Thursday, October 17, 2013

Just Intonation compared to Pythagorean Tuning and Equal temprament

There have been many different tuning methods throughout time and none of them are perfect for all music. This is because music is based on intervals between notes, and those intervals do not always add up when yous switch key.

According to Ptolemy's intense diatonic scale, which is considered the only tuning that could be reasonably sung, and corresponding with modern just intonation. Gandharva Veda uses this system of tuning which means that the resonance between all the different notes will be preserved. The C major scale looks like this if we use 528 Hz as the starting note.

C = 528 Hz
D = 594 Hz (528 x 9 / 8)
E = 660 Hz (528 x 5 / 4)
F = 704 Hz (528 x 4 / 3)
G = 792 Hz (528 x 3 / 2)
A = 880 Hz (528 x 5 / 3)
B = 990 Hz (528 x 15 / 8)
Next octave of C = 1056 Hz (528 x 2)

All of these frequencies interact harmoniously with each other and all intervals are perfect equations with small . It also works with A minor, since that scale uses the same notes. However, if someone played a C major song and switched to D major, A would be the fifth and should equal 594 Hz x 3 / 2 = 891 Hz, which is quite different from the A = 880 Hz in C major. Your ear can hear difference a difference of 1 Hz between two notes that are sustained, so 11 Hz is a large difference.

Pythagorean tuning is not even harmonious within a single key and uses only perfect fifths (3:2) and octaves (2:1) which creates very large integers, such as 243:128 for a major seventh which comes from five fifths up and two octaves down (3/2)5 x (1/2)2. The big downside is that thirds (which form the middle note in chords) are dissonant - they are 81:64 instead of 5:4, which means for the above example E = 668.25 Hz instead of 660 Hz. Those extra 8.25 Hz means that musicians working with Pythagorean tuning can't play regular chords, but have to stick to simpler music using mainly fifths instead.

With Equal Temperament musicians figured out a way to play all different keys on the same instrument with a harmonic sound. Even though Equal Temperament is often viewed as a Western invention, it has been historically discovered by a Chinese man in 1584 and a Dutch man in 1585, independent of each other. Instead of working with intervals that relate to each other in mathematical harmony, equal temperament simply divides the octave into 12 equal pieces.

The downside of Equal Temperament is that some tones are more than 4 Hz higher or lower than their Just counterparts, which is a clear audible difference. This means that a perfect fifth, which is 3:2 in Just Intonation, will instead be 2.996614:2 in Equal Temperament. In Just Intonation the fifth and the unison would resonate with each other every 2 beats for the fifth and 3 beats for the unison. However, in Equal Temperament the fifth will slowly go out of beat with the unison since there is no exact mathematical relationship.

This means that instead tones strengthening each other, they destructively interfere with each other, as can be seen in the following image from a lecture held at Maharishi Vedic University, Vlodrop, Holland, in January 2011.


"The two upper waves are the sounds, while the wave under is the combined sound that we hear. The two sounds have the same amplitude. The changing amplitude of the lower wave shows the change in volume of the combined sound. At point A the two sounds are somewhat synchronous, and the combined amplitude is at its largest. Then they become less synchronous and the combined amplitude becomes less. At B they vibrate opposite each other and the combined amplitude becomes zero, making no sound. Then they gradually move back to synchrony, while the combined amplitude gradually increases and reaches its maximum when the two waves again become synchronous, and so on."

So, even if you have tuned your guitar to A = 432 Hz, the guitar itself does not use Just Intonation and so even if A is the right frequency, no other tones will be. The easiest way is to play a fretless instrument, such as the violin, since you can adjust each note as you please. However, with guitar and keyboard there are no easy solutions to this, unless you want to build your own guitar like this guy did!

Monday, August 12, 2013

Point of Vantage: Guitar vs Piano

This post is inspired by David Hurlin's post Vantage Point where he talks about how drumming on unconventional instruments such as mailboxes can unlock innocent creativity. I would recommend you to read the full post!

This brought to life an idea I've had for a while. In my mind, the guitar is a more creative instrument than the piano. Now, don't get me wrong, pianos are beautiful and great music has been written through playing the piano. However, a piano is linear, whereas a guitar is two dimensional. Each string on a guitar is like a mini piano. In addition to this, a guitar presents all tones as equal since it does not distinguish between black and white keys, whereas a piano tells you which tones you should play for C major and all other keys are played in relation to C major, as far as the black and white piano keys are concerned.

Sure, the piano has potential for grandiose pieces of music since you can use all ten fingers at the same time, whereas with the guitar you only have six strings and five fingers to play with. In my experience though, the guitar has inspired me to create more original music without referring to music theory. When I first started writing "The Sound of Rain" I simply took an open C major chord and moved it down on the fret board three steps. This jumbled all the notes somewhat and when I played the different strings there was a new sound that I really liked and started to play around with.

