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Vibratory clarity: Sharpen your conceptual toolbox with tuning-themed definitions – unpacked using analogies, audio clips, images, & more. Scroll around and see what you find! (everything as plain-term as possible…)

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—Tuning terms—

(12-)tet | A440 | Alpha-melodics | Amplitude | Anti-Pythagorean | Beat rate | Beau Geste effect | Binaural beats | Blackjack scale | Bohlen-Pierce scale | Cent | Comma | Consonance | Cross-note | Decibel (dB) | Dissonance | Double-siding | Drone | EDO | Equal temperament | Frequency | Fundamental | Gamelan | Generator | Harmonic series | Helmholtz resonator | Hertz (Hz) | Hyperpiano | Imperfect root | Inharmonicity | Just intonation | Lefty involution | Limit | Linear temperament | Maqam | Magic temperament | Mauna Loa | Meantone | Microtonality | Miracle temperament | Nada brahma | Non-octave scale | Open string | Oscillation | Otonality/utonality | Overtone | Paucitonality | Phasing | Pitch | Polytonality | Psychoacoustics | Pythagorean | Quarter-tone | Raga | Ratio | Re-entrant | Regular temperament | Sargam | Schismatic temperament | Scordatura | Sine wave | Slack-key (‘kī hō’alu’) | Slack thwack | Solfège | Solmization | Sruti | Stretched tuning | String theory | Swara | Sweetened tuning | Temperament | Tempering | Tetrachord | Third bridge | Tremolo | Tritave | Tuning | Twists | Undertone | Wahine | Wavelength | Wolf fifth | Xenharmonic

red = term defined here

green = article on my site

blue = external hyperlink

• (12-)tet: Abbreviation of ‘(12)-tone equal temperament’ – i.e. our modern system of dividing the octave into 12 semitones, all of proportionally equal size (hence 12 frets/piano keys to one octave). Other ‘equally tempered’ divisions are also used: e.g. 5-tet (used in gamelan) and 24-tet (a.k.a. quarter-tones). All ‘tet’ systems give rise to microtonality except 12-tet and its exact divisors (6, 4, 3, 2, and 1-tet). Here’s the chromatic sequence of two 12-tet octaves on the guitar:

• A440: The tone produced by an oscillation of 440Hz (cycles per second). Used as a tuning standard in much of Western music, having been adopted by European classical traditions from around the mid-19th century. Produced by playing 1str 5fr on an EADGBE-tuned guitar:

• Alpha-melodics: A word I came up with to describe the general process of ‘making melodies from words’, or, more formally, ‘creating music by using note names to spell out words, codes, phrases, and other semantically meaningful sequences’ (full article: Alpha-melodics: the hidden sounds of words). Here are my alpha-melodics for ‘BABA’, ‘EDGE’, and ‘DEFACE’:

• Amplitude: Essentially the ‘height’ of an oscillation – i.e. the property which determines the volume of the resulting sounds (hence an ‘amplifier’ makes things louder). All other things being equal, a wave with greater amplitude (measured in decibels: dB) will sound louder – however this doesn’t equate to a simple ‘more dB=louder’ scale overall (e.g. we perceive very low or high sounds as being softer than middle frequencies, even if their amplitudes are identical – and we won’t perceive oscillations outside our 20Hz-20kHz hearing range as sound at all).

• Anti-Pythagorean: Any tuning philosophy which seeks to reject, according to avant-garde mastermind Tony Conrad, “the tyranny of the Pythagorean worldview – whereby the proportions found in the intervals [are] elevated to a cosmic hierarchy, a divinely endowed ‘harmony of the spheres’, fixed for all time”. To Conrad, this “reeked of aristocratic oppression, [with] no role for the agency of the individual…any dogmatic system was a force to be joyfully resisted!” (…maybe he’d have got on with Cylon of Croton, who led a revolt against Pythagoras and his disciples in 509 B.C.)

• Beat rate: The ‘interference pattern’ caused when two tones of similar frequency are played simultaneously, perceived as a rapid, tremolo-like variation in volume (caused by the two waveforms alternately adding to and subtracting from each other). On the guitar, this is clearest when playing near-identical natural harmonics (e.g. as a tuning method), with the ‘beat rate’ equalling the difference of their frequencies (more from Stanford – and also see Hz, frequency, & binaural beats).

• Beau Geste effect: Describes the sonic intensification brought by particular modulation and echo patterns – most famously evident in wolf-howls, where it helps packs to sound ‘larger’ (“trees, ridges, rock cliffs, and valleys reflect and scatter [the vibrations]. As a result, competing packs hear a very complex mix…two wolves may sound like four or more”). Coined in 1977 by zoologist John Krebs, in reference to a 1924 British adventure novel in which three stranded soldiers create the illusion of strength by propping the corpses of dead colleagues up against the visible wall of their fortress (more info in Tales, Quotes, & Musings). Here’s what it sounds like:

• Binaural beats: An auditory phenomenon arising when two sine waves of similar frequency are presented to a listener separately (i.e. one via each ear) – causing the perception of a wavering, ‘beating’ effect. The sine waves must be lower than ~1500Hz, and differ by less than ~40Hz: with the ‘beat rate’ equalling the frequency difference between them. While the precise mechanisms remain unclear, binaural beating is known to be a construction of our own auditory systems, rather than arising from any ‘real’ air vibrations (also see beat rate). Try this combination through headphones:

• Blackjack scale: A microtonal scale derived by Paul Erlich, named after the card game for its 21 steps. Each step comprises 1 ‘secor’: a jump of ~116.7 cents (=1/6th of a 12-tet perfect 5th: like an ‘extra-wide semitone’) – related to the ‘Miracle temperament‘ of George Secor and others. Check out some Blackjack-tuned Rachmaninoff – and an experimental showcase of the scale from Joseph Pehrson below:

• Bohlen-Pierce scale: A 13-note microtonal scale characterised by its repetition at the ‘tritave‘ (3:1 ratio) rather than the octave (2:1). Its equal-tempered form has steps of ~146.3 cents each, with 13 of them making a tritave (=a perfect 12th: essentially the jump from 0fr to 19fr). Hear what it sounds like in Sevish’s synthesized and D’n’B settings, and watch 12tone explain:

• Cent: 1/100th of a semitone (i.e. if you sliced each fret-span into 100 pieces). For example, a jump of 1200 cents, or 12 semitones = 1 octave, while (in 12-tet) a perfect 5th = 700 cents. Like all other intervals (but unlike Hz frequencies), cents are a relative measure: i.e. they describe the relationship between notes, rather than some ‘absolute’ property (e.g. an octave is always 1200 cents, regardless of pitch).

