~ music intervals ~

'measure, label and aurally understand the theories of distance, space and gravity between musical pitches.'

minor 3rd

major 3rd

interval filter studies

interval filter studies

 

~

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In a nutshell. The space between pitches is a true determiner of their potential influence on one another. This is their numerics page for accurate identity.

Definition / Overview: Most of us probably use the word distance to describe the space between two things. In music that distance can be a range of actual pitch that we might try to understand ways; listening (aural), a numerical labeling (intellectual), or through our 1000 year old system of notation (written symbols).

So really there's some interesting ways to think and muse about musical distance. And that's the idea behind the following discission of this term 'interval', we're just measuring the interval or distance between two pitches. We'll use the same labeling and measuring process through all of our musical styles.

Advanced theorist. For the advanced theorist reading here, there's really just one idea for the general topic of this page; measuring and labeling the distance intervals between a root pitch and each greater degree of the chromatic scale. This entire exercise helps to prove up the perfect closure of our pitches.

Simply that our 'groups of pitches' today are the perfectly closed loops of pitches from which we create our ideas of melody, harmony etc. Subbing for the term 'scale' to a certain extent, a 'group' includes the multifaceted properties that each pitch in a 'scale' brings to the conversation.

These properties include; modes, shades of major / minor, apeggios, colortones, 'parent scales' for phrases, intervals, sequences, soloing through chord changes. Our chosen group creates what is diatonic, thus establishing the boundaries of a select group of pitches. Combined we create a stabilizing perspective of the theory for venturing on beyond.

melody / harmony / modes

arpeggios

sequences

soloing

venturing beyond

The whole tamale. With the majority of melodies being created from the diatonic major scale group of pitches, an initial examination of the intervals within this group for emerging theorists just makes good sense. Continue here for a survey of our complete 12 tone resource.

Common symbols. These symbols are used to identify the various aspects of our musical interval measurings. Example 1.

Survey the whole tamale. This next idea includes all of the intervals we'll commonly find in our musics all labeled generically. Used in creating the building blocks of scales, arpeggios and chords, each interval can have other names or numerical descriptions. It extends for two full octaves and includes each nook and cranny along the way. We term theintervals of the first octave 'simple.' Intervals of the second octave are said to be 'compound.' This sort of charting helps us get our arms completely around the resource. Example 2.

Well that looks fairly complete. Some interesting fingerings yes? This all might be easier at the keyboard. If available, use the sustain pedal to sound, hear and sing along with each pairing. Also, these interval numbers are the ones used in creating a part of the main navigational chart for this book. Example 2a.

Chromatic scale ~ a 1/2 step ~ one fret ~ half step interval. A core center of the theoretical American musical universal is the 12 pitch loop of the chromatic scale. This symmetrical group of pitches is simply created by using only one interval; the half step.

As theorists, we tend to want to slice and dice our musical intervals every which way and when we do, we want to try to label our dicing results with standard musical vocabulary. This labeling usually happens a couple of ways, which we often combine, to consistently dial in the aural sound with music theory terms.

ex numbers

So to begin this interval discovery process, examine the 12 pitches of the chromatic scale using middle C as our root or fundamental pitch. Sing or hum along as you go and find the pitches on your instrument. Example 3.

Sharps and flats. Lots of black dots yes? No worries for that's all of these we have for the most part. For while we can extend our range by additional octaves, this in theory is our complete set of pitches to work with. Those so impassioned will rote memorize the lick.

Of our 12 pitches, the C, D, E, F, G, A and B are said to be natural and as such, are simply identified without a sharp or flat. We can find these as the white keys on the piano. We use the sharps (#) and flats (b) to identify pitches as well as to make adjustments by half step.

In the above idea we used sharps going up and flats coming down to label certain pitches. While cool here, which of these two we use is more dependent on key center than a line's overall direction. We'll always try to notate the music the way it will be most easily read, give the musicians reading the work the best chance of success. Theory be banished!

So can you accurately sing the pitches along with the mp3 audio file? Perhaps without the audio? Surely developing this ability to sing the chromatic pitches within the octave is a giant step in helping our ears to hear the theory. For the career musician, this is one of our seven skills.

Where are the half steps in our music? Thinking along our theory spectrum of style, we commonly find the half step as a 'lead in' to a diatonic pitch within the key center of a song. So when making folk music, this occurs mostly with our voices until our guitar chords develop into more movable forms. Once there; game on but only for a moment really, of musical time. For most often the half step lead in sounds barely get a full beat. We use this motion to charge up the swing.