I also like that my guitar doesn't have marks for the 5th, 7th 9th and 12th fret, because leaving room to make mistakes also means you can find combinations you never would have thought of. As one of my teachers always say, "There are no mistakes, only happy accidents".

Friday, June 21, 2013

Wholeness is Greater than the Sum of the Parts

When I play music with others, there is an interesting meeting taking place. I started playing music to express myself and to get to know myself better. Playing with others allows me to know myself in terms of how I'm different and unique compared to others. I discover that as a musician, I'm stable and steady. I know a large repertoire of songs. I also grow in unexpected ways from being influenced by the people I play with. I become more fluid and free. I start to improvise songs never written before.

I recently recorded one of my songs, The Sound of Rain, with my friend Kurtis Kujawski freely improvising to the song. To me, it really shows how the interaction between structure and flow can create a wholeness more beautiful than each part.



When I play with other people I play less for my own sake and more for the sake of the music itself. Being part of something greater makes me realize what my true talents are and inspires me to develop new ones too.

Monday, June 3, 2013

528 Hz Experiment

A few days ago I did an experiment with my friend Nick Tucco, similar to the previous post where the frequency of 432 Hz created symmetric patterns. This time we are using 528 Hz, which is one of the Solfeggio Frequencies.

We used my guitar amp, his drum, and a bunch of sand. Connecting my amp to a computer, we played the tone 528 Hz on pretty high volume which made the drum vibrate and distribute the sand over its surface in patterns.



Initially we had too little sand, which only showed a hole in the middle surrounded by two rings of sand.
Later, when we added more sand to the drum, the hold in the middle didn't show up, but instead seven empty circles around the edge of the drum were seen. Both times we used 528 Hz.

The sounds we create have an impact on the environment and can create something beautiful. Taking this to a deeper level, our thoughts are nothing but unmanifest sounds and have similar capabilities. Before we can speak, we have to have a thought, even if it is unconscious. If we can fine tune our amplifiers to create sand patterns on a drum, who says we can't fine tune our consciousness to create patterns in our life?

If you want to delve deeper into the mystery of frequencies, read about the difference between 440 Hz and 432 Hz here.

Sunday, December 2, 2012

432 Hz compared to 440 Hz

I've been reading about alternate tuning and done some of my own research into the subject. The standard tuning for instruments is A = 440 Hz  This was decided in 1939 and this is the only official standard tuning around the world. My preferred tuning is A = 432 Hz which according to some studies is a more harmonious frequency, in tune with natural law. You can see for yourself with these two water sound images of the two frequencies.


Worth to mention is that there are many alternative frequencies for tuning. Some people say 444 Hz is the "sacred frequency" but so far there is no "right" or "wrong" tuning defined. There are claims that 432 Hz was the standard tuning for classical composers, but this is not true. There was no such thing as a standard tuning before electromagnetism was discovered in the 19th century, which enabled the precise measurement of frequencies. Old organ pipes are tuned to a large variety of frequencies. 

"For example, an English pitchpipe from 1720 plays the A above middle C at 380 Hz, while the organs played by Johann Sebastian Bach in Hamburg, Leipzig and Weimar were pitched at A = 480 Hz, a difference of around four semitones. In other words, the A produced by the 1720 pitchpipe would have been at the same frequency as the F on one of Bach's organs."

With this being said, my own personal experience with the different frequencies has been clear. I feel a lot more relaxed when playing 432 Hz on my guitar, maybe partly because there is less tension on the strings. However, there is also a connection to sacred numbers. An lower octave is half the frequency and a higher octave is double frequency. The A string (second lowest) on a guitar that is the one being tuned is two octaves below the tuning A, which means four times lower frequency. For 440 Hz this becomes 110 Hz, but for 432 Hz it becomes 108 Hz, which is a sacred number. (See Wikipedia)

You can also see a practical experiment I did with some friends on the Solfeggio frequency 528 Hz in this article.

For a more philosophical article, read about the Source of Music.

Saturday, November 17, 2012

Performing vs Recording

When I started singing my strongest motivation was the chance to perform. Being in front of an audience and meeting them through music has always been a profound experience for me. I want to thank my music teacher Ingeborg Axner FranzĂ©n who has a deep and profound philosophy in her teaching.

I learned that a performance is always a meeting between the audience and the performers. Ingeborg helped me understand that the audience is part of the performance and actively create the music together with me. My song is something I wish to express to them, a gift of myself that I can share, but their attention is an equal gift in return because they create the space that I fill with music. Ingeborg and I would take different angles on every song in preparation of a performance and figure out what the essential message and feeling in the song I wanted to give the audience. This way, I've always been very conscious about the deeper layers of music.