• Comma: A small interval resulting from tuning a note two different ways. Most prominently, the ‘syntonic’ comma equals ‘the difference between a pure major 3rd and four pure 5ths, minus 2 octaves’ (~21.5 cents = 81:80 ratio) – while the ‘Pythagorean‘ comma is the difference between 7 octaves and 12 pure 5ths (~23.5 cents = 531441:524288). Commas arise primarily as ‘remainders’ in the construction processes of non-equally tempered tuning systems – in fact, equal temperaments are primarily about eliminating commas altogether.

• Consonance & dissonance: In music, these terms refer to the perception of ‘stability and clash’ in sound combinations – particularly, the relative impression of how ‘settled’ or ‘tense’ particular sets of notes may sound when played simultaneously (music is about tension and release…). Intervals generally classed as consonant include the octave (2:1), perfect 5th (3:2), and other particularly ‘simple ratios’, and most would assign the label ‘dissonant’ to intervals such as the tritone and wolf fifth – however the precise categorisations are somewhat arbitrary (for one thing, paradigms have shifted over time: and all human perception is filtered through infinite layers of cultural, social, and individual variance). According to global guitar icon John McLaughlin, who speaks of ‘hard consonances’ and ‘soft dissonances’, our common use of the terms “comes from an invalid, completely conditioned viewpoint…it steals something from the music, because you don’t even give [it] the first chance of being listened to…for what it is”. Also see frequency, paucitonality and beat rate.

• Cross-note: The set of minor tunings with only one open-string minor 3rd – named this way as you can easily ‘cross over’ to a major chord using just one finger, on 1fr of that string – e.g. in Open Dm, ‘0-0-0-1-0-0’ = Dmaj (something less straightforward in the other direction, i.e. Dm shapes in Open Dmaj tuning). Named by Skip James, who offering the somewhat unclear explanation that, “the major crosses the minor” (I guess that a ‘0-0-0-1-0-0′ major shape ‘crosses the straight line’). 

• Decibel (dB): A unit of ‘sound intensity’, describing the relative power of a pressure wave using a logarithmic scale (i.e. where the corresponding values for 10, 100, 1000, & 10000 are equally-spaced). This roughly equates to the ‘loudness’ of a given sound source: humans are able to perceive sounds up to ~140 decibels, with whispers, dishwashers, and chainsaws coming in at around 20, 80, and 120dB if you stand next to them – while an unamplified steel-string acoustic guitar falls between 60-85Hz. Also see amplitude, wavelength, and Hertz.

• Dissonance: explained along with consonance.

• Double-siding: A term I made up to describe the technique of ‘plucking on both sides of a capo’ – e.g. if you capo at 11fr, you can play the strings on either side of it (creating, in a way, a 12-string microtonal harp). A form of ‘third-bridge‘ technique (basically, wedging an object under the string to ‘split’ its length into different tones). More in my full Double-siding article.

• Drone: A broadly-applied term, which in the context of music relates to ‘continuous humming’ sounds – for example the rich buzz of the Indian tanpura (listen below), or the uninterrupted use of open bass strings to accompany higher melodies. Sounds commonly described as ‘droning’ tend to feature low pitches, although the concept of a ‘high drone’ is more rare than incoherent. The word itself evolved from the Old English for ‘male honeybee’ around five centuries ago (along with its counterpart meaning of ‘idler, lazy worker’: as drone bees produce no honey for the hive – even the ‘unmanned flying robot’ meaning is now over 70 years old). Learn more about the long history of India’s divine raga drones in my Tanpura Samples article – and also check out my drone tuning tags (layouts which, in tanpuristic manner, consisit of nothing but a root and a perfect 5th either above or below).

• EDO: short for ‘equal divisions of the octave’ – and is thus synonymous with ‘tet’, or (n-)’tone equal temperament‘). Also see 12-tet (=12-EDO).

• Equal temperament: Tuning systems which divide each octave into a given number of equal segments (see 12-tet).

• Frequency: The number of times an event is repeated per unit of time. In the context of sound, this is essentially the ‘speed of vibration’ – i.e. the number of full wave-cycle oscillations which occur each second (measured in Hz). More generally, frequency can apply to the ‘repetition rate’ of any other musical element (e.g. the patterns of how a particular melodic motif is featured throughout a composition).

• Fundamental: A sound source’s ‘base pitch’, from which all its overtones arise – in other words, the lowest frequency in its periodic waveform (measured in Hz). Ordinarily, the fundamental is the main tone we ‘hear’ – and the one we use to classify a note’s pitch (i.e. while the timbre of an open guitar string contains its full harmonic series, the overall sound is dominated by the strength of the low fundamental). A pure sine wave comprises nothing but a fundamental (i.e. no overtones):

• Gamelan: Refers to the traditional percussion-based ensembles of Indonesia‘s Balinese, Javanese, and Sundanese island traditions (‘gamelans’) – and more generally to the music played on their instruments: principally comprising ‘metallophones’ such as the bonang (kettle gong) and saron (bronze bars). Accompaniment comes from the kendhang (hand drum), suling (bamboo flute), gambang kayu (wood xylophone), and also singers – for example as part of Java’s wayang (theatrical performances). Gamelan draws on a wide variety of xenharmonic tuning systems – such as the pentatonic sléndro (which somewhat approximates 5-tet) and pélog (an uneven 7-note sequence loosely resembling 9-tet). Witness some Balinese microtonality from the Pelitan Ensemble below – and see more on gamelan tuning, history, and myth in my Global Instruments article. 