In the blues. Anytime we sense the blue hue in the music, there's a chance the half step is involved. For blues' singers, finding the sweet spots is probably all by ear as the story being told is the energizer. For we theorists, we'll measure the intervals too :)

blues hue

In jazz. There's a unique spectrum of chromaticism through our American jazz library of songs. As the blues historically preceded and base jazz, all of the blues' hue mentioned above is common all throughout. In getting the music to rhythmically swing from each participant in a jazz group, the half step lead in becomes a seamless, continuous process as the music is being created.

In the more modern jazz of the last 75 years or so, in some genres, the written melodies have become more chromatic in construction. Do remember here that when the pitches are this close together, that with practice, they can be played very very fast.

As a part of the jazz artform, the half step / chromatic color is also used as a way to obscure the sense of tonal direction in the music, create momentary (or longer) respites to tonal gravity and forward motion, create those lovely blurs of modern color and to jazz up the more common cycles so often found within the music.

Within the octave span. In this next idea we simply break down the chromatic scale into its 12 component parts and measure each of the intervals from our root pitch C. Do sing or hum along as the mp3 file plays back the written music. Gently close of an ear with a finger to better hear your vocalized pitches. Or perhaps scat sing along as you work through the pitches with your guitar. Example 3a.

Labeling intervals. Our purest sounding intervals we label perfect, abbreviated (p. / per.). These are in order of aural purity the perfect octave, 5th and 4th. Next in sound purity come our major (maj) and minor (min) third, then major and minor intervals. These three labels; perfect, major and minor are the most common.

We can further resize our perfect intervals, making them larger termed augmenting (aug) or smaller termed diminishing (dim). We'll explore each of these in turn during the following survey measuring between pitches.

Looping intervals. Each of these intervals also becomes a sort of portal into our whole system of theory. For if were to choose any one interval and loop it, as we examine this loop we'll find each interval as the organic building block of the larger compositional components we use in composing and creating music.

Music intervals / quality of sound. Written history reminds us that our system of tonal organization is based upon the perfect octave interval, the interval notated in last measure just above. For it is this interval between two pitches when struck together that resonates most purely, or simply that which sounds the best to our ears, that becomes the foundational basis we build our entire system of music theory upon.

So of all of our possible interval combinations, the pitches of an intune, properly struck octave perfectly melt into one another, making either the lower or upper near indistinguishable from one another in their combined sound. This purity of sound between two struck pitches, whose interval is a perfect octave apart, is the basis of our theory from which we create our entire system of tonal organization.

 

Science weighs in / measures of aural purity. And while our ears will often tell us which of the intervals sound best, and this of course is about one's own art, mathematical science can provide another way into this discovery process. It turns out that the simpler the numerical ratio between pitches, the purer its sound and aural perfection.

More than one way to label our intervals. Perhaps needless to say that there is more than one way to name an interval. Depending on one's experience, existing information and artistic directions, there are variables to consider and navigate. As theorists, how we name an interval is nearly always dependent upon where we find it and how it is used in the actual music we're studying. Here at Essentials this where and how is often called "by the numbers." But having to start somewhere, we simply do what we can with what we have n'est-ce pas?

Diatonic major scale intervals / purity of sound. Stylistic and genre considerations aside for the moment, turns out that the majority of compositions in the American songbook are written in a major key. In this next idea, we simply arrange the intervals found within the diatonic major scale according to their degree of purity of sound.

For those into the numbers, purity of sound is reflected in simplicity of the ratio between the pitches. All things considered, the simpler the ratio, the purer the sound. In this next example we borrow the ratios from a system of tuning known as 'just intonation' based on the natural overtone / harmonic series, which provides us with a 'close enough' approximation of the pitch ratios for our comparative purposes here. Example 3b.

What to listen for. In the above example, the less we can hear the purer the sound. Thus, when sounding the two pitch octave, can you distinguish between the lower and upper C's? Or do they perfectly melt or merge together into one sound? As we move towards the right, as each successive interval becomes less consonant thus more dissonant, can you better distinguish between the two pitches used in creating the interval?

If so, you're not alone Amigo, for this simple illustration is the core of our tonal gravity / aural predictability of the music we create. I conclude the above idea with the premiere octave consonance to provide a glimpse of the perfect closure of equal temper tuning.

