7-limit tuning

(Playⓘ) Compositions with septimal tunings include La Monte Young's The Well-Tuned Piano, Ben Johnston's String Quartet No.Those considering 7 to be consonant include Marin Mersenne,[5] Giuseppe Tartini, Leonhard Euler, François-Joseph Fétis, J.A. Serre, Moritz Hauptmann, Alexander John Ellis, Wilfred Perrett, Max Friedrich Meyer.LaMonte Young created a lattice containing only identities 3 and 7, thus requiring only two axes, for The Well-Tuned Piano.[7] One, called by Ptolemy the "tonic diatonic," is ascribed to the Pythagorean philosopher and statesman Archytas of Tarentum.

Harmonic seventh, septimal seventh

Septimal chromatic semitone on C

9/7 major third from C to E . ^{[

1

]} This, "extremely large third", may resemble a neutral third or blue note . ^{[

2

]}

Septimal minor third on C

9/7 major thirdneutral thirdblue noteSeptimal minor thirdintervalsinterval ratiospitchesminor seventh5-limitharmonic seventhseptimal chromatic semitonebarbershop seventh chordLa Monte YoungThe Well-Tuned PianoBen JohnstonLou HarrisonMichael HarrisonGreat Highland bagpipePtolemyArchytasTarantumconsonantMarin MersenneGiuseppe TartiniLeonhard EulerFrançois-Joseph FétisMoritz HauptmannAlexander John EllisMax Friedrich MeyerGioseffo ZarlinoRené DescartesJean-Philippe RameauHermann von HelmholtzArthur von OettingenHugo RiemannPaul Hindemithpitch latticeClaudius PtolemydiatonicchromaticPythagoreanArchytas of Tarentumtetrachord:peripatetic philosopherAristoxenusĐàn bầuFonville, JohnPerspectives of New MusicPartch, HarryGenesis of a MusicHindemith, PaulMusical tuningsMillioctaveSavartIntervalInterval ratioPitch classConsonance and dissonanceList of musical intervalsList of intervals in 5-limit just intonationList of meantone intervalsMicrotoneJust intonationEuler–Fokker genusHarmonic scaleHarry Partch's 43-tone scaleHexanyList of compositionsOtonalityPtolemy's intense diatonic scalePythagorean tuningScale of harmonicsTonality diamondTonality fluxTemperaments6-tone12-tone15-tone17-tone19-tone22-tone23-tone24-tonepieces31-tone34-tone41-tone53-tone58-tone72-tone96-toneLinearMeantonequarter-commaseptimalSchismaticMiracleRegular diatonicWell temperamentTemperament ordinaireKirnbergerVallottiWerckmeisterChinese musicologyShí-èr-lǜDastgahArabic maqamTurkish makamMughamOctoechosCarnatic ragaSlendroTetrachord833 cents scaleA12 scaleAlpha scaleBeta scaleGamma scaleDelta scaleLambda scale