• Generator: In the context of intervals, this describes the ‘building blocks’ required to construct regular temperaments. All equal temperaments (‘rank 1’) can be ‘generated’ by stacking up a single interval (e.g. our familiar 12-tet system is ‘generated’ by a full cycle of 12 equally-tempered 5ths of 700 cents each), while other systems require more than one generator (e.g. ‘rank 2’ quarter-comma meantone uses two intervals: ‘pure’ major 3rds of 386 cents, and ‘narrowed’ 5ths of 696 cents). Generators can also be used to construct non-octave systems, such as Wendy Carlos’ ‘Alpha‘ scales (derived from the ratio 9:5).

• Harmonic series: The subset of overtones produced by exact whole-number ratios of the sound source’s fundamental. The harmonic series comprises the (theoretically infinite) progression of these harmonics, which are produced by dividing the string into ever-smaller fractions (i.e. open string 1/1=fundamental, 1/2=octave, 1/3=fifth, 1/4=second octave, 1/5=major 3rd, etc). The resulting tones match the ‘pure’ intervals of just intonation, rather than the equally-tempered frequencies of the frets. Hear this microtonality below in the overtones of the open 6str (N.H. at <12>, <7>, <5>, <3.8>, <3.2>, <2.7>, <2.3>). Also see undertone – and my Overtonal Scale Explorer and Fretless Fretboard articles.

• Helmholtz resonator: An open-holed chamber which produces sound via spring-like oscillations of the air inside it – for example an ocarina, a blown bottle, or the body of a guitar (it’s also responsible for the sound when you open a window in a fast-moving car). Named for German physicist Hermann von Helmholtz (1821-1894), author of foundational acoustics textbook On the Sensations of Tone. Watch ‘Helmholtz resonation’ below, captured in smoke clouds using a high-speed camera:

• Hertz (Hz): A frequency unit of 1 ‘cycle per second’. On the guitar, this means ‘how many times every second does a vibrating string complete its full oscillation cycle?’ – although the measurement can be used to describe any other time-based regularity (e.g. clocks tick at a rate of 1Hz). Human hearing spans approximately 20Hz to 20kHz (‘kilohertz’ = x1000), with EADGBE‘s open 6 & 1str coming in at 82.4Hz & 329.6Hz respectively. Named for Heinrich Hertz (1857-1894), the first scientist to prove the existence of electromagnetic waves.

• Hyperpiano: A modified piano designed by Bill Sethares and Kevin Hobby, based around the principle of ‘inharmonic‘ string construction. Each string comprises “three segments: two equal unwound segments surrounding a thicker wound portion”. The experimental instrument’s unique timbres are tuned to microtonal ‘hyperoctave’ scales, built from ratios based on the 12th root of 4 (=1.122). Read their writeup, and hear it in a glitch-hop track.

• Imperfect root: A term I coined to refer to melodic frameworks which deliberately include a ‘nudged root note’ – i.e. the base note of the scale, when actually performed, does not ring out at exactly zero cents. While this may seem like a contradiction in terms, it only leads to incoherence when considered in the abstract: while the maths behind creating tuning systems may assume a zero-cent root, the actual root notes we play can deviate from any otherwise-implied ‘home tone’ (e.g. pressing the 6str a little too hard, or just tuning a little sharp or flat of A440 concert pitch…). For example, Indian rudra veena master Bahauddin Dagar employs ‘seven shades of Sa’: deliberately intoning the 1st degree of some ragas with pitches other than the precise root of the background tanpura – tuned in accordance with the arc of the sun, and selected to bring out each scale’s unique tensions (see him demo it below, and read my interview with him here). In this sense, an ‘imperfect root’ functions more like a melodic scale tone, rather than as a starting point for constructing a tuning system – perhaps revealing a little of the ambiguity behind how we use words like ‘root’. Also see inharmonicity and stretched tuning.

• Inharmonicity: The deviation of a sound source’s overtones from exact whole-number multiples of its fundamental frequency. On the guitar, this ‘imperfection’ mainly arises from the fact that a string’s vibration is essentially just a moving ‘bend’ – which, like any other bend, raises the pitch. The effect is stronger with looser, thicker strings (detune your 6str and pluck hard to hear the effect: e.g. below). Learn more in my article James Taylor’s puzzle: the microtonal ‘stretch’:

• Just intonation: A category of tuning system where all intervals are constructed using ‘simple’ whole-number ratios. A ‘justly-intoned’ twist on our 7-note major scale could take intervals (from the root) of 1:1, 9:8, 5:4, 4:3, 3:2, 5:3, 15:8, and 2:1 (in cents: 0, 204, 386, 498, 702, 884, 1088, 1200). While the guitar isn’t set up for just intonation (as no fret intervals match to a ‘just’ ratio except the 2:1 octave), in tunings such as Open G, many artists slightly drop the pitch of the maj. 3rd string – bringing it closer to the Gmaj chord’s ‘pure’ interval (=14 cents lower: the same as the root string’s <3.7fr> natural harmonic). Watch a chordal comparison of JI vs. 12-tet below:

• Lefty involution: The ability to turn a guitar tuning ‘upside-down’ and play all shapes the same way (i.e. if you top-to-bottom flipped each line of a tab, the same shapes would produce the same chords – if you ignore octave transpositions). The only two 6-string tunings to possess this property are Unison (as all strings are the same) and Tritones (as all adjacent strings are separated by a half-octave of 6 semitones up and down: like you’d placed a ‘mirror’ halfway along the octave, giving the same view in both directions). Also see Lefty Flip tuning.