Diatonic major scale intervals. Thinking C major, let's examine and name the pitches of the diatonic C major scale. Here we measure and label each of its pitches all from our root pitch C. Example 3c.

OK so far? Major scale created by major and perfect intervals. Do find them on your instrument. Can we project this same theory from each of the 12 pitches? Sure can.

Inverting the diatonic major scale intervals. So what goes up must come down n'est-ce pas? So it is with our intervals. In the following chart and musical example, we invert each of our diatonic intervals of the major scale. Example 3a.

C up to D

major 2nd
C down to D
minor 7th

C up to E

major 3rd
C down to E
minor 6th

C up to F

perfect 4th
C down to F
perfect 5th

C up to G

perfect 5th
C down to G
perfect 4th

C up to A

major 6th
C down to A
minor 3rd

C up to B

major 7th
C down to B
minor 2nd

C up to C

perfect octave
C down to C
perfect unison

Easy enough yes? Surely lots to memorize for the emerging theorist. A bit each day will feed the bulldog over time. So 'triangle' is major, ' - ' minus is minor and 'p.' is perfect. Interesting how the inverted interval always numbers add up to nine? I wonder why that is.

Blue notes / the remaining five pitches. So if our chromatic scale has 12 pitches and we use seven to create the major scale, that leaves us five more pitches to negotiate. While we term these five remaining pitches non-diatonic, in a more American theoretical vernacular, they are the essential blue notes. They're blue in their interval relation to our tonic pitch C, of the C major scale. Hip to the idea of the blues rub? Examine the blue note intervals and ratios. Example 4.

Where in the music. Well, we're starting to get a wee bit more tense in our relation to our tonic pitch C. On one end is our purest octave with a ratio if 2:1 to the diminished fifth, that checks in at a confusing 45:32. This tension is what creates what I call the blues rub, we rub mostly diatonic, consonant pitches against dissonant. This lives pretty much everywhere in the American sounds we love.

Traditional Folk music too? Well yes, that probably would be a bit of a stretch for sure but in anything even remotely or directly linked stylistically to our blues, rock, pop, jazz and beyond, mixing the blue notes into the diatonic major / relative minor grouping is an American certainty we've come to enjoy.

The minor tonal environment. For many players, the minor keys and the colors within are the ones that they base their core sound on. The whole blues thing fits right in this zone. It's interesting in that while we'll often use the five nondiatonic pitches to spice things up in songs written in a major key, the reverse it not nearly as true.

Honking on the major 3rd in a minor tune is often just plain awful. Same with the major 7th, although fairly often we find this color as a passing tone. So we really do not get it both ways here, but artistically using the minor pitches in a major key is very common and cool. Honking the minor 3rd over V7 creates the American essential blues rub, a strong current that flows in most of the American styles throughout all of the eras.

~ super theory game changer ~
Interval studies.

What they are. Musical interval studies are about diatonically creating the same amount of distance or interval from each pitch within a select group of pitches. Once we decide on which interval to sequence, we just string the pitches together using that distance between them to create melodic sequences. While the following ideas are more academic than musical, they become way more musical as we place them into songs and our compositions. These sorts of studies often make for good warmup exercises also.

Grist for the mill. 'Grist for the mill' was what my college professor Dr. Miller used to call the musical material we needed to shed to thoroughly learn our instruments. The 'learn and forget' creed of the beboppers. Of course we each tend to gravitate towards certain sounds and in discovering our own artistic / pro balance, we end up shedding what'll keep the lights on.

The following studies are all diatonic, arranged by interval, and give suggestions for the basic permutations for a place to start. Sky's the limit of course and there is a ton of additional ideas out there for those so inclined. The following lines are suggestions of course. Oftentimes they start and end on the tonic pitch. In doing this we're just trying to create a sense of tonal closure for the emerging talent while getting our pitches, scales and intervals under our fingers by rote.

Where in the music. Melodic intervals are everywhere in the music. The interval studies are about exploring and developing our melodic and improvisational strength with our pitch resource with various intervals. In a longer view of these and additional interval studies, we're simply are looking for musical ways to get more mileage out of our best melodic ideas. These initial studies often lead to the more advanced permutation and sequence possibilities.