In this video I'm performing two original songs:
On my own (starts at 1:50)
Unspoken Dialogue (starts at 5:10)

I started taking vocal lessons at the age of 13, just as my voice started to deepen. Now that I'm almost 26, it means half of my life I've been singing as a hobby, so it has become an intimate part of who I am. I've known Ingeborg, my music teacher, since I was 6 years old and started taking piano lessons from her. I still meet with Ingeborg whenever I go home to Sweden and continue to have coaching sessions, and we stay in touch through emails as well.

Ingeborg taught me different song styles, such as classical singing or being more raw and expressive, but always reminded me to go back and sing as Patrik would have done it. This way I could develop a versatile voice while still retaining a strong identity and unique style of singing. She noticed that I put particular attention on the lyrics when I was singing and so she helped me develop my lyrical singing, along with an appreciation for the melody. I am grateful to have a music teacher who never criticized me in a negative way, and instead pointed out something good before making a caring suggestion for improvement.


Now I have started to get into a whole different field, which is recording. Compared to a caring music teacher, the microphone can seem cold and critical sometimes, as it picks up any slight mistake I might make and mechanically repeats it to me when I listen to the recording. I've learned to be less self-critical through listening to my own recordings and realized that there is a great advantage to this medium: I can now enjoy my own music and have a self-referral feedback loop.

This is great for songwriting, as I can sit and fiddle with different chords, song structures and instrumental parts and then listen to the wholeness. Transitions, how different parts fit together and the overall theme of the song becomes clear in a way that isn't possible otherwise when I listen to my recorded self. I can make changes to intonation, smoother transitions between verse and chorus or simply just enjoy the sound of my own music.

Monday, October 22, 2012

The Source of Music

Where does music come from?

The source of music is silence. Is this really true or just a poetic statement? I will argue my case through using the language of science. Music is composed of sound, and sound is nothing but waves. Two sound waves of the same frequency and amplitude with opposite phase cancel each other out and together create silence. This may sound really weird, but science confirms it and calls it "destructive interference". Below you can see how two identical waves can either amplify or cancel each other out, depending on their phase. Taking this a quantum leap forward, if all possible sound waves were to exist together, they would all cancel each other out and create... silence.
Animation courtesy of Dr. Dan Russell, Grad. Prog. Acoustics, Penn State.

In other words, silence is infinitely dynamic, since it contains all possible sounds. If you listen to the silence, then you have access to all these sounds and can create any piece of music. The natural question that follows is: How do you listen to silence? I would argue that it's not enough to simply be in a silent room, but that you have to also silence your mind while remaining aware. Being asleep, the mind is silent but there isn't any awareness. However, in the morning right before fully waking up (especially without an alarm after a good night's sleep) there can be a brief period where the mind doesn't hold any thoughts but awareness is still there. This can also happen just before falling asleep, when the last thoughts are gone but awareness is still there.

I experience this state of consciousness through Transcendental Meditation, a technique I've practiced for almost twenty years (since I was six years old). It takes twenty minutes in the morning and twenty minutes in the evening. I've found this technique to be the major source of inspiration for my music and songwriting.

When I perform, the silence just before the performance is what creates the connection between me and the audience, and from there the music is born. When I write music, I spend months and sometimes years taking in experiences of the world and soaking up impressions that in a short moment of inspirations gets compiled into a song. To respect and recognize this silent phase of songwriting, is to realize that spending two hours every week writing songs is only the tip of an iceberg for a dedicated musician. Being a musician is a calling that permeates my whole life.

Silence is not just the source of music, but is also an intimate part of any song. Without silence in between notes and words, music would just be noise. Imagine a good song you like with no pauses in between words or notes, and it all suddenly seems very jumbled together and not as enjoyable. A skilled musician can use the silence between words to accentuate what will come next and build up anticipation within the audience, making them wonder and long for what they are about to hear.

To further explain what happens between two sounds I'm going to use a model from Maharishi Vedic Science, called the Fourfold Structure of the Gap. (You can read more on page 9 in Dr. William Sand's Ph.D. dissertation.)



The first sound fades away into nothingness of all sounds existing simultaneously in a state of silence, and from this state the next sound starts to manifest. What makes this perspective even more interesting is that what goes into the gap - the first sound - is the exact cause of what comes next.

I have had this experience several times when I write music. A song starts in silence with infinite possibilities of what it could become. Then, I have a subtle impulse that makes me sing that first word, strum that first chord or play that first note, and from there the rest of the song flows effortlessly, like a stream bursting out from its spring. There is no doubt about what chord I shall play next, or which word shall follow the previous. They are all connected, and each one is unfolding from what came before.

What is your experience of the silence in music, and the music in silence?
(Comments are appreciated!)

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