• Limit: A term popularised by composer Harry Partsch (1901-1974), used to describe the complexity of a tuning system’s interval construction. The ‘limit’ of an interval is the largest odd factor in its ratio – in other words, the ‘upper limit’ of its fractional complexity (limits are always expressed as odd numbers, since dividing a ratio by 2 just equates to lowering it an octave: i.e. ‘octave equivalence’). Thus, in an ‘p-limit’ tuning system, ‘p’ is the largest odd factor in any of the interval’s frequency ratios. Two distinct conceptions exist: ‘odd-limit’ (in which, broadly speaking, ‘p’ is the largest number which divides any of the factors) and ‘prime-limit’ (in which every interval can be written using integer ratios made of products of the primes up to and including ‘p’: e.g. in ‘7-prime-limit’ tuning, every interval ratio can be written using integers which are products of 2, 3, 5 and 7). Confusingly, these methods will produce different results even when ‘p’ is both odd and prime (i.e. ‘5-odd-limit’ and ‘5-prime-limit’ are not the same). Listen to some 7-limit just intonation drones from Ben Luca Robinson (recorded on an ‘electro-magnetically actuated zither’).

• Linear temperament: Refers to any tuning system in which all intervals can be constructed using only two generators – one of which must be the 2:1 octave (=1200 cents). The most prominent linear temperament is probably meantone (e.g. quarter-comma meantone is generated using octaves and ‘narrowed’ 5ths of ~696 cents) – with Miracle and Schismatic temperaments matching the criteria too. 12-tet can also be considered linear: while it can be formed with just one interval (i.e. the cycle of 700-cent 5ths), it can also be built from others: stacking jumps of 1, 5, 7, and 11 semitones will work too (i.e. perfect 5ths and minor 2nds both up and down).

• Maqam: The main melodic systems of Arabic and Middle Eastern classical music (particularly in traditions arising from Egypt, Lebanon, Jordan, Palestine, and Syria). Each individual maqam, in the words of Sami Abu Shumays, contains “habitual melodic phrases, modulation possibilities, ornamentation techniques, and aesthetic conventions, that together form a rich melodic framework and artistic tradition. The maqam’s melodic course…within that framework is called sayr“. The overall concept, combining theoretical abstraction, aesthetic reflection, and cultural association, is something of a ‘distant cousin’ to North Indian raga – both systems share elements of common ancestry (e.g. via the diffusion of Islamic ideas in the Mughal period). Watch qanun player Maya Youssef play some Syrian melodies below:

• Magic temperament: A group of tuning systems in which major 3rds are set somewhere closer to their ‘pure’ 5:4 ratio, so that 5 of them approximate a ‘tritave’ (octave + perfect 5th = ~1902 cents). This approach makes it a ‘regular’ temperament (as all its tones can be generated by stacking up these 3rds) – while also meaning that it doesn’t repeat at the octave (its 3rds are ‘narrowed’ from 12-tet’s 400 cents to ~1902/5=380.2 cents: so stacking up three of them comes in short of the 1200 cents octave by most of a semitone). A variety of ‘Magic’ systems exist, with one derived 7-note scale taking cent values of 0, 322, 381, 703, 762, 1084, 1142, & 1201 (plus, 19-tet very closely approximates ‘magic’). More from x31, and hear the scale here:

• Mauna Loa: A Hawaiian kī hō’alu (slack-key) concept, referring to any tuning where the two highest-pitched strings are separated by a perfect 5th (such as C6 Mauna Loa: below). Named for the ‘high-up stability’ of the world’s largest active volcano, located on Hawaii Island, which has erupted non-stop since rising from the Pacific seabed over 400,000 years ago. (n.b. ‘Old Mauna Loa’ is also a tuning category: for layouts with an adjacent string pair set a maj. 6th & maj. 2nd above the slack-key root, with the maj. 6th being the lower of these two notes. Confusingly, it is rare for a tuning to satisfy both the ‘old’ and ‘normal’ conditions…).

• Meantone: A tuning system based on prioritising ‘pure‘ (or almost-pure) 3rds, via ‘tempering‘ the size of the 5ths (i.e. narrowing them slightly from their pure ratio of 3:2). ‘Quarter-comma’ meantone, which enjoyed popularity in the Renaissance and Baroque eras, preserves pure major 3rds (~386 cents) by stacking 5ths of size ~696 cents (a ‘quarter of a syntonic comma‘ less than the pure 5th of ~702 cents). Other meantone variants, which employ subtly different narrowings, also exist. Hear a meantone take on Haydn’s Flötenuhrstücke below:

• Microtonality: A broad term, which can refer to any music tuned to systems outside 12-tone equal temperament (and its exact subsets). Despite the connotations of ‘micro’, such systems do not necessarily include intervals narrower than our familiar 100 cent semitone (e.g. the gamelan sléndro splits the octave into only 5 parts) – although many microtonal systems do use small divisions (e.g. India’s sruti pitches, or Dolores Catherino’s 106-tet ‘Polychromatic’ synth: below). Composer Margo Schulter takes a broader, less Western-centric view, defining microtonalism as “the use of any interval or tuning system deemed ‘unusual’ or ‘different’ in a given cultural setting…the ‘dimension’ or ‘continuum of variation’ among [all] intervals and tuning systems”. (Also see paucitonality and xenharmonicity).