Stronger cats will work one melodic idea, often drawn from the melody of the song being performed, and will permutate that idea through the song's form, oftentimes using intervallic ideas similar to the ones which follow here. Towards the close of the chorus, they'll present a new idea and start this improvisational process over. Thus, the interval studies are like calisthenics, to strengthen our melodic abilities enabling us to create cool ways to develop our best ideas.

Interval sequences / what they create. In our AmerEuro music over the last 500 years or so that we have record of, musical sequencing plays a nice role in creating the art. The melodic intervals studies which follow are in reality also simple exercises for the emerging talent in creating melodic sequence.

For from these melodic studies we often harmonize the lines, creating harmonic sequences more commonly known as our chord progressions. Rhythm patterns are also applied to our pitch sequences, which when added to our pitches and chords creates the sequences that help our music flow, find a balance and become art.

Stepwise or scaler motion ~ major and minor seconds. This melodic motion, surely at the core of all melodic motions, simply follows along with each pitch of the group of pitches we're working with. In the following idea we'll start with the major scale and then its relative minor. Moving stepwise, our intervals are whole steps and half steps, the major and minor seconds respectively. Example 5.

Relative minor. Here we use the same pitches and follow the same stepwise interval motion as above but start on the 6th scale degree to create the relative / Aeolian minor. Example 5a.

Motion in thirds. This next idea is very common and we'll find it all throughout the literature. By simply skipping every other pitch in our scale group, we'll create a line of major and minor thirds. First ascending, then descending. Example 6.

Descending motion in thirds. In this next idea, we simply flip things around. By changing up the rhythms a bit we can transform our interval studies into near melodies. These ideas in major and minor thirds just might be perfect for creating our melodic sequences over tertian harmony, the American apple pie combination for a true core of thoughtful composing, both written out and in our improvisations. Example 6a.

Alternating the direction. In this next idea, we simply alternate our interval motion by moving upward first, find the next pitch in the group and then use a descending third. We then find the next pitch and ascend by third etc. This alternating of pitch direction is the next challenge level of our interval studies. Example 6b.

Upside / downside. This next idea comes from to us via trumpeter Brian Lynch of NYC. I got to hear Mr. Lynch up north here a few years back and heard this bit on an interval study and just thought ... 'now how cool is that.' Pretty sure the 'upside / downside' is a title of a jazz fusion monster guitarist Mike Stern composition. In this idea we ascend by third while descending stepwise. Example 6c.

wiki ~ Brian Lynch
wiki ~ Mike Stern

Pretty cool huh? Apply these alternating melodic treatments to any and all of your interval studies as you deem essential to developing your wizardry. The rhythmic consistency hurts the artistic melodic nature of the line for sure but this is just grist for the mill :)

Motion in fourths. Here we begin to get a bit out there, for while bass pitch motion by fourth is super common, melodic lines in fourths tend to neatly obscure our tonal direction toute suite. This type of motion became popular for jazz cats in the 70's as the music became modal with a rock influence and chords stacked in fourths; i.e., quartile. Players blowing over one chord for extended periods and patterns in fourths became cool. For when executed accurately and quickly, they do sound stellar. Example 7.

Inverting the intervals. Following along the above progression, we simply invert the intervals and descend the line. Example 7a.

A serious fingering challenge. These types of melodic ideas create some serious challenges for the advancing guitarist. For here we are in one key and basically hanging in the same area of the fretboard. Aspiring jazz players will to eventually run this through all of our 12 keys over the entire pitch range of the instrument.

A tall order for sure but there is surely a method, actually lots of them, to conquer this madness. Examine the ideas in the method section for a way into the 'anything from anywhere' concept.

Motion in fifths. As the intervals get wider, we approach what players often call the 'wide interval' studies. That exercises in the 5th's and beyond set the stage for bolder motions for those so inclined. Here we stick to our diatonic motion in C major, ascending fifths. Example 8.

Descending in alternating 5th's. Following along in our general studies here, this next idea alternates the intervals as we descend the line. Example 8a.

A sequence. Very cool how even this academic line creates a very solid melodic sequence. It almost has a Baroque quality to it. Of course it is a bit mechanical but even so, provides a good starting point in the process of sequencing our ideas. Can any artistic idea be filtered through an interval and sequenced? Probably so.

Motion in 6th's. The interval of the 6th, actually the 6th scale degree of the major scale, is home to the relative minor, Aeolian mode and a key pitch in the major pentatonic color. In this next idea, a simple vanilla ascension up then down. Example 9.

