quality of a triad (comprising two minor thirds), or quality of a seventh chord<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_85_935\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_85_935\"><div tabindex=\"-1\"><p>term denoting quality of an interval (one half step larger than its major or perfect counterpart), or quality of a triad (comprising two major thirds)<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_85_947\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_85_947\"><div tabindex=\"-1\"><p>intervals larger than an octave<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_85_978\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_85_978\"><div tabindex=\"-1\"><p>\"the perceptual quality of sound\u201d (Eidsheim 2008, 158)<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><\/div>","protected":false},"author":3,"menu_order":5,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-85","chapter","type-chapter","status-publish","hentry"],"part":3,"_links":{"self":[{"href":"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/wp-json\/pressbooks\/v2\/chapters\/85","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/wp-json\/wp\/v2\/users\/3"}],"version-history":[{"count":109,"href":"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/wp-json\/pressbooks\/v2\/chapters\/85\/revisions"}],"predecessor-version":[{"id":6983,"href":"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/wp-json\/pressbooks\/v2\/chapters\/85\/revisions\/6983"}],"part":[{"href":"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/wp-json\/pressbooks\/v2\/chapters\/85\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/wp-json\/wp\/v2\/media?parent=85"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/wp-json\/pressbooks\/v2\/chapter-type?post=85"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/wp-json\/wp\/v2\/contributor?post=85"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.macalester.digital\/multimodalmusicianship\/wp-json\/wp\/v2\/license?post=85"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}