• Miracle temperament: Describes a particular set of 10-note scales – which must be made of 9 smaller intervals (‘secors’) and 1 larger one. The difference between the interval sizes is known as the ‘quomma’ (as it lies between a comma and a quarter-tone) – meaning that all Miracle scales span precisely ‘10 secors + 1 quomma’ (=9 short ‘secor’ steps and 1 long ‘secor+quomma’). Thus, equal temperaments with 31, 41, and 72 steps can be considered ‘miraculous’ (as ‘n=10s+q’ can be solved with integers in each case: respectively, 31=(10*3)+1, 41=(10*4)+1, and 72=(10*7)+2). Related to the theories of George Secor, and also to the Blackjack scale – with the term ‘miracle’ itself being chosen as a playful acronym of ‘Multiple Integer Ratios Approximated Consistently, Linearly, and Evenly’. Read Secor’s own writeup of it here, and watch 12tone explain the system below:

• Nada brahma: Derives from a Sanskrit term loosely translatable as ‘universal vibration’, or ‘god as sound’. A fundamental tenet of Indian classical music, it refers to the belief that sound vibration is the fundamental essence of all creation, and the primary route by which to know the divine.

• Non-octave scale: Any scale or tuning system which does not repeat at the 2:1 octave (=1200 cents). These come in wide variety: many are based around dividing up some other interval instead (e.g. the Bohlen-Pierce scale divides the 1902 cent ‘tritave’ into 13 steps of ~146 cents each), while others draw from elsewhere (e.g. the ‘Golden Ratio’ scale uses jumps of 833.09 cents, derived from Fibonacci-like combination tones). In literal terms, any stretched tuning (in which each octave is slightly ‘widened’) is also a non-octave tuning – although here, the stretch is primarily designed to compensate for inharmonicity (i.e. the aim is to eliminate non-consonant octaves when the instrument is played). Check out Wendy Carlos’ Alpha scales – and see imperfect root.

• Open string: Describes a string which vibrates at its full length – i.e. it rings unfretted/unstopped along the instrument’s whole scale length. Under usual circumstances, the frequency produced will be the string’s fundamental tone.

• Oscillation: A single segment of a repetitive physical motion – e.g. in the context of the guitar, one back-and-forth movement of a plucked string as it vibrates. Also see Hz and wavelength.

• Otonality / utonality: Two interlinked concepts coined by microtonalist Harry Partsch (1901-1974). ‘Otonality’ refers to interval sets built from only ‘equal denominators and consecutive numerators’ of a fundamental (e.g. interval ratios of 1/1, 2/1, 3/1) – while ‘utonality’ describes the inversion of an otonality (i.e. building the same interval sequence downwards, below the fundamental – essentially ‘flipping the fractions’ to 1/1, 1/2, 1/3… instead of 1/1, 2/1, 3/1…: see undertone series). More on the Xenharmonic Wiki.

• Overtone: Any frequency which is higher than the same sound source’s fundamental – comprising both the neat order of its harmonic series (e.g. the sound of an open guitar string), and also any messier, ‘inharmonic‘ overtones produced (e.g. the resonance of a snare drum). The harmonic series, also known as the ‘overtone series’, numbers these harmonic overtones by the progression of their fractions (e.g. the ‘1st & 2nd overtones’ of a guitar string are found at its first two natural harmonic positions: at <12fr> & <7fr>, which are 1/2 and 1/3 of the way along its length). Also see harmonics: the subset of overtones produced by whole-number ratios of the fundamental – and hear some of Ondar’s Tuvan ‘overtone singing’ below:

• Paucitonality: A term coined by Margo Schulter to describe ‘scarce-tonedness’ – in other words, “a state of musical and cultural myopia in which the use of intervals and intonational nuances routinely occurring in many world-musical traditions…[are] relegated to a special ‘microtonal‘ category…an ideology (often unspoken) restricting musicians (at least in theory) to a single tuning system”. (Also see xenharmonic and anti-Pythagorean).

• Pitch: The ‘position’ of a sound wave’s frequency – relative to the other pitches present in the scenario (e.g. ‘higher, lower’), or to an absolute scale of Hertz: cycles per second (e.g. open E1str’s pitch = 330Hz). Broadly speaking, pitch functions like the ‘perceptual counterpart’ of frequency – primarily referring to our inner conception of this objectively-measurable property. It is thus laden with more subjectivity than scientific analysis of vibration patterns: e.g. the exact same ‘up/down’ interval motions can sound ambiguous to different listeners, as shown by the tritone paradox – and even the equivalence of the 2:1 octave, long thought to be a human perceptual universal, seems to vary by culture. The word ‘pitch’ (which, fittingly, offers unusual ambiguity in the broader English language) has been used in its modern musical sense since at least the 1630s, possibly evolving from a maritime use of the term (“alternate fall and rise of the bow and stern…as in, passing over waves”). Also see consonance/dissonance.

• Phasing: In scientific terms, the ‘phase’ of an oscillation specifies a particular timing or position along its waveform. In the context of music, this concept usually relates to ‘phase difference’ – i.e. the positional difference between two sound waves at a given point in time (hence ‘out-of-phase’ meaning ‘clashing’). Creatively, this manifests on a variety of scales: e.g. two copies of an oscillation can be ‘nudged’ slightly apart to give a ‘shimmering, wavering’ effect, as the waveforms alternately add to and subtract from each other (e.g. playing through a ‘phase pedal’) – or the whole musical pattern can be shifted on a beat-by-beat basis (e.g. Steve Reich’s Clapping Music is simply a 12-beat pattern, successively ‘jumped back’ a beat until it comes back in sync with the original loop, 12 steps later: see below). The concept also presents other quirks, such as ‘phase cancellation’: when waveforms align to ‘cancel each other out’ (i.e. their signals are a 180-degree flip of each other):

• Polytonality: The simultaneous use of more than one distinct key. Present in traditions from South Indian folk to Lithuanian sutartines, as well as classical composers: e.g. Stravinsky’s Petrushka stacks F#maj on top of Cmaj – a clashing tritone separation. (n.b. ‘polyvalence’ is the simultaneous use of more than one harmonic function within the same key). More from Adam Neely.