Into the wayback machine. Permutating the wide interval up, then by diatonic step then leaping downward to create the sequence. Again the sound to me is very Baroque. Guitarist Ted Greene often talked about the music of the European Baroque period of the 18th century being so similar to the harmonic and melodic cycles we find in American jazz. Example 9a.

Intervals ~ motion in major 7th's / leading tone. The interval of the major 7th, the first leap in the following line, surely gives us a sense of its ability as the leading tone to our tonic pitch. The smaller minor or blue 7th, the key component in our V7 chords, also lends its abilities in moving towards each successive pitch in the line. Example 10.

Permutating the pitches. Again the sense of a cycle emerges as does the tonal direction of the line. When we do achieve the final pitch it surely is not unexpected, i.e., tonal gravity. Example 10a.

Motion in 8th's / octaves. Flat picks probably down first here as the last of our simple intervals is the octave. These are often played as written below or as a double stop sounded together. Bass players often create lines similar to the following idea. Example 11.

The 'Wes Montgomery' sound. In this next idea we simply play the octave pitches together. Commonly known as 'in octaves', they can become a very powerful melodic component of the modern guitarist's palette. Jazz guitarist Wes Montgomery of the later 50's and forward developed a very keen sense and ability of what these octaves could do in a wide range of musical settings. Common bottom line? Swings.

Octave sounded lines are not only deep in pitch but can also have a very deep rhythmic strength that swings hard. Sound these 'a la Wes' ideas by fanning the pitches with your thumb. Another approach is to claw the pitches together with the thumb and index or middle finger. Or flat pick and claw (not easy at all). Example 11a.

Octave melodies. Playing lines in octaves can surely be a tricky process at first. For there are nuances as to how each of us physically play that can factor in. The easiest way into this is to simply find melodies we dig and figure out ways to 'octavize' the lines. All of the Americana melodies included in this text make great octave studies. For all of the lines are diatonic, easy to hear for the most part and we just might already know them. Click the links to the right for suggestions.

So, a bit cooler with the intervals? Newer players often find these studies fascinating as they open up a new world of melodic possibilities. When we figure in different rhythms, we just might end up in awe at the possibilities. Most of our music lives in various cycles and the interval studies can help to organize our most diverse creative ideas.

There are patterns within beautiful art. The creative artist can recognize and invent cool pattern 'cells', which are then expanded into full works. Top 40 crafters call this their hook. Advanced improvising musicians often do this while the music is being created in real time. This surely is something to behold for those in the know ... and now you know too :)

The ideas above are academic in their approach. For all of the American styles they provide a solid place to begin. As we mature over our careers and look for ever greater challenges in our art, interval studies and permutation of the pitches provides a solid source for new challenges and ideas.

Run these down in A minor. Hear some hints of minor in these ideas? Not really too big a shift to rerun the lines through the 'perspective' of A minor. Same relative pitches as C major yes? Just a slight shifting of the intervals within the same loop of pitches.

Where in the music. Of course this type of study is mostly a jazz thing. Most of the other musical style's improvisational melodic demands are considerably less and the interval studies not nearly so essential to building one's melodic strengths. Improvisation in the blues / rock traditions are often based on paraphrasing the melody of the song, two and four bar riffs, repeated hooks and of course the wow factor. Thus, the interval studies are not as key in developing improvisational strength as soloists generally just do not get the extended ride time or the consistent brighter tempos of the jazz.

Soloing in the folk styles is generally limited. Folk artists might get a couple of bars usually the intro of the tune. Of course in folk's cousins, bluegrass, country and beyond, sky's the limit although eight and sixteen bar 'breaks' are the norm. In most of the rock and pop worlds, soloing is usually limited to four, eight and sixteen bar phrases.

In the blues, the 12 bar form is king and two choruses, thus 24 bars, is generally what most cats need to work the magic. First chorus can be time to settle things a bit to 'bring it' on the second. In stronger players, of course all of this 'generally happens thing' goes out the window.

Jazz players. Jazz players will inevitably follow all of the above guidelines included in the other styles and then extend all of their parameters. One chorus in a typical jazz song is generally 32 bars. Stronger players most often solo with a two chorus minimum. Extra strong players solo till they are done, no limit to the blowing as that is in many performance settings, the core component of the artform. Thus, taking a half a dozen choruses in a blues solo is not all that uncommon.

