Some Interesting Keyboards Some books about music refer to a persistent "myth" that it is possible, using only two keyboards, to construct an instrument on which it is possible to play music in any key using just intonation. Indeed, it is true that it is not possible, with only 24 keys to the octave, to construct an instrument that will play in perfect just intonation in every key. However, it is possible to exhibit an example of the type of keyboard that has given rise to this "myth", so that its capabilities, as well as its limitations, can be seen. Thus, what may be constructed with 24 keys to the octave is a keyboard which allows playing diatonic music in just intonation in any of the twelve conventionally designated keys, even if nothing can be ensured concerning the pitch of accidentals, and with the provision that one has to make a jump in pitch when one transposes around the far end of the circle of fifths. This will be shown explicitly below. The most obvious design: This is the Wicki-Hayden keyboard.
An Introduction to Historical Tunings Or if G vibrates at 100 cycles per second, then B vibrates at 125, and so on. (If you'd like this explained in more detail, visit my Just Intonation Explained page.) The size of a pure 5:4 major third is 386.3 cents, a cent being one 1200th of an octave, or one 100th of a half-step. A pure perfect fifth is a 3 to 2 frequency ratio; if vibrates at 440 cycles per second, then E vibrates at 660 cycles per second. A pure perfect fifth should be 702 cents wide, which is just about 7/12 of an octave; our current equal-tempered tuning accomodates perfect fifths (at 700 cents) within 2 cents, which is closer than most people can distinguish, but the thirds (at 400 cents) are way off, and form audible beats that are ugly once you're sensitized to hear them. Let's look at the meantone solution. A major third and perfect fifth on the same pitch, of course, make up a major triad, the most common chord in European music from 1500 to 1900 - the meantone era. One last point: Why is it called meantone? 3.
Music Theory for Musicians and Normal People by Toby W. Rush This page includes links to each of the individual Music Theory pages I've created in PDF form. This is a work in progress; I am writing new ones regularly and fixing errors and omissions on existing ones as I find them. If you find them useful for your theory studies, you are welcome to use them, and if you find errors or have suggestions, I invite you to contact me. Click the thumbnails to view or download each page as a PDF for free! These pages are available for free under a Creative Commons BY-NC-ND license. This collection is a work in progress, but if you would prefer, you can download all the current pages as a single PDF. Each and every one of these pages is available is an 18" x 24" poster. These pages are available in multiple translations and localizations! Interested in helping translate these pages to your own language? What is Music Theory? And why are all these cool and attractive people studying it? Notation: Pitch Notation: Rhythm Notation: Meter Beaming Triads
Just Intonation Explained You can figure out the rest. There is a rather complicated formula for figuring out how many cents large an interval is: Divide 1200 by the logarithm of 2. If you use base 10 logarithms (any base is permitted), 1200/log 2 = 3986.3137... For any ratio n/p, the number of cents in the interval is log (n/p) x 1200/log 2 If you're using log 10, then cents = log (n/p) x 3986.3137... Using this formula, we can obtain the following interval sizes: 16/15 = 111.73... cents 9/8 = 203.91 cents 8/7 = 231.17... cents 7/6 = 266.87... cents 6/5 = 315.64... cents 11/9 = 347.4... cents 5/4 = 386.31... cents 9/7 = 435.08... cents 1323/1024 = 443.52... cents 21/16 = 470.78... cents 4/3 = 498 cents 7/5 = 582.51... cents 3/2 = 702 cents And so on, and so on. The smaller the numbers in an interval's ratio, the more consonant (sweet-sounding) it is, and the more useful it is for purposes of musical intelligibility. By the way, it's really not so difficult to learn to recognize these intervals by ear. 3. 4. David B.
A different way to visualize rhythm - John Varney To learn more on circular perceptions of rhythm with specific reference to African music, read this paper and then watch this Five(ish) Minute Drum Lesson on African Drumming. How has drumming played an essential role in African culture? What do specific rhythms represent? Interested in the software applications of a circular rhythmic approach? What exactly is rhythm? How does the beat of a song differ from its rhythm? As seen from this TED Ed lesson, different cultures share similar rhythms. Rhythm and Math are related? Just love music and want to learn more? How playing an instrument benefits your brain - Anita Collins Why we love repetition in music - Elizabeth Hellmuth Margulis Music as a language -Victor Wooten
Relating Tuning and Timbre This is the full text of the article (more or less) as it first appeared in Experimental Musical Instruments. It was the catalyst for much of the work that resulted in Tuning Timbre Spectrum Scale, and it contains links to computer programs that will make it easy for you to draw dissonance curves yourself. James Forrest has recently created a Java applet for interactive exploration of dissonance curves. Introduction If you've ever attempted to play music in weird tunings (where "weird" means anything other than 12 tone equal temperament), then you've probably noticed that certain timbres (or tones) sound good in some scales and not in others. 17 and 19 tone equal temperament are easy to play in, for instance, because many of the standard timbres in synthesizers sound fine in these tunings. The principle of local consonance describes a relationship between the timbre of a sound and a tuning (or scale) in which the timbre will sound most consonant. What Exactly is Consonance?
Music theory Music theory considers the practices and possibilities of music. It is generally derived from observation of how musicians and composers actually make music, but includes hypothetical speculation. Most commonly, the term describes the academic study and analysis of fundamental elements of music such as pitch, rhythm, harmony, and form, but also refers to descriptions, concepts, or beliefs related to music. Because of the ever-expanding conception of what constitutes music (see Definition of music), a more inclusive definition could be that music theory is the consideration of any sonic phenomena, including silence, as it relates to music. Music theory is a subfield of musicology, which is itself a subfield within the overarching field of the arts and humanities. The development, preservation, and transmission of music theory may be found in oral and practical music-making traditions, musical instruments, and other artifacts. History of music theory[edit] Fundamentals of music[edit] Play .
The Utopian Blues Why is the spirituality of the musician in "High" cultures so often a low-down spirituality? In India, for example, the musician belongs to a caste so low it hovers on the verge of untouchability. This lowness relates, in popular attitudes, to the musician's invariable use of forbidden intoxicants. Islam is popularly believed to "ban" music; obviously this is not the case, since so many Indian musicians converted. Other musicians were known as hearty drinkers or otherwise louche and bohemian types -- the few exceptions were pious Sufis in other, more disciplined orders, such as the Nematollahiyya or Ahl-i Haqq. In the rituals of Afro-American religions, such as Santeria, Voudoun, and Candomblé, the all-important drummers and musicians are often non-initiates, professionals hired by the congregation -- this is no doubt a reflection of the quasi-nomadic "minstrel" status of musicians in the highly evolved pastoral-agricultural societies of West Africa. And what music! . . . . Thanks to:
How maths helps us understand why music moves people Music is known to provoke the senses, give pleasure and sometimes move people to tears. Surely this has little to do with mathematical models which are so frequently associated with cold and rational logic. So what can maths tell us about this powerful phenomenon closely connected to the emotions? Can mathematics help us measure what’s sublime or ineffable about a piece of music? Music evokes strong emotions such as frisson (goose bumps), awe and laughter – and has been found to use the same reward pathways as food, drugs and sex to induce pleasure. On one end of the spectrum, a performance or a piece of music that does just what you’d expect runs the risk of becoming banal. Author provided Listen PDQ Bach: The Short-tempered Clavier: Minuet in C Download MP3 / 735 KB The craving that comes from musical anticipation and the euphoria that follows the reward have both been found to be linked to dopamine release. Playing with expectations Listen Happy Birthday (first part) Download MP3 / 284 KB