• Psychoacoustics: The systematic, scientific study of sound perception (typically in humans, but not in principle confined to any particular species). Psychoacoustics is a truly interdisciplinary field, combining concepts from neuroscience, anatomy, psychology, sociology, electronics, physics, computer science, music theory, and more – and extending beyond music, encompassing other forms of sound perception too (e.g. how we process speech or birdsong). Read a brief history in Acoustics Today – & also see consonance, dissonance, and raga.

• Pythagorean: A tuning system based around stacking up ‘pure’ 5ths (3:2 ratio=702 cents). This interval is used as the generator due to its consonance, offering decisive downward resolutions to every note – but the method presents issues with triads and major 3rds, which, if created by stacking four 5ths, come out at ​​81:64 (~408 cents). The system enjoyed its heyday in the age before the Renaissance (listen here)…despite being named after Pythagoras, there is little evidence that the Ancient Greek philosopher actually used it (although he did derive the string ratios of the overtone series using a monochord: or, as is erroneously fabled, by comparing the dissonance patterns of different-sized blacksmith’s hammers). Listen to a Pythagorean-tuned guitar duet here – and also see comma, just intonation, and anti-Pythagorean.

• Quarter-tone: An interval of half a semitone, or 50 cents (like having 24 frets in the space of 12: i.e. 24-tet). While Middle Eastern systems are said to employ quarter tones, such intervals are often nearby microtones, intoned with subtle differences depending on the maqam at hand. Here’s what ‘true’ quarter-tones sound like:

• Raga: The main melodic system of Indian classical music – central to both the Hindustani and Carnatic (Northern and Southern) traditions. To oversimplify, ragas function like ‘melodic mood recipes’: each presenting their own ‘ingredients’, such as core phrases, note hierarchies, ascending & descending lines, and ornamentation patterns – as well as accompanying rules and guidelines for how to blend them into a coherent whole. Despite this detail, ragas are much more about aesthetics than exacting technique or theory, aimed first and foremost at summoning their own unique set of sentiments and colours (the word raga derives from the Sanskrit for ‘that which colours the mind’: hence my site’s name and tagline). For more, start with my Raga Index articles on Parameshwari and Chandranandan – and watch the playfulness on display in Rupak Kulkarni & Ojas Adhiya’s Darbar 2018 performance:

• Ratio: Expresses the relative frequencies of an interval’s tones – e.g. EADGBE‘s open 5str is 110Hz, and its 12fr is 220Hz, giving a ratio of 2:1 (=220/110). Commonly used to describe microtonal intervals, which are often produced by fractional methods (e.g. in just intonation, a perfect 5th is 3:2, and a major 3rd is 5:4).

• Re-entrant: Describes tunings in which the open strings are not arranged in strict ‘low>high’ (or ‘high>low’) sequence – such as the ukulele, banjo, and charango (but not the Standard-tuned guitar). See Re-entrant Menu category.

• Regular temperament: Refers to any tuning system in which all interval ratios can be derived from a finite number of generators. Essentially, they come in two varieties: equal temperaments (which build a finite number of intervals from a specific division of the octave), and ‘infinite’ temperaments (which lack neat octave-division repetitions, and loop around themselves indefinitely, theoretically passing through an infinite sequence of tones). Crucially, all regular tunings will ‘look the same’ as themselves regardless of which note you start on (i.e. the same intervals are available from all tones present in the system) – as opposed to ‘irregular’ tunings, which lose this property by representing pure intervals with different combinations of tempered intervals.

• Sargam: The Indian classical ‘solmization’ system of assigning particular syllables to each swara of a raga. These are typically close variants of ‘Sa, Re, Ga, Ma, Pa, Dha, Ni’ (see image & my quick sitar demo below), although subtle differences exist between the Hindustani (Northern) and Carnatic (Southern) traditions. Much like the ‘moveable Do’ variant of European solfège, the system is always ‘relative’, setting ‘Sa’ as the scale’s root regardless of pitch (Indian classical music is predominantly ‘modal’: i.e. based on exploring within particular scalar frameworks, rather than modulating between them). Sargam can also refer to the practice of singing these note-names out loud (a common feature of khayal vocal performances) – and it can even be used to spell out semantically-meaningful words and phrases (e.g. Ravi Shankar included the motif ‘Ga-Na-Dha’ [3-b7-b6] in his Raag Mohan Kauns, to honour the passing of Mahatma ‘Ga-n-dhi’: read more examples of global word-melody in my Alpha-melodics article).

• Schismatic temperament: Refers to tuning systems in which the ‘schisma’ (comma of ratio 32805:32768, or ~1.95 cents) is ‘tempered’ to a unison (i.e. counted as zero cents). Major thirds are generally constructed by stacking of 8*4ths (rather than the more usual 4*5ths), to produce 12-note scales, each with 5 larger and 7 smaller intervals. Different schismatic concepts may be referred to as ‘schismic’, ‘Helmholtz’ and ‘quasi-Pythagorean’ temperaments – read more on x31.

• Scordatura: A European classical term for the altered tuning of string instruments (from the Italian for ‘discord’) – employed by Bach, Vivaldi, Haydn, Bartók, Stravinsky, and many more. Often, scordatura parts are notated by ‘usual’ finger position rather than literal pitch (…not an issue with guitar tab).

• Sine wave: An oscillation consisting of a single fundamental frequency and nothing else (i.e. no overtones). In other words, the simplest possible waveform (a pure ‘sinusoidal’ tone, derived from a simple, smooth periodic oscillation). Often produced electronically – although some ‘real’ sound sources get very close (e.g. a tuning fork). Theoretically, all oscillation patterns can be modelled with combinations of sines. Here’s what sine waves of 100, 150, 240, 400, 600, & 900Hz sound like:

• Slack-key (‘kī hō’alu’): Hawaii’s acoustic guitar traditions, which employ various open major-chord tunings (kī hō’alu translates as ‘to loosen the key/string’). Hammer-ons, natural harmonics, and other expressive techniques are also common in the style, which likely originated with guitars brought to Hawaii by Mexican cowboys in the early 19th century (more from Dancing Cat Records & also see my slack-key tuning pages).