There's a second aspect of these studies with the five scale shapes that pattern together the pitches for the jazz guitar method. Surely a more thorough diatonic go at the resource over the range of the lower 12 frets; scale shapes, diatonic intervals, arpeggios and chords and their color tones. And while most of these simply increase our initial challenge, they also strengthen our knowledge of the instrument, what we say and how we say it.

Do remember that in jazz performance, the tempos are often brighter than our other musical styles, this in itself ramps up the challenge. Successfully meeting ramped up challenges ramps up the fun. Thus, thorough and ingrained knowledge by rote memorization of resources is really just the easiest and quickest way to go.

"Music washes away the dust of everyday life."

Art Blakey

Review. Here is a chart to review the musical intervals we have by combining our first octave melodic numbers one through eight with our more harmonic leaning numbers nine through fifteen.

Simple intervals. Intervals found within the octave span.

pitches
interval
# of half steps
# of whole steps
commonly called
C to C unison / prime 0 0 unison / prime
C up to C# augmented unison 1 .5 sharp one
C up to Db minor second 1 .5 flat two
C up to D major second 2 1 two
C up to D# augmented 2nd 3 1.5 sharp two
C up to Eb minor third 3 1.5 flat 3 / blue 3rd
C up to E major third 4 2 major third
C up to F perfect fourth 5 2.5 fourth
C up to F# augmented 4th 6 3 sharp four / tritone / blue 4th
C up to Gb diminished fifth 6 3 flat five / tritone / blue 5th
C up to G perfect fifth 7 3.5 fifth / dominant
C up to G# augmented fifth 8 4 sharp five
C up to Ab minor sixth 8 4 flat six
C up to A major sixth 9 4.5 six
C up to A# augmented sixth 10 5 sharp six
C up to Bb minor seventh 10 5 flat seven / blue 7th / dominant 7th
C up to B major seventh 11 5.5 major seventh leading tone
C up octave to C octave 12 6 octave
C up octave to C# augmented octave 13 6.5 sharp octave?
C up octave to Db minor ninth 13 6.5 flat nine
C up octave to D major ninth 14 7 ninth

Compund intervals. Moving into the second octave above our starting pitch. We often associate these elevated numbers in association with our harmony or chordal explorations.

by the #'s 8 thru 15
harmony / chords
pitches
interval
# of half steps
# of whole steps
commonly called
C up octave to C# augmented octave 13 6.5 sharp octave?
C up octave to Db minor ninth 13 6.5 flat nine
C up octave to D major ninth 14 7 ninth
C up octave to D# augmented ninth 15 7.5 sharp nine
C up octave to Eb minor tenth 15 7.5 minor tenth
C up octave to E major tenth 16 8 tenth
C up octave to F perfect eleventh 17 8.5 eleventh
C up octave to F# augmented eleventh 18 9 sharp eleven
C up octave to Gb diminished twelfth 18 9 diminished twelfth
C up octave to G perfect twelfth 19 9.5 twelfth
C up octave to G# augmented twelfth 20 10 sharp twelve
C up octave to Ab minor thirteenth 20 10 flat thirteen
C up octave to A major thirteenth 21 10.5 thirteenth
C up octave to A# augmented thirteenth 22 11 sharp thirteen
C up octave to Bb minor fourteenth 22 11 flat seven
C up octave to B major fourteenth 23 11.5 leading tone
C up 2 octaves to C major fifteenth 24 12 octave
C up 2 octaves + 1/2 step to C# augmented fifteenth 25 12.5 sharp fifteen
C up 2 octaves + 1/2 step to Db minor sixteenth 25 12.5 flat nine
C up 2 octaves + whole step to D major seventeenth 26 13 ninth
C up 2 octaves + 3 1/2 steps to D# augmented seventeenth 27 13.5 sharp nine
C up 2 octaves + 3 1/2 steps to Eb minor eighteenth 27 13.5 minor third
C up 2 octaves + 2 whole steps to E major eighteenth 28 14 8 av. tenth?
 

Footnotes:

(1)Mauleon-Santana, Rebeca. 101Montunos, p. iv. USA Sher Music Co.,Ca. 1999

(1) Isacoff, Stuart. Temperament ... The Idea That Solved Music's Greatest Riddle, p. 40-42. USA Alfred A. Knopf, New York. 2001

(2)Aebersold, Jamey and Slone, Ken. The Charlie Parker Omnibook. New York: Atlantic Music Corp., 1978.