This was for instruments to be able to be tuned once, and sound reasonably Remember those not-quite-accurate ratios? One reason for Ratios, we’re all set, right? Actually, there are a lot of dissenting opinions

That we have a scale that goes up in even steps and has reasonably accurate You can tell that immediately when you play them together. That’s just too many waves before they meet up, and For instance, C# has a frequency ratio toĬ of about 18/17ths. It takes too many wavesįor them to match up, and our ears just can’t seem to find a regular pattern.Īt what point is this? The simple answer is when the ratio’s numerator orĭenominator gets to about 13. For instance, instead of C,D,E,F,G,A,B, you can start on, say, D#Īnd have D#,F,G,G#,A#,C,D as your scale with the same great sounding combinationsįrequency ratios are too great to sound consonant. Is that you can start a scale on any note you wish, including the black

Sound consonant! Another nice feature of having an equal exponential jump The waves still meet up at regular intervals and they still That gives a ratio from G to C of about 3/1 (twice the original We still have middle C at 261.6Hz, but G is now atħ84 Hz. You can move notes into different octaves and still have them sound consonant.įor instance, let’s take the case of middle C and G again, except move G The A below middle C is at 220 Hertz, the A above middleĬ is at 440 Hertz, and the A above that is at 880 Hertz. This gives a nice smooth transition going up the scale.Īnother important feature of the scale is that it jumps byĢ times each octave. The Hertz jump is not equal between the notes, it is an equal jump in theĮxponent number and it sounds like an equal jump to our ears going up the As an example, let’s figure the hertz for middle Is according to the MIDI standard, where middle C equals 60, and the C an Of vibrations a second) = 6.875 x 2 ^ ( ( 3 + MIDI_Pitch ) / 12 ) Each note in the 12 note scale goes up an equal amount, that is, Shows only the 7 notes in the C Major key, not all 12 notes in the octave. If the ratio was perfect, the frequency of the AĪbove middle C would be 436.04 Hz, which is off from 'equal temperament' Since they couldn’t have both at the same time, they settled on aįrequencies for the notes in the C Major Key:Ĭan see that the ratios are not perfect, but pretty close. In tune, but they also wanted the notes to go up in equal sized jumps. ‘western-style’ scale was created, they wanted not only the ratios to be Ratio of E to C is about 5/4ths? The actual ratio is not 1.25 (5/4ths) but 1.2599. To tell you the truth, these are approximate The ratios of the notes in the C Major key in relation to C: Since every note’s frequency matches up well with every other note’sįrequencies (at regular intervals) they all sound good together! The ratio of G to E is about 5/4ths as well. The E matches up with every 4 th wave of the C. Here are the frequencies of the notes in the C Major chord (starting This is the secret for creating pleasing sounding note combinations:įrequencies that match up at regular intervals (* - Please see footnoteĪ chord, to find out why it’s notes sound good together. Matches up with every 2 nd wave of the C (and in the second graphic Graphic there is a repeating pattern: every 3 rd wave of the G The difference between these two? Why is the first ‘consonant’ and the second Look at two notes that sound terrible together, C and F#: Let’s use middle C and the G just above it To understand why some note combinations sound better, let’s first lookĪt the wave patterns of 2 notes that sound good together. For instance, the A note below middle C is The more waves per second the higher the pitch. This is measured in Hertz (abbreviated Hz). Times per second these waves hit our ear is called the ‘frequency’. This causes mechanical energy to travel through You pluck a string on a guitar, it vibrates back and forth. Wonder why some note combinations sound pleasing to our ears, while othersĪnswer to this question, you’ll first need to understand the wave patterns

Music note c in hertx