• Slack thwack: An informal term I use throughout this project to refer to tunings with a low-side ‘adjacent octave’ – i.e. the two deepest strings are tuned exactly an octave apart (e.g. AADGBE). This typically brings a rough, percussive quality to their timbre: by loosening the 6str, you widen its vibration path, making it easier to ‘slap’ it against the metal frets, somewhat like a snare drum (the slackness also intensifies the pitch-instability via increasing inharmonicity).

• Solfège: The European-derived ‘solmization’ system of assigning syllables to each scale step – ‘Do, Re, Mi, Fa, So, La, Ti’ are matched to the 7 tones of the (diatonic) scale (like in The Sound of Music). Primarily intended as a tool to aid with interval recognition, sight-reading, and general ear skills, solfège (also called solfèggio) comes in two main varieties: ‘fixed Do’ (where Do is always the note C), and ‘moveable Do’ (which always sets Do as the scale’s root, regardless of pitch: my global, modal bias leads me to heavily favour this method…although India’s similarly-moveable sargam system sounds even better). Also read about solfège’s use in ‘spelling-based melodies’ in my Alpha-melodics article.

• Solmization: See solfège and sargam.

• Sruti: Refers to the microtones used in Indian classical music, both Hindustani (North) and Carnatic (South). Many sources, both ancient and modern, cite a list of 22 specific sruti – but this is a case of ‘theory disconnecting from practice’: a 22-note reckoning doesn’t really match up to the infinite microtonal shades which are actually used. Also see raga and sargam.

• Stretched tuning: A tuning approach which subtly ‘expands’ the span of each octave to slightly wider than an exact 2:1 ratio (=1200 cents). The technique is most relevant to lower, looser-strung instruments such as the piano and guitar – where it is used to compensate for the greater inharmonicity of deeper, slacker strings (e.g. an upright piano’s bass strings need to be ultra-wide and ultra-slack to achieve the right frequencies, which also makes their pitch more liable to ‘bend’ upwards, especially if struck hard: thus, the octaves above them are ‘stretched’ by a few cents so the combinations still sound ‘in’). For some guitar context, check out my article James Taylor’s puzzle: the microtonal ‘stretch’. (n.b. a ‘compressed’ tuning is one which narrows the octave to below 1200 cents).

• String theory: A set of concepts in theoretical physics which take the fundamental constituents of the universe to be one-dimensional vibrating ‘strings’ (rather than point-like ‘particles’). Proposed as a way of bridging quantum mechanics (the science of the very small) with Einstein’s general relativity theory (a description of universe-scale forces), it is one candidate for a ‘unified field theory’ – aimed at uniting gravity, electromagnetism, and the strong & weak nuclear forces into a single coherent framework. However, it remains a theoretical construct, still far from the reaches of experimental observation and testing. (Also see nada brahma).

• Subharmonic: see undertone

• Swara: While this can be oversimplified to mean ‘note name’ or ‘scale step’ in Indian classical music, the concept is much broader than this – encompassing not just the tone itself, but also implying raga-specific details such as its microtonal sruti position, characteristic articulations, and function within the broader melodic geometry. The word itself derives from the Sanskrit svar: ‘to sound’ (also see raga, sargam, & nada brahma).

• Sweetened tuning: A tuning practice which subtly ‘nudges’ some intervals away from their 12-tet cent values, in order to improve the sound in some way. On the guitar, this has a variety of manifestations: e.g. the major 3rd strings of Open D and G are (often subconsciously) nudged closer to the ‘pure’ 3rd of 386 cents (useful for ‘justly-intoned’ slide playing) – and James Taylor subtly ‘stretches’ his open-string intervals to counteract his frequent retunings and capo-related inharmonicity (stretching is just a particular form of sweetening: more in my full article). While I prefer making these adjustments by ear, the Peterson company offers intriguing electronic tuners with dozens of preset ‘sweetenings’, designed to improve the frequency balances of particular chords and keys.

• Temperament: see tuning (system), equal temperament and 12tet

• Tempering: The process of slightly adjusting the sizes of some or all intervals (often 5ths and 3rds) – usually to preserve exact 2:1 octaves (which are not produced by chains of any other pure interval) and accommodate other ‘useful repetitions’ (e.g. the capacity to modulate evenly). A tuning system is ‘tempered’ if it alters the ‘pure’ ratios of just intonation in order to fulfil other criteria (e.g. 12-tet tempers its 5ths from 702 to 700 cents, bringing a neat, equilateral design: i.e. the ‘cycle of 5ths’). The practice is of particular importance for keyboards and other fixed-pitch instruments, which otherwise struggle with even modulations between keys (without tempering, each key would have a different ‘shape’). Also see stretched tuning.

• Tetrachord: A grouping of intervals which span a perfect 4th overall (~498 cents) – typically comprising 4 notes (tetra=’four’, chordon=’tone’). In Ancient Greek music theory, ‘descending tetrachords’ of exact 4:3 ratios served as the basic unit of harmonic construction – with chains of these tetrachords (which varied in their inner notes only) forming the ‘Greater & Lesser Perfect Systems’ (e.g. in the 2nd-century A.D. work of Cleonides). In modern Western parlance the term still implies a 4th-like gap, but can refer to any 4-note adjacent sequence divided by 3 intervals – while South India’s Carnatic system uses both ‘adjunct’ (overlapping) and ‘disjunct’ (non-overlapping) tetrachords in the Melakarta process of raga derivation. Here are the E Mixolydian scale’s tetrachords (‘lower’: 1-2-3-4, ‘upper’: 5-6-b7-8):

• Third bridge: The technique of splitting a string into more than one vibrating segment, usually by wedging an object somewhere along its length (i.e. ‘bridge + extra thing + nut’). This is achievable on the guitar in a variety of ways (e.g. Kaki King’s ‘Passerelle bridge‘ below) – see my Double-siding article for more, including how to do it with a capo.

• Tremolo: A general musical term for a ‘trembling’ effect. Strictly, this refers to either the ‘rapid reiteration’ of a note (i.e. picking it continuously), or a ‘variation of amplitude‘ (i.e. fast rise-fall cycles of its volume, as produced by a tremolo pedal: listen below). The ‘whammy bar’ found on some electric guitars is also commonly called a ‘tremolo arm’ – however its effect is actually a change of pitch rather than volume.

• Tritave: An interval of ratio 3:1 (i.e. an octave + a perfect 5th = 1902 cents). Used as a central component in the construction of microtonal systems such as Magic temperament (where the tritave is divided into 5 major 3rds of ~380 cents each), and the Bohlen-Pierce scale (where it is divided into 13 steps of ~146 cents each). On the guitar, a tritave comprises a 19-fret jump (octave=12 + fifth=7):

• Tuning: A broad term, relating to various processes of ‘adjustment’, ‘fine-setting’, or ‘bringing closer to a desired order’. In the context of music, a ‘tuning’ (noun) is the ‘system of frequencies’ underlying a sonic phenomenon – while the act of ‘tuning’ (verb) is to ‘adjust the pitches of a sound source’ in some implicitly deliberate fashion. Any and all philosophies of interval construction can be referred to as ‘tuning systems’: ranging from the ancient, ear-derived sruti of Indian raga to the abstruse mathematical derivations of modern xenharmonic composers. Oddly, ‘detuning’ and ‘tuning’ are only approximate antonyms: amongst string players, ‘detune’ is often used as a synonym for ‘downtune’ (as in ‘decreasing tension’: e.g. ‘I detuned the 6str right down to a low A’). In the broader English language, the word ‘tune’ – which can also just mean ‘melody’ – has expanded outwards from its original musical associations, now used in relation to such things as radios (‘tuning the wireless’), conscious awareness (‘tune in/out’), and car modifications (…the only ‘world of tuning’ I can find apart from this one is a defunct FB fan page for body & engine mods). See my Tuning Tales & Quotes page and Impatient Meditation essay for more tuning insights from around the world – and, I guess, everything else in the whole World of Tuning project!

• Twists: A shorthand term I use in this project for ‘the number of strings altered from EADGBE’ – i.e. a ‘3-twist’ tuning has 3 strings set differently to Standard. See tag pages for 1, 2, 3, 4, 5, and 6-twist tunings.

• Undertone (series): The frequencies produced by ‘inverting’ the harmonic series (i.e. using the same intervals to extend downwards from the fundamental, with fractions 1/1, 1/2, 1/3…). While often derived in abstraction, undertones (sometimes referred to as ‘subharmonics’) can also be simulated by real instruments under certain conditions – such as through ‘overblowing’ certain flutes, or forcefully bowing violins at specific points on the string. By ‘flipping’ the overtone series, the undertone series can be used to derive an ‘inverted’ version of 12-tone just intonation: with descending cent values of 0, -112, -204, -316, -386, -498, -583, -702, -814, -884, -996, -1088, & -1200. Also see otonality/utonality. More from Adam Neely – and this is what the intervals of F’s undertone series sound like:

• Wahine: A Hawaiian kī hō’alu (slack-key) concept, referring to any tuning based around a maj. 7th interval from the slack root (e.g. Keola’s C: listen below). Consequently, Wahine-tuned songs tend to feature prominent leading-tone resolutions (e.g. ‘0-1’ on the maj. 7th string). In Keola Beamer’s words, Wahine tunings are “generally darker and more evocative than the Major tunings. There is the very real element of tonal coloration…”.

• Wavelength: The distance between one wave peak to the next – i.e. the length taken up by one complete cycle of its oscillation. Designated with the lambda symbol (λ), it is calculated as ‘speed/frequency’ (v/f) – meaning that, all other things being equal, raising the frequency leads to a shortening of wavelength (as more cycles must fit within the same unit of time/length). The wavelength of the guitar’s open E6str can thus be calculated as ‘v/f=λ’, using the speed of sound (‘v’=770mph=344 m/s), and E6str’s pitch (‘f’=82.4Hz): giving (344/82.4=) 4.17m (while the highest fret’s wavelength is around 3.1cm).

• Wolf fifth: A sharply dissonant interval in meantone-style temperaments, arising due to the fact that a cycle of ‘narrowed’ 5ths will not lead back to the exact octave, without the inclusion of a ‘stretched’ 5th somewhere to compensate for the shortfall (e.g. quarter-comma meantone creates a wolf of ~738 cents: listen below). This gives rise to a dissonant ‘beating’ effect, likened to a wolf’s howl (see Beau Geste effect). Also called the ‘Procrustean’ fifth: after Procrustes, the murderous blacksmith of Greek myth, fabled to have stretched his victims on a rack. Sometimes used more generally to refer to other gap-filling intervals which differ significantly from their ‘pure‘ equivalents.

• Xenharmonic: In the words of Ivor Darreg, who coined the term (from the Greek xenos/xenia: ‘foreign/hospitable’), xenharmonic music encompasses “everything that does not sound like 12-tone equal temperament“. Essentially, an alternative word for ‘microtonal‘, with implications that the system in question deviates significantly from 12-tet. Also see sruti, maqam, gamelan, and paucitonality.

(Ivor Darreg & his xenharmonic self-creations)

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—Let me know what to add!—

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• Blackadder: Dr. Johnson’s Dictionary (